1
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Slöetjes SD, Grassi MP, Kapaklis V. Modelling nanomagnet vertex dynamics through Coulomb charges. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:405804. [PMID: 38906128 DOI: 10.1088/1361-648x/ad5acc] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2024] [Accepted: 06/21/2024] [Indexed: 06/23/2024]
Abstract
We investigate the magnetization dynamics in nanomagnet vertices often found in artificial spin ices. Our analysis involves creating a simplified model that depicts edge magnetization using magnetic charges. We utilize the model to explore the energy landscape, its associated curvatures, and the fundamental modes. Our study uncovers specific magnonic regimes and transitions between magnetization states, marked by zero-modes, which can be understood within the framework of Landau theory. To verify our model, we compare it with micromagnetic simulations, demonstrating a noteworthy agreement.
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Affiliation(s)
- Samuel D Slöetjes
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
| | - Matías P Grassi
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
| | - Vassilios Kapaklis
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
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2
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Jensen JH, Strømberg A, Breivik I, Penty A, Niño MA, Khaliq MW, Foerster M, Tufte G, Folven E. Clocked dynamics in artificial spin ice. Nat Commun 2024; 15:964. [PMID: 38302504 PMCID: PMC10834408 DOI: 10.1038/s41467-024-45319-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 01/19/2024] [Indexed: 02/03/2024] Open
Abstract
Artificial spin ice (ASI) are nanomagnetic metamaterials with a wide range of emergent properties. Through local interactions, the magnetization of the nanomagnets self-organize into extended magnetic domains. However, controlling when, where and how domains change has proven difficult, yet is crucial for technological applications. Here, we introduce astroid clocking, which offers significant control of ASI dynamics in both time and space. Astroid clocking unlocks a discrete, step-wise and gradual dynamical process within the metamaterial. Notably, our method employs global fields to selectively manipulate local features within the ASI. Sequences of these clock fields drive domain dynamics. We demonstrate, experimentally and in simulations, how astroid clocking of pinwheel ASI enables ferromagnetic domains to be gradually grown or reversed at will. Richer dynamics arise when the clock protocol allows both growth and reversal to occur simultaneously. With astroid clocking, complex spatio-temporal behaviors of magnetic metamaterials become easily controllable with high fidelity.
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Affiliation(s)
- Johannes H Jensen
- Department of Computer Science, Norwegian University of Science and Technology, Trondheim, Norway.
| | - Anders Strømberg
- Department of Electronic Systems, Norwegian University of Science and Technology, Trondheim, Norway.
| | - Ida Breivik
- Department of Electronic Systems, Norwegian University of Science and Technology, Trondheim, Norway
| | - Arthur Penty
- Department of Computer Science, Norwegian University of Science and Technology, Trondheim, Norway
| | - Miguel Angel Niño
- ALBA Synchrotron Light Facility, Carrer de la Llum 2 - 26, Cerdanyola del Vallés, 08290, Barcelona, Spain
| | - Muhammad Waqas Khaliq
- ALBA Synchrotron Light Facility, Carrer de la Llum 2 - 26, Cerdanyola del Vallés, 08290, Barcelona, Spain
| | - Michael Foerster
- ALBA Synchrotron Light Facility, Carrer de la Llum 2 - 26, Cerdanyola del Vallés, 08290, Barcelona, Spain
| | - Gunnar Tufte
- Department of Computer Science, Norwegian University of Science and Technology, Trondheim, Norway
| | - Erik Folven
- Department of Electronic Systems, Norwegian University of Science and Technology, Trondheim, Norway
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3
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Alfonso-Moro M, Guisset V, David P, Canals B, Coraux J, Rougemaille N. Geometrical Frustration, Correlated Disorder, and Emerging Order in a Corrugated C_{60} Monolayer. PHYSICAL REVIEW LETTERS 2023; 131:186201. [PMID: 37977638 DOI: 10.1103/physrevlett.131.186201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2022] [Revised: 01/31/2023] [Accepted: 09/13/2023] [Indexed: 11/19/2023]
Abstract
Under certain experimental conditions, the deposition of C_{60} molecules onto an atomically flat copper surface gives rise to the formation of corrugated islands. This corrugation, which reflects a molecular displacement perpendicular to the surface plane, presents an astonishing pattern: It is well described by a frustrated Ising spin Hamiltonian whose thermodynamics is compatible with a spin liquid about to transit toward an ordered zigzag state. Here we study the statistical properties of such a molecular corrugation using a structure factor analysis, a tool generally employed in frustrated magnetism. More specifically, the real and reciprocal space analysis of pairwise molecule correlations allows us to demonstrate that the C_{60}/Cu system, in which magnetism is totally absent, has all the characteristics of a triangular Ising antiferromagnet. Our results indicate that the organization of two-dimensional matter, at the molecular length scale, sometimes turns out to be particularly close to that encountered in highly frustrated magnets.
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Affiliation(s)
- M Alfonso-Moro
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
| | - V Guisset
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
| | - P David
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
| | - B Canals
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
| | - J Coraux
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
| | - N Rougemaille
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
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4
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Goryca M, Zhang X, Ramberger J, Watts JD, Nisoli C, Leighton C, Schiffer P, Crooker SA. Deconstructing magnetization noise: Degeneracies, phases, and mobile fractionalized excitations in tetris artificial spin ice. Proc Natl Acad Sci U S A 2023; 120:e2310777120. [PMID: 37851675 PMCID: PMC10614600 DOI: 10.1073/pnas.2310777120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2023] [Accepted: 09/11/2023] [Indexed: 10/20/2023] Open
Abstract
Direct detection of spontaneous spin fluctuations, or "magnetization noise," is emerging as a powerful means of revealing and studying magnetic excitations in both natural and artificial frustrated magnets. Depending on the lattice and nature of the frustration, these excitations can often be described as fractionalized quasiparticles possessing an effective magnetic charge. Here, by combining ultrasensitive optical detection of thermodynamic magnetization noise with Monte Carlo simulations, we reveal emergent regimes of magnetic excitations in artificial "tetris ice." A marked increase of the intrinsic noise at certain applied magnetic fields heralds the spontaneous proliferation of fractionalized excitations, which can diffuse independently, without cost in energy, along specific quasi-1D spin chains in the tetris ice lattice.
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Affiliation(s)
- Mateusz Goryca
- National High Magnetic Field Lab, Los Alamos National Laboratory, Los Alamos, NM87545
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw02-093, Poland
| | - Xiaoyu Zhang
- Department of Applied Physics, Yale University, New Haven, CT06520
| | - Justin Ramberger
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN55455
| | - Justin D. Watts
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN55455
- School of Physics and Astronomy, University of Minnesota, Minneapolis, MN55455
| | - Cristiano Nisoli
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM87545
| | - Chris Leighton
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN55455
| | - Peter Schiffer
- Department of Applied Physics, Yale University, New Haven, CT06520
- Department of Physics, Yale University, New Haven, CT06520
| | - Scott A. Crooker
- National High Magnetic Field Lab, Los Alamos National Laboratory, Los Alamos, NM87545
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5
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King AD, Coraux J, Canals B, Rougemaille N. Magnetic Arctic Circle in a Square Ice Qubit Lattice. PHYSICAL REVIEW LETTERS 2023; 131:166701. [PMID: 37925737 DOI: 10.1103/physrevlett.131.166701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2023] [Accepted: 09/15/2023] [Indexed: 11/07/2023]
Abstract
Under certain boundary conditions, the square ice model exhibits a phase separation in which the core of the system is disordered while its outer region remains ordered. This phenomenon, known as the "arctic circle," has been studied theoretically in combinatorial mathematics and statistical mechanics. Here, we realize the physics of the arctic circle experimentally for the first time, using a programmable lattice of superconducting qubits, and investigate its properties under the prism of a highly frustrated magnet. Our work reveals two unexpected properties. First, the disordered spin manifold confined within the arctic curve is a spin liquid whose average spin texture resembles that of an antivortex, i.e., it is a topologically charged Coulomb phase. Second, monopole quasiparticle excitations, which are totally absent in theoretical works, can be isolated in a phase-separated system. Remarkably, a monopole segregation mechanism is observed, in which the monopoles are sorted according to the magnetic charge and magnetic moment they carry, without the application of an external driving force.
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Affiliation(s)
- A D King
- D-Wave Systems, Burnaby, British Columbia V5G 4M9, Canada
| | - J Coraux
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
| | - B Canals
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
| | - N Rougemaille
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
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6
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Yun C, Liang Z, Hrabec A, Liu Z, Huang M, Wang L, Xiao Y, Fang Y, Li W, Yang W, Hou Y, Yang J, Heyderman LJ, Gambardella P, Luo Z. Electrically programmable magnetic coupling in an Ising network exploiting solid-state ionic gating. Nat Commun 2023; 14:6367. [PMID: 37821464 PMCID: PMC10567909 DOI: 10.1038/s41467-023-41830-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2023] [Accepted: 09/20/2023] [Indexed: 10/13/2023] Open
Abstract
Two-dimensional arrays of magnetically coupled nanomagnets provide a mesoscopic platform for exploring collective phenomena as well as realizing a broad range of spintronic devices. In particular, the magnetic coupling plays a critical role in determining the nature of the cooperative behavior and providing new functionalities in nanomagnet-based devices. Here, we create coupled Ising-like nanomagnets in which the coupling between adjacent nanomagnetic regions can be reversibly converted between parallel and antiparallel through solid-state ionic gating. This is achieved with the voltage-control of the magnetic anisotropy in a nanosized region where the symmetric exchange interaction favors parallel alignment and the antisymmetric exchange interaction, namely the Dzyaloshinskii-Moriya interaction, favors antiparallel alignment of the nanomagnet magnetizations. Applying this concept to a two-dimensional lattice, we demonstrate a voltage-controlled phase transition in artificial spin ices. Furthermore, we achieve an addressable control of the individual couplings and realize an electrically programmable Ising network, which opens up new avenues to design nanomagnet-based logic devices and neuromorphic computers.
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Affiliation(s)
- Chao Yun
- State Key Laboratory of Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, 100871, Beijing, China
- School of Materials Science and Engineering, Peking University, 100871, Beijing, China
| | - Zhongyu Liang
- State Key Laboratory of Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, 100871, Beijing, China
| | - Aleš Hrabec
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
- Laboratory for Multiscale Materials Experiments, Paul Scherrer Institute, 5232, Villigen PSI, Switzerland
- Laboratory for Magnetism and Interface Physics, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
| | - Zhentao Liu
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
- Laboratory for Multiscale Materials Experiments, Paul Scherrer Institute, 5232, Villigen PSI, Switzerland
| | - Mantao Huang
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Leran Wang
- State Key Laboratory of Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, 100871, Beijing, China
| | - Yifei Xiao
- Division of Functional Materials, Central Iron and Steel Research Institute Group, 100081, Beijing, China
| | - Yikun Fang
- Division of Functional Materials, Central Iron and Steel Research Institute Group, 100081, Beijing, China
| | - Wei Li
- Division of Functional Materials, Central Iron and Steel Research Institute Group, 100081, Beijing, China
| | - Wenyun Yang
- State Key Laboratory of Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, 100871, Beijing, China
| | - Yanglong Hou
- School of Materials Science and Engineering, Peking University, 100871, Beijing, China
| | - Jinbo Yang
- State Key Laboratory of Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, 100871, Beijing, China
| | - Laura J Heyderman
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland.
- Laboratory for Multiscale Materials Experiments, Paul Scherrer Institute, 5232, Villigen PSI, Switzerland.
| | - Pietro Gambardella
- Laboratory for Magnetism and Interface Physics, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland.
| | - Zhaochu Luo
- State Key Laboratory of Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, 100871, Beijing, China.
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7
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Saccone M, Caravelli F, Hofhuis K, Dhuey S, Scholl A, Nisoli C, Farhan A. Real-space observation of ergodicity transitions in artificial spin ice. Nat Commun 2023; 14:5674. [PMID: 37704596 PMCID: PMC10499874 DOI: 10.1038/s41467-023-41235-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2022] [Accepted: 08/23/2023] [Indexed: 09/15/2023] Open
Abstract
Ever since its introduction by Ludwig Boltzmann, the ergodic hypothesis became a cornerstone analytical concept of equilibrium thermodynamics and complex dynamic processes. Examples of its relevance range from modeling decision-making processes in brain science to economic predictions. In condensed matter physics, ergodicity remains a concept largely investigated via theoretical and computational models. Here, we demonstrate the direct real-space observation of ergodicity transitions in a vertex-frustrated artificial spin ice. Using synchrotron-based photoemission electron microscopy we record thermally-driven moment fluctuations as a function of temperature, allowing us to directly observe transitions between ergodicity-breaking dynamics to system freezing, standing in contrast to simple trends observed for the temperature-dependent vertex populations, all while the entropy features arise as a function of temperature. These results highlight how a geometrically frustrated system, with thermodynamics strictly adhering to local ice-rule constraints, runs back-and-forth through periods of ergodicity-breaking dynamics. Ergodicity breaking and the emergence of memory is important for emergent computation, particularly in physical reservoir computing. Our work serves as further evidence of how fundamental laws of thermodynamics can be experimentally explored via real-space imaging.
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Affiliation(s)
- Michael Saccone
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
| | - Francesco Caravelli
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Kevin Hofhuis
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
- Laboratory for Multiscale Materials Experiments (LMX), Paul Scherrer Institute, 5232, Villigen PSI, Switzerland
| | - Scott Dhuey
- Molecular Foundry, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA, 94720, USA
| | - Andreas Scholl
- Advanced Light Source, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA, 94720, USA
| | - Cristiano Nisoli
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Alan Farhan
- Department of Physics, Baylor University, Waco, TX, 76798, USA.
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8
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Hu W, Zhang Z, Liao Y, Li Q, Shi Y, Zhang H, Zhang X, Niu C, Wu Y, Yu W, Zhou X, Guo H, Wang W, Xiao J, Yin L, Liu Q, Shen J. Distinguishing artificial spin ice states using magnetoresistance effect for neuromorphic computing. Nat Commun 2023; 14:2562. [PMID: 37142614 PMCID: PMC10160026 DOI: 10.1038/s41467-023-38286-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2023] [Accepted: 04/24/2023] [Indexed: 05/06/2023] Open
Abstract
Artificial spin ice (ASI) consisting patterned array of nano-magnets with frustrated dipolar interactions offers an excellent platform to study frustrated physics using direct imaging methods. Moreover, ASI often hosts a large number of nearly degenerated and non-volatile spin states that can be used for multi-bit data storage and neuromorphic computing. The realization of the device potential of ASI, however, critically relies on the capability of transport characterization of ASI, which has not been demonstrated so far. Using a tri-axial ASI system as the model system, we demonstrate that transport measurements can be used to distinguish the different spin states of the ASI system. Specifically, by fabricating a tri-layer structure consisting a permalloy base layer, a Cu spacer layer and the tri-axial ASI layer, we clearly resolve different spin states in the tri-axial ASI system using lateral transport measurements. We have further demonstrated that the tri-axial ASI system has all necessary required properties for reservoir computing, including rich spin configurations to store input signals, nonlinear response to input signals, and fading memory effect. The successful transport characterization of ASI opens up the prospect for novel device applications of ASI in multi-bit data storage and neuromorphic computing.
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Affiliation(s)
- Wenjie Hu
- State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai, China
- Shanghai Qi Zhi Institute, Shanghai, China
| | - Zefeng Zhang
- Frontier Institute of Chip and System, Fudan University, Shanghai, China
- Research Institute of Intelligent Complex Systems and ISTBI, Fudan University, Shanghai, China
| | - Yanghui Liao
- State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai, China
- Shanghai Qi Zhi Institute, Shanghai, China
| | - Qiang Li
- State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai, China
- Shanghai Qi Zhi Institute, Shanghai, China
| | - Yang Shi
- State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai, China
- Shanghai Qi Zhi Institute, Shanghai, China
| | - Huanyu Zhang
- State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai, China
- Shanghai Qi Zhi Institute, Shanghai, China
| | - Xumeng Zhang
- Frontier Institute of Chip and System, Fudan University, Shanghai, China
| | - Chang Niu
- State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai, China
- Shanghai Qi Zhi Institute, Shanghai, China
| | - Yu Wu
- State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai, China
- Shanghai Qi Zhi Institute, Shanghai, China
| | - Weichao Yu
- State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai, China
- Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai, China
| | - Xiaodong Zhou
- State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai, China
- Shanghai Qi Zhi Institute, Shanghai, China
- Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai, China
| | - Hangwen Guo
- State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai, China
- Shanghai Qi Zhi Institute, Shanghai, China
- Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai, China
| | - Wenbin Wang
- State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai, China
- Shanghai Qi Zhi Institute, Shanghai, China
- Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai, China
| | - Jiang Xiao
- State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai, China
- Shanghai Qi Zhi Institute, Shanghai, China
- Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai, China
- Shanghai Research Center for Quantum Sciences, Shanghai, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing, China
| | - Lifeng Yin
- State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai, China.
- Shanghai Qi Zhi Institute, Shanghai, China.
- Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai, China.
- Shanghai Research Center for Quantum Sciences, Shanghai, China.
- Collaborative Innovation Center of Advanced Microstructures, Nanjing, China.
- State Key Laboratory of Integrated Chips and Systems, Fudan University, Shanghai, China.
| | - Qi Liu
- Frontier Institute of Chip and System, Fudan University, Shanghai, China.
- State Key Laboratory of Integrated Chips and Systems, Fudan University, Shanghai, China.
| | - Jian Shen
- State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai, China.
- Shanghai Qi Zhi Institute, Shanghai, China.
- Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai, China.
- Shanghai Research Center for Quantum Sciences, Shanghai, China.
- Collaborative Innovation Center of Advanced Microstructures, Nanjing, China.
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, Shanghai, China.
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9
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Lopez-Bezanilla A, Raymond J, Boothby K, Carrasquilla J, Nisoli C, King AD. Kagome qubit ice. Nat Commun 2023; 14:1105. [PMID: 36849545 PMCID: PMC9970994 DOI: 10.1038/s41467-023-36760-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2022] [Accepted: 02/13/2023] [Indexed: 03/01/2023] Open
Abstract
Topological phases of spin liquids with constrained disorder can host a kinetics of fractionalized excitations. However, spin-liquid phases with distinct kinetic regimes have proven difficult to observe experimentally. Here we present a realization of kagome spin ice in the superconducting qubits of a quantum annealer, and use it to demonstrate a field-induced kinetic crossover between spin-liquid phases. Employing fine control over local magnetic fields, we show evidence of both the Ice-I phase and an unconventional field-induced Ice-II phase. In the latter, a charge-ordered yet spin-disordered topological phase, the kinetics proceeds via pair creation and annihilation of strongly correlated, charge conserving, fractionalized excitations. As these kinetic regimes have resisted characterization in other artificial spin ice realizations, our results demonstrate the utility of quantum-driven kinetics in advancing the study of topological phases of spin liquids.
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Affiliation(s)
- Alejandro Lopez-Bezanilla
- grid.148313.c0000 0004 0428 3079Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 USA
| | | | | | - Juan Carrasquilla
- grid.17063.330000 0001 2157 2938Vector Institute, University of Toronto, Toronto, ON M5G 1M1 Canada ,grid.46078.3d0000 0000 8644 1405Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 3G1 Canada
| | - Cristiano Nisoli
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
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10
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Searching for the ground state of complex spin-ice systems using deep learning techniques. Sci Rep 2022; 12:15026. [PMID: 36056094 PMCID: PMC9440018 DOI: 10.1038/s41598-022-19312-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2022] [Accepted: 08/26/2022] [Indexed: 11/08/2022] Open
Abstract
Searching for the ground state of a given system is one of the most fundamental and classical questions in scientific research fields. However, when the system is complex and large, it often becomes an intractable problem; there is essentially no possibility of finding a global energy minimum state with reasonable computational resources. Recently, a novel method based on deep learning techniques was devised as an innovative optimization method to estimate the ground state. We apply this method to one of the most complicated spin-ice systems, aperiodic Penrose P3 patterns. From the results, we discover new configurations of topologically induced emergent frustrated spins, different from those previously known. Additionally, a candidate of the ground state for a still unexplored type of Penrose P3 spin-ice system is first proposed through this study. We anticipate that the capabilities of the deep learning techniques will not only improve our understanding on the physical properties of artificial spin-ice systems, but also bring about significant advances in a wide range of scientific research fields requiring computational approaches for optimization.
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11
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Yue WC, Yuan Z, Lyu YY, Dong S, Zhou J, Xiao ZL, He L, Tu X, Dong Y, Wang H, Xu W, Kang L, Wu P, Nisoli C, Kwok WK, Wang YL. Crystallizing Kagome Artificial Spin Ice. PHYSICAL REVIEW LETTERS 2022; 129:057202. [PMID: 35960577 DOI: 10.1103/physrevlett.129.057202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2022] [Revised: 03/16/2022] [Accepted: 07/11/2022] [Indexed: 06/15/2023]
Abstract
Artificial spin ices are engineered arrays of dipolarly coupled nanobar magnets. They enable direct investigations of fascinating collective phenomena from their diverse microstates. However, experimental access to ground states in the geometrically frustrated systems has proven difficult, limiting studies and applications of novel properties and functionalities from the low energy states. Here, we introduce a convenient approach to control the competing diploar interactions between the neighboring nanomagnets, allowing us to tailor the vertex degeneracy of the ground states. We achieve this by tuning the length of selected nanobar magnets in the spin ice lattice. We demonstrate the effectiveness of our method by realizing multiple low energy microstates in a kagome artificial spin ice, particularly the hardly accessible long range ordered ground state-the spin crystal state. Our strategy can be directly applied to other artificial spin systems to achieve exotic phases and explore new emergent collective behaviors.
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Affiliation(s)
- Wen-Cheng Yue
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
- Jiangsu Provincial Key Laboratory of Advanced Photonic and Electronic Materials, School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, China
| | - Zixiong Yuan
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
- Jiangsu Provincial Key Laboratory of Advanced Photonic and Electronic Materials, School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, China
| | - Yang-Yang Lyu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
| | - Sining Dong
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
| | - Jian Zhou
- Jiangsu Provincial Key Laboratory of Advanced Photonic and Electronic Materials, School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, China
| | - Zhi-Li Xiao
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - Liang He
- Jiangsu Provincial Key Laboratory of Advanced Photonic and Electronic Materials, School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, China
| | - Xuecou Tu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
- Purple Mountain Laboratories, Nanjing 211111, China
| | - Ying Dong
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou, Zhejiang 311121, China
| | - Huabing Wang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
- Purple Mountain Laboratories, Nanjing 211111, China
| | - Weiwei Xu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
| | - Lin Kang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
- Purple Mountain Laboratories, Nanjing 211111, China
| | - Peiheng Wu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
- Purple Mountain Laboratories, Nanjing 211111, China
| | - Cristiano Nisoli
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Wai-Kwong Kwok
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Yong-Lei Wang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
- Jiangsu Provincial Key Laboratory of Advanced Photonic and Electronic Materials, School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, China
- Purple Mountain Laboratories, Nanjing 211111, China
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12
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Schánilec V, Brunn O, Horáček M, Krátký S, Meluzín P, Šikola T, Canals B, Rougemaille N. Approaching the Topological Low-Energy Physics of the F Model in a Two-Dimensional Magnetic Lattice. PHYSICAL REVIEW LETTERS 2022; 129:027202. [PMID: 35867462 DOI: 10.1103/physrevlett.129.027202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Revised: 04/11/2022] [Accepted: 06/15/2022] [Indexed: 06/15/2023]
Abstract
We demonstrate that the physics of the F model can be approached very closely in a two-dimensional artificial magnetic system. Faraday lines spanning across the lattice and carrying a net polarization, together with chiral Faraday loops characterized by a zero magnetic susceptibility, are imaged in real space using magnetic force microscopy. Our measurements reveal the proliferation of Faraday lines and Faraday loops as the system is brought from low- to high-energy magnetic configurations. They also reveal a link between the Faraday loop density and icelike spin-spin correlations in the magnetic structure factor. Key for this Letter, the density of topological defects remains small, on the order of 1% or less, and negligible compared to the density of Faraday loops. This is made possible by replacing the spin degree of freedom used in conventional lattices of interacting nanomagnets by a micromagnetic knob, which can be finely tuned to adjust the vertex energy directly, rather than modifying the two-body interactions.
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Affiliation(s)
- V Schánilec
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut NEEL, 38000 Grenoble, France
- Central European Institute of Technology, CEITEC BUT, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic
| | - O Brunn
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut NEEL, 38000 Grenoble, France
- Institute of Scientific Instruments of the Czech Academy of Sciences, Královopolská 147, 612 64 Brno, Czech Republic
- Institute of Physical Engineering, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic
| | - M Horáček
- Institute of Scientific Instruments of the Czech Academy of Sciences, Královopolská 147, 612 64 Brno, Czech Republic
| | - S Krátký
- Institute of Scientific Instruments of the Czech Academy of Sciences, Královopolská 147, 612 64 Brno, Czech Republic
| | - P Meluzín
- Institute of Scientific Instruments of the Czech Academy of Sciences, Královopolská 147, 612 64 Brno, Czech Republic
| | - T Šikola
- Central European Institute of Technology, CEITEC BUT, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic
- Institute of Physical Engineering, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic
| | - B Canals
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut NEEL, 38000 Grenoble, France
| | - N Rougemaille
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut NEEL, 38000 Grenoble, France
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13
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Puttock R, Andersen IM, Gatel C, Park B, Rosamond MC, Snoeck E, Kazakova O. Defect-induced monopole injection and manipulation in artificial spin ice. Nat Commun 2022; 13:3641. [PMID: 35752624 PMCID: PMC9233697 DOI: 10.1038/s41467-022-31309-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2022] [Accepted: 06/13/2022] [Indexed: 11/17/2022] Open
Abstract
Lithographically defined arrays of nanomagnets are well placed for application in areas such as probabilistic computing or reconfigurable magnonics due to their emergent collective dynamics and writable magnetic order. Among them are artificial spin ice (ASI), which are arrays of binary in-plane macrospins exhibiting geometric frustration at the vertex interfaces. Macrospin flips in the arrays create topologically protected magnetic charges, or emergent monopoles, which are bound to an antimonopole to conserve charge. In the absence of controllable pinning, it is difficult to manipulate individual monopoles in the array without also influencing other monopole excitations or the counter-monopole charge. Here, we tailor the local magnetic order of a classic ASI lattice by introducing a ferromagnetic defect with shape anisotropy into the array. This creates monopole injection sites at nucleation fields below the critical lattice switching field. Once formed, the high energy monopoles are fixed to the defect site and may controllably propagate through the lattice under stimulation. Defect programing of bound monopoles within the array allows fine control of the pathways of inverted macrospins. Such control is a necessary prerequisite for the realization of functional devices, e. g. reconfigurable waveguide in nanomagnonic applications. Artificial spin ice systems offer a promising platform to study the motion of emergent magnetic monopoles, but controlled nucleation of monopoles is challenging. Here the authors demonstrate controlled injection and propagation of emergent monopoles in an artificial spin ice utilizing ferromagnetic defects.
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Affiliation(s)
- Robert Puttock
- Quantum Materials and Sensors, National Physical Laboratory, Teddington, UK.
| | - Ingrid M Andersen
- Centre d'Elaboration de Materiaux et d'Etudes Structurales, Toulouse, France
| | - Christophe Gatel
- Centre d'Elaboration de Materiaux et d'Etudes Structurales, Toulouse, France
| | - Bumsu Park
- Centre d'Elaboration de Materiaux et d'Etudes Structurales, Toulouse, France
| | - Mark C Rosamond
- School of Electronic and Electrical Engineering, University of Leeds, Leeds, UK
| | - Etienne Snoeck
- Centre d'Elaboration de Materiaux et d'Etudes Structurales, Toulouse, France
| | - Olga Kazakova
- Quantum Materials and Sensors, National Physical Laboratory, Teddington, UK
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14
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Nourhani A, Crespi VH, Lammert PE. Mutual information and breakdown of the Perron-Frobenius scenario in zero-temperature triangular Ising antiferromagnets on cylinders. Phys Rev E 2022; 105:044105. [PMID: 35590530 DOI: 10.1103/physreve.105.044105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Accepted: 03/04/2022] [Indexed: 06/15/2023]
Abstract
A nominally two-dimensional spin model wrapped onto a cylinder can profitably be viewed, especially for long cylinders, as a one-dimensional chain. Each site of such a chain is a ring of spins with a complex state space. Traditional correlation functions are inadequate for the study of correlations in such a system and need to be replaced with something like mutual information. Being induced purely by frustration, the disorder of a cylindrical zero-temperature triangular Ising antiferromagnet (TIAFM) and attendant correlations have a chance of evading the consequences of the Perron-Frobenius theorem which describes and constrains correlations in thermally disordered one-dimensional systems. Correlations in such TIAFM systems and the aforementioned evasion are studied here through a fermionic representation. For cylindrical TIAFM models with open boundary conditions, we explain and derive the following characteristics of end-to-end mutual information: period-three oscillation of the decay length, halving of the decay length compared to what Perron-Frobenius predicts on the basis of transfer matrix eigenvalues, and subexponential decay-inverse square in the length-for certain systems.
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Affiliation(s)
- Amir Nourhani
- Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA
- Biomimicry Research and Innovation Center, University of Akron, Akron, Ohio 44325, USA
- Departments of Biology, Mathematics, and Chemical, Biomolecular and Corrosion Engineering, University of Akron, Akron, Ohio 44325, USA
| | - Vincent H Crespi
- Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Paul E Lammert
- Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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15
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Kempinger S, Huang YS, Lammert P, Vogel M, Hoffmann A, Crespi VH, Schiffer P, Samarth N. Field-Tunable Interactions and Frustration in Underlayer-Mediated Artificial Spin Ice. PHYSICAL REVIEW LETTERS 2021; 127:117203. [PMID: 34558933 DOI: 10.1103/physrevlett.127.117203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2021] [Revised: 07/24/2021] [Accepted: 08/11/2021] [Indexed: 06/13/2023]
Abstract
Artificial spin ice systems have opened experimental windows into a range of model magnetic systems through the control of interactions among nanomagnet moments. This control has previously been enabled by altering the nanomagnet size and the geometry of their placement. Here we demonstrate that the interactions in artificial spin ice can be further controlled by including a soft ferromagnetic underlayer below the moments. Such a substrate also breaks the symmetry in the array when magnetized, introducing a directional component to the correlations. Using spatially resolved magneto-optical Kerr effect microscopy to image the demagnetized ground states, we show that the correlation of the demagnetized states depends on the direction of the underlayer magnetization. Further, the relative interaction strength of nearest and next-nearest neighbors varies significantly with the array geometry. We exploit this feature to induce frustration in an inherently unfrustrated square lattice geometry, demonstrating new possibilities for effective geometries in two-dimensional nanomagnetic systems.
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Affiliation(s)
- Susan Kempinger
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA
- Department of Physics, North Central College, Naperville, Illinois 60540, USA
| | - Yu-Sheng Huang
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA
| | - Paul Lammert
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA
| | - Michael Vogel
- Institute of Physics and Center for Interdisciplinary Nanostructure Science and Technology (CINSaT), University of Kassel, Heinrich-Platt-Straße 40, 34132 Kassel, Germany
| | - Axel Hoffmann
- Materials Research Laboratory and Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Vincent H Crespi
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA
| | - Peter Schiffer
- Department of Applied Physics and Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Nitin Samarth
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA
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16
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Realization of macroscopic ratchet effect based on nonperiodic and uneven potentials. Sci Rep 2021; 11:16617. [PMID: 34400750 PMCID: PMC8368205 DOI: 10.1038/s41598-021-96192-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Accepted: 08/04/2021] [Indexed: 11/28/2022] Open
Abstract
Ratchet devices allow turning an ac input signal into a dc output signal. A ratchet device is set by moving particles driven by zero averages forces on asymmetric potentials. Hybrid nanostructures combining artificially fabricated spin ice nanomagnet arrays with superconducting films have been identified as a good choice to develop ratchet nanodevices. In the current device, the asymmetric potentials are provided by charged Néel walls located in the vertices of spin ice magnetic honeycomb array, whereas the role of moving particles is played by superconducting vortices. We have experimentally obtained ratchet effect for different spin ice I configurations and for vortex lattice moving parallel or perpendicular to magnetic easy axes. Remarkably, the ratchet magnitudes are similar in all the experimental runs; i. e. different spin ice I configurations and in both relevant directions of the vortex lattice motion. We have simulated the interplay between vortex motion directions and a single asymmetric potential. It turns out vortices interact with uneven asymmetric potentials, since they move with trajectories crossing charged Néel walls with different orientations. Moreover, we have found out the asymmetric pair potentials which generate the local ratchet effect. In this rocking ratchet the particles (vortices) on the move are interacting each other (vortex lattice); therefore, the ratchet local effect turns into a global macroscopic effect. In summary, this ratchet device benefits from interacting particles moving in robust and topological protected type I spin ice landscapes.
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17
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King AD, Nisoli C, Dahl ED, Poulin-Lamarre G, Lopez-Bezanilla A. Qubit spin ice. Science 2021; 373:576-580. [PMID: 34326242 DOI: 10.1126/science.abe2824] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Accepted: 06/17/2021] [Indexed: 11/02/2022]
Abstract
Artificial spin ices are frustrated spin systems that can be engineered, in which fine tuning of geometry and topology has allowed the design and characterization of exotic emergent phenomena at the constituent level. Here, we report a realization of spin ice in a lattice of superconducting qubits. Unlike conventional artificial spin ice, our system is disordered by both quantum and thermal fluctuations. The ground state is classically described by the ice rule, and we achieved control over a fragile degeneracy point, leading to a Coulomb phase. The ability to pin individual spins allows us to demonstrate Gauss's law for emergent effective monopoles in two dimensions. The demonstrated qubit control lays the groundwork for potential future study of topologically protected artificial quantum spin liquids.
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Affiliation(s)
- Andrew D King
- D-Wave Systems, Burnaby, British Columbia V5G 4M9, Canada.
| | - Cristiano Nisoli
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87544, USA.
| | - Edward D Dahl
- D-Wave Systems, Burnaby, British Columbia V5G 4M9, Canada
- Associate Laboratory Directorate for Simulation and Computation, Los Alamos National Laboratory, Los Alamos, NM 87544, USA
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18
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Chaurasiya AK, Mondal AK, Gartside JC, Stenning KD, Vanstone A, Barman S, Branford WR, Barman A. Comparison of Spin-Wave Modes in Connected and Disconnected Artificial Spin Ice Nanostructures Using Brillouin Light Scattering Spectroscopy. ACS NANO 2021; 15:11734-11742. [PMID: 34132521 DOI: 10.1021/acsnano.1c02537] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Artificial spin ice systems have seen burgeoning interest due to their intriguing physics and potential applications in reprogrammable memory, logic, and magnonics. Integration of artificial spin ice with functional magnonics is a relatively recent research direction, with a host of promising results. As the field progresses, direct in-depth comparisons of distinct artificial spin systems are crucial to advancing the field. While studies have investigated the effects of different lattice geometries, little comparison exists between systems comprising continuously connected nanostructures, where spin-waves propagate via dipole-exchange interaction, and systems with nanobars disconnected at vertices, where spin-wave propagation occurs via stray dipolar field. Gaining understanding of how these very different coupling methods affect both spin-wave dynamics and magnetic reversal is key for the field to progress and provides crucial system-design information including for future systems containing combinations of connected and disconnected elements. Here, we study the magnonic response of two kagome spin ices via Brillouin light scattering, a continuously connected system and a disconnected system with vertex gaps. We observe distinct high-frequency dynamics and magnetization reversal regimes between the systems, with key distinctions in spin-wave localization and mode quantization, microstate trajectory during reversal and internal field profiles. These observations are pertinent for the fundamental understanding of artificial spin systems and broader design and engineering of reconfigurable functional magnonic crystals.
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Affiliation(s)
- Avinash Kumar Chaurasiya
- Department of Condensed Matter Physics and Material Sciences, S. N. Bose National Centre for Basic Sciences, Block - JD, Sector-III, Salt Lake, Kolkata 700 106, India
| | - Amrit Kumar Mondal
- Department of Condensed Matter Physics and Material Sciences, S. N. Bose National Centre for Basic Sciences, Block - JD, Sector-III, Salt Lake, Kolkata 700 106, India
| | - Jack C Gartside
- Blackett Laboratory, Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Kilian D Stenning
- Blackett Laboratory, Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Alex Vanstone
- Blackett Laboratory, Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Saswati Barman
- Institute of Engineering and Management, Sector-V, Salt Lake, Kolkata 700 091, India
| | - Will R Branford
- Blackett Laboratory, Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
- London Centre for Nanotechnology, Imperial College London, London SW7 2AZ, United Kingdom
| | - Anjan Barman
- Department of Condensed Matter Physics and Material Sciences, S. N. Bose National Centre for Basic Sciences, Block - JD, Sector-III, Salt Lake, Kolkata 700 106, India
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19
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Controlled creation and annihilation of isolated robust emergent magnetic monopole like charged vertices in square artificial spin ice. Sci Rep 2021; 11:13593. [PMID: 34193911 PMCID: PMC8245615 DOI: 10.1038/s41598-021-92877-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2021] [Accepted: 06/09/2021] [Indexed: 11/21/2022] Open
Abstract
Magnetic analogue of an isolated free electric charge, i.e., a magnet with a single north or south pole, is a long sought-after particle which remains elusive so far. In magnetically frustrated pyrochlore solids, a classical analogue of monopole was observed as a result of excitation of spin ice vertices. Direct visualization of such excitations were proposed and later confirmed in analogous artificial spin ice (ASI) systems of square as well as Kagome geometries. However, such magnetically charged vertices are randomly created as they are thermally driven and are always associated with corresponding equal and opposite emergent charges, often termed as monopole–antimonopole pairs, connected by observable strings. Here, we demonstrate a controlled stabilisation of a robust isolated emergent monopole-like magnetically charged vertices in individual square ASI systems by application of an external magnetic field. The excitation conserves the magnetic charge without the involvement of a corresponding excitation of opposite charge. Well supported by Monte Carlo simulations our experimental results enable, in absence of a true elemental magnetic monopole, creation of electron vortices and studying electrodynamics in presence of a monopole-like field in a solid state environment.
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20
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Sahoo S, May A, van Den Berg A, Mondal AK, Ladak S, Barman A. Observation of Coherent Spin Waves in a Three-Dimensional Artificial Spin Ice Structure. NANO LETTERS 2021; 21:4629-4635. [PMID: 34048252 PMCID: PMC8289297 DOI: 10.1021/acs.nanolett.1c00650] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Harnessing high-frequency spin dynamics in three-dimensional (3D) nanostructures may lead to paradigm-shifting, next-generation devices including high density spintronics and neuromorphic systems. Despite remarkable progress in fabrication, the measurement and interpretation of spin dynamics in complex 3D structures remain exceptionally challenging. Here, we take a first step and measure coherent spin waves within a 3D artificial spin ice (ASI) structure using Brillouin light scattering. The 3D-ASI was fabricated by using a combination of two-photon lithography and thermal evaporation. Two spin-wave modes were observed in the experiment whose frequencies showed nearly monotonic variation with the applied field strength. Numerical simulations qualitatively reproduced the observed modes. The simulated mode profiles revealed the collective nature of the modes extending throughout the complex network of nanowires while showing spatial quantization with varying mode quantization numbers. The study shows a well-defined means to explore high-frequency spin dynamics in complex 3D spintronic and magnonic structures.
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Affiliation(s)
- Sourav Sahoo
- Department
of Condensed Matter Physics and Material Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700 106, India
| | - Andrew May
- School
of Physics and Astronomy, Cardiff University, Cardiff CF24 3AA, U.K.
| | - Arjen van Den Berg
- School
of Physics and Astronomy, Cardiff University, Cardiff CF24 3AA, U.K.
| | - Amrit Kumar Mondal
- Department
of Condensed Matter Physics and Material Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700 106, India
| | - Sam Ladak
- School
of Physics and Astronomy, Cardiff University, Cardiff CF24 3AA, U.K.
| | - Anjan Barman
- Department
of Condensed Matter Physics and Material Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700 106, India
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21
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Paterson GW, Macauley GM, Macêdo R. Field‐Driven Reversal Models in Artificial Spin Ice. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202100109] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Gary W. Paterson
- SUPA, School of Physics and Astronomy University of Glasgow Glasgow G12 8QQ UK
- James Watt School of Engineering Electronics and Nanoscale Engineering Division University of Glasgow Glasgow G12 8QQ UK
| | - Gavin M. Macauley
- SUPA, School of Physics and Astronomy University of Glasgow Glasgow G12 8QQ UK
| | - Rair Macêdo
- James Watt School of Engineering Electronics and Nanoscale Engineering Division University of Glasgow Glasgow G12 8QQ UK
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22
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May A, Saccone M, van den Berg A, Askey J, Hunt M, Ladak S. Magnetic charge propagation upon a 3D artificial spin-ice. Nat Commun 2021; 12:3217. [PMID: 34050163 PMCID: PMC8163774 DOI: 10.1038/s41467-021-23480-7] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2020] [Accepted: 04/30/2021] [Indexed: 11/09/2022] Open
Abstract
Magnetic charge propagation in spin-ice materials has yielded a paradigm-shift in science, allowing the symmetry between electricity and magnetism to be studied. Recent work is now suggesting the spin-ice surface may be important in mediating the ordering and associated phase space in such materials. Here, we detail a 3D artificial spin-ice, which captures the exact geometry of bulk systems, allowing magnetic charge dynamics to be directly visualized upon the surface. Using magnetic force microscopy, we observe vastly different magnetic charge dynamics along two principal directions. For a field applied along the surface termination, local energetics force magnetic charges to nucleate over a larger characteristic distance, reducing their magnetic Coulomb interaction and producing uncorrelated monopoles. In contrast, applying a field transverse to the surface termination yields highly correlated monopole-antimonopole pairs. Detailed simulations suggest it is the difference in effective chemical potential as well as the energy landscape experienced during dynamics that yields the striking differences in monopole transport.
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Affiliation(s)
- A May
- School of Physics and Astronomy, Cardiff University, Cardiff, UK
| | - M Saccone
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA.,Theoretical Division (T4), Los Alamos National Laboratory, Los Alamos, NM, USA
| | - A van den Berg
- School of Physics and Astronomy, Cardiff University, Cardiff, UK
| | - J Askey
- School of Physics and Astronomy, Cardiff University, Cardiff, UK
| | - M Hunt
- School of Physics and Astronomy, Cardiff University, Cardiff, UK
| | - S Ladak
- School of Physics and Astronomy, Cardiff University, Cardiff, UK.
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23
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Rodríguez-Gallo C, Ortiz-Ambriz A, Tierno P. Topological Boundary Constraints in Artificial Colloidal Ice. PHYSICAL REVIEW LETTERS 2021; 126:188001. [PMID: 34018772 DOI: 10.1103/physrevlett.126.188001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2020] [Revised: 03/17/2021] [Accepted: 04/07/2021] [Indexed: 06/12/2023]
Abstract
The effect of boundaries and how these can be used to influence the bulk behavior in geometrically frustrated systems are both long-standing puzzles, often relegated to a secondary role. Here, we use numerical simulations and "proof of concept" experiments to demonstrate that boundaries can be engineered to control the bulk behavior in a colloidal artificial ice. We show that an antiferromagnetic frontier forces the system to rapidly reach the ground state (GS), as opposed to the commonly implemented open or periodic boundary conditions. We also show that strategically placing defects at the corners generates novel bistable states, or topological strings, which result from competing GS regions in the bulk. Our results could be generalized to other frustrated micro- and nanostructures where boundary conditions may be engineered with lithographic techniques.
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Affiliation(s)
- Carolina Rodríguez-Gallo
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028, Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028, Barcelona, Spain
| | - Antonio Ortiz-Ambriz
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028, Barcelona, Spain
- Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028, Barcelona, Spain
| | - Pietro Tierno
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028, Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028, Barcelona, Spain
- Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028, Barcelona, Spain
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24
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Gartside JC, Vanstone A, Dion T, Stenning KD, Arroo DM, Kurebayashi H, Branford WR. Reconfigurable magnonic mode-hybridisation and spectral control in a bicomponent artificial spin ice. Nat Commun 2021; 12:2488. [PMID: 33941786 PMCID: PMC8093262 DOI: 10.1038/s41467-021-22723-x] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Accepted: 03/22/2021] [Indexed: 02/02/2023] Open
Abstract
Strongly-interacting nanomagnetic arrays are finding increasing use as model host systems for reconfigurable magnonics. The strong inter-element coupling allows for stark spectral differences across a broad microstate space due to shifts in the dipolar field landscape. While these systems have yielded impressive initial results, developing rapid, scaleable means to access a broad range of spectrally-distinct microstates is an open research problem. We present a scheme whereby square artificial spin ice is modified by widening a 'staircase' subset of bars relative to the rest of the array, allowing preparation of any ordered vertex state via simple global-field protocols. Available microstates range from the system ground-state to high-energy 'monopole' states, with rich and distinct microstate-specific magnon spectra observed. Microstate-dependent mode-hybridisation and anticrossings are observed at both remanence and in-field with dynamic coupling strength tunable via microstate-selection. Experimental coupling strengths are found up to g/2π = 0.16 GHz. Microstate control allows fine mode-frequency shifting, gap creation and closing, and active mode number selection.
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Affiliation(s)
| | - Alex Vanstone
- Blackett Laboratory, Imperial College London, London, UK
| | - Troy Dion
- Blackett Laboratory, Imperial College London, London, UK
- London Centre for Nanotechnology, University College London, London, UK
| | | | - Daan M Arroo
- London Centre for Nanotechnology, University College London, London, UK
- Department of Materials, Imperial College London, London, UK
| | | | - Will R Branford
- Blackett Laboratory, Imperial College London, London, UK
- London Centre for Nanotechnology, Imperial College London, London, UK
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25
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Meng F, Donnelly C, Abert C, Skoric L, Holmes S, Xiao Z, Liao JW, Newton PJ, Barnes CH, Sanz-Hernández D, Hierro-Rodriguez A, Suess D, Cowburn RP, Fernández-Pacheco A. Non-Planar Geometrical Effects on the Magnetoelectrical Signal in a Three-Dimensional Nanomagnetic Circuit. ACS NANO 2021; 15:6765-6773. [PMID: 33848131 PMCID: PMC8155340 DOI: 10.1021/acsnano.0c10272] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/08/2020] [Accepted: 03/30/2021] [Indexed: 06/12/2023]
Abstract
Expanding nanomagnetism and spintronics into three dimensions (3D) offers great opportunities for both fundamental and technological studies. However, probing the influence of complex 3D geometries on magnetoelectrical phenomena poses important experimental and theoretical challenges. In this work, we investigate the magnetoelectrical signals of a ferromagnetic 3D nanodevice integrated into a microelectronic circuit using direct-write nanofabrication. Due to the 3D vectorial nature of both electrical current and magnetization, a complex superposition of several magnetoelectrical effects takes place. By performing electrical measurements under the application of 3D magnetic fields, in combination with macrospin simulations and finite element modeling, we disentangle the superimposed effects, finding how a 3D geometry leads to unusual angular dependences of well-known magnetotransport effects such as the anomalous Hall effect. Crucially, our analysis also reveals a strong role of the noncollinear demagnetizing fields intrinsic to 3D nanostructures, which results in an angular dependent magnon magnetoresistance contributing strongly to the total magnetoelectrical signal. These findings are key to the understanding of 3D spintronic systems and underpin further fundamental and device-based studies.
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Affiliation(s)
- Fanfan Meng
- Cavendish
Laboratory, University of Cambridge, Cambridge, CB3 0HE, U.K.
| | - Claire Donnelly
- Cavendish
Laboratory, University of Cambridge, Cambridge, CB3 0HE, U.K.
| | - Claas Abert
- Faculty
of Physics, University of Vienna, Vienna, 1090, Austria
- Research
Platform MMM Mathematics-Magnetism-Materials, University of Vienna, Vienna, 1090, Austria
| | - Luka Skoric
- Cavendish
Laboratory, University of Cambridge, Cambridge, CB3 0HE, U.K.
| | - Stuart Holmes
- London
Centre for Nanotechnology, UCL, London, WC1H 0AH, U.K.
| | - Zhuocong Xiao
- Nanoscience
Centre, University of Cambridge, Cambridge, CB3 0FF, U.K.
| | - Jung-Wei Liao
- Cavendish
Laboratory, University of Cambridge, Cambridge, CB3 0HE, U.K.
| | - Peter J. Newton
- Cavendish
Laboratory, University of Cambridge, Cambridge, CB3 0HE, U.K.
| | | | - Dédalo Sanz-Hernández
- Cavendish
Laboratory, University of Cambridge, Cambridge, CB3 0HE, U.K.
- Unité
Mixte de Physique, CNRS, Thales, Université
Paris-Saclay, Palaiseau, 91767, France
| | - Aurelio Hierro-Rodriguez
- Depto.
Física, Universidad de Oviedo, Oviedo, 33007, Spain
- SUPA,
School of Physics and Astronomy, University
of Glasgow, Glasgow, G12 8QQ, U.K.
| | - Dieter Suess
- Faculty
of Physics, University of Vienna, Vienna, 1090, Austria
- Research
Platform MMM Mathematics-Magnetism-Materials, University of Vienna, Vienna, 1090, Austria
| | | | - Amalio Fernández-Pacheco
- Cavendish
Laboratory, University of Cambridge, Cambridge, CB3 0HE, U.K.
- SUPA,
School of Physics and Astronomy, University
of Glasgow, Glasgow, G12 8QQ, U.K.
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26
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Woods JS, Chen XM, Chopdekar RV, Farmer B, Mazzoli C, Koch R, Tremsin AS, Hu W, Scholl A, Kevan S, Wilkins S, Kwok WK, De Long LE, Roy S, Hastings JT. Switchable X-Ray Orbital Angular Momentum from an Artificial Spin Ice. PHYSICAL REVIEW LETTERS 2021; 126:117201. [PMID: 33798337 DOI: 10.1103/physrevlett.126.117201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2020] [Accepted: 12/23/2020] [Indexed: 06/12/2023]
Abstract
Artificial spin ices (ASI) have been widely investigated as magnetic metamaterials with exotic properties governed by their geometries. In parallel, interest in x-ray photon orbital angular momentum (OAM) has been rapidly growing. Here we show that a square ASI with a patterned topological defect, a double edge dislocation, imparts OAM to scattered x rays. Unlike single dislocations, a double dislocation does not introduce magnetic frustration, and the ASI equilibrates to its antiferromagnetic (AFM) ground state. The topological charge of the defect differs with respect to the structural and magnetic order; thus, x-ray diffraction from the ASI produces photons with even and odd OAM quantum numbers at the structural and AFM Bragg conditions, respectively. The magnetic transitions of the ASI allow the AFM OAM beams to be switched on and off by modest variations of temperature and applied magnetic field. These results demonstrate ASIs can serve as metasurfaces for reconfigurable x-ray optics that could enable selective probes of electronic and magnetic properties.
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Affiliation(s)
- Justin S Woods
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Xiaoqian M Chen
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Department of Electrical and Computer Engineering, University of Kentucky, Lexington, Kentucky 40506, USA
| | - Rajesh V Chopdekar
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Barry Farmer
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA
| | - Claudio Mazzoli
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Roland Koch
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Anton S Tremsin
- Space Sciences Laboratory, University of California, Berkeley, California 94720, USA
| | - Wen Hu
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Andreas Scholl
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Steve Kevan
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Stuart Wilkins
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Wai-Kwong Kwok
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Lance E De Long
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA
| | - Sujoy Roy
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - J Todd Hastings
- Department of Electrical and Computer Engineering, University of Kentucky, Lexington, Kentucky 40506, USA
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27
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Yumnam G, Chen Y, Guo J, Keum J, Lauter V, Singh DK. Quantum Disordered State of Magnetic Charges in Nanoengineered Honeycomb Lattice. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2021; 8:2004103. [PMID: 33747751 PMCID: PMC7967061 DOI: 10.1002/advs.202004103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/26/2020] [Indexed: 06/12/2023]
Abstract
A quantum magnetic state due to magnetic charges is never observed, even though they are treated as quantum mechanical variables in theoretical calculations. Here, the occurrence of a novel quantum disordered state of magnetic charges in a nanoengineered magnetic honeycomb lattice of ultra-small connecting elements is demonstrated. The experimental research, performed using spin resolved neutron scattering, reveals a massively degenerate ground state, comprised of low integer and energetically forbidden high integer magnetic charges, that manifests cooperative paramagnetism at low temperature. The system tends to preserve the degenerate configuration even under large magnetic field application. It exemplifies the robustness of disordered correlation of magnetic charges in a 2D honeycomb lattice. The realization of quantum disordered ground state elucidates the dominance of exchange energy, which is enabled due to the nanoscopic magnetic element size in nanoengineered honeycomb. Consequently, an archetypal platform is envisaged to study quantum mechanical phenomena due to emergent magnetic charges.
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Affiliation(s)
- George Yumnam
- Department of Physics and AstronomyUniversity of MissouriColumbiaMO65211USA
| | - Yiyao Chen
- Department of Physics and AstronomyUniversity of MissouriColumbiaMO65211USA
| | - Jiasen Guo
- Department of Physics and AstronomyUniversity of MissouriColumbiaMO65211USA
| | - Jong Keum
- Oak Ridge National LaboratoryOak RidgeTN37831USA
| | | | - Deepak Kumar Singh
- Department of Physics and AstronomyUniversity of MissouriColumbiaMO65211USA
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28
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Parakkat VM, Macauley GM, Stamps RL, Krishnan KM. Configurable Artificial Spin Ice with Site-Specific Local Magnetic Fields. PHYSICAL REVIEW LETTERS 2021; 126:017203. [PMID: 33480755 DOI: 10.1103/physrevlett.126.017203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Accepted: 12/18/2020] [Indexed: 06/12/2023]
Abstract
We demonstrate ground state tunability for a hybrid artificial spin ice composed of Fe nanomagnets which are subject to site-specific exchange-bias fields, applied in integer multiples of the lattice along one sublattice of the classic square artificial spin ice. By varying this period, three distinct magnetic textures are identified: a striped ferromagnetic phase; an antiferromagnetic phase attainable through an external field protocol alone; and an unconventional ground state with magnetically charged pairs embedded in an antiferromagnetic matrix. Monte Carlo simulations support the results of field protocols and demonstrate that the pinning tunes relaxation timescales and their critical behavior.
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Affiliation(s)
- Vineeth Mohanan Parakkat
- Department of Materials Science and Engineering, 323 Roberts Hall, University of Washington, Seattle, Washington 98195, USA
| | - Gavin M Macauley
- SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
| | - Robert L Stamps
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
| | - Kannan M Krishnan
- Department of Materials Science and Engineering, 323 Roberts Hall, University of Washington, Seattle, Washington 98195, USA
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29
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Farhan A, Saccone M, Petersen CF, Dhuey S, Hofhuis K, Mansell R, Chopdekar RV, Scholl A, Lippert T, van Dijken S. Geometrical Frustration and Planar Triangular Antiferromagnetism in Quasi-Three-Dimensional Artificial Spin Architecture. PHYSICAL REVIEW LETTERS 2020; 125:267203. [PMID: 33449705 DOI: 10.1103/physrevlett.125.267203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Revised: 10/01/2020] [Accepted: 12/04/2020] [Indexed: 06/12/2023]
Abstract
We present a realization of highly frustrated planar triangular antiferromagnetism achieved in a quasi-three-dimensional artificial spin system consisting of monodomain Ising-type nanomagnets lithographically arranged onto a deep-etched silicon substrate. We demonstrate how the three-dimensional spin architecture results in the first direct observation of long-range ordered planar triangular antiferromagnetism, in addition to a highly disordered phase with short-range correlations, once competing interactions are perfectly tuned. Our work demonstrates how escaping two-dimensional restrictions can lead to new types of magnetically frustrated metamaterials.
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Affiliation(s)
- Alan Farhan
- NanoSpin, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland
- Laboratory for Multiscale Materials Experiments (LMX), Paul Scherrer Institut, 5232 Villigen, Switzerland
- Advanced Light Source, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, California 94720, USA
| | - Michael Saccone
- NanoSpin, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland
- Physics Department, University of California, 1156 High Street, Santa Cruz, California 95064, USA
| | - Charlotte F Petersen
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Scott Dhuey
- Molecular Foundry, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, California 94720, USA
| | - Kevin Hofhuis
- Laboratory for Multiscale Materials Experiments (LMX), Paul Scherrer Institut, 5232 Villigen, Switzerland
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland
| | - Rhodri Mansell
- NanoSpin, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland
| | - Rajesh V Chopdekar
- Advanced Light Source, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, California 94720, USA
| | - Andreas Scholl
- Advanced Light Source, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, California 94720, USA
| | - Thomas Lippert
- Laboratory for Multiscale Materials Experiments (LMX), Paul Scherrer Institut, 5232 Villigen, Switzerland
- Department of Chemistry and Applied Biosciences, Laboratory of Inorganic Chemistry, ETH Zurich, 8093 Zurich, Switzerland
| | - Sebastiaan van Dijken
- NanoSpin, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland
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30
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Pip P, Donnelly C, Döbeli M, Gunderson C, Heyderman LJ, Philippe L. Electroless Deposition of Ni-Fe Alloys on Scaffolds for 3D Nanomagnetism. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2020; 16:e2004099. [PMID: 33025737 DOI: 10.1002/smll.202004099] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Revised: 08/17/2020] [Indexed: 06/11/2023]
Abstract
3D magnetic nanostructures are of great interest due to the possibility to design novel properties and the benefits for both technological applications such as high-density data storage, as well as more fundamental studies. One of the main challenges facing the realization of these three-dimensional systems is their fabrication, which includes the deposition of magnetic materials on 3D surfaces. In this work, the electroless deposition of Ni-Fe on a 3D-printed, non-conductive microstructure is presented. The deposited films exhibit low coercivity, with the saturation magnetization and composition corresponding to the archetypal soft magnetic material permalloy. For fundamental studies of 3D micromagnetism, this new development in fabrication offers the possibility to combine the flexibility of 3D nanofabrication techniques such as two-photon lithography for the fabrication of 3D scaffolds with a homogeneous soft ferromagnetic thin film, and thus represents an important step toward exploring the rich physics of complex 3D magnetic architectures with tailored properties and the development of advanced applications.
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Affiliation(s)
- Petai Pip
- Laboratory for Mechanics of Materials and Nanostructures, Empa (Swiss Federal Laboratories for Materials Testing and Research), Thun, 3602, Switzerland
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, Zurich, 8093, Switzerland
- Laboratory for Multiscale Materials Experiments, Paul Scherrer Institute, Forschungsstrasse 111, Villigen PSI, 5232, Switzerland
| | - Claire Donnelly
- Cavendish Laboratory, University of Cambridge, JJ Thomson Ave, Cambridge, CB3 0HT, UK
| | - Max Döbeli
- Ion Beam Physics, Department of Physics, ETH Zurich, Zurich, 8093, Switzerland
| | - Christopher Gunderson
- Laboratory for Mechanics of Materials and Nanostructures, Empa (Swiss Federal Laboratories for Materials Testing and Research), Thun, 3602, Switzerland
| | - Laura J Heyderman
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, Zurich, 8093, Switzerland
- Laboratory for Multiscale Materials Experiments, Paul Scherrer Institute, Forschungsstrasse 111, Villigen PSI, 5232, Switzerland
| | - Laetitia Philippe
- Laboratory for Mechanics of Materials and Nanostructures, Empa (Swiss Federal Laboratories for Materials Testing and Research), Thun, 3602, Switzerland
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31
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Schánilec V, Canals B, Uhlíř V, Flajšman L, Sadílek J, Šikola T, Rougemaille N. Bypassing Dynamical Freezing in Artificial Kagome Ice. PHYSICAL REVIEW LETTERS 2020; 125:057203. [PMID: 32794868 DOI: 10.1103/physrevlett.125.057203] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2020] [Revised: 07/01/2020] [Accepted: 07/10/2020] [Indexed: 06/11/2023]
Abstract
Spin liquids are correlated, disordered states of matter that fluctuate even at low temperatures. Experimentally, the extensive degeneracy characterizing their low-energy manifold is expected to be lifted, for example, because of dipolar interactions, leading to an ordered ground state at absolute zero. However, this is not what is usually observed, and many systems, whether they are chemically synthesized or nanofabricated, dynamically freeze before magnetic ordering sets in. In artificial realizations of highly frustrated magnets, ground state configurations, and even low-energy manifolds, thus remain out of reach for practical reasons. Here, we show how dynamical freezing can be bypassed in an artificial kagome ice. We illustrate the efficiency of our method by demonstrating that the a priori dynamically inaccessible ordered ground state and fragmented spin liquid configurations can be obtained reproducibly, imaged in real space at room temperature, and studied conveniently. We then identify the mechanism by which dynamical freezing occurs in the dipolar kagome ice.
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Affiliation(s)
- V Schánilec
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut NEEL, 38000 Grenoble, France
- Central European Institute of Technology, CEITEC BUT, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic
| | - B Canals
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut NEEL, 38000 Grenoble, France
| | - V Uhlíř
- Central European Institute of Technology, CEITEC BUT, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic
| | - L Flajšman
- Central European Institute of Technology, CEITEC BUT, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic
| | - J Sadílek
- Central European Institute of Technology, CEITEC BUT, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic
| | - T Šikola
- Central European Institute of Technology, CEITEC BUT, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic
- Institute of Physical Engineering, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, Brno, 616 69, Czech Republic
| | - N Rougemaille
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut NEEL, 38000 Grenoble, France
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32
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Di Pietro Martínez M, Buceta RC. Energetic analysis of disorder effects in an artificial spin ice with dipolar interactions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:285801. [PMID: 32155604 DOI: 10.1088/1361-648x/ab7e58] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study the effect of quenched disorder in square artificial spin ice by means of numerical simulations. We introduce disorder in the length of magnetic islands using two kinds of distributions: Gaussian and uniform. As the system behavior depends on its geometrical parameters, we focus on studying it in the proximity of the ice regime which is quite difficult to thermalize both in experiments and simulations. We show how length disorder affect the antiferromagnetic and (locally) ferromagnetic ordering, by inducing the system, in the case of weak disorder, to intermediate or mix states. Moreover, in the case of strong disorder, ferromagnetic plaquettes prevail regardless of whether the mean length of the islands corresponds to an antiferromagnetic ordering.
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33
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Effects of magnetic monopoles charge on the cracking reversal processes in artificial square ices. Sci Rep 2020; 10:9959. [PMID: 32561787 PMCID: PMC7305124 DOI: 10.1038/s41598-020-66794-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2020] [Accepted: 05/12/2020] [Indexed: 11/24/2022] Open
Abstract
In this paper we perform nanofabrication of square artificial spin ices with different lattice parameters, in order to investigate the roles of vertex excitation on the features of the system. In particular, the character of magnetic charge distribution asymmetry on the vertices are observed under magnetic hysteresis loop experiments. We then compare our results with simulation using an emergent Hamiltonian containing objects such as magnetic monopoles and dipoles in the vertices of the array (instead of the usual Hamiltonian based on the dipolar interactions among the magnetic nanoislands). All possible interactions between these objects are considered (monopole-monopole, monopole-dipole and dipole-dipole). Using realistic parameters we observe very good match between experiments and theory, which allow us to better understand the system dynamics in function of monopole charge intensity.
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34
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Bramwell ST, Harris MJ. The history of spin ice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:374010. [PMID: 32554893 DOI: 10.1088/1361-648x/ab8423] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2019] [Accepted: 03/27/2020] [Indexed: 06/11/2023]
Abstract
This review is a study of how the idea of spin ice has evolved over the years, with a focus on the scientific questions that have come to define the subject. Since our initial discovery of spin ice in 1997, there have been well over five thousand papers that discuss it, and in the face of such detail, it must be difficult for the curious observer to 'see the wood for the trees'. To help in this task, we go in search of the biggest insight to have emerged from the study of spin ice. On the way, we identify highlights and outstanding puzzles, and celebrate the inspirational role that Roger Cowley played in the early years.
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Affiliation(s)
- Steven T Bramwell
- London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London WC1H 0AH, United Kingdom
| | - Mark J Harris
- School of Divinity, University of Edinburgh, New College, Edinburgh, EH1 2LX, United Kingdom
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35
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Oğuz EC, Ortiz-Ambriz A, Shem-Tov H, Babià-Soler E, Tierno P, Shokef Y. Topology Restricts Quasidegeneracy in Sheared Square Colloidal Ice. PHYSICAL REVIEW LETTERS 2020; 124:238003. [PMID: 32603179 DOI: 10.1103/physrevlett.124.238003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2020] [Accepted: 05/26/2020] [Indexed: 06/11/2023]
Abstract
Recovery of ground-state degeneracy in two-dimensional square ice is a significant challenge in the field of geometric frustration with far-reaching fundamental implications, such as realization of vertex models and understanding the effect of dimensionality reduction. We combine experiments, theory, and numerical simulations to demonstrate that sheared square colloidal ice partially recovers the ground-state degeneracy for a wide range of field strengths and lattice shear angles. Our method could inspire engineering a novel class of frustrated microstructures and nanostructures based on sheared magnetic lattices in a wide range of soft- and condensed-matter systems.
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Affiliation(s)
- Erdal C Oğuz
- School of Mechanical Engineering, Tel Aviv University, Tel Aviv 69978, Israel
- School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
- Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Antonio Ortiz-Ambriz
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona 08028, Spain
- Institut de Nanociència i Nanotecnologia, Universitat de Barcelona, Barcelona 08028, Spain
| | - Hadas Shem-Tov
- School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
| | - Eric Babià-Soler
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona 08028, Spain
| | - Pietro Tierno
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona 08028, Spain
- Institut de Nanociència i Nanotecnologia, Universitat de Barcelona, Barcelona 08028, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona 08028, Spain
| | - Yair Shokef
- School of Mechanical Engineering, Tel Aviv University, Tel Aviv 69978, Israel
- Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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36
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Saccone M, Hofhuis K, Bracher D, Kleibert A, van Dijken S, Farhan A. Elevated effective dimension in tree-like nanomagnetic Cayley structures. NANOSCALE 2020; 12:189-194. [PMID: 31803884 DOI: 10.1039/c9nr07510k] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Using state-of-the-art electron-beam lithography, Ising-type nanomagnets may be defined onto nearly any two-dimensional pattern imaginable. The ability to directly observe magnetic configurations achieved in such artificial spin systems makes them a perfect playground for the realization of artificial spin glasses. However, no experimental realization of a finite-temperature artificial spin glass has been achieved so far. Here, we aim to get a significant step closer in achieving that goal by introducing an artificial spin system with random interactions and increased effective dimension: dipolar Cayley tree. Through synchrotron-based photoemission electron microscopy, we show that an improved balance of ferro- and antiferromagnetic ordering can be achieved in this type of system. This combined with an effective dimension as high as d = 2.72 suggests that future systems generated out of these building blocks can host finite temperature spin glass phases, allowing for real-time observation of glassy dynamics.
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Affiliation(s)
- Michael Saccone
- Physics Department, University of California, 1156 High Street, Santa Cruz, CA 95064, USA. and NanoSpin, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland.
| | - Kevin Hofhuis
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland and Laboratory for Multiscale Materials Experiments, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
| | - David Bracher
- Swiss Light Source, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
| | - Armin Kleibert
- Swiss Light Source, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
| | - Sebastiaan van Dijken
- NanoSpin, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland.
| | - Alan Farhan
- NanoSpin, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland. and Laboratory for Multiscale Materials Experiments, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
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37
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Thermally and field-driven mobility of emergent magnetic charges in square artificial spin ice. Sci Rep 2019; 9:15989. [PMID: 31690773 PMCID: PMC6831649 DOI: 10.1038/s41598-019-52460-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2019] [Accepted: 10/14/2019] [Indexed: 12/03/2022] Open
Abstract
Designing and constructing model systems that embody the statistical mechanics of frustration is now possible using nanotechnology. We have arranged nanomagnets on a two-dimensional square lattice to form an artificial spin ice, and studied its fractional excitations, emergent magnetic monopoles, and how they respond to a driving field using X-ray magnetic microscopy. We observe a regime in which the monopole drift velocity is linear in field above a critical field for the onset of motion. The temperature dependence of the critical field can be described by introducing an interaction term into the Bean-Livingston model of field-assisted barrier hopping. By analogy with electrical charge drift motion, we define and measure a monopole mobility that is larger both for higher temperatures and stronger interactions between nanomagnets. The mobility in this linear regime is described by a creep model of zero-dimensional charges moving within a network of quasi-one-dimensional objects.
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38
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Abstract
Vertex models are an important class of statistical mechanical system that admit exact solutions and exotic physics. Applications include water ice, ferro- and antiferro-electrics, spin ice and artificial spin ice. Here we show that it is possible to engineer spin ice films with atomic-layer precision down to the monolayer limit. Specific heat measurements show that these films, which have a fundamentally different symmetry to bulk spin ice, realise systems close to the two-dimensional F-model, with exotic phase transitions on topologically-constrained configurational manifolds. Our results show how spin ice thin films can release the celebrated Pauling entropy of spin ice without an anomaly in the specific heat. They also significantly expand the class of vertex models available to experiment.
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39
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Li Y, Paterson GW, Macauley GM, Nascimento FS, Ferguson C, Morley SA, Rosamond MC, Linfield EH, MacLaren DA, Macêdo R, Marrows CH, McVitie S, Stamps RL. Superferromagnetism and Domain-Wall Topologies in Artificial "Pinwheel" Spin Ice. ACS NANO 2019; 13:2213-2222. [PMID: 30588800 DOI: 10.1021/acsnano.8b08884] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
For over ten years, arrays of interacting single-domain nanomagnets, referred to as artificial spin ices, have been engineered with the aim to study frustration in model spin systems. Here, we use Fresnel imaging to study the reversal process in "pinwheel" artificial spin ice, a modified square ASI structure obtained by rotating each island by some angle about its midpoint. Our results demonstrate that a simple 45° rotation changes the magnetic ordering from antiferromagnetic to ferromagnetic, creating a superferromagnet which exhibits mesoscopic domain growth mediated by domain wall nucleation and coherent domain propagation. We observe several domain-wall configurations, most of which are direct analogues to those seen in continuous ferromagnetic films. However, charged walls also appear due to the geometric constraints of the system. Changing the orientation of the external magnetic field allows control of the nature of the spin reversal with the emergence of either one- or two-dimensional avalanches. This property of pinwheel ASI could be employed to tune devices based on magnetotransport phenomena such as Hall circuits.
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Affiliation(s)
- Yue Li
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
| | - Gary W Paterson
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
| | - Gavin M Macauley
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
| | - Fabio S Nascimento
- Departamento de Física , Universidade Federal de Viçosa , Viçosa 36570-900 , Minas Gerais , Brazil
| | - Ciaran Ferguson
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
| | - Sophie A Morley
- School of Physics and Astronomy , University of Leeds , Leeds LS2 9JT , United Kingdom
- Department of Physics , University of California , Santa Cruz , California 95064 , United States
| | - Mark C Rosamond
- School of Electronic and Electrical Engineering , University of Leeds , Leeds LS2 9JT , United Kingdom
| | - Edmund H Linfield
- School of Electronic and Electrical Engineering , University of Leeds , Leeds LS2 9JT , United Kingdom
| | - Donald A MacLaren
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
| | - Rair Macêdo
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
| | - Christopher H Marrows
- School of Physics and Astronomy , University of Leeds , Leeds LS2 9JT , United Kingdom
| | - Stephen McVitie
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
| | - Robert L Stamps
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
- Department of Physics and Astronomy , University of Manitoba , Manitoba R3T 2N2 , Canada
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40
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Farhan A, Saccone M, Petersen CF, Dhuey S, Chopdekar RV, Huang YL, Kent N, Chen Z, Alava MJ, Lippert T, Scholl A, van Dijken S. Emergent magnetic monopole dynamics in macroscopically degenerate artificial spin ice. SCIENCE ADVANCES 2019; 5:eaav6380. [PMID: 30783629 PMCID: PMC6368442 DOI: 10.1126/sciadv.aav6380] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2018] [Accepted: 12/21/2018] [Indexed: 05/26/2023]
Abstract
Magnetic monopoles, proposed as elementary particles that act as isolated magnetic south and north poles, have long attracted research interest as magnetic analogs to electric charge. In solid-state physics, a classical analog to these elusive particles has emerged as topological excitations within pyrochlore spin ice systems. We present the first real-time imaging of emergent magnetic monopole motion in a macroscopically degenerate artificial spin ice system consisting of thermally activated Ising-type nanomagnets lithographically arranged onto a pre-etched silicon substrate. A real-space characterization of emergent magnetic monopoles within the framework of Debye-Hückel theory is performed, providing visual evidence that these topological defects act like a plasma of Coulomb-type magnetic charges. In contrast to vertex defects in a purely two-dimensional artificial square ice, magnetic monopoles are free to evolve within a divergence-free vacuum, a magnetic Coulomb phase, for which features in the form of pinch-point singularities in magnetic structure factors are observed.
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Affiliation(s)
- Alan Farhan
- Advanced Light Source, Lawrence Berkeley National Laboratory (LBNL), 1 Cyclotron Road, Berkeley, CA 94720, USA
- Laboratory for Multiscale Materials Experiments (LMX), Paul Scherrer Institute, 5232 Villigen, Switzerland
| | - Michael Saccone
- Physics Department, University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA
| | - Charlotte F. Petersen
- COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Espoo, Finland
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Scott Dhuey
- Molecular Foundry, LBNL, 1 Cyclotron Road, Berkeley, CA 94720, USA
| | - Rajesh V. Chopdekar
- Advanced Light Source, Lawrence Berkeley National Laboratory (LBNL), 1 Cyclotron Road, Berkeley, CA 94720, USA
| | - Yen-Lin Huang
- Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, CA 94720, USA
| | - Noah Kent
- Physics Department, University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA
- Materials Sciences Division, LBNL, 1 Cyclotron Road, Berkeley, CA 94720, USA
| | - Zuhuang Chen
- School of Materials Science and Engineering, Harbin Institute of Technology, Shenzhen, Guangdong 518055, China
| | - Mikko J. Alava
- COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Espoo, Finland
| | - Thomas Lippert
- Laboratory for Multiscale Materials Experiments (LMX), Paul Scherrer Institute, 5232 Villigen, Switzerland
- Department of Chemistry and Applied Biosciences, Laboratory of Inorganic Chemistry, ETH Zurich, Switzerland
| | - Andreas Scholl
- Advanced Light Source, Lawrence Berkeley National Laboratory (LBNL), 1 Cyclotron Road, Berkeley, CA 94720, USA
| | - Sebastiaan van Dijken
- NanoSpin, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland
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41
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Loreto RP, Nascimento FS, Gonçalves RS, Borme J, Cezar JC, Nisoli C, Pereira AR, de Araujo CIL. Experimental and theoretical evidences for the ice regime in planar artificial spin ices. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:025301. [PMID: 30521491 DOI: 10.1088/1361-648x/aaeeef] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
In this work, we explore a kind of geometrical effect in the thermodynamics of artificial spin ices (ASI). In general, such artificial materials are athermal. Here, We demonstrate that geometrically driven dynamics in ASI can open up the panorama of exploring distinct ground states and thermally magnetic monopole excitations. It is shown that a particular ASI lattice will provide a richer thermodynamics with nanomagnet spins experiencing less restriction to flip precisely in a kind of rhombic lattice. This can be observed by analysis of only three types of rectangular artificial spin ices (RASI). Denoting the horizontal and vertical lattice spacings by [Formula: see text] and [Formula: see text], respectively, then, a RASI material can be described by its aspect ratio [Formula: see text]. The rhombic lattice emerges when [Formula: see text]. So, by comparing the impact of thermal effects on the spin flips in these three appropriate different RASI arrays, it is possible to find a system very close to the ice regime.
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Affiliation(s)
- R P Loreto
- Laboratory of Spintronics and Nanomagnetism (LabSpiN), Departamento de Física, Universidade Federal de Viçosa, 36570-900, Viçosa, Minas Gerais, Brazil
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42
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Louis D, Lacour D, Hehn M, Lomakin V, Hauet T, Montaigne F. A tunable magnetic metamaterial based on the dipolar four-state Potts model. NATURE MATERIALS 2018; 17:1076-1080. [PMID: 30374201 DOI: 10.1038/s41563-018-0199-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2018] [Accepted: 09/18/2018] [Indexed: 06/08/2023]
Abstract
Metamaterials, tunable artificial materials, are useful playgrounds to investigate magnetic systems. So far, artificial Ising spin systems have revealed features such as emergent magnetic monopoles1,2 and charge fragmentation3. Here we present a metasystem composed of a lattice of dipolarly coupled nanomagnets. The magnetic spin of each nanomagnet is constrained to lie along a body diagonal, which yields four possible spin states. We show that the magnetic ordering of this metasystem (antiferromagnetic, ferromagnetic or spin ice like) is determined by the spin states orientation relative to the underlying lattice. The dipolar four-state Potts model explains our experimental observations and sheds light on the role of symmetry, as well as short- and long-range dipolar magnetic interactions, in such non-Ising spin systems.
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Affiliation(s)
- D Louis
- Institut Jean Lamour, CNRS-Université de Lorraine, Nancy, France
| | - D Lacour
- Institut Jean Lamour, CNRS-Université de Lorraine, Nancy, France
| | - M Hehn
- Institut Jean Lamour, CNRS-Université de Lorraine, Nancy, France
| | - V Lomakin
- University of California San Diego, Department of Electrical and Computer Engineering, La Jolla, CA, USA
| | - T Hauet
- Institut Jean Lamour, CNRS-Université de Lorraine, Nancy, France
| | - F Montaigne
- Institut Jean Lamour, CNRS-Université de Lorraine, Nancy, France.
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43
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Libál A, Lee DY, Ortiz-Ambriz A, Reichhardt C, Reichhardt CJO, Tierno P, Nisoli C. Ice rule fragility via topological charge transfer in artificial colloidal ice. Nat Commun 2018; 9:4146. [PMID: 30297820 PMCID: PMC6175946 DOI: 10.1038/s41467-018-06631-1] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2018] [Accepted: 09/05/2018] [Indexed: 11/09/2022] Open
Abstract
Artificial particle ices are model systems of constrained, interacting particles. They have been introduced theoretically to study ice-manifolds emergent from frustration, along with domain wall and grain boundary dynamics, doping, pinning-depinning, controlled transport of topological defects, avalanches, and memory effects. Recently such particle-based ices have been experimentally realized with vortices in nano-patterned superconductors or gravitationally trapped colloids. Here we demonstrate that, although these ices are generally considered equivalent to magnetic spin ices, they can access a novel spectrum of phenomenologies that are inaccessible to the latter. With experiments, theory and simulations we demonstrate that in mixed coordination geometries, entropy-driven negative monopoles spontaneously appear at a density determined by the vertex-mixture ratio. Unlike its spin-based analogue, the colloidal system displays a "fragile ice" manifold, where local energetics oppose the ice rule, which is instead enforced through conservation of the global topological charge. The fragile colloidal ice, stabilized by topology, can be spontaneously broken by topological charge transfer.
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Affiliation(s)
- András Libál
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.,Mathematics and Computer Science Department, Babeş-Bolyai University, Cluj, 400084, Romania
| | - Dong Yun Lee
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, 08028, España
| | - Antonio Ortiz-Ambriz
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, 08028, España.,Institut de Nanociència i Nanotecnologia, Universitat de Barcelona, Barcelona, 08028, Spain
| | - Charles Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | | | - Pietro Tierno
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, 08028, España.,Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona, 08028, Spain.,Institut de Nanociència i Nanotecnologia, Universitat de Barcelona, Barcelona, 08028, Spain
| | - Cristiano Nisoli
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA. .,Institute for Materials Science, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
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44
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Tunable and switchable magnetic dipole patterns in nanostructured superconductors. Nat Commun 2018; 9:2576. [PMID: 29968732 PMCID: PMC6030140 DOI: 10.1038/s41467-018-05045-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2017] [Accepted: 06/08/2018] [Indexed: 11/08/2022] Open
Abstract
Design and manipulation of magnetic moment arrays have been at the focus of studying the interesting cooperative physical phenomena in various magnetic systems. However, long-range ordered magnetic moments are rather difficult to achieve due to the excited states arising from the relatively weak exchange interactions between the localized moments. Here, using a nanostructured superconductor, we investigate a perfectly ordered magnetic dipole pattern with the magnetic poles having the same distribution as the magnetic charges in an artificial spin ice. The magnetic states can simply be switched on/off by applying a current flowing through nanopatterned area. Moreover, by coupling magnetic dipoles with the pinned vortex lattice, we are able to erase the positive/negative poles, resulting in a magnetic dipole pattern of only one polarity, analogous to the recently predicted vortex ice. These switchable and tunable magnetic dipole patterns open pathways for the study of exotic ordering phenomena in magnetic systems.
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45
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Wang YL, Ma X, Xu J, Xiao ZL, Snezhko A, Divan R, Ocola LE, Pearson JE, Janko B, Kwok WK. Switchable geometric frustration in an artificial-spin-ice-superconductor heterosystem. NATURE NANOTECHNOLOGY 2018; 13:560-565. [PMID: 29892018 DOI: 10.1038/s41565-018-0162-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2017] [Accepted: 05/03/2018] [Indexed: 06/08/2023]
Abstract
Geometric frustration emerges when local interaction energies in an ordered lattice structure cannot be simultaneously minimized, resulting in a large number of degenerate states. The numerous degenerate configurations may lead to practical applications in microelectronics1, such as data storage, memory and logic2. However, it is difficult to achieve very high degeneracy, especially in a two-dimensional system3,4. Here, we showcase in situ controllable geometric frustration with high degeneracy in a two-dimensional flux-quantum system. We create this in a superconducting thin film placed underneath a reconfigurable artificial-spin-ice structure5. The tunable magnetic charges in the artificial-spin-ice strongly interact with the flux quanta in the superconductor, enabling switching between frustrated and crystallized flux quanta states. The different states have measurable effects on the superconducting critical current profile, which can be reconfigured by precise selection of the spin-ice magnetic state through the application of an external magnetic field. We demonstrate the applicability of these effects by realizing a reprogrammable flux quanta diode. The tailoring of the energy landscape of interacting 'particles' using artificial-spin-ices provides a new paradigm for the design of geometric frustration, which could illuminate a path to control new functionalities in other material systems, such as magnetic skyrmions6, electrons and holes in two-dimensional materials7,8, and topological insulators9, as well as colloids in soft materials10-13.
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Affiliation(s)
- Yong-Lei Wang
- Materials Science Division, Argonne National Laboratory, Argonne, IL, USA.
- Department of Physics, University of Notre Dame, Notre Dame, IN, USA.
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China.
| | - Xiaoyu Ma
- Department of Physics, University of Notre Dame, Notre Dame, IN, USA
| | - Jing Xu
- Materials Science Division, Argonne National Laboratory, Argonne, IL, USA
- Department of Physics, Northern Illinois University, DeKalb, IL, USA
| | - Zhi-Li Xiao
- Materials Science Division, Argonne National Laboratory, Argonne, IL, USA.
- Department of Physics, Northern Illinois University, DeKalb, IL, USA.
| | - Alexey Snezhko
- Materials Science Division, Argonne National Laboratory, Argonne, IL, USA
| | - Ralu Divan
- Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL, USA
| | - Leonidas E Ocola
- Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL, USA
- IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA
| | - John E Pearson
- Materials Science Division, Argonne National Laboratory, Argonne, IL, USA
| | - Boldizsar Janko
- Department of Physics, University of Notre Dame, Notre Dame, IN, USA.
| | - Wai-Kwong Kwok
- Materials Science Division, Argonne National Laboratory, Argonne, IL, USA
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46
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Direct-write of free-form building blocks for artificial magnetic 3D lattices. Sci Rep 2018; 8:6160. [PMID: 29670129 PMCID: PMC5906635 DOI: 10.1038/s41598-018-24431-x] [Citation(s) in RCA: 68] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2018] [Accepted: 03/29/2018] [Indexed: 11/30/2022] Open
Abstract
By the fabrication of periodically arranged nanomagnetic systems it is possible to engineer novel physical properties by realizing artificial lattice geometries that are not accessible via natural crystallization or chemical synthesis. This has been accomplished with great success in two dimensions in the fields of artificial spin ice and magnetic logic devices, to name just two. Although first proposals have been made to advance into three dimensions (3D), established nanofabrication pathways based on electron beam lithography have not been adapted to obtain free-form 3D nanostructures. Here we demonstrate the direct-write fabrication of freestanding ferromagnetic 3D nano-architectures. By employing micro-Hall sensing, we have determined the magnetic stray field generated by our free-form structures in an externally applied magnetic field and we have performed micromagnetic and macro-spin simulations to deduce the spatial magnetization profiles in the structures and analyze their switching behavior. Furthermore we show that the magnetic 3D elements can be combined with other 3D elements of different chemical composition and intrinsic material properties.
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47
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Al Mamoori MKI, Keller L, Pieper J, Barth S, Winkler R, Plank H, Müller J, Huth M. Magnetic Characterization of Direct-Write Free-Form Building Blocks for Artificial Magnetic 3D Lattices. MATERIALS (BASEL, SWITZERLAND) 2018; 11:E289. [PMID: 29439553 PMCID: PMC5848986 DOI: 10.3390/ma11020289] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/22/2017] [Revised: 02/07/2018] [Accepted: 02/07/2018] [Indexed: 11/16/2022]
Abstract
Three-dimensional (3D) nanomagnetism, where spin configurations extend into the vertical direction of a substrate plane allow for more complex, hierarchical systems and the design of novel magnetic effects. As an important step towards this goal, we have recently demonstrated the direct-write fabrication of freestanding ferromagnetic 3D nano-architectures of ferromagnetic CoFe in shapes of nano-tree and nano-cube structures by means of focused electron beam induced deposition. Here, we present a comprehensive characterization of the magnetic properties of these structures by local stray-field measurements using a high-resolution micro-Hall magnetometer. Measurements in a wide range of temperatures and different angles of the externally applied magnetic field with respect to the surface plane of the sensor are supported by corresponding micromagnetic simulations, which explain the overall switching behavior of in part rather complex magnetization configurations remarkably well. In particular, the simulations yield coercive and switching fields that are in good quantitative correspondence with the measured coercive and switching fields assuming a bulk metal content of 100 at % consisting of bcc Co 3 Fe. We show that thermally-unstable magnetization states can be repetitively prepared and their lifetime controlled at will, a prerequisite to realizing dynamic and thermally-active magnetic configurations if the building blocks are to be used in lattice structures.
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Affiliation(s)
| | - Lukas Keller
- Institute of Physics, Goethe University, 60438 (M) Frankfurt, Germany.
| | - Jonathan Pieper
- Institute of Physics, Goethe University, 60438 (M) Frankfurt, Germany.
| | - Sven Barth
- Institute of Materials Chemistry, Vienna University of Technology, 1060 Vienna, Austria.
| | - Robert Winkler
- Graz Centre for Electron Microscopy, 8010 Graz, Austria.
| | - Harald Plank
- Institute of Electron Microscopy and Nanoanalysis, Graz University of Technology, 8010 Graz, Austria.
| | - Jens Müller
- Institute of Physics, Goethe University, 60438 (M) Frankfurt, Germany.
| | - Michael Huth
- Institute of Physics, Goethe University, 60438 (M) Frankfurt, Germany.
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48
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Abstract
Many liquid or liquid-like states remain stable down to temperatures well below the interaction energy scale, where mean-field theory predicts an ordering transition. In magnetism, correlated states such as spin ice and the spin liquid have been described as Coulomb phases, governed by an emergent gauge principle. In the physical chemistry of polar liquids, systems that evade mean field order have, in contrast, been described by Onsager’s theory of the reaction field. Here we observe that in the low-temperature limit, Onsager’s theory may be cast as a prototypical theory of the Coulomb phase. However at finite temperature, it describes a distinct geometrical state, characterised by harmonic functions. This state, labelled here the ‘harmonic phase’, is shown to occur experimentally in spin ice, a dipolar lattice system. It is suggested to be relevant to more general dipolar liquids. Spin ice materials can be described using idealised models of frustrated magnetism and have motivated a revisiting of the theory of interacting dipolar systems. Bramwell shows that Onsager’s theory of polar liquids describes the Coulomb phase and predicts a distinct ‘harmonic phase’ at finite temperature.
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49
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Bramwell ST. Artificial spin ice: A ratchet made of tiny magnets. NATURE MATERIALS 2017; 16:1053-1054. [PMID: 29058726 DOI: 10.1038/nmat5004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Affiliation(s)
- Steven T Bramwell
- Department of Physics and Astronomy and at the London Centre for Nanotechnology, University College London, 17-19 Gordon Street, London WC1H 0AJ, UK
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50
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Realization of Rectangular Artificial Spin Ice and Direct Observation of High Energy Topology. Sci Rep 2017; 7:13982. [PMID: 29070908 PMCID: PMC5656638 DOI: 10.1038/s41598-017-14421-w] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2017] [Accepted: 10/10/2017] [Indexed: 11/29/2022] Open
Abstract
In this work, we have constructed and experimentally investigated frustrated arrays of dipoles forming two-dimensional artificial spin ices with different lattice parameters (rectangular arrays with horizontal and vertical lattice spacings denoted by a and b respectively). Arrays with three different aspect ratios γ = a/b = \documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{{\bf{4}}}$$\end{document}4 are studied. Theoretical calculations of low-energy demagnetized configurations for these same parameters are also presented. Experimental data for demagnetized samples confirm most of the theoretical results. However, the highest energy topology (doubly-charged monopoles) does not emerge in our theoretical model, while they are seen in experiments for large enough γ. Our results also insinuate that the string tension connecting two magnetic monopoles in a pair vanishes in rectangular lattices with a critical ratio γ = γc = \documentclass[12pt]{minimal}
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