1
|
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.
Collapse
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
| |
Collapse
|
2
|
Lendinez S, Jungfleisch MB. Magnetization dynamics in artificial spin ice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:013001. [PMID: 31600143 DOI: 10.1088/1361-648x/ab3e78] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
In this topical review, we present key results of studies on magnetization dynamics in artificial spin ice (ASI), which are arrays of magnetically interacting nanostructures. Recent experimental and theoretical progress in this emerging area, which is at the boundary between research on frustrated magnetism and high-frequency studies of artificially created nanomagnets, is reviewed. The exploration of ASI structures has revealed fascinating discoveries in correlated spin systems. Artificially created spin ice lattices offer unique advantages as they allow for a control of the interactions between the elements by their geometric properties and arrangement. Magnonics, on the other hand, is a field that explores spin dynamics in the gigahertz frequency range in magnetic micro- and nanostructures. In this context, magnonic crystals are particularly important as they allow the modification of spin-wave properties and the observation of band gaps in the resonance spectra. Very recently, there has been considerable progress, experimentally and theoretically, in combining aspects of both fields-artificial spin ice and magnonics-enabling new functionalities in magnonic and spintronic applications using ASI, as well as providing a deeper understanding of geometrical frustration in the gigahertz range. Different approaches for the realization of ASI structures and their experimental characterization in the high-frequency range are described and the appropriate theoretical models and simulations are reviewed. Special attention is devoted to linking these findings to the quasi-static behavior of ASI and dynamic investigations in magnonics in an effort to bridge the gap between both areas further and to stimulate new research endeavors.
Collapse
Affiliation(s)
- S Lendinez
- Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, United States of America
| | | |
Collapse
|
3
|
Magnetization dynamics of weakly interacting sub-100 nm square artificial spin ices. Sci Rep 2019; 9:19967. [PMID: 31882867 PMCID: PMC6934880 DOI: 10.1038/s41598-019-56219-y] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2019] [Accepted: 12/06/2019] [Indexed: 12/02/2022] Open
Abstract
Artificial Spin Ice (ASI), consisting of a two dimensional array of nanoscale magnetic elements, provides a fascinating opportunity to observe the physics of out-of-equilibrium systems. Initial studies concentrated on the static, frozen state, whilst more recent studies have accessed the out-of-equilibrium dynamic, fluctuating state. This opens up exciting possibilities such as the observation of systems exploring their energy landscape through monopole quasiparticle creation, potentially leading to ASI magnetricity, and to directly observe unconventional phase transitions. In this work we have measured and analysed the magnetic relaxation of thermally active ASI systems by means of SQUID magnetometry. We have investigated the effect of the interaction strength on the magnetization dynamics at different temperatures in the range where the nanomagnets are thermally active. We have observed that they follow an Arrhenius-type Néel-Brown behaviour. An unexpected negative correlation of the average blocking temperature with the interaction strength is also observed, which is supported by Monte Carlo simulations. The magnetization relaxation measurements show faster relaxation for more strongly coupled nanoelements with similar dimensions. The analysis of the stretching exponents obtained from the measurements suggest 1-D chain-like magnetization dynamics. This indicates that the nature of the interactions between nanoelements lowers the dimensionality of the ASI from 2-D to 1-D. Finally, we present a way to quantify the effective interaction energy of a square ASI system, and compare it to the interaction energy computed with micromagnetic simulations.
Collapse
|
4
|
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.
Collapse
|
5
|
Leleu T, Yamamoto Y, Utsunomiya S, Aihara K. Combinatorial optimization using dynamical phase transitions in driven-dissipative systems. Phys Rev E 2017; 95:022118. [PMID: 28297856 DOI: 10.1103/physreve.95.022118] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2016] [Indexed: 11/07/2022]
Abstract
The dynamics of driven-dissipative systems is shown to be well-fitted for achieving efficient combinatorial optimization. The proposed method can be applied to solve any combinatorial optimization problem that is equivalent to minimizing an Ising Hamiltonian. Moreover, the dynamics considered can be implemented using various physical systems as it is based on generic dynamics-the normal form of the supercritical pitchfork bifurcation. The computational principle of the proposed method relies on an hybrid analog-digital representation of the binary Ising spins by considering the gradient descent of a Lyapunov function that is the sum of an analog Ising Hamiltonian and archetypal single or double-well potentials. By gradually changing the shape of the latter potentials from a single to double well shape, it can be shown that the first nonzero steady states to become stable are associated with global minima of the Ising Hamiltonian, under the approximation that all analog spins have the same amplitude. In the more general case, the heterogeneity in amplitude between analog spins induces the stabilization of local minima, which reduces the quality of solutions to combinatorial optimization problems. However, we show that the heterogeneity in amplitude can be reduced by setting the parameters of the driving signal near a regime, called the dynamic phase transition, where the analog spins' DC components map more accurately the global minima of the Ising Hamiltonian which, in turn, increases the quality of solutions found. Last, we discuss the possibility of a physical implementation of the proposed method using networks of degenerate optical parametric oscillators.
Collapse
Affiliation(s)
- Timothée Leleu
- Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
| | - Yoshihisa Yamamoto
- ImPACT program, The Japan Science and Technology Agency, Gobancho 7, Chiyoda-ku, Tokyo 102-0076, Japan.,E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - Shoko Utsunomiya
- National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda, Tokyo 101-0003, Japan
| | - Kazuyuki Aihara
- Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
| |
Collapse
|
6
|
Real-space observation of magnetic excitations and avalanche behavior in artificial quasicrystal lattices. Sci Rep 2016; 6:34384. [PMID: 27694973 PMCID: PMC5046066 DOI: 10.1038/srep34384] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2016] [Accepted: 09/05/2016] [Indexed: 11/08/2022] Open
Abstract
Artificial spin ice lattices have emerged as model systems for studying magnetic frustration in recent years. Most work to date has looked at periodic artificial spin ice lattices. In this paper, we observe frustration effects in quasicrystal artificial spin ice lattices that lack translational symmetry and contain vertices with different numbers of interacting elements. We find that as the lattice state changes following demagnetizing and annealing, specific vertex motifs retain low-energy configurations, which excites other motifs into higher energy configurations. Additionally, we find that unlike the magnetization reversal process for periodic artificial spin ice lattices, which occurs through 1D avalanches, quasicrystal lattices undergo reversal through a dendritic 2D avalanche mechanism.
Collapse
|
7
|
Wang YL, Xiao ZL, Snezhko A, Xu J, Ocola LE, Divan R, Pearson JE, Crabtree GW, Kwok WK. Rewritable artificial magnetic charge ice. Science 2016; 352:962-6. [DOI: 10.1126/science.aad8037] [Citation(s) in RCA: 106] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2015] [Accepted: 04/13/2016] [Indexed: 11/02/2022]
|
8
|
Magnetic-charge ordering and phase transitions in monopole-conserved square spin ice. Sci Rep 2015; 5:15875. [PMID: 26511870 PMCID: PMC4625371 DOI: 10.1038/srep15875] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2015] [Accepted: 10/06/2015] [Indexed: 11/16/2022] Open
Abstract
Magnetic-charge ordering and corresponding magnetic/monopole phase transitions in spin ices are the emergent topics of condensed matter physics. In this work, we investigate a series of magnetic-charge (monopole) phase transitions in artificial square spin ice model using the conserved monopole density algorithm. It is revealed that the dynamics of low monopole density lattices is controlled by the effective Coulomb interaction and the Dirac string tension, leading to the monopole dimerization which is quite different from the dynamics of three-dimensional pyrochlore spin ice. The condensation of the monopole dimers into monopole crystals with staggered magnetic-charge order can be predicted clearly. For the high monopole density cases, the lattice undergoes two consecutive phase transitions from high-temperature paramagnetic/charge-disordered phase into staggered charge-ordered phase before eventually toward the long-range magnetically-ordered phase as the ground state which is of staggered charge order too. A phase diagram over the whole temperature-monopole density space, which exhibits a series of emergent spin and monopole ordered states, is presented.
Collapse
|
9
|
Kityk IV, Fedorchuk AO, Ozga K, AlZayed NS. Band Structure Simulations of the Photoinduced Changes in the MgB₂:Cr Films. NANOMATERIALS (BASEL, SWITZERLAND) 2015; 5:541-553. [PMID: 28347024 PMCID: PMC5312910 DOI: 10.3390/nano5020541] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/16/2015] [Revised: 03/25/2015] [Accepted: 03/26/2015] [Indexed: 11/17/2022]
Abstract
An approach for description of the photoinduced nonlinear optical effects in the superconducting MgB₂:Cr₂O₃ nanocrystalline film is proposed. It includes the molecular dynamics step-by-step optimization of the two separate crystalline phases. The principal role for the photoinduced nonlinear optical properties plays nanointerface between the two phases. The first modified layers possess a form of slightly modified perfect crystalline structure. The next layer is added to the perfect crystalline structure and the iteration procedure is repeated for the next layer. The total energy here is considered as a varied parameter. To avoid potential jumps on the borders we have carried out additional derivative procedure.
Collapse
Affiliation(s)
- Iwan V Kityk
- Faculty of Electrical Engineering, Czestochowa University of Technology, Armii Krajowej Street 17, 42-200 Czestochowa, Poland.
| | - Anatolii O Fedorchuk
- Department of Inorganic and Organic Chemistry, Lviv National University of Veterinary Medicine and Biotechnologies, Pekarska Street 50, 79010 Lviv, Ukraine.
| | - Katarzyna Ozga
- Faculty of Electrical Engineering, Czestochowa University of Technology, Armii Krajowej Street 17, 42-200 Czestochowa, Poland.
| | - Nasser S AlZayed
- Physics and Astronomy Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.
| |
Collapse
|
10
|
Montaigne F, Lacour D, Chioar IA, Rougemaille N, Louis D, Mc Murtry S, Riahi H, Burgos BS, Menteş TO, Locatelli A, Canals B, Hehn M. Size distribution of magnetic charge domains in thermally activated but out-of-equilibrium artificial spin ice. Sci Rep 2014; 4:5702. [PMID: 25029620 PMCID: PMC4100542 DOI: 10.1038/srep05702] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2014] [Accepted: 06/26/2014] [Indexed: 11/09/2022] Open
Abstract
A crystal of emerging magnetic charges is expected in the phase diagram of the dipolar kagomé spin ice. An observation of charge crystallites in thermally demagnetized artificial spin ice arrays has been recently reported by S. Zhang and coworkers and explained through the thermodynamics of the system as it approaches a charge-ordered state. Following a similar approach, we have generated a partial order of magnetic charges in an artificial kagomé spin ice lattice made out of ferrimagnetic material having a Curie temperature of 475 K. A statistical study of the size of the charge domains reveals an unconventional sawtooth distribution. This distribution is in disagreement with the predictions of the thermodynamic model and is shown to be a signature of the kinetic process governing the remagnetization.
Collapse
Affiliation(s)
- F Montaigne
- Institut Jean Lamour, Université de Lorraine and CNRS, Vandoeuvre lès Nancy, F-54506, France
| | - D Lacour
- Institut Jean Lamour, Université de Lorraine and CNRS, Vandoeuvre lès Nancy, F-54506, France
| | - I A Chioar
- 1] CNRS, Institut NEEL, F-38042 Grenoble, France [2] Univ. Grenoble Alpes, Institut NEEL, F-38042 Grenoble, France
| | - N Rougemaille
- 1] CNRS, Institut NEEL, F-38042 Grenoble, France [2] Univ. Grenoble Alpes, Institut NEEL, F-38042 Grenoble, France
| | - D Louis
- Institut Jean Lamour, Université de Lorraine and CNRS, Vandoeuvre lès Nancy, F-54506, France
| | - S Mc Murtry
- Institut Jean Lamour, Université de Lorraine and CNRS, Vandoeuvre lès Nancy, F-54506, France
| | - H Riahi
- Institut Jean Lamour, Université de Lorraine and CNRS, Vandoeuvre lès Nancy, F-54506, France
| | - B Santos Burgos
- Elettra-Sincrotrone Trieste S.C.p.A. S.S. 14 - km 163,5 in AREA Science Park, 34149 Basovizza, Trieste, Italy
| | - T O Menteş
- Elettra-Sincrotrone Trieste S.C.p.A. S.S. 14 - km 163,5 in AREA Science Park, 34149 Basovizza, Trieste, Italy
| | - A Locatelli
- Elettra-Sincrotrone Trieste S.C.p.A. S.S. 14 - km 163,5 in AREA Science Park, 34149 Basovizza, Trieste, Italy
| | - B Canals
- 1] CNRS, Institut NEEL, F-38042 Grenoble, France [2] Univ. Grenoble Alpes, Institut NEEL, F-38042 Grenoble, France
| | - M Hehn
- Institut Jean Lamour, Université de Lorraine and CNRS, Vandoeuvre lès Nancy, F-54506, France
| |
Collapse
|
11
|
Chern GW, Morrison MJ, Nisoli C. Degeneracy and criticality from emergent frustration in artificial spin ice. PHYSICAL REVIEW LETTERS 2013; 111:177201. [PMID: 24206515 DOI: 10.1103/physrevlett.111.177201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2012] [Indexed: 06/02/2023]
Abstract
Although initially introduced to mimic the spin-ice pyrochlores, no artificial spin ice has yet exhibited the expected degenerate ice phase with critical correlations similar to the celebrated Coulomb phase in the pyrochlore lattice. Here we study a novel artificial spin ice based on a vertex-frustrated rather than pairwise frustrated geometry and show that it exhibits a quasicritical ice phase of extensive residual entropy and, significantly, algebraic correlations. Interesting in its own regard as a novel realization of frustration in a vertex system, our lattice opens new pathways to study defects in a critical manifold and to design degeneracy in artificial magnetic nanoarrays, a task so far elusive.
Collapse
Affiliation(s)
- Gia-Wei Chern
- Theoretical Division and Center for Nonlinear Studies, LANL, Los Alamos, New Mexico 87545, USA
| | | | | |
Collapse
|
12
|
Heyderman LJ, Stamps RL. Artificial ferroic systems: novel functionality from structure, interactions and dynamics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:363201. [PMID: 23948652 DOI: 10.1088/0953-8984/25/36/363201] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Lithographic processing and film growth technologies are continuing to advance, so that it is now possible to create patterned ferroic materials consisting of arrays of sub-1 μm elements with high definition. Some of the most fascinating behaviour of these arrays can be realised by exploiting interactions between the individual elements to create new functionality. The properties of these artificial ferroic systems differ strikingly from those of their constituent components, with novel emergent behaviour arising from the collective dynamics of the interacting elements, which are arranged in specific designs and can be activated by applying magnetic or electric fields. We first focus on artificial spin systems consisting of arrays of dipolar-coupled nanomagnets and, in particular, review the field of artificial spin ice, which demonstrates a wide range of fascinating phenomena arising from the frustration inherent in particular arrangements of nanomagnets, including emergent magnetic monopoles, domains of ordered macrospins, and novel avalanche behaviour. We outline how demagnetisation protocols have been employed as an effective thermal anneal in an attempt to reach the ground state, comment on phenomena that arise in thermally activated systems and discuss strategies for selectively generating specific configurations using applied magnetic fields. We then move on from slow field and temperature driven dynamics to high frequency phenomena, discussing spinwave excitations in the context of magnonic crystals constructed from arrays of patterned magnetic elements. At high frequencies, these arrays are studied in terms of potential applications including magnetic logic, linear and non-linear microwave optics, and fast, efficient switching, and we consider the possibility to create tunable magnonic crystals with artificial spin ice. Finally, we discuss how functional ferroic composites can be incorporated to realise magnetoelectric effects. Specifically, we discuss artificial multiferroics (or multiferroic composites), which hold promise for new applications that involve electric field control of magnetism, or electric and magnetic field responsive devices for high frequency integrated circuit design in microwave and terahertz signal processing. We close with comments on how enhanced functionality can be realised through engineering of nanostructures with interacting ferroic components, creating opportunities for novel spin electronic devices that, for example, make use of the transport of magnetic charges, thermally activated elements, and reprogrammable nanomagnet systems.
Collapse
Affiliation(s)
- L J Heyderman
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland.
| | | |
Collapse
|
13
|
Crystallites of magnetic charges in artificial spin ice. Nature 2013; 500:553-7. [DOI: 10.1038/nature12399] [Citation(s) in RCA: 179] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2013] [Accepted: 06/14/2013] [Indexed: 11/09/2022]
|
14
|
Zhang S, Li J, Gilbert I, Bartell J, Erickson MJ, Pan Y, Lammert PE, Nisoli C, Kohli KK, Misra R, Crespi VH, Samarth N, Leighton C, Schiffer P. Perpendicular magnetization and generic realization of the Ising model in artificial spin ice. PHYSICAL REVIEW LETTERS 2012; 109:087201. [PMID: 23002770 DOI: 10.1103/physrevlett.109.087201] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2012] [Indexed: 06/01/2023]
Abstract
We have studied frustrated kagome arrays and unfrustrated honeycomb arrays of magnetostatically interacting single-domain ferromagnetic islands with magnetization normal to the plane. The measured pairwise spin correlations of both lattices can be reproduced by models based solely on nearest-neighbor correlations. The kagome array has qualitatively different magnetostatics but identical lattice topology to previously studied artificial spin ice systems composed of in-plane moments. The two systems show striking similarities in the development of moment pair correlations, demonstrating a universality in artificial spin ice behavior independent of specific realization in a particular material system.
Collapse
Affiliation(s)
- Sheng Zhang
- Department of Physics and Materials Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
15
|
Libál A, Reichhardt C, Olson Reichhardt CJ. Hysteresis and return-point memory in colloidal artificial spin ice systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:021406. [PMID: 23005762 DOI: 10.1103/physreve.86.021406] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2011] [Revised: 06/22/2012] [Indexed: 06/01/2023]
Abstract
Using computer simulations, we investigate hysteresis loops and return-point memory for artificial square and kagome spin ice systems by cycling an applied bias force and comparing microscopic effective spin configurations throughout the hysteresis cycle. Return-point memory loss is caused by motion of individual defects in kagome ice or of grain boundaries in square ice. In successive cycles, return-point memory is recovered rapidly in kagome ice. Memory is recovered more gradually in square ice due to the extended nature of the grain boundaries. Increasing the amount of quenched disorder increases the defect density but also enhances the return-point memory since the defects become trapped more easily.
Collapse
Affiliation(s)
- A Libál
- Faculty of Mathematics and Computer Science, Babes-Bolyai University, RO-400591 Cluj-Napoca, Romania
| | | | | |
Collapse
|
16
|
Budrikis Z, Morgan JP, Akerman J, Stein A, Politi P, Langridge S, Marrows CH, Stamps RL. Disorder strength and field-driven ground state domain formation in artificial spin ice: experiment, simulation, and theory. PHYSICAL REVIEW LETTERS 2012; 109:037203. [PMID: 22861890 DOI: 10.1103/physrevlett.109.037203] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2011] [Indexed: 06/01/2023]
Abstract
Quenched disorder affects how nonequilibrium systems respond to driving. In the context of artificial spin ice, an athermal system comprised of geometrically frustrated classical Ising spins with a twofold degenerate ground state, we give experimental and numerical evidence of how such disorder washes out edge effects and provide an estimate of disorder strength in the experimental system. We prove analytically that a sequence of applied fields with fixed amplitude is unable to drive the system to its ground state from a saturated state. These results should be relevant for other systems where disorder does not change the nature of the ground state.
Collapse
Affiliation(s)
- Zoe Budrikis
- School of Physics, The University of Western Australia, 35 Stirling Highway, Crawley 6009, Australia.
| | | | | | | | | | | | | | | |
Collapse
|
17
|
Budrikis Z, Politi P, Stamps RL. Diversity enabling equilibration: disorder and the ground state in artificial spin ice. PHYSICAL REVIEW LETTERS 2011; 107:217204. [PMID: 22181919 DOI: 10.1103/physrevlett.107.217204] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2011] [Indexed: 05/31/2023]
Abstract
We report a novel approach to the question of whether and how the ground state can be achieved in square artificial spin ices where frustration is incomplete. We identify two sources of randomness that affect the approach to ground state: quenched disorder in the island response to fields and randomness in the sequence of driving fields. Numerical simulations show that quenched disorder can lead to final states with lower energy, and randomness in the sequence of driving fields always lowers the final energy attained by the system. We use a network picture to understand these two effects: disorder in island responses creates new dynamical pathways, and a random sequence of driving fields allows more pathways to be followed.
Collapse
Affiliation(s)
- Zoe Budrikis
- School of Physics, The University of Western Australia, Australia.
| | | | | |
Collapse
|
18
|
Zhang S, Li J, Bartell J, Ke X, Nisoli C, Lammert PE, Crespi VH, Schiffer P. Ignoring your neighbors: moment correlations dominated by indirect or distant interactions in an ordered nanomagnet array. PHYSICAL REVIEW LETTERS 2011; 107:117204. [PMID: 22026700 DOI: 10.1103/physrevlett.107.117204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2011] [Indexed: 05/31/2023]
Abstract
We have studied the moment correlations within triangular lattice arrays of single-domain coaligned nanoscale ferromagnetic islands. Independent variation of lattice spacing along and perpendicular to the island axis tunes the magnetostatic interactions between islands through a broad range of relative strengths. For certain lattice parameters, the sign of the correlations between near-neighbor island moments is opposite to that favored by the pairwise interaction. This finding, supported by analysis of the total correlation in terms of direct and convoluted indirect contributions across multiple pairwise interactions, indicates that indirect interactions and/or those mediated by further neighbors can be tuned to be dominant, with implications for the wide range of systems composed of interacting nanomagnets.
Collapse
Affiliation(s)
- Sheng Zhang
- Department of Physics and Materials Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | | | | | | | | | | | | | | |
Collapse
|
19
|
Chern GW, Mellado P, Tchernyshyov O. Two-stage ordering of spins in dipolar spin ice on the kagome lattice. PHYSICAL REVIEW LETTERS 2011; 106:207202. [PMID: 21668259 DOI: 10.1103/physrevlett.106.207202] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2009] [Revised: 04/28/2011] [Indexed: 05/30/2023]
Abstract
Spin ice, a peculiar thermal state of a frustrated ferromagnet on the pyrochlore lattice, has a finite entropy density and excitations carrying magnetic charge. By combining analytical arguments and Monte Carlo simulations, we show that spin ice on the two-dimensional kagome lattice orders in two stages. The intermediate phase has ordered magnetic charges and is separated from the paramagnetic phase by an Ising transition. The transition to the low-temperature phase is of the three-state Potts or Kosterlitz-Thouless type, depending on the presence of defects in the charge order.
Collapse
Affiliation(s)
- Gia-Wei Chern
- Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
| | | | | |
Collapse
|
20
|
Rougemaille N, Montaigne F, Canals B, Duluard A, Lacour D, Hehn M, Belkhou R, Fruchart O, El Moussaoui S, Bendounan A, Maccherozzi F. Artificial kagome arrays of nanomagnets: a frozen dipolar spin ice. PHYSICAL REVIEW LETTERS 2011; 106:057209. [PMID: 21405433 DOI: 10.1103/physrevlett.106.057209] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2010] [Revised: 12/10/2010] [Indexed: 05/30/2023]
Abstract
Magnetic frustration effects in artificial kagome arrays of nanomagnets are investigated using x-ray photoemission electron microscopy and Monte Carlo simulations. Spin configurations of demagnetized networks reveal unambiguous signatures of long range, dipolar interaction between the nanomagnets. As soon as the system enters the spin ice manifold, the kagome dipolar spin ice model captures the observed physics, while the short range kagome spin ice model fails.
Collapse
Affiliation(s)
- N Rougemaille
- Institut Néel, CNRS-UJF, BP 166, 38042 Grenoble Cedex 9, France
| | | | | | | | | | | | | | | | | | | | | |
Collapse
|
21
|
Mellado P, Petrova O, Shen Y, Tchernyshyov O. Dynamics of magnetic charges in artificial spin ice. PHYSICAL REVIEW LETTERS 2010; 105:187206. [PMID: 21231135 DOI: 10.1103/physrevlett.105.187206] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2010] [Indexed: 05/30/2023]
Abstract
Artificial spin ice has been recently implemented in two-dimensional arrays of mesoscopic magnetic wires. We propose a theoretical model of magnetization dynamics in artificial spin ice under the action of an applied magnetic field. Magnetization reversal is mediated by domain walls carrying two units of magnetic charge. They are emitted by lattice junctions when the local field exceeds a critical value Hc required to pull apart magnetic charges of opposite sign. Positive feedback from Coulomb interactions between magnetic charges induces avalanches in magnetization reversal.
Collapse
Affiliation(s)
- Paula Mellado
- Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | | | | | | |
Collapse
|
22
|
Nisoli C, Li J, Ke X, Garand D, Schiffer P, Crespi VH. Effective temperature in an interacting vertex system: theory and experiment on artificial spin ice. PHYSICAL REVIEW LETTERS 2010; 105:047205. [PMID: 20867881 DOI: 10.1103/physrevlett.105.047205] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2009] [Indexed: 05/29/2023]
Abstract
Frustrated arrays of interacting single-domain nanomagnets provide important model systems for statistical mechanics, as they map closely onto well-studied vertex models and are amenable to direct imaging and custom engineering. Although these systems are manifestly athermal, we demonstrate that an effective temperature, controlled by an external magnetic drive, describes their microstates and therefore their full statistical properties.
Collapse
Affiliation(s)
- Cristiano Nisoli
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | | | | | | | | | |
Collapse
|
23
|
Budrikis Z, Politi P, Stamps RL. Vertex dynamics in finite two-dimensional square spin ices. PHYSICAL REVIEW LETTERS 2010; 105:017201. [PMID: 20867472 DOI: 10.1103/physrevlett.105.017201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2010] [Indexed: 05/29/2023]
Abstract
Local magnetic ordering in artificial spin ices is discussed from the point of view of how geometrical frustration controls dynamics and the approach to steady state. We discuss the possibility of using a particle picture based on vertex configurations to interpret the time evolution of magnetic configurations. Analysis of possible vertex processes allows us to anticipate different behaviors for open and closed edges and the existence of different field regimes. Numerical simulations confirm these results and also demonstrate the importance of correlations and long-range interactions in understanding particle population evolution. We also show that a mean-field model of vertex dynamics gives important insights into finite size effects.
Collapse
Affiliation(s)
- Zoe Budrikis
- School of Physics M013, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia
| | | | | |
Collapse
|
24
|
Libál A, Reichhardt CJO, Reichhardt C. Creating artificial ice states using vortices in nanostructured superconductors. PHYSICAL REVIEW LETTERS 2009; 102:237004. [PMID: 19658964 DOI: 10.1103/physrevlett.102.237004] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2008] [Indexed: 05/28/2023]
Abstract
We demonstrate that it is possible to realize vortex ice states that are analogous to square and kagome ice. With numerical simulations, we show that the system can be brought into a state that obeys either global or local ice rules by applying an external current according to an annealing protocol. We explore the breakdown of the ice rules due to disorder in the nanostructure array and show that in square ice, topological defects appear along grain boundaries, while in kagome ice, individual defects appear. We argue that the vortex system offers significant advantages over other artificial ice systems.
Collapse
Affiliation(s)
- A Libál
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| | | | | |
Collapse
|