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Adamantopoulos T, Merte M, Go D, Freimuth F, Blügel S, Mokrousov Y. Orbital Rashba Effect as a Platform for Robust Orbital Photocurrents. Phys Rev Lett 2024; 132:076901. [PMID: 38427860 DOI: 10.1103/physrevlett.132.076901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Revised: 07/03/2023] [Accepted: 01/09/2024] [Indexed: 03/03/2024]
Abstract
Orbital current has emerged over the past years as one of the key novel concepts in magnetotransport. Here, we demonstrate that laser pulses can be used to generate large and robust nonrelativistic orbital currents in systems where the inversion symmetry is broken by the orbital Rashba effect. By referring to model and first principles tools, we demonstrate that orbital Rashba effect, accompanied by crystal field splitting, can mediate robust orbital photocurrents without a need for spin-orbit interaction even in metallic systems. We show that such nonrelativistic orbital photocurrents are translated into derivative photocurrents of spin when relativistic effects are taken into account. We thus promote orbital photocurrents as a promising platform for optical generation of currents of angular momentum, and discuss their possible applications.
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Affiliation(s)
- T Adamantopoulos
- Peter Grünberg Institut, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
- Department of Physics, RWTH Aachen University, 52056 Aachen, Germany
| | - M Merte
- Peter Grünberg Institut, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
- Department of Physics, RWTH Aachen University, 52056 Aachen, Germany
- Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
| | - D Go
- Peter Grünberg Institut, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
- Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
| | - F Freimuth
- Peter Grünberg Institut, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
- Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
| | - S Blügel
- Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
| | - Y Mokrousov
- Peter Grünberg Institut, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
- Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
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2
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Seifert TS, Go D, Hayashi H, Rouzegar R, Freimuth F, Ando K, Mokrousov Y, Kampfrath T. Publisher Correction: Time-domain observation of ballistic orbital-angular-momentum currents with giant relaxation length in tungsten. Nat Nanotechnol 2023; 18:1254. [PMID: 37605046 PMCID: PMC10575767 DOI: 10.1038/s41565-023-01504-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/23/2023]
Affiliation(s)
- Tom S Seifert
- Department of Physics, Freie Universität Berlin, Berlin, Germany.
- Department of Physical Chemistry, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany.
| | - Dongwook Go
- Peter-Grünberg-Institut, Forschungszentrum Jülich, Jülich, Germany
- Institute of Physics, Johannes-Gutenberg-Universität Mainz, Mainz, Germany
| | - Hiroki Hayashi
- Department of Applied Physics and Physico-Informatics, Keio University, Yokohama, Japan
- Keio Institute of Pure and Applied Sciences, Keio University, Yokohama, Japan
| | - Reza Rouzegar
- Department of Physics, Freie Universität Berlin, Berlin, Germany
- Department of Physical Chemistry, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany
| | - Frank Freimuth
- Peter-Grünberg-Institut, Forschungszentrum Jülich, Jülich, Germany
- Keio Institute of Pure and Applied Sciences, Keio University, Yokohama, Japan
| | - Kazuya Ando
- Department of Applied Physics and Physico-Informatics, Keio University, Yokohama, Japan
- Keio Institute of Pure and Applied Sciences, Keio University, Yokohama, Japan
- Center for Spintronics Research Network, Keio University, Yokohama, Japan
| | - Yuriy Mokrousov
- Peter-Grünberg-Institut, Forschungszentrum Jülich, Jülich, Germany
- Institute of Physics, Johannes-Gutenberg-Universität Mainz, Mainz, Germany
| | - Tobias Kampfrath
- Department of Physics, Freie Universität Berlin, Berlin, Germany
- Department of Physical Chemistry, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany
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3
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Seifert TS, Go D, Hayashi H, Rouzegar R, Freimuth F, Ando K, Mokrousov Y, Kampfrath T. Time-domain observation of ballistic orbital-angular-momentum currents with giant relaxation length in tungsten. Nat Nanotechnol 2023; 18:1132-1138. [PMID: 37550573 PMCID: PMC10575790 DOI: 10.1038/s41565-023-01470-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Accepted: 06/29/2023] [Indexed: 08/09/2023]
Abstract
The emerging field of orbitronics exploits the electron orbital momentum L. Compared to spin-polarized electrons, L may allow the transfer of magnetic information with considerably higher density over longer distances in more materials. However, direct experimental observation of L currents, their extended propagation lengths and their conversion into charge currents has remained challenging. Here, we optically trigger ultrafast angular-momentum transport in Ni|W|SiO2 thin-film stacks. The resulting terahertz charge-current bursts exhibit a marked delay and width that grow linearly with the W thickness. We consistently ascribe these observations to a ballistic L current from Ni through W with a giant decay length (~80 nm) and low velocity (~0.1 nm fs-1). At the W/SiO2 interface, the L flow is efficiently converted into a charge current by the inverse orbital Rashba-Edelstein effect, consistent with ab initio calculations. Our findings establish orbitronic materials with long-distance ballistic L transport as possible candidates for future ultrafast devices and an approach to discriminate Hall-like and Rashba-Edelstein-like conversion processes.
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Affiliation(s)
- Tom S Seifert
- Department of Physics, Freie Universität Berlin, Berlin, Germany.
- Department of Physical Chemistry, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany.
| | - Dongwook Go
- Peter-Grünberg-Institut, Forschungszentrum Jülich, Jülich, Germany
- Institute of Physics, Johannes-Gutenberg-Universität Mainz, Mainz, Germany
| | - Hiroki Hayashi
- Department of Applied Physics and Physico-Informatics, Keio University, Yokohama, Japan
- Keio Institute of Pure and Applied Sciences, Keio University, Yokohama, Japan
| | - Reza Rouzegar
- Department of Physics, Freie Universität Berlin, Berlin, Germany
- Department of Physical Chemistry, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany
| | - Frank Freimuth
- Peter-Grünberg-Institut, Forschungszentrum Jülich, Jülich, Germany
- Keio Institute of Pure and Applied Sciences, Keio University, Yokohama, Japan
| | - Kazuya Ando
- Department of Applied Physics and Physico-Informatics, Keio University, Yokohama, Japan
- Keio Institute of Pure and Applied Sciences, Keio University, Yokohama, Japan
- Center for Spintronics Research Network, Keio University, Yokohama, Japan
| | - Yuriy Mokrousov
- Peter-Grünberg-Institut, Forschungszentrum Jülich, Jülich, Germany
- Institute of Physics, Johannes-Gutenberg-Universität Mainz, Mainz, Germany
| | - Tobias Kampfrath
- Department of Physics, Freie Universität Berlin, Berlin, Germany
- Department of Physical Chemistry, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany
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4
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Kammerbauer F, Choi WY, Freimuth F, Lee K, Frömter R, Han DS, Lavrijsen R, Swagten HJM, Mokrousov Y, Kläui M. Controlling the Interlayer Dzyaloshinskii-Moriya Interaction by Electrical Currents. Nano Lett 2023; 23:7070-7075. [PMID: 37466639 DOI: 10.1021/acs.nanolett.3c01709] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/20/2023]
Abstract
The recently discovered interlayer Dzyaloshinskii-Moriya interaction (IL-DMI) in multilayers with perpendicular magnetic anisotropy favors canting of spins in the in-plane direction. It could thus stabilize intriguing spin textures such as Hopfions. A key requirement for nucleation is to control the IL-DMI. Therefore, we investigate the influence of an electric current on a synthetic antiferromagnet with growth-induced IL-DMI. The IL-DMI is quantified by using out-of-plane hysteresis loops of the anomalous Hall effect while applying a static in-plane magnetic field at varied azimuthal angles. We observe a shift in the azimuthal dependence with an increasing current, which we conclude to originate from the additional in-plane symmetry breaking introduced by the current flow. Fitting the angular dependence, we demonstrate the presence of an additive current-induced term that linearly increases the IL-DMI in the direction of current flow. This opens the possibility of easily manipulating 3D spin textures by currents.
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Affiliation(s)
- Fabian Kammerbauer
- Institute of Physics, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
| | - Won-Young Choi
- Institute of Physics, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
- Center for Spintronics, Korea Institute of Science and Technology, 34141 Seoul, Republic of Korea
| | - Frank Freimuth
- Institute of Physics, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Kyujoon Lee
- Division of Display and Semiconductor Physics, Korea University, 30019 Sejong, Republic of Korea
| | - Robert Frömter
- Institute of Physics, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
| | - Dong-Soo Han
- Center for Spintronics, Korea Institute of Science and Technology, 34141 Seoul, Republic of Korea
| | - Reinoud Lavrijsen
- Department of Applied Physics, Institute for Photonic Integration, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands
| | - Henk J M Swagten
- Department of Applied Physics, Institute for Photonic Integration, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands
| | - Yuriy Mokrousov
- Institute of Physics, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Mathias Kläui
- Institute of Physics, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
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5
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Alahmed L, Zhang X, Wen J, Xiong Y, Li Y, Zhang LC, Lux F, Freimuth F, Mahdi M, Mokrousov Y, Novosad V, Kwok WK, Yu D, Zhang W, Lee YS, Li P. Evidence of Magnon-Mediated Orbital Magnetism in a Quasi-2D Topological Magnon Insulator. Nano Lett 2022; 22:5114-5119. [PMID: 35699946 DOI: 10.1021/acs.nanolett.2c00562] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
We explore spin dynamics in Cu(1,3-bdc), a quasi-2D topological magnon insulator. The results show that the thermal evolution of the Landé g factor (g) is anisotropic: gin-plane decreases while gout-of-plane increases with increasing temperature T. Moreover, the anisotropy of the g factor (Δg) and the anisotropy of saturation magnetization (ΔMs) are correlated below 4 K, but they diverge above 4 K. We show that the electronic orbital moment contributes to the g anisotropy at lower T, while the topological orbital moment induced by thermally excited spin chirality dictates the g anisotropy at higher T. Our work suggests an interplay among topology, spin chirality, and orbital magnetism in Cu(1,3-bdc).
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Affiliation(s)
- Laith Alahmed
- Department of Electrical and Computer Engineering, Auburn University, Auburn, Alabama 36849, United States
| | - Xiaoqian Zhang
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Jiajia Wen
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States
| | - Yuzan Xiong
- Department of Electrical and Computer Engineering, Oakland University, Rochester, Michigan 48309 United States
| | - Yi Li
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Li-Chuan Zhang
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Fabian Lux
- Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
| | - Frank Freimuth
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
- Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
| | - Muntasir Mahdi
- Department of Electrical and Computer Engineering, Auburn University, Auburn, Alabama 36849, United States
| | - Yuriy Mokrousov
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
- Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
| | - Valentine Novosad
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Wai-Kwong Kwok
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Dapeng Yu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Wei Zhang
- Department of Physics, Oakland University, Rochester, Michigan 48309 United States
- Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
| | - Young S Lee
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States
- Department of Applied Physics, Stanford University, Stanford, California 94305, United States
| | - Peng Li
- Department of Electrical and Computer Engineering, Auburn University, Auburn, Alabama 36849, United States
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6
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Freimuth F, Blügel S, Mokrousov Y. Theory of unidirectional magnetoresistance and nonlinear Hall effect. J Phys Condens Matter 2021; 34:055301. [PMID: 34678787 DOI: 10.1088/1361-648x/ac327f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Accepted: 10/22/2021] [Indexed: 06/13/2023]
Abstract
We study the unidirectional magnetoresistance (UMR) and the nonlinear Hall effect (NLHE) in the ferromagnetic Rashba model. For this purpose we derive expressions to describe the response of the electric current quadratic in the applied electric field. We compare two different formalisms, namely the standard Keldysh nonequilibrium formalism and the Moyal-Keldysh formalism, to derive the nonlinear conductivities of UMR and NLHE. We find that both formalisms lead to identical numerical results when applied to the ferromagnetic Rashba model. The UMR and the NLHE nonlinear conductivities tend to be comparable in magnitude according to our calculations. Additionally, their dependencies on the Rashba parameter and on the quasiparticle broadening are similar. The nonlinear zero-frequency response considered here is several orders of magnitude higher than the one at optical frequencies that describes the photocurrent generation in the ferromagnetic Rashba model. Additionally, we compare our Keldysh nonequilibrium expression in the independent-particle approximation to literature expressions of the UMR that have been obtained within the constant relaxation time approximation of the Boltzmann formalism. We find that both formalisms converge to the same analytical formula in the limit of infinite relaxation time. However, remarkably, we find that the Boltzmann result does not correspond to the intraband term of the Keldysh expression. Instead, the Boltzmann result corresponds to the sum of the intraband term and an interband term that can be brought into the form of an effective intraband term due to thef-sum rule.
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Affiliation(s)
- Frank Freimuth
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
- Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
| | - Stefan Blügel
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Yuriy Mokrousov
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
- Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
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7
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Shao Q, Li P, Liu L, Yang H, Fukami S, Razavi A, Wu H, Wang K, Freimuth F, Mokrousov Y, Stiles MD, Emori S, Hoffmann A, Åkerman J, Roy K, Wang JP, Yang SH, Garello K, Zhang W. Roadmap of spin-orbit torques. IEEE Trans Magn 2021; 57:10.48550/arXiv.2104.11459. [PMID: 37057056 PMCID: PMC10091395 DOI: 10.48550/arxiv.2104.11459] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
Spin-orbit torque (SOT) is an emerging technology that enables the efficient manipulation of spintronic devices. The initial processes of interest in SOTs involved electric fields, spin-orbit coupling, conduction electron spins and magnetization. More recently interest has grown to include a variety of other processes that include phonons, magnons, or heat. Over the past decade, many materials have been explored to achieve a larger SOT efficiency. Recently, holistic design to maximize the performance of SOT devices has extended material research from a nonmagnetic layer to a magnetic layer. The rapid development of SOT has spurred a variety of SOT-based applications. In this Roadmap paper, we first review the theories of SOTs by introducing the various mechanisms thought to generate or control SOTs, such as the spin Hall effect, the Rashba-Edelstein effect, the orbital Hall effect, thermal gradients, magnons, and strain effects. Then, we discuss the materials that enable these effects, including metals, metallic alloys, topological insulators, two-dimensional materials, and complex oxides. We also discuss the important roles in SOT devices of different types of magnetic layers, such as magnetic insulators, antiferromagnets, and ferrimagnets. Afterward, we discuss device applications utilizing SOTs. We discuss and compare three-terminal and two-terminal SOT-magnetoresistive random-access memories (MRAMs); we mention various schemes to eliminate the need for an external field. We provide technological application considerations for SOT-MRAM and give perspectives on SOT-based neuromorphic devices and circuits. In addition to SOT-MRAM, we present SOT-based spintronic terahertz generators, nano-oscillators, and domain wall and skyrmion racetrack memories. This paper aims to achieve a comprehensive review of SOT theory, materials, and applications, guiding future SOT development in both the academic and industrial sectors.
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Affiliation(s)
- Qiming Shao
- Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology
| | - Peng Li
- Department of Electrical and Computer Engineering, Auburn University
| | - Luqiao Liu
- Electrical Engineering and Computer Science, Massachusetts Institute of Technology
| | - Hyunsoo Yang
- Department of Electrical and Computer Engineering, National University of Singapore
| | - Shunsuke Fukami
- Research Institute of Electrical Communication, Tohoku University
| | - Armin Razavi
- Department of Electrical and Computer Engineering, University of California, Los Angeles
| | - Hao Wu
- Department of Electrical and Computer Engineering, University of California, Los Angeles
| | - Kang Wang
- Department of Electrical and Computer Engineering, University of California, Los Angeles
| | | | | | - Mark D Stiles
- Alternative Computing Group, National Institute of Standards and Technology
| | | | - Axel Hoffmann
- Department of Materials Science and Engineering, University of Illinois Urbana-Champaign
| | | | - Kaushik Roy
- Department of Electrical and Computer Engineering, Purdue University
| | - Jian-Ping Wang
- Electrical and Computer Engineering Department, University of Minnesota
| | | | - Kevin Garello
- IMEC, Leuven, Belgium; CEA-Spintec, Grenoble, France
| | - Wei Zhang
- Physics Department, Oakland University
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8
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Kerber N, Ksenzov D, Freimuth F, Capotondi F, Pedersoli E, Lopez-Quintas I, Seng B, Cramer J, Litzius K, Lacour D, Zabel H, Mokrousov Y, Kläui M, Gutt C. Faster chiral versus collinear magnetic order recovery after optical excitation revealed by femtosecond XUV scattering. Nat Commun 2020; 11:6304. [PMID: 33298908 PMCID: PMC7726566 DOI: 10.1038/s41467-020-19613-z] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2020] [Accepted: 10/12/2020] [Indexed: 11/09/2022] Open
Abstract
While chiral spin structures stabilized by Dzyaloshinskii-Moriya interaction (DMI) are candidates as novel information carriers, their dynamics on the fs-ps timescale is little known. Since with the bulk Heisenberg exchange and the interfacial DMI two distinct exchange mechanisms are at play, the ultrafast dynamics of the chiral order needs to be ascertained and compared to the dynamics of the conventional collinear order. Using an XUV free-electron laser we determine the fs-ps temporal evolution of the chiral order in domain walls in a magnetic thin film sample by an IR pump - X-ray magnetic scattering probe experiment. Upon demagnetization we observe that the dichroic (CL-CR) signal connected with the chiral order correlator mzmx in the domain walls recovers significantly faster than the (CL + CR) sum signal representing the average collinear domain magnetization mz2 + mx2. We explore possible explanations based on spin structure dynamics and reduced transversal magnetization fluctuations inside the domain walls and find that the latter can explain the experimental data leading to different dynamics for collinear magnetic order and chiral magnetic order. Chiral spin structures have great promise for future information processing applications, however little is known about their ultrafast dynamics. In this experimental study, the authors use femtosecond temporal evolution to observe the fast recovery of chiral magnetic order.
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Affiliation(s)
- Nico Kerber
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099, Mainz, Germany.,Graduate School of Excellence Materials Science in Mainz, 55128, Mainz, Germany
| | - Dmitriy Ksenzov
- Department Physik, Universität Siegen, Walter-Flex-Strasse 3, 57072, Siegen, Germany
| | - Frank Freimuth
- Peter Grünberg Institute and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425, Jülich, Germany
| | | | | | | | - Boris Seng
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099, Mainz, Germany.,Graduate School of Excellence Materials Science in Mainz, 55128, Mainz, Germany.,Institut Jean Lamour, UMR CNRS 7198, Université de Lorraine, 54506, Vandoeuvre-lès-Nancy, France
| | - Joel Cramer
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099, Mainz, Germany.,Graduate School of Excellence Materials Science in Mainz, 55128, Mainz, Germany
| | - Kai Litzius
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099, Mainz, Germany.,Graduate School of Excellence Materials Science in Mainz, 55128, Mainz, Germany
| | - Daniel Lacour
- Institut Jean Lamour, UMR CNRS 7198, Université de Lorraine, 54506, Vandoeuvre-lès-Nancy, France
| | - Hartmut Zabel
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099, Mainz, Germany.,Graduate School of Excellence Materials Science in Mainz, 55128, Mainz, Germany.,Department of Physics, Ruhr-University Bochum, 44780, Bochum, Germany
| | - Yuriy Mokrousov
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099, Mainz, Germany.,Graduate School of Excellence Materials Science in Mainz, 55128, Mainz, Germany.,Peter Grünberg Institute and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425, Jülich, Germany
| | - Mathias Kläui
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099, Mainz, Germany. .,Graduate School of Excellence Materials Science in Mainz, 55128, Mainz, Germany.
| | - Christian Gutt
- Department Physik, Universität Siegen, Walter-Flex-Strasse 3, 57072, Siegen, Germany.
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9
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Ding S, Ross A, Go D, Baldrati L, Ren Z, Freimuth F, Becker S, Kammerbauer F, Yang J, Jakob G, Mokrousov Y, Kläui M. Harnessing Orbital-to-Spin Conversion of Interfacial Orbital Currents for Efficient Spin-Orbit Torques. Phys Rev Lett 2020; 125:177201. [PMID: 33156648 DOI: 10.1103/physrevlett.125.177201] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2020] [Revised: 08/05/2020] [Accepted: 09/03/2020] [Indexed: 06/11/2023]
Abstract
Current-induced spin-orbit torques (SOTs) allow for the efficient electrical manipulation of magnetism in spintronic devices. Engineering the SOT efficiency is a key goal that is pursued by maximizing the active interfacial spin accumulation or modulating the nonequilibrium spin density that builds up through the spin Hall and inverse spin galvanic effects. Regardless of the origin, the fundamental requirement for the generation of the current-induced torques is a net spin accumulation. We report on the large enhancement of the SOT efficiency in thulium iron garnet (TmIG)/Pt by capping with a CuO_{x} layer. Considering the weak spin-orbit coupling (SOC) of CuO_{x}, these surprising findings likely result from an orbital current generated at the interface between CuO_{x} and Pt, which is injected into the Pt layer and converted into a spin current by strong SOC. The converted spin current decays across the Pt layer and exerts a "nonlocal" torque on TmIG. This additional torque leads to a maximum colossal enhancement of the SOT efficiency of a factor 16 for 1.5 nm of Pt at room temperature, thus opening a path to increase torques while at the same time offering insights into the underlying physics of orbital transport, which has so far been elusive.
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Affiliation(s)
- Shilei Ding
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
- Graduate School of Excellence Materials Science in Mainz, 55128 Mainz, Germany
| | - Andrew Ross
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
- Graduate School of Excellence Materials Science in Mainz, 55128 Mainz, Germany
| | - Dongwook Go
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Lorenzo Baldrati
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Zengyao Ren
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
- Graduate School of Excellence Materials Science in Mainz, 55128 Mainz, Germany
- School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China
| | - Frank Freimuth
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Sven Becker
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Fabian Kammerbauer
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Jinbo Yang
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing, 100871, China
- Beijing Key Laboratory for Magnetoelectric Materials and Devices, Beijing 100871, China
| | - Gerhard Jakob
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
- Graduate School of Excellence Materials Science in Mainz, 55128 Mainz, Germany
| | - Yuriy Mokrousov
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Mathias Kläui
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
- Graduate School of Excellence Materials Science in Mainz, 55128 Mainz, Germany
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
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10
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Pizzi G, Vitale V, Arita R, Blügel S, Freimuth F, Géranton G, Gibertini M, Gresch D, Johnson C, Koretsune T, Ibañez-Azpiroz J, Lee H, Lihm JM, Marchand D, Marrazzo A, Mokrousov Y, Mustafa JI, Nohara Y, Nomura Y, Paulatto L, Poncé S, Ponweiser T, Qiao J, Thöle F, Tsirkin SS, Wierzbowska M, Marzari N, Vanderbilt D, Souza I, Mostofi AA, Yates JR. Wannier90 as a community code: new features and applications. J Phys Condens Matter 2020; 32:165902. [PMID: 31658458 DOI: 10.1088/1361-648x/ab51ff] [Citation(s) in RCA: 215] [Impact Index Per Article: 53.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
Wannier90 is an open-source computer program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used electronic-structure codes thanks to its independence from the basis sets representing these Bloch states. In the past few years the development of Wannier90 has transitioned to a community-driven model; this has resulted in a number of new developments that have been recently released in Wannier90 v3.0. In this article we describe these new functionalities, that include the implementation of new features for wannierisation and disentanglement (symmetry-adapted Wannier functions, selectively-localised Wannier functions, selected columns of the density matrix) and the ability to calculate new properties (shift currents and Berry-curvature dipole, and a new interface to many-body perturbation theory); performance improvements, including parallelisation of the core code; enhancements in functionality (support for spinor-valued Wannier functions, more accurate methods to interpolate quantities in the Brillouin zone); improved usability (improved plotting routines, integration with high-throughput automation frameworks), as well as the implementation of modern software engineering practices (unit testing, continuous integration, and automatic source-code documentation). These new features, capabilities, and code development model aim to further sustain and expand the community uptake and range of applicability, that nowadays spans complex and accurate dielectric, electronic, magnetic, optical, topological and transport properties of materials.
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Affiliation(s)
- Giovanni Pizzi
- Theory and Simulation of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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11
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Lux FR, Freimuth F, Blügel S, Mokrousov Y. Chiral Hall Effect in Noncollinear Magnets from a Cyclic Cohomology Approach. Phys Rev Lett 2020; 124:096602. [PMID: 32202897 DOI: 10.1103/physrevlett.124.096602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Revised: 12/22/2019] [Accepted: 02/06/2020] [Indexed: 06/10/2023]
Abstract
We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect. Instead, it appears already at linear order in the gradients of the magnetization texture and exists for one-dimensional magnetic textures such as domain walls and spin spirals. It receives a natural interpretation in the language of Alain Connes' noncommutative geometry. We show that this chiral Hall effect resembles the familiar topological Hall effect in essential properties while its phenomenology is distinctly different. Our findings make the reinterpretation of experimental data necessary, and offer an exciting twist in engineering the electrical transport through magnetic skyrmions.
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Affiliation(s)
- Fabian R Lux
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
- Department of Physics, RWTH Aachen University, 52056 Aachen, Germany
| | - Frank Freimuth
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Stefan Blügel
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Yuriy Mokrousov
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
- Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
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12
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Go D, Freimuth F, Hanke JP, Xue F, Gomonay O, Lee KJ, Blügel S, Haney PM, Lee HW, Mokrousov Y. Theory of Current-Induced Angular Momentum Transfer Dynamics in Spin-Orbit Coupled Systems. Phys Rev Res 2020; 2:10.1103/physrevresearch.2.033401. [PMID: 33655217 PMCID: PMC7919697 DOI: 10.1103/physrevresearch.2.033401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Motivated by the importance of understanding various competing mechanisms to the current-induced spin-orbit torque on magnetization in complex magnets, we develop a theory of current-induced spin-orbital coupled dynamics in magnetic heterostructures. The theory describes angular momentum transfer between different degrees of freedom in solids, e.g., the electron orbital and spin, the crystal lattice, and the magnetic order parameter. Based on the continuity equations for the spin and orbital angular momenta, we derive equations of motion that relate spin and orbital current fluxes and torques describing the transfer of angular momentum between different degrees of freedom, achieved in a steady state under an applied external electric field. We then propose a classification scheme for the mechanisms of the current-induced torque in magnetic bilayers. We evaluate the sources of torque using density functional theory, effectively capturing the impact of the electronic structure on these quantities. We apply our formalism to two different magnetic bilayers, Fe/W(110) and Ni/W(110), which are chosen such that the orbital and spin Hall effects in W have opposite sign and the resulting spin- and orbital-mediated torques can compete with each other. We find that while the spin torque arising from the spin Hall effect of W is the dominant mechanism of the current-induced torque in Fe/W(110), the dominant mechanism in Ni/W(110) is the orbital torque originating in the orbital Hall effect of the non-magnetic substrate. Thus the effective spin Hall angles for the total torque are negative and positive in the two systems. Our prediction can be experimentally identified in moderately clean samples, where intrinsic contributions dominate. This clearly demonstrates that our formalism is ideal for studying the angular momentum transfer dynamics in spin-orbit coupled systems as it goes beyond the "spin current picture" by naturally incorporating the spin and orbital degrees of freedom on an equal footing. Our calculations reveal that, in addition to the spin and orbital torque, other contributions such as the interfacial torque and self-induced anomalous torque within the ferromagnet are not negligible in both material systems.
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Affiliation(s)
- Dongwook Go
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
- Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
- Department of Physics, Pohang University of Science and Technology, Pohang 37673, Korea
- Basic Science Research Institute, Pohang University of Science and Technology, Pohang 37673, Korea
| | - Frank Freimuth
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Jan-Philipp Hanke
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Fei Xue
- Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
- Institute for Research in Electronics and Applied Physics & Maryland Nanocenter, University of Maryland, College Park, MD 20742
| | - Olena Gomonay
- Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
| | - Kyung-Jin Lee
- Department of Materials Science and Engineering, Korea University, Seoul 02841, Korea
- KU-KIST Graduate School of Converging Science and Technology, Korea University, Seoul 02841, Korea
| | - Stefan Blügel
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Paul M. Haney
- Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Hyun-Woo Lee
- Department of Physics, Pohang University of Science and Technology, Pohang 37673, Korea
| | - Yuriy Mokrousov
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
- Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
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13
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Karnad GV, Freimuth F, Martinez E, Lo Conte R, Gubbiotti G, Schulz T, Senz S, Ocker B, Mokrousov Y, Kläui M. Modification of Dzyaloshinskii-Moriya-Interaction-Stabilized Domain Wall Chirality by Driving Currents. Phys Rev Lett 2018; 121:147203. [PMID: 30339435 DOI: 10.1103/physrevlett.121.147203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2018] [Indexed: 06/08/2023]
Abstract
We measure and analyze the chirality of Dzyaloshinskii-Moriya-interaction (DMI) stabilized spin textures in multilayers of Ta|Co_{20}F_{60}B_{20}|MgO. The effective DMI is measured experimentally using domain wall motion measurements, both in the presence (using spin-orbit torques) and absence of driving currents (using magnetic fields). We observe that the current-induced domain wall motion yields a change in effective DMI magnitude and opposite domain wall chirality when compared to field-induced domain wall motion (without current). We explore this effect, which we refer to as current-induced DMI, by providing possible explanations for its emergence, and explore the possibility of its manifestation in the framework of recent theoretical predictions of DMI modifications due to spin currents.
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Affiliation(s)
- G V Karnad
- Institut für Physik, Johannes Gutenberg-Universität, Staudinger Weg 7, 55128 Mainz, Germany
| | - F Freimuth
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - E Martinez
- Departamento Fisica Aplicada, Facultad de Ciencias, University of Salamanca, 37008 Salamanca, Spain
| | - R Lo Conte
- Institut für Physik, Johannes Gutenberg-Universität, Staudinger Weg 7, 55128 Mainz, Germany
- Graduate School of Excellence "Materials Science in Mainz" (MAINZ), Staudinger Weg 9, 55128 Mainz, Germany
| | - G Gubbiotti
- Istituto Officina dei Materiali del CNR (CNR-IOM), Sede Secondaria di Perugia, c/o Dipartimento di Fisica e Geologia, Universitá di Perugia, I-06123 Perugia, Italy
| | - T Schulz
- Institut für Physik, Johannes Gutenberg-Universität, Staudinger Weg 7, 55128 Mainz, Germany
| | - S Senz
- Max-Planck-Institut für Mikrostrukturphysik, 06120 Halle(Saale), Germany
| | - B Ocker
- Singulus Technology AG, 63796 Kahl am Main, Germany
| | - Y Mokrousov
- Institut für Physik, Johannes Gutenberg-Universität, Staudinger Weg 7, 55128 Mainz, Germany
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
- Graduate School of Excellence "Materials Science in Mainz" (MAINZ), Staudinger Weg 9, 55128 Mainz, Germany
| | - M Kläui
- Institut für Physik, Johannes Gutenberg-Universität, Staudinger Weg 7, 55128 Mainz, Germany
- Graduate School of Excellence "Materials Science in Mainz" (MAINZ), Staudinger Weg 9, 55128 Mainz, Germany
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14
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Freimuth F. Tailor-made currents. Nat Mater 2018; 17:478-479. [PMID: 29795218 DOI: 10.1038/s41563-018-0086-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Affiliation(s)
- Frank Freimuth
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich, Germany.
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15
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Go D, Hanke JP, Buhl PM, Freimuth F, Bihlmayer G, Lee HW, Mokrousov Y, Blügel S. Toward surface orbitronics: giant orbital magnetism from the orbital Rashba effect at the surface of sp-metals. Sci Rep 2017; 7:46742. [PMID: 28440289 PMCID: PMC5404270 DOI: 10.1038/srep46742] [Citation(s) in RCA: 47] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2016] [Accepted: 03/27/2017] [Indexed: 11/09/2022] Open
Abstract
As the inversion symmetry is broken at a surface, spin-orbit interaction gives rise to spin-dependent energy shifts - a phenomenon which is known as the spin Rashba effect. Recently, it has been recognized that an orbital counterpart of the spin Rashba effect - the orbital Rashba effect - can be realized at surfaces even without spin-orbit coupling. Here, we propose a mechanism for the orbital Rashba effect based on sp orbital hybridization, which ultimately leads to the electric polarization of surface states. For the experimentally well-studied system of a BiAg2 monolayer, as a proof of principle, we show from first principles that this effect leads to chiral orbital textures in k-space. In predicting the magnitude of the orbital moment arising from the orbital Rashba effect, we demonstrate the crucial role played by the Berry phase theory for the magnitude and variation of the orbital textures. As a result, we predict a pronounced manifestation of various orbital effects at surfaces, and proclaim the orbital Rashba effect to be a key platform for surface orbitronics.
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Affiliation(s)
- Dongwook Go
- Peter Grünberg Institut and Institute of Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany.,Department of Physics, Pohang University of Science and Technology, Pohang 37673, Korea
| | - Jan-Philipp Hanke
- Peter Grünberg Institut and Institute of Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Patrick M Buhl
- Peter Grünberg Institut and Institute of Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Frank Freimuth
- Peter Grünberg Institut and Institute of Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Gustav Bihlmayer
- Peter Grünberg Institut and Institute of Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Hyun-Woo Lee
- Department of Physics, Pohang University of Science and Technology, Pohang 37673, Korea
| | - Yuriy Mokrousov
- Peter Grünberg Institut and Institute of Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Stefan Blügel
- Peter Grünberg Institut and Institute of Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
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16
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Freimuth F, Blügel S, Mokrousov Y. The inverse thermal spin-orbit torque and the relation of the Dzyaloshinskii-Moriya interaction to ground-state energy currents. J Phys Condens Matter 2016; 28:316001. [PMID: 27301682 DOI: 10.1088/0953-8984/28/31/316001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Using the Kubo linear-response formalism we derive expressions to calculate the electronic contribution to the heat current generated by magnetization dynamics in ferromagnetic metals with broken inversion symmetry and spin-orbit interaction (SOI). The effect of producing heat currents by magnetization dynamics constitutes the Onsager reciprocal of the thermal spin-orbit torque (TSOT), i.e. the generation of torques on the magnetization due to temperature gradients. We find that the energy current driven by magnetization dynamics contains a contribution from the Dzyaloshinskii-Moriya interaction (DMI), which needs to be subtracted from the Kubo linear response of the energy current in order to extract the heat current. We show that the expressions of the DMI coefficient can be derived elegantly from the DMI energy current. Guided by formal analogies between the Berry phase theory of DMI on the one hand and the modern theory of orbital magnetization on the other hand we are led to an interpretation of the latter in terms of energy currents as well. Based on ab initio calculations we investigate the electronic contribution to the heat current driven by magnetization dynamics in Mn/W(0 0 1) magnetic bilayers. We predict that fast domain walls drive strong heat currents.
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Affiliation(s)
- Frank Freimuth
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
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17
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Huisman TJ, Mikhaylovskiy RV, Costa JD, Freimuth F, Paz E, Ventura J, Freitas PP, Blügel S, Mokrousov Y, Rasing T, Kimel AV. Femtosecond control of electric currents in metallic ferromagnetic heterostructures. Nat Nanotechnol 2016; 11:455-8. [PMID: 26854566 DOI: 10.1038/nnano.2015.331] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2015] [Accepted: 12/14/2015] [Indexed: 05/06/2023]
Abstract
The idea to use not only the charge but also the spin of electrons in the operation of electronic devices has led to the development of spintronics, causing a revolution in how information is stored and processed. A novel advancement would be to develop ultrafast spintronics using femtosecond laser pulses. Employing terahertz (10(12) Hz) emission spectroscopy and exploiting the spin-orbit interaction, we demonstrate the optical generation of electric photocurrents in metallic ferromagnetic heterostructures at the femtosecond timescale. The direction of the photocurrent is controlled by the helicity of the circularly polarized light. These results open up new opportunities for realizing spintronics in the unprecedented terahertz regime and provide new insights in all-optical control of magnetism.
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Affiliation(s)
- T J Huisman
- Radboud University, Institute for Molecules and Materials, 6525 AJ Nijmegen, The Netherlands
| | - R V Mikhaylovskiy
- Radboud University, Institute for Molecules and Materials, 6525 AJ Nijmegen, The Netherlands
| | - J D Costa
- INL - International Iberian Nanotechnology Laboratory, Av. Mestre José Veiga s/n, 4715-330 Braga, Portugal
- IN-IFIMUP, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal
| | - F Freimuth
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - E Paz
- INL - International Iberian Nanotechnology Laboratory, Av. Mestre José Veiga s/n, 4715-330 Braga, Portugal
| | - J Ventura
- IN-IFIMUP, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal
| | - P P Freitas
- INL - International Iberian Nanotechnology Laboratory, Av. Mestre José Veiga s/n, 4715-330 Braga, Portugal
| | - S Blügel
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Y Mokrousov
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Th Rasing
- Radboud University, Institute for Molecules and Materials, 6525 AJ Nijmegen, The Netherlands
| | - A V Kimel
- Radboud University, Institute for Molecules and Materials, 6525 AJ Nijmegen, The Netherlands
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18
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Wadley P, Howells B, Železný J, Andrews C, Hills V, Campion RP, Novák V, Olejník K, Maccherozzi F, Dhesi SS, Martin SY, Wagner T, Wunderlich J, Freimuth F, Mokrousov Y, Kuneš J, Chauhan JS, Grzybowski MJ, Rushforth AW, Edmonds KW, Gallagher BL, Jungwirth T. Electrical switching of an antiferromagnet. Science 2016; 351:587-90. [PMID: 26841431 DOI: 10.1126/science.aab1031] [Citation(s) in RCA: 294] [Impact Index Per Article: 36.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2015] [Accepted: 01/04/2016] [Indexed: 11/02/2022]
Abstract
Antiferromagnets are hard to control by external magnetic fields because of the alternating directions of magnetic moments on individual atoms and the resulting zero net magnetization. However, relativistic quantum mechanics allows for generating current-induced internal fields whose sign alternates with the periodicity of the antiferromagnetic lattice. Using these fields, which couple strongly to the antiferromagnetic order, we demonstrate room-temperature electrical switching between stable configurations in antiferromagnetic CuMnAs thin-film devices by applied current with magnitudes of order 10(6) ampere per square centimeter. Electrical writing is combined in our solid-state memory with electrical readout and the stored magnetic state is insensitive to and produces no external magnetic field perturbations, which illustrates the unique merits of antiferromagnets for spintronics.
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Affiliation(s)
- P Wadley
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK.
| | - B Howells
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
| | - J Železný
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic. Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Prague 2, Czech Republic
| | - C Andrews
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
| | - V Hills
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
| | - R P Campion
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
| | - V Novák
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic
| | - K Olejník
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic
| | - F Maccherozzi
- Diamond Light Source, Chilton, Didcot, Oxfordshire, OX11 0DE, UK
| | - S S Dhesi
- Diamond Light Source, Chilton, Didcot, Oxfordshire, OX11 0DE, UK
| | - S Y Martin
- Hitachi Cambridge Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, UK
| | - T Wagner
- Hitachi Cambridge Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, UK. Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0HE, UK
| | - J Wunderlich
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic. Hitachi Cambridge Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, UK
| | - F Freimuth
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Y Mokrousov
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - J Kuneš
- Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Praha 8, Czech Republic
| | - J S Chauhan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
| | - M J Grzybowski
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK. Institute of Physics, Polish Academy of Sciences, al. Lotnikow 32/46, PL-02-668 Warsaw, Poland
| | - A W Rushforth
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
| | - K W Edmonds
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
| | - B L Gallagher
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
| | - T Jungwirth
- Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha 6, Czech Republic. School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
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19
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Gayles J, Freimuth F, Schena T, Lani G, Mavropoulos P, Duine RA, Blügel S, Sinova J, Mokrousov Y. Dzyaloshinskii-Moriya Interaction and Hall Effects in the Skyrmion Phase of Mn(1-x) Fe(x)Ge. Phys Rev Lett 2015; 115:036602. [PMID: 26230813 DOI: 10.1103/physrevlett.115.036602] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2015] [Indexed: 06/04/2023]
Abstract
We carry out density functional theory calculations which demonstrate that the electron dynamics in the Skyrmion phase of Fe-rich Mn_{1-x}Fe_{x}Ge alloys is governed by Berry phase physics. We observe that the magnitude of the Dzyaloshinskii-Moriya interaction directly related to the mixed space-momentum Berry phases, changes sign and magnitude with concentration x in direct correlation with the data of Shibata et al. [Nat. Nanotechnol. 8, 723 (2013)]. The computed anomalous and topological Hall effects in FeGe are also in good agreement with available experiments. We further develop a simple tight-binding model able to explain these findings. Finally, we show that the adiabatic Berry phase picture is violated in the Mn-rich limit of the alloys.
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Affiliation(s)
- J Gayles
- Institut für Physik, Johannes Gutenberg Universität Mainz, D-55099 Mainz, Germany
- Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
| | - F Freimuth
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - T Schena
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - G Lani
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - P Mavropoulos
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - R A Duine
- Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
| | - S Blügel
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - J Sinova
- Institut für Physik, Johannes Gutenberg Universität Mainz, D-55099 Mainz, Germany
- Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
- Institute of Physics ASCR, Cukrovarnicka 10, 162 53 Praha 6, Czech Republic
| | - Y Mokrousov
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
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20
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Zhang W, Jungfleisch MB, Jiang W, Pearson JE, Hoffmann A, Freimuth F, Mokrousov Y. Spin Hall effects in metallic antiferromagnets. Phys Rev Lett 2014; 113:196602. [PMID: 25415914 DOI: 10.1103/physrevlett.113.196602] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2014] [Indexed: 06/04/2023]
Abstract
We investigate four CuAu-I-type metallic antiferromagnets for their potential as spin current detectors using spin pumping and inverse spin Hall effect. Nontrivial spin Hall effects were observed for FeMn, PdMn, and IrMn while a much higher effect was obtained for PtMn. Using thickness-dependent measurements, we determined the spin diffusion lengths of these materials to be short, on the order of 1 nm. The estimated spin Hall angles of the four materials follow the relationship PtMn>IrMn>PdMn>FeMn, highlighting the correlation between the spin-orbit coupling of nonmagnetic species and the magnitude of the spin Hall effect in their antiferromagnetic alloys. These experiments are compared with first-principles calculations. Engineering the properties of the antiferromagnets as well as their interfaces can pave the way for manipulation of the spin dependent transport properties in antiferromagnet-based spintronics.
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Affiliation(s)
- Wei Zhang
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | | | - Wanjun Jiang
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - John E Pearson
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Axel Hoffmann
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Frank Freimuth
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany
| | - Yuriy Mokrousov
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany
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21
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Franz C, Freimuth F, Bauer A, Ritz R, Schnarr C, Duvinage C, Adams T, Blügel S, Rosch A, Mokrousov Y, Pfleiderer C. Real-space and reciprocal-space Berry phases in the Hall effect of Mn(1-x)Fe(x)Si. Phys Rev Lett 2014; 112:186601. [PMID: 24856709 DOI: 10.1103/physrevlett.112.186601] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2013] [Indexed: 06/03/2023]
Abstract
We report an experimental and computational study of the Hall effect in Mn(1-x)Fe(x)Si, as complemented by measurements in Mn(1-x)Co(x)Si, when helimagnetic order is suppressed under substitutional doping. For small x the anomalous Hall effect (AHE) and the topological Hall effect (THE) change sign. Under larger doping the AHE remains small and consistent with the magnetization, while the THE grows by over a factor of 10. Both the sign and the magnitude of the AHE and the THE are in excellent agreement with calculations based on density functional theory. Our study provides the long-sought material-specific microscopic justification that, while the AHE is due to the reciprocal-space Berry curvature, the THE originates in real-space Berry phases.
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Affiliation(s)
- C Franz
- Physik-Department, Technische Universität München, James-Franck-Straße, D-85748 Garching, Germany
| | - F Freimuth
- Institute for Advanced Simulation and Peter Grünberg Institut, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany
| | - A Bauer
- Physik-Department, Technische Universität München, James-Franck-Straße, D-85748 Garching, Germany
| | - R Ritz
- Physik-Department, Technische Universität München, James-Franck-Straße, D-85748 Garching, Germany
| | - C Schnarr
- Physik-Department, Technische Universität München, James-Franck-Straße, D-85748 Garching, Germany
| | - C Duvinage
- Physik-Department, Technische Universität München, James-Franck-Straße, D-85748 Garching, Germany
| | - T Adams
- Physik-Department, Technische Universität München, James-Franck-Straße, D-85748 Garching, Germany
| | - S Blügel
- Institute for Advanced Simulation and Peter Grünberg Institut, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany
| | - A Rosch
- Institute for Theoretical Physics, Universität zu Köln, Zülpicher Straße 77, D-50937 Köln, Germany
| | - Y Mokrousov
- Institute for Advanced Simulation and Peter Grünberg Institut, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany
| | - C Pfleiderer
- Physik-Department, Technische Universität München, James-Franck-Straße, D-85748 Garching, Germany
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22
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Abstract
Recent experiments on current-induced domain-wall motion in chiral domain walls reveal important contributions both from spin-orbit torques (SOTs) and from the Dzyaloshinskii-Moriya interaction (DMI). We derive a Berry phase expression for the DMI and show that within this Berry phase theory DMI and SOTs are intimately related, in a way formally analogous to the relation between orbital magnetization (OM) and anomalous Hall effect (AHE). We introduce the concept of the twist torque moment, which probes the internal twist of wavepackets in chiral magnets in a similar way as the orbital moment probes the wavepacket's internal self-rotation. We propose to interpret the Berry phase theory of DMI as a theory of spiralization in analogy to the modern theory of OM. We show that the twist torque moment and the spiralization together give rise to a Berry phase governing the response of the SOT to thermal gradients, in analogy to the intrinsic anomalous Nernst effect. The Berry phase theory of DMI is computationally very efficient because it only needs the electronic structure of the collinear magnetic system as input. As an application of the formalism we compute the DMI in Co/Pt(111), O/Co/Pt(111) and Al/Co/Pt(111) magnetic bi- and trilayers and show that the DMI is highly anisotropic in these systems.
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Affiliation(s)
- F Freimuth
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany
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23
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Garello K, Miron IM, Avci CO, Freimuth F, Mokrousov Y, Blügel S, Auffret S, Boulle O, Gaudin G, Gambardella P. Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures. Nat Nanotechnol 2013; 8:587-93. [PMID: 23892985 DOI: 10.1038/nnano.2013.145] [Citation(s) in RCA: 226] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2012] [Accepted: 06/25/2013] [Indexed: 05/17/2023]
Abstract
Recent demonstrations of magnetization switching induced by in-plane current injection in heavy metal/ferromagnetic heterostructures have drawn increasing attention to spin torques based on orbital-to-spin momentum transfer. The symmetry, magnitude and origin of spin-orbit torques (SOTs), however, remain a matter of debate. Here we report on the three-dimensional vector measurement of SOTs in AlOx/Co/Pt and MgO/CoFeB/Ta trilayers using harmonic analysis of the anomalous and planar Hall effects. We provide a general scheme to measure the amplitude and direction of SOTs as a function of the magnetization direction. Based on space and time inversion symmetry arguments, we demonstrate that heavy metal/ferromagnetic layers allow for two different SOTs having odd and even behaviour with respect to magnetization reversal. Such torques include strongly anisotropic field-like and spin transfer-like components, which depend on the type of heavy metal layer and annealing treatment. These results call for SOT models that go beyond the spin Hall and Rashba effects investigated thus far.
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Affiliation(s)
- Kevin Garello
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), E-08193 Barcelona, Spain.
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24
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Mokrousov Y, Zhang H, Freimuth F, Zimmermann B, Long NH, Weischenberg J, Souza I, Mavropoulos P, Blügel S. Anisotropy of spin relaxation and transverse transport in metals. J Phys Condens Matter 2013; 25:163201. [PMID: 23511040 DOI: 10.1088/0953-8984/25/16/163201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Using first-principles methods we explore the anisotropy of the spin relaxation and transverse transport properties in bulk metals with respect to the real-space direction of the spin-quantization axis in paramagnets or of the spontaneous magnetization in ferromagnets. Owing to the presence of the spin-orbit coupling the orbital and spin character of the Bloch states depends sensitively on the orientation of the spins relative to the crystal axes. This leads to drastic changes in quantities which rely on interband mixing induced by the spin-orbit interaction. The anisotropy is particularly striking for quantities which exhibit spiky and irregular distributions in the Brillouin zone, such as the spin-mixing parameter or the Berry curvature of the electronic states. We demonstrate this for three cases: (i) the Elliott-Yafet spin-relaxation mechanism in paramagnets with structural inversion symmetry; (ii) the intrinsic anomalous Hall effect in ferromagnets; and (iii) the spin Hall effect in paramagnets. We discuss the consequences of the pronounced anisotropic behavior displayed by these properties for spin-polarized transport applications.
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Affiliation(s)
- Yuriy Mokrousov
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, Jülich, Germany.
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25
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Kampfrath T, Battiato M, Maldonado P, Eilers G, Nötzold J, Mährlein S, Zbarsky V, Freimuth F, Mokrousov Y, Blügel S, Wolf M, Radu I, Oppeneer PM, Münzenberg M. Terahertz spin current pulses controlled by magnetic heterostructures. Nat Nanotechnol 2013; 8:256-60. [PMID: 23542903 DOI: 10.1038/nnano.2013.43] [Citation(s) in RCA: 130] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2012] [Accepted: 02/25/2013] [Indexed: 05/23/2023]
Abstract
In spin-based electronics, information is encoded by the spin state of electron bunches. Processing this information requires the controlled transport of spin angular momentum through a solid, preferably at frequencies reaching the so far unexplored terahertz regime. Here, we demonstrate, by experiment and theory, that the temporal shape of femtosecond spin current bursts can be manipulated by using specifically designed magnetic heterostructures. A laser pulse is used to drive spins from a ferromagnetic iron thin film into a non-magnetic cap layer that has either low (ruthenium) or high (gold) electron mobility. The resulting transient spin current is detected by means of an ultrafast, contactless amperemeter based on the inverse spin Hall effect, which converts the spin flow into a terahertz electromagnetic pulse. We find that the ruthenium cap layer yields a considerably longer spin current pulse because electrons are injected into ruthenium d states, which have a much lower mobility than gold sp states. Thus, spin current pulses and the resulting terahertz transients can be shaped by tailoring magnetic heterostructures, which opens the door to engineering high-speed spintronic devices and, potentially, broadband terahertz emitters.
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Affiliation(s)
- T Kampfrath
- Department of Physical Chemistry, Fritz Haber Institute, Faradayweg 4-6, 14195 Berlin, Germany.
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26
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Seemann KM, Garcia-Sanchez F, Kronast F, Miguel J, Kákay A, Schneider CM, Hertel R, Freimuth F, Mokrousov Y, Blügel S. Disentangling the physical contributions to the electrical resistance in magnetic domain walls: a multiscale study. Phys Rev Lett 2012; 108:077201. [PMID: 22401245 DOI: 10.1103/physrevlett.108.077201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2011] [Indexed: 05/31/2023]
Abstract
We analyze the origin of the electrical resistance arising in domain walls of perpendicularly magnetized materials by considering a superposition of anisotropic magnetoresistance and the resistance implied by the magnetization chirality. The domain wall profiles of L1(0)-FePd and L1(0)-FePt are determined by micromagnetic simulations based on which we perform first-principles calculations to quantify electron transport through the core and closure region of the walls. The wall resistance, being twice as high in L1(0)-FePd than in L1(0)-FePt, is found to be clearly dominated in both cases by a high gradient of magnetization rotation, which agrees well with experimental observations.
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Affiliation(s)
- K M Seemann
- Peter Grünberg Institute, Forschungszentrum Jülich and Jülich-Aachen Research Alliance, Jülich, Germany.
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27
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Weischenberg J, Freimuth F, Sinova J, Blügel S, Mokrousov Y. Ab initio theory of the scattering-independent anomalous Hall effect. Phys Rev Lett 2011; 107:106601. [PMID: 21981517 DOI: 10.1103/physrevlett.107.106601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2011] [Indexed: 05/31/2023]
Abstract
We report on first-principles calculations of the side-jump contribution to the anomalous Hall conductivity (AHC) directly from the electronic structure of a perfect crystal. We implemented our approach for a short-range scattering disorder model within the density functional theory and computed the full scattering-independent AHC in elemental bcc Fe, hcp Co, fcc Ni, and L1(0) FePd and FePt alloys. The full AHC thus calculated agrees systematically with experiment to a degree unattainable so far, correctly capturing the previously missing elements of side-jump contributions, hence paving the way to a truly predictive theory of the anomalous Hall effect and turning it from a characterization tool to a probing tool of multiband complex electronic band structures.
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Affiliation(s)
- Jürgen Weischenberg
- Peter Grünberg Institut, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
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28
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Seemann KM, Freimuth F, Zhang H, Blügel S, Mokrousov Y, Bürgler DE, Schneider CM. Origin of the planar Hall effect in nanocrystalline Co60Fe20B20. Phys Rev Lett 2011; 107:086603. [PMID: 21929187 DOI: 10.1103/physrevlett.107.086603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2010] [Indexed: 05/31/2023]
Abstract
An angle dependent analysis of the planar Hall effect (PHE) in nanocrystalline single-domain Co(60)Fe(20)B(20) thin films is reported. In a combined experimental and theoretical study we show that the transverse resistivity of the PHE is entirely driven by anisotropic magnetoresistance (AMR). Our results for Co(60)Fe(20)B(20) obtained from first principles theory in conjunction with a Boltzmann transport model take into account the nanocrystallinity and the presence of 20 at. % boron. The ab initio AMR ratio of 0.12% agrees well with the experimental value of 0.22%. Furthermore, we experimentally demonstrate that the anomalous Hall effect contributes negligibly in the present case.
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Affiliation(s)
- K M Seemann
- Peter Grünberg Institute (PGI-6) and Jülich-Aachen Research Alliance (JARA-FIT), Forschungszentrum Jülich, D-52425 Jülich, Germany.
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29
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Zhang H, Freimuth F, Blügel S, Mokrousov Y, Souza I. Role of spin-flip transitions in the anomalous Hall effect of FePt alloy. Phys Rev Lett 2011; 106:117202. [PMID: 21469892 DOI: 10.1103/physrevlett.106.117202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2010] [Indexed: 05/30/2023]
Abstract
We carry out ab initio calculations which demonstrate the importance of the non-spin-conserving part of the spin-orbit interaction for the intrinsic anomalous Hall conductivity of ordered FePt alloys. The impact of this interaction is strongly reduced if Pt is replaced by the lighter isoelectronic element Pd. An analysis of the interband transitions responsible for the anomalous velocity reveals that spin-flip transitions occur not only at avoided band crossings near the Fermi level, but also between well-separated pairs of bands with similar dispersions. We also predict a strong anisotropy in the anomalous Hall conductivity of FePt caused entirely by low-frequency spin-flip transitions.
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Affiliation(s)
- Hongbin Zhang
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany
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30
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Abstract
We report on first principles calculations of the anisotropy of the intrinsic spin Hall conductivity (SHC) in nonmagnetic hcp metals and in antiferromagnetic Cr. For most of the metals of this study we find large anisotropies. We derive the general relation between the SHC vector and the direction of spin polarization and discuss its consequences for hcp metals. Especially, it is predicted that for systems where the SHC changes sign due to the anisotropy the spin Hall effect may be tuned such that the spin polarization is parallel either to the electric field or to the spin current.
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Affiliation(s)
- Frank Freimuth
- Institut für Festkörperforschung and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
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