One of the most powerful ways to manipulate spins in nanometer-scale devices is by converting a charge current to a spin current via spin–orbit coupling. The resulting spin–orbit torques (SOTs) have been investigated and utilized extensively in the past decade. Quantitatively, however, SOTs may exhibit a non-trivial angular dependence, which is not well explored. Here, we develop a nested iterative analysis to determine the magnitude of SOTs from harmonic Hall measurements. This updated method largely improves the fit quality in the full magnetic field range and accurately retrieves even higher order, anisotropic spin–orbit torque coefficients. The numerical implementation of our algorithm is fast, robust, and designed for easy integration into existing analysis schemes. We verify our code using simulated data with and without anisotropic SOTs. Accurately quantifying higher order SOT terms can be especially useful for modeling non-uniform magnetic textures such as domain walls and skyrmions and current-induced magnetization switching characteristics.
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26 April 2021
Research Article|
April 26 2021
Accurate extraction of anisotropic spin–orbit torques from harmonic measurements
Special Collection:
Mesoscopic Magnetic Systems: From Fundamental Properties to Devices
D. M. J. van Elst
;
D. M. J. van Elst
1
Department of Applied Physics, Eindhoven University of Technology
, P.O. Box 513, 5600MB Eindhoven, The Netherlands
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M. R. A. Peters
;
M. R. A. Peters
1
Department of Applied Physics, Eindhoven University of Technology
, P.O. Box 513, 5600MB Eindhoven, The Netherlands
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F. Büttner
;
F. Büttner
a)
2
Department of Materials Science and Engineering, Massachusetts Institute of Technology
, Cambridge, Massachusetts 02139, USA
3
Helmholtz-Zentrum für Materialien und Energie GmbH
, 14109 Berlin, Germany
a)Author to whom correspondence should be addressed: felix.buettner@helmholtz-berlin.de
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A. Wittmann
;
A. Wittmann
2
Department of Materials Science and Engineering, Massachusetts Institute of Technology
, Cambridge, Massachusetts 02139, USA
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E. A. Tremsina;
E. A. Tremsina
2
Department of Materials Science and Engineering, Massachusetts Institute of Technology
, Cambridge, Massachusetts 02139, USA
4
Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology
, Cambridge, Massachusetts 02139, USA
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C. O. Avci
;
C. O. Avci
5
Department of Materials, ETH Zürich
, CH-8093 Zürich, Switzerland
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R. Lavrijsen
;
R. Lavrijsen
1
Department of Applied Physics, Eindhoven University of Technology
, P.O. Box 513, 5600MB Eindhoven, The Netherlands
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H. J. M. Swagten;
H. J. M. Swagten
1
Department of Applied Physics, Eindhoven University of Technology
, P.O. Box 513, 5600MB Eindhoven, The Netherlands
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G. S. D. Beach
G. S. D. Beach
2
Department of Materials Science and Engineering, Massachusetts Institute of Technology
, Cambridge, Massachusetts 02139, USA
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a)Author to whom correspondence should be addressed: felix.buettner@helmholtz-berlin.de
Note: This paper is part of the APL Special Collection on Mesoscopic Magnetic Systems: From Fundamental Properties to Devices.
Appl. Phys. Lett. 118, 172403 (2021)
Article history
Received:
January 29 2021
Accepted:
April 05 2021
Citation
D. M. J. van Elst, M. R. A. Peters, F. Büttner, A. Wittmann, E. A. Tremsina, C. O. Avci, R. Lavrijsen, H. J. M. Swagten, G. S. D. Beach; Accurate extraction of anisotropic spin–orbit torques from harmonic measurements. Appl. Phys. Lett. 26 April 2021; 118 (17): 172403. https://doi.org/10.1063/5.0045855
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