Symmetry and magnitude of spin–orbit torques in ferromagnetic heterostructures



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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Figure 1: Torque schematics and magnetization measurements.
Figure 2: Second-harmonic Hall resistance and current-induced spin–orbit fields.
Figure 3: Angular dependence of the Hall resistance and SOT components.
Figure 4: Dependence of the field-like and spin transfer-like SOT components on the injected current density.
Figure 5: Effect of thermal annealing and stack composition on current-induced spin–orbit fields.


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This work was supported by the European Research Council (StG 203239 NOMAD), the European Commission under the Seventh Framework Programme (GA 318144, SPOT), Ministerio de Economía y Competitividad (ERA-Net EUI2008-03884, MAT2010-15659), Agència de Gestió d'Ajuts Universitaris i de Recerca (2009 SGR 695) and the Agence Nationale de la Recherche (ANR-10-BLANC-1011-3 ‘SPINHALL’). F.F. and Y.M. acknowledge funding under the HGF-YIG programme VH-NG-513. The samples were patterned at the NANOFAB facility of the Institut Néel (CNRS).

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K.G., I.M.M. and P.G. planned the experiment. I.M.M., C.O.A., G.G. and S.A. fabricated the samples. K.G., I.M.M. and C.O.A. performed the measurements. K.G., I.M.M., C.O.A. and P.G. analysed the data. F.F. derived the general expression for the torques. K.G. and P.G. wrote the manuscript. All authors discussed the results and commented on the manuscript.

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Correspondence to Kevin Garello or Pietro Gambardella.

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Garello, K., Miron, I., Avci, C. et al. Symmetry and magnitude of spin–orbit torques in ferromagnetic heterostructures. Nature Nanotech 8, 587–593 (2013).

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