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We measure spin-orbit torque generated by exfoliated layers of the low-symmetry semi-metal ZrTe3 using the spin-torque ferromagnetic resonance (ST-FMR) technique. When the ZrTe3 has a thickness greater than about 10 nm, artifacts due to spin pumping and/or resonant heating can cause the standard ST-FMR analysis to overestimate the true magnitude of the torque efficiency by as much as a factor of 30, and to indicate incorrectly that the spin-orbit torque depends strongly on the ZrTe3 layer thickness. Artifact-free measurements can still be achieved over a substantial thickness range by the method developed recently to detect ST-FMR signals in the Hall geometry as well as the longitudinal geometry. ZrTe3/Permalloy samples generate a conventional in-plane anti-damping spin torque efficiency ξDL|| = 0.014 ± 0.004, and an unconventional in-plane field-like torque efficiency |ξFL||| = 0.003 ± 0.001. The out-of-plane anti-damping torque is negligible. We suggest that artifacts similarly interfere with the standard ST-FMR analysis for other van der Waals samples thicker than about 10 nm. 

We adapt Sagnac interferometry for magneto-optic Kerr effect measurements of spin-orbit-torque-induced magnetic tilting in thin-film magnetic samples. The high sensitivity of Sagnac interferometry permits for the first time optical quantification of spin-orbit torque from small-angle magnetic tilting of samples with perpendicular magnetic anisotropy (PMA). We find significant disagreement between Sagnac measurements and simultaneously-performed harmonic Hall (HH) measurements of spin-orbit torque on Pt/Co/MgO and Pd/Co/MgO samples with PMA. The Sagnac results for PMA samples are consistent with both HH and Sagnac measurements for the in-plane geometry, so we conclude that the conventional analysis framework for PMA HH measurements is flawed. We suggest that the explanation for this discrepancy is that although magnetic-field induced magnetic tilting in PMA samples can produce a strong planar Hall effect, when tilting is instead generated by spin-orbit torque it produces negligible change in the planar Hall signal. This very surprising result demonstrates an error in the most-popular method for measuring spin-orbit torques in PMA samples, and represents an unsolved puzzle in understanding the planar Hall effect in magnetic thin films. 

Abstract The interconversion of charge and spin currents via spin-Hall effect is essential for spintronics. Energy-efficient and deterministic switching of magnetization can be achieved when spin polarizations of these spin currents are collinear with the magnetization. However, symmetry conditions generally restrict spin polarizations to be orthogonal to both the charge and spin flows. Spin polarizations can deviate from such direction in nonmagnetic materials only when the crystalline symmetry is reduced. Here, we show control of the spin polarization direction by using a non-collinear antiferromagnet Mn 3 GaN, in which the triangular spin structure creates a low magnetic symmetry while maintaining a high crystalline symmetry. We demonstrate that epitaxial Mn 3 GaN/permalloy heterostructures can generate unconventional spin-orbit torques at room temperature corresponding to out-of-plane and Dresselhaus-like spin polarizations which are forbidden in any sample with two-fold rotational symmetry. Our results demonstrate an approach based on spin-structure design for controlling spin-orbit torque, enabling high-efficient antiferromagnetic spintronics. 

Lecture notes used in a graduate-level Introduction to Solid State Physics course at Cornell University, to serve as a supplement to textbooks at the level of Ashcroft & Mermin. 

Spin-orbit coupling (SOC), the interaction between the electron spin and the orbital angular momentum, can unlock rich phenomena at interfaces, in particular interconverting spin and charge currents. Conventional heavy metals have been extensively explored due to their strong SOC of conduction electrons. However, spin-orbit effects in classes of materials such as epitaxial 5 d -electron transition-metal complex oxides, which also host strong SOC, remain largely unreported. In addition to strong SOC, these complex oxides can also provide the additional tuning knob of epitaxy to control the electronic structure and the engineering of spin-to-charge conversion by crystalline symmetry. Here, we demonstrate room-temperature generation of spin-orbit torque on a ferromagnet with extremely high efficiency via the spin-Hall effect in epitaxial metastable perovskite SrIrO 3 . We first predict a large intrinsic spin-Hall conductivity in orthorhombic bulk SrIrO 3 arising from the Berry curvature in the electronic band structure. By manipulating the intricate interplay between SOC and crystalline symmetry, we control the spin-Hall torque ratio by engineering the tilt of the corner-sharing oxygen octahedra in perovskite SrIrO 3 through epitaxial strain. This allows the presence of an anisotropic spin-Hall effect due to a characteristic structural anisotropy in SrIrO 3 with orthorhombic symmetry. Our experimental findings demonstrate the heteroepitaxial symmetry design approach to engineer spin-orbit effects. We therefore anticipate that these epitaxial 5 d transition-metal oxide thin films can be an ideal building block for low-power spintronics.