Kimata et al. (Nature 565, 627–630, 2019) established the magnetic spin Hall effect (MSHE) and magnetic inverse spin Hall effect (MISHE) in the non-collinear antiferromagnet Mn3Sn — time-reversal-odd spin–charge conversion responses tied to magnetic order — using a quantum-kinetic theory truncated at the relaxation-time approximation (RTA) and a two-layer kagome toy model. The analysis explicitly neglected skew scattering and other disorder-dependent Fermi-surface terms, left unidentified the microscopic origin of a sharp d.c. voltage jump observed at the Mn3Sn switching field (about ±1,200 Oe) in ferromagnetic-resonance spin pumping on Ni81Fe19/Mn3Sn, and did not provide a systematic, quantitative account of MSHE/MISHE magnitudes across other magnetic materials and interfaces. Later work has clarified the intrinsic mechanism (spin-current vorticity in the Fermi sea, symmetry classification by magnetic Laue group), computed MSHE-type tensors from first principles in ferromagnets and other non-collinear antiferromagnets, demonstrated MSHE-based field-free magnetization switching, and observed interfacial and ferromagnetic MSHE in new systems; however, the quantitative extrinsic (skew-scattering/side-jump) contribution to the time-reversal-odd spin response, the origin of the switching-field voltage jump, and a disorder-aware, interface-aware quantitative materials mapping remain unresolved.

Background

The spin Hall effect (SHE) converts a longitudinal charge current into a transverse pure spin current, and its reciprocal, the inverse spin Hall effect (ISHE), converts a spin current into a transverse charge voltage; together they are the workhorse mechanisms for generating and detecting spin currents in spintronics. In non-magnetic heavy metals these effects are time-reversal-even (T-even), dissipative Fermi-surface responses rooted in spin–orbit coupling. A standard ISHE experiment is spin pumping: a ferromagnetic layer driven into ferromagnetic resonance (FMR) by microwave radiation precesses its magnetization and injects a time-dependent spin current into an adjacent conductor, whose ISHE produces a d.c. voltage that is decomposed into symmetric (Lorentzian) and antisymmetric (dispersive) parts with characteristic angular dependences. Mn3Sn is a metallic non-collinear antiferromagnet in which the Mn moments on a distorted kagome lattice (a two-dimensional network of corner-sharing triangles) form an inverse triangular (120-degree) spin structure with a tiny canting moment, characterized by a cluster magnetic octupole (the collective order parameter of the triangular spin arrangement); the Berry curvature of its band structure — momentum-space curvature accumulated near Weyl points (linear band-touching points that act as monopoles of Berry curvature) — generates a large anomalous Hall effect (a transverse charge response odd under time reversal, even though the net magnetization nearly vanishes). Because magnetic order lowers the symmetry of the spin–charge conversion tensor, magnetic crystals can host spin Hall responses that are odd under time reversal (T-odd) and reverse with the magnetic order, which Kimata et al. (2019) named the magnetic spin Hall effect (MSHE) and magnetic inverse spin Hall effect (MISHE). In a lateral Ni81Fe19/MgO/Mn3Sn spin-accumulation device they observed a spin signal that changes sign when the triangular spin order is reversed, and in FMR spin pumping on Ni81Fe19 (permalloy, a soft ferromagnetic Ni–Fe alloy; 10 nm)/Mn3Sn(100 nm) bilayers they found that roughly 80% of the symmetric d.c. voltage component is even under reversal of the applied d.c. field, which they attributed to the intraband (relaxation-proportional) MISHE. The theory in that work solved the quantum-kinetic (Liouville) equation for the density matrix in the relaxation-time approximation (RTA), which represents disorder by a single relaxation time τ and retains only the lowest-order impurity scattering: the diagonal (intraband) terms scale with τ while the off-diagonal (interband) terms are τ-independent. A minimal toy model of two kagome layers with on-site exchange fields in the inverse triangular pattern, a layer potential and a Rashba-type interface spin–orbit coupling reproduced the measured angular dependences, showing that non-collinear magnetic order — rather than large atomic spin–orbit coupling — can generate large MSHE and MISHE. The extrinsic mechanisms of transverse transport familiar from anomalous-Hall physics — skew scattering (asymmetric deflection of carriers by impurities, arising at higher order in the impurity potential) and the side-jump effect (coordinate shift during scattering) — were explicitly neglected, as was any realistic description of disorder; and the microscopic origin of a sharp d.c. voltage jump observed near the Mn3Sn switching field of about ±1,200 Oe in the spin-pumping device was left unidentified. Subsequent theory has clarified the intrinsic side of the problem: Mook et al. (2020) related the MSHE to the vorticity of spin currents in the Fermi sea, tabulated all magnetic Laue groups (the point symmetries of the crystal's diffraction pattern, magnetic order included) that permit it, and concluded that it should appear in all ferromagnets with sizable spin–orbit coupling, while ab initio calculations have computed MSHE-type tensors in ferromagnets and in other non-collinear antiferromagnets. What remains missing is the quantitative extrinsic and disorder-dependent part of the T-odd spin response, the explanation of the unexplained device signal, and a systematic, materials-level quantitative account.

Problem Statement

The magnetic spin Hall effect (MSHE) and magnetic inverse spin Hall effect (MISHE) — time-reversal-odd spin–charge conversion responses allowed by magnetic order — were established in Mn3Sn by Kimata et al. (2019) using a quantum-kinetic theory truncated at the relaxation-time approximation and a two-layer kagome toy model. The open problem, as acknowledged in that work, is to complete this picture quantitatively, with three linked components serving one objective — a complete, predictive, quantitative theory of time-reversal-odd spin–charge conversion in magnetic crystals, validated against the measured Mn3Sn phenomenology. First, determine the role and quantitative importance of extrinsic, disorder-dependent Fermi-surface terms — skew scattering (higher-order impurity-potential contributions) and side-jump — in producing the magnetization-odd (MSHE/MISHE) and magnetization-even spin–charge responses of magnetic crystals, by extending the formalism beyond the relaxation-time approximation; this includes evaluating how such terms modify the decomposition of measured spin-pumping voltages into conventional (field-odd) ISHE and magnetic (field-even) MISHE parts. Second, identify the microscopic origin of the sharp d.c. voltage jump observed at the Mn3Sn switching field of about ±1,200 Oe in ferromagnetic-resonance spin-pumping measurements on Ni81Fe19/Mn3Sn bilayers — a signal attributed in the source possibly to a rectified anomalous Hall contribution or other interface effects, whose control is needed to secure the ~80% MISHE attribution of the symmetric voltage. Third, establish a systematic, quantitative account of MSHE/MISHE magnitudes across other single-crystal magnetic materials and interfaces — including the influence of interface symmetry breaking and realistic disorder — sufficient to serve as a predictive, first-principles-aided basis for discovering materials with large magnetic spin Hall responses.

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