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Register a new userSpin-orbit torques in strained PtMnSb from first principles
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We compute spin-orbit torques (SOTs) in strained PtMnSb from first principles. We consider both tetragonal strain and shear strain. We find a strong linear dependence of the field-like SOTs on these strains, while the antidamping SOT is only moderately sensitive to shear strain and even insensitive to tetragonal strain. We also study the dependence of the SOT on the magnetization direction. In order to obtain analytical expressions suitable for fitting our numerical textit{ab-initio} results we derive a general expansion of the SOT in terms of all response tensors that are allowed by crystal symmetry. Our expansion includes also higher-order terms beyond the usually considered lowest order. We find that the dependence on the strain is much smaller for the higher-order terms than for the lowest order terms. In order to judge the sensitivity of the SOT on the exchange correlation potential we compute the SOT in both GGA and LDA. We find that the higher-order terms depend significantly on the exchange-correlation potential, while the lowest order terms are insensitive to it. Since the higher-order terms are small in comparison to the lowest order terms the total SOT is insensitive to the exchange correlation potential in strained PtMnSb.
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We review a unified approach for computing: (i) spin-transfer torque in magnetic trilayers like spin-valves and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces; and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupled-material, where injected charge current flows parallel to the interface. Our approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Greens functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. We provide illustrative examples by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin-valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations; as well as spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide.
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The spin currents generated by spin-orbit coupling (SOC) in the nonmagnetic metal layer or at the interface with broken inversion symmetry are of particular interest and importance. Here, we have explored the spin current generation mechanisms through the spin-orbit torques (SOTs) measurements in the Ru/Fe heterostructures with weak perpendicular magnetic anisotropy (PMA). Although the spin Hall angle (SHA) of Ru is smaller than that in Pt, Ta or W, reversible SOT in Ru/Fe heterostructures can still be realized. Through non-adiabatic harmonic Hall voltage measurements and macrospin simulation, the effective SHA in Ru/Fe heterostructures is compared with Pt. Moreover, we also explore that the spin current driven by interface strongly depends on the electrical conductivities. Our results suggest a new method for efficiently generating finite spin currents in ferromagnet/nonmagnetic metal bilayers, which establishes new opportunities for fundamental study of spin dynamics and transport in ferromagnetic systems.
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