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Register a new userTheory of spin Hall magnetoresistance
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We present a theory of the spin Hall magnetoresistance (SMR) in multilayers made from an insulating ferromagnet F, such as yttrium iron garnet (YIG), and a normal metal N with spin-orbit interactions, such as platinum (Pt). The SMR is induced by the simultaneous action of spin Hall and inverse spin Hall effects and therefore a non-equilibrium proximity phenomenon. We compute the SMR in F$|$N and F$|$N$|$F layered systems, treating N by spin-diffusion theory with quantum mechanical boundary conditions at the interfaces in terms of the spin-mixing conductance. Our results explain the experimentally observed spin Hall magnetoresistance in N$|$F bilayers. For F$|$N$|$F spin valves we predict an enhanced SMR amplitude when magnetizations are collinear. The SMR and the spin-transfer torques in these trilayers can be controlled by the magnetic configuration.
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We present a theory of the spin Hall magnetoresistance of metals in contact with magnetic insulators. We express the spin-mixing conductances, which govern the phenomenology of the effect, in terms of the microscopic parameters of the interface and the spin-spin correlation functions of the local moments on the surface of the magnetic insulator. The magnetic field and temperature dependence of the spin-mixing conductances leads to a rich behaviour of the resistance due to an interplay between the Hanle effect and spin mixing at the interface. Our theory provides a useful tool for understanding the experiments on heavy metals in contact with magnetic insulators of different kinds, and it predicts striking behaviours of magnetoresistance.
In bilayers consisting of a normal metal (N) with spin-orbit coupling and a ferromagnet (F), the combination of the spin-Hall effect, the spin-transfer torque, and the inverse spin-Hall effect gives a small correction to the in-plane conductivity of N, which is referred to as spin-Hall magnetoresistance (SMR). We here present a theory of the SMR and the associated off-diagonal conductivity corrections for frequencies up to the terahertz regime. We show that the SMR signal has pronounced singularities at the spin-wave frequencies of F, which identifies it as a potential tool for all-electric spectroscopy of magnon modes. A systematic change of the magnitude of the SMR at lower frequencies is associated with the onset of a longitudinal magnonic contribution to spin transport across the F-N interface.
We present a formalism that simultaneously incorporates the effect of quantum tunneling and spin diffusion on spin Hall magnetoresistance observed in normal metal/ferromagnetic insulator bilayers (such as Pt/YIG) and normal metal/ferromagnetic metal bilayers (such as Pt/Co), in which the angle of magnetization influences the magnetoresistance of the normal metal. In the normal metal side the spin diffusion is known to affect the landscape of the spin accumulation caused by spin Hall effect and subsequently the magnetoresistance, while on the ferromagnet side the quantum tunneling effect is detrimental to the interface spin current which also affects the spin accumulation. The influence of generic material properties such as spin diffusion length, layer thickness, interface coupling, and insulating gap can be quantified in a unified manner, and experiments that reveal the quantum feature of the magnetoresistance are suggested.
We have studied the spin Hall magnetoresistance (SMR), the magnetoresistance within the plane transverse to the current flow, of Pt/Co bilayers. We find that the SMR increases with increasing Co thickness: the effective spin Hall angle for bilayers with thick Co exceeds the reported values of Pt when a conventional drift-diffusion model is used. An extended model including spin transport within the Co layer cannot account for the large SMR. To identify its origin, contributions from other sources are studied. For most bilayers, the SMR increases with decreasing temperature and increasing magnetic field, indicating that magnon-related effects in the Co layer play little role. Without the Pt layer, we do not observe the large SMR found for the Pt/Co bilayers with thick Co. Implementing the effect of the so-called interface magnetoresistance and the textured induced anisotropic scattering cannot account for the Co thickness dependent SMR. Since the large SMR is present for W/Co but its magnitude reduces in W/CoFeB, we infer its origin is associated with a particular property of Co.
We review the recently discovered spin Hall magnetoresistance (SMR) and related effects from a theoretical point of view. The SMR is observed in bilayers of a magnetic insulator and a metal, in which spin currents aregenerated in the normal metal due to the spin Hall effect. The associated angular momentum transfer to the ferromagnetic layer and thereby the electrical resistance is modulated by the angle between the applied current and the magnetization direction. The SMR provides a convenient tool to non-invasively measure the magnetization direction and spin-transfer torque to an insulator. We introduce the minimal theoretical instruments to calculate the SMR, i.e. spin diffusion theory and quantum mechanical boundary conditions. This leads to a small set of parameters that can be fitted to experiments. We discuss the limitations of the theory as well as alternative mechanisms such as the ferromagnetic proximity effect and Rashba spin-orbit torques, and point out new developments related to the SMR.
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