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The coset construction is a tool for systematically building low energy effective actions for Nambu-Goldstone modes. This technique is typically used to compute time-ordered correlators appropriate for S-matrix computations for systems in their ground state. In this paper, we extend this technique to the Schwinger-Keldysh formalism, which enables one to calculate a wider variety of correlators and applies also to systems in a mixed state. We focus our attention on internal symmetries and demonstrate that, after identifying the appropriate symmetry breaking pattern, Schwinger-Keldysh effective actions for Nambu-Goldstone modes can be constructed using the standard rules of the coset construction. Particular emphasis is placed on the thermal state and ensuring that correlators satisfy the KMS relation. We also discuss explicitly the power counting scheme underlying our effective actions. We comment on the similarities and differences between our approach and others that have previously appeared in the literature. In particular, our prescription does not require the introduction of additional "diffusive" symmetries and retains the full non-linear structure generated by the coset construction. We conclude with a series of explicit examples, including a computation of the finite-temperature two-point functions of conserved spin currents in non-relativistic paramagnets, antiferromagnets, and ferromagnets. Along the way, we also clarify the discrete symmetries that set antiferromagnets apart from ferromagnets, and point out that the dynamical KMS symmetry must be implemented in different ways in these two systems. [ABSTRACT FROM AUTHOR]

Magnetoresistive effects are usually invariant on inversion of the magnetization direction. In non-centrosymmetric conductors, however, nonlinear resistive terms can give rise to a current dependence that is quadratic in the applied voltage and linear in the magnetization. Here we demonstrate that such conditions are realized in simple bilayer metal films where the spin-orbit interaction and spin-dependent scattering couple the current-induced spin accumulation to the electrical conductivity. We show that the longitudinal resistance of Ta|Co and Pt|Co bilayers changes when reversing the polarity of the current or the sign of the magnetization. This unidirectional magnetoresistance scales linearly with current density and has opposite sign in Ta and Pt, which we associate with the modification of the interface scattering potential induced by the spin Hall effect in these materials. Our results suggest a route to control the resistance and detect magnetization switching in spintronic devices using a two-terminal geometry, which applies also to heterostructures including topological insulators. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]