Generalized spin-transfer torque and collective spin dynamics in disordered magnets*

We provide a generalized theory of spin transfer and reciprocal pumping effects at interfaces between metals and non-collinear magnets, including the cases of spin glasses and amorphous magnets. The theory is based on energetics rather than spin conservation, albeit the latter is recovered in the appropriate language. The generalized spin-mixing conductance tensor is parametrized by three coefficients, corresponding to the three independent generators of spin rotations. In the limit of exchange-dominated interactions, those correspond to the soft modes of the macroscopic, coarse-grained dynamics, restoring the fully broken rotational symmetry. We employ this formalism to demonstrate that disordered magnets represent a very versatile platform for spin transport, sustaining long-range drag signals between metal contacts even in the presence of damping sources.