Spin transport study in a disordered-metal/ferromagnetic-insulator heterostructure based on full counting statistics within the coherent potential approximation

We present a theoretical formalism to investigate quantum spin transport in a two-dimensional metal/ferromagnetic insulator (FI) heterostructure in the presence of disorder. The formalism is based on the full counting statistics (FCS) within coherent potential approximation (CPA), which is capable of calculating the disorder average of an arbitrary number of Green's functions. Due to the convolutional structure of the self-energy of the FI lead, the conventional FCS-CPA formalism breaks down in our system. We propose two solutions to solve this problem. We numerically examine the formalism by calculating the average spin conductance in a disordered nonmagnetic metal/FI (NM/FI) heterostructure and apply it to a disordered altermagnetic metal/FI (AM/FI) heterostructure. The FCS-CPA results exhibit excellent agreement with brute force calculations in weak disorders. In AM/FI systems, the spin transport is enhanced in weak disorders and suppressed in strong disorders. Stronger anisotropic hopping suppresses the spin transport in AM/FI systems. The average spin conductance is notably sensitive to the spin polarization of AM states. The methods proposed here are also applicable to the convolutional self-energy in electron-phonon coupling systems.