![]() This approach requires to construct torque operator for a given Hamiltonian of the junction whose trace with current-driven density matrix, split into four components and expressed in terms of nonequilibrium Green functions, automatically generates field-like and damping-like components of STT or SOT vector. ![]() We review a unified approach for computing both spin-transfer torque (STT) in spin-valves and magnetic tunnel junctions (MTJs), where charge current is injected perpendicularly to interfaces, and spin-orbit torque (SOT) in ferromagnet/spin-orbit-coupled-material (where experimentally explored spin-orbit-coupled-materials include 5 d heavy metals, topological insulators, Weyl semimetals and monolayers of transition metal dichalcogenides) with charge current injected parallel to the interface.
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