Spin-memory loss due to spin-orbit coupling at ferromagnet/heavy-metal interfaces: Ab initio spin-density matrix approach

Spin-memory loss (SML) of electrons traversing ferromagnetic-metal/heavy-metal (FM/HM), FM/normal-metal (FM/NM) and HM/NM interfaces is a fundamental phenomenon that must be invoked to explain consistently large number of spintronic experiments. However, its strength extracted by fitting experimental data to phenomenological semiclassical theory, which replaces each interface by a fictitious bulk layer, is poorly understood from a microscopic quantum framework and/or materials properties. Here we describe ensemble of flowing spin quantum states using spin-density matrix, so that SML is measured like any decoherence process by the decay of its off-diagonal elements or, equivalently, by the reduction of the magnitude of polarization vector. By combining this framework with density functional theory (DFT) calculations, we examine how all three components of the polarization vector change at Co/Ta, Co/Pt, Co/Cu, Pt/Cu and Pt/Au interfaces embedded within Cu/FM/HM/Cu vertical heterostructures. In addition, we use ab initio Green's functions to compute spectral function and spin texture over FM, HM and NM monolayers around these interfaces which quantify interfacial spin-orbit coupling, thereby explaining the microscopic origin of SML [Reference: arXiv:1708.07105].