Spin transport at finite temperatures: A first-principles study for ferromagnetic|nonmagnetic interfaces

Abstract

Symmetry lowering at an interface leads to an enhancement of the effect of spin-orbit coupling and to a discontinuity of spin currents passing through the interface. This discontinuity is characterized by a "spin-memory loss" (SML) parameter δ that has only been determined directly at low temperatures. Although δ is believed to be significant in experiments involving interfaces between ferromagnetic and nonmagnetic metals, especially heavy metals like Pt, it is more often than not neglected to avoid introducing too many unknown interface parameters in addition to often poorly known bulk parameters like the spin-flip diffusion length l sf . In this work, we calculate δ along with the interface resistance AR I and the spin-asymmetry parameter γ as a function of temperature for Co|Pt and Py|Pt interfaces where Py is the ferromagnetic Ni 80 Fe 20 alloy, permalloy. We use first-principles scattering theory to calculate the conductance as well as local charge and spin currents, modeling temperature-induced disorder with frozen thermal lattice and, for ferromagnetic materials, spin disorder within the adiabatic approximation. The bulk and interface parameters are extracted from the spin currents using a Valet-Fert model generalized to include SML.

Calculating the spin memory loss at Cu$|$metal interfaces from first principles

“…In this section, we present the formulation [51] that we use to extract the parameters from the first-principles calculations when combined with a "layer-averaged local current scheme" [42]. Further details of the formulation are provided elsewhere [56,74]. The results of semiclassical transport theory that we will need are summarized in Sec.…”

“…We therefore construct a symmetric NM|FM|NM trilayer with the origin z = 0 at the centre of the FM layer and inject an electric current from a NM lead imposing the boundary conditions j s (−∞) = j s (∞) = 0. The calculated spin current in the FM metal can be fitted using (5) to extract β, l FM [42] and j s (z I − η) [51,56]. In the NM metal, the fitting using ( 6) is still applicable resulting in l NM and j s (z I + η) where because of the symmetry and without loss of generality, we just consider the rightmost FM|NM interface.…”

“…IV. In Appendix A, the formalism required to determine the SML for NM|FM interfaces using a bilayer structure is derived and it is shown to yield the same results for Pt|Py interface parameters as were obtained for a Pt|Py|Pt trilayer in [56].…”

“…Studies based on firstprinciples scattering theory can model many types of interface disorder [8,[46][47][48][49] as well as temperature-induced bulk disorder [50] and thereby shed light on the SML and its relationship with microscopic scattering mechanisms [51]. A number of theoretical studies of the SML have recently been reported for interfaces between nonmagnetic (NM) materials [51][52][53] and between ferromagnetic (FM) and NM materials [51,[54][55][56] with a strong focus on interfaces between the transition metal Pt and another metal.…”

“…In this paper, we present a systematic study of the transport parameters AR I , γ and δ for interfaces comprising Cu and Pd, Pt, Co and Py using first-principles relativistic scattering calculations [70] that take into account temperature-induced lattice and spin disorder [50] as well as alloy disorder [71] and lattice mismatch [40,51,56]. The SML parameters for Cu|Py and Cu|Co interfaces are found to decrease monotonically with increasing temperature and become negligibly small at room temperature.…”