Generalized magnetoelectronic circuit theory and spin relaxation at interfaces in magnetic multilayers

Abstract

Spin transport at metallic interfaces is an essential ingredient of various spintronic device concepts, such as giant magnetoresistance, spin-transfer torque, and spin pumping. Spin-orbit coupling plays an important role in many such devices. In particular, spin current is partially absorbed at the interface due to spin-orbit coupling. We develop a general magnetoelectronic circuit theory and generalize the concept of spin-mixing conductance, accounting for various mechanisms responsible for spin-flip scattering. For the special case when exchange interactions dominate, we give a simple expression for the spin-mixing conductance in terms of the contributions responsible for spin relaxation (i.e., spin memory loss), spin torque, and spin precession. The spin memory loss parameter δ is related to spin-flip transmission and reflection probabilities. There is no straightforward relation between spin torque and spin memory loss. We calculate the spin-flip scattering rates for N|N, F|N, and F|F interfaces using the Landauer-Büttiker method within the linear muffin-tin orbital method and determine the values of δ using circuit theory.

Spin superfluidity in noncollinear antiferromagnets

“…(59) in Ref. [48]). Here, r σ σ mn stands for reflection amplitudes for electrons reflected from channel n into channel m in the normal metal and l is the quantization axis for σ, σ =↑, ↓.…”

“…A buildup of spin accumulation in a normal metal will then lead to injection of spin current into the magnetic insulator layer. The boundary condition on the interface can be derived via the magnetoelectronic circuit theory [44][45][46][47][48]. When exchange interactions dominate, the spin injection and pumping together give the total spin current across the interface (see details in Supplemental Material [40])…”

“…where ω is the instantaneous angular velocity for slow dynamics of the order parameter andĜ m is the generalized spin-mixing conductance tensor [48]. Under assumption of C 3 symmetry (or axial symmetry with respect to the l axis), the tensorĜ m takes the following form…”

Atomic scale control of spin current transmission at interfaces

“…SML has first been considered in magnetoresistance experiments [26,27]. The possible underlying mechanisms for SML are still debated, nevertheless it is believed to be related to interface spin orbit coupling (i-SOC) [25,[28][29][30][31], non collinear magnetization, disorder [22,32], and lattice mismatch [22]. SML due to i-SOC is often evoked in order to explain inconsistencies of the value of the spin Hall angle in spin transport experiments [33][34][35][36].…”

Spin-circuit representation of spin-torque ferromagnetic resonance

“…Such circuits when complex can be simply solved using a circuit solver and therefore helps in analysis, benchmarking experimental results, and proposing creative designs of functional devices. We do need to consider the interfacial spin memory loss, [42][43][44][45][46][47] which lowers the conductivity. Recent calculations 42,[48][49][50][51][52] signify the Elliott-Yafet spin relaxation mechanism in heavy metals for which λ is dependent on thickness as conductivity varies with thickness of the samples.…”