Spin current and spin transfer torque in ferromagnet/superconductor spin valves

TL;DR

This paper investigates spin transport, spin current, and spin transfer torque in ferromagnet/superconductor spin valves using self-consistent methods, revealing how these phenomena depend on geometry, bias, and interface quality.

Contribution

It provides a detailed, realistic analysis of spin dynamics in spin valves, incorporating interface imperfections and geometry, which advances understanding beyond idealized models.

Findings

Spin current precesses around exchange fields within ferromagnets.

Spin current penetrates into the superconductor above a critical bias.

Spin accumulation oscillates in the normal metal with parameter-dependent peaks.

Abstract

Using fully self consistent methods, we study spin transport in realistic, fabricable experimental spin valve systems consisting of two magnetic layers, a superconducting layer, and a spacer normal layer between the ferromagnets. Our methods ensure that the proper relations between spin current gradients and spin transfer torques are satisfied. We present results as a function of geometrical parameters, interfacial barrier values, misalignment angle between the ferromagnets, and bias voltage. Our main results are for the spin current and spin accumulation as functions of position within the spin valve structure. We see precession of the spin current about the exchange fields within the ferromagnets, and penetration of the spin current into the superconductor for biases greater than the critical bias, defined in the text. The spin accumulation exhibits oscillating behavior in the normal metal, with a strong dependence on the physical parameters both as to the structure and formation of the peaks. We also study the bias dependence of the spatially averaged spin transfer torque and spin accumulation. We examine the critical bias effect of these quantities, and their dependence on the physical parameters. Our results are predictive of the outcome of future experiments, as they take into account imperfect interfaces and a realistic geometry.