Landauer theory of ballistic torkances in non-collinear spin valves

TL;DR

This paper develops a Landauer-based theory for voltage-induced spin-transfer torques in ballistic non-collinear spin valves, revealing quantum size effects and oscillations in torkance related to magnetic structure.

Contribution

It introduces a novel Landauer-like formula for torkance in non-collinear spin valves and predicts long-range oscillations due to quantum size effects.

Findings

Oscillations of Ni-torkance as a function of Ni thickness.

Contrast between oscillatory torkance and thickness-independent conductance.

Quantum size effects influence spin-transfer torques in non-collinear magnetic structures.

Abstract

We present a theory of voltage-induced spin-transfer torques in ballistic non-collinear spin valves. The torkance on one ferromagnetic layer is expressed in terms of scattering coefficients of the whole spin valve, in analogy to the Landauer conductance formula. The theory is applied to Co/Cu/Ni(001)-based systems where long-range oscillations of the Ni-torkance as a function of Ni thickness are predicted. The oscillations represent a novel quantum size effect due to the non-collinear magnetic structure. The oscillatory behavior of the torkance contrasts a thickness-independent trend of the conductance.