Charge and Spin Transport in Magnetic Tunnel Junctions: Microscopic Theory

TL;DR

This paper develops a microscopic theory for charge and spin transport in magnetic tunnel junctions, revealing how currents depend on magnetization dynamics and providing expressions for damping and conductance.

Contribution

It introduces a perturbative approach to evaluate charge and spin currents in MTJs, deriving explicit formulas that relate currents to magnetization dynamics and tunnel conductance.

Findings

Charge current depends on magnetization dynamics and vanishes for insulators.

Derived microscopic expression for enhanced Gilbert damping constant.

Found that damping is proportional to tunnel conductance and bias voltage.

Abstract

We study the charge and spin currents passing through a magnetic tunnel junction (MTJ) on the basis of a tight-binding model. The currents are evaluated perturbatively with respect to the tunnel Hamiltonian. The charge current has the form $A[\bm M_1(t)\times\dot{\bm M}_1(t)]\cdot\bm M_2+B\dot{\bm M}_1(t)\cdot\bm M_2$, where $\bm M_1(t)$ and $\bm M_2$ denote the directions of the magnetization in the free layer and fixed layer, respectively. The constant $A$ vanishes when one or both layers are insulators, {while the constant $B$ disappears when both layers are insulators or the same ferromagnets.} The first term in the expression for charge current represents dissipation driven by the effective electric field induced by the dynamic magnetization. In addition, from an investigation of the spin current, we obtain the microscopic expression for the enhanced Gilbert damping constant $\varDelta \alpha$. We show that $\varDelta\alpha$ is proportional to the tunnel conductance and depends on the bias voltage.