Spin pumping and torque statistics in the quantum noise limit

TL;DR

This paper develops a quantum noise analysis framework for charge, energy, and spin current fluctuations in a nanomagnet system, incorporating geometric phases and quantum corrections relevant at high precession rates.

Contribution

It introduces a Keldysh action approach that includes geometric phases to analyze stochastic currents and spin torque statistics in quantum nanomagnetic systems.

Findings

Derivation of spintronic fluctuation relations.

Identification of quantum limits of pumped current noise.

Analysis of magnetization switching and precession stability.

Abstract

We analyze the statistics of charge and energy currents and spin torque in a metallic nanomagnet coupled to a large magnetic metal via a tunnel contact. We derive a Keldysh action for the tunnel barrier, describing the stochastic currents in the presence of a magnetization precessing with the rate $\Omega$. In contrast to some earlier approaches, we include the geometric phases that affect the counting statistics. We illustrate the use of the action by deriving spintronic fluctuation relations, the quantum limit of pumped current noise, and consider the fluctuations in two specific cases: the situation with a stable precession of magnetization driven by spin transfer torque, and the torque-induced switching between the minima of a magnetic anisotropy. The quantum corrections are relevant when the precession rate exceeds the temperature $T$, i.e., for $\hbar \Omega \gtrsim k_B T$.