Spin pumping and torque statistics in the quantum noise limit

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 $\hslash \Omega \gtrsim k_{B}T$.

10 pages, 4 figures

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• Spin Transfer Torques
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• Fluctuation Relations for Spintronics
• Geometric Quantum Noise of Spin
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• Strong non-equilibrium effects in spin torque systems
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• Current noise geometrically generated by a driven magnet
• A thermally driven spin-transfer-torque system far from equilibrium: enhancement of the thermoelectric current via pumping current
• Charge conservation in spin torque oscillators leads to a self-induced torque
• Breaking of Coulomb blockade by macrospin-assisted tunneling