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

Spin pumping and torque statistics in the quantum noise limit