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Magnon-mediated spin current noise in ferromagnet$|$non-magnetic conductor hybrids

The quantum excitations of the collective magnetization dynamics in a ferromagnet (F) - magnons - enable spin transport without an associated charge current. This pure spin current can be transferred to electrons in an adjacent non-magnetic conductor (N). We evaluate the finite temperature noise of the magnon-mediated spin current injected into N by an adjacent F driven by a coherent microwave field. We find that the dipolar interaction leads to squeezing of the magnon modes giving them wavevector dependent non-integral spin, which directly manifests itself in the shot noise. For temperatures higher than the magnon gap, the thermal noise is dominated by large wavevector magnons which exhibit negligible squeezing. The noise spectrum is white up to the frequency corresponding to the maximum of the temperature or the magnon gap. At larger frequencies, the noise is dominated by vacuum fluctuations. The shot noise is found to be much larger than its thermal counterpart over a broad temperature range, making the former easier to be measured experimentally.