Spin Current Cross-Correlations as a Probe of Magnon Coherence

Motivated by the important role of the normalized second-order coherence function, often called $g^{(2)}$, in the field of quantum optics, we propose a method to determine magnon coherence in solid-state devices. Namely, we show that the cross-correlations of pure spin currents injected by a ferromagnet into two metal leads, normalized by their dc value, replicate the behavior of $g^{(2)}$ when magnons are driven far from equilibrium. We consider two scenarios: driving by ferromagnetic resonance, which leads to the coherent occupation of a single mode, and driving by heating of the magnons, which leads to an excess of incoherent magnons. We find an enhanced normalized cross-correlation in the latter case, thereby demonstrating bunching of nonequilibrium thermal magnons due to their bosonic statistics. Our results contribute to the burgeoning field of quantum magnonics, which seeks to explore and exploit the quantum nature of magnons.

Figure 1

Magnetic heterostucture, with ferromagnetic insulator (FI) and metallic leads (LNM and RNM). The arrow in the FI depicts its total spin. Spin currents ${\widehat{I}}_L$ and ${\widehat{I}}_R$ are injected into the LNM and RNM, respectively, when the FI is excited.

Figure 2

Normalized spin-current cross-correlation $c^{(2)}$ for FI driven via heating (left) and FMR (right). The coherent mode number $N_c=(\chi h{)}^2$ is assumed to be driven by a circularly polarized FMR field $h$, with $\chi$ as the susceptibility. Solid lines, blue to red, represent electronic temperatures $T/E_m=0.01$, 2.5, 5, 7.5, 10.