Magnonic noise and Wiedemann-Franz law

We theoretically establish mutual relations among magnetic momentum, heat, and fluctuations of propagating magnons in a ferromagnetic insulating junction in terms of noise and the bosonic Wiedemann-Franz (WF) law. Using the Schwinger-Keldysh formalism, we calculate all transport coefficients of a noise spectrum for both magnonic spin and heat currents, and establish Onsager relations between the thermomagnetic currents and the zero-frequency noise. Making use of the magnonic WF law and the Seebeck coefficient in the low-temperature limit, we theoretically discover universal relations, i.e.,being independent of material parameters, for both the nonequilibrium and equilibrium noise, and show that each noise is described solely in terms of thermal conductance. Finally, we introduce a magnonic spin analog of the Fano factor, noise-to-current ratio, and demonstrate that the magnonic spin-Fano factor reduces to a universal value in the low-temperature limit and it remains valid even beyond a linear response regime.