Breaking down the magnonic Wiedemann-Franz law in the hydrodynamic regime

Quantum transport has attracted a profound growth of interest owing to its fundamental importance and many applications in condensed matter physics. Recent developments in experimental techniques have boosted the study of quantum transport. Notably in ultraclean systems, strong interactions between quasi-particles drastically affect the transport properties, resulting in an emergent hydrodynamic behavior. The most-studied example is the hydrodynamic charge transport in metals, which gives rise to an active research field called electron hydrodynamics. This concept has revealed various unconventional transport phenomena such as the violation of the Wiedemann-Franz (WF) law.

Recent experiments on ultrapure ferromagnetic insulators have opened up new pathways for magnon hydrodynamics. Hydrodynamic magnon transport implies exhibiting extraordinary features as well as electron hydrodynamics and has a potential for innovative functionalities beyond the conventional non-interacting magnon picture. However, the direct observation of magnon fluids remains an open issue due to the lack of probes to access the time and length scales characteristics of this regime.

In this work, we derive a set of coupled hydrodynamic equations for a magnon fluid and study the spin and thermal conductivities by focusing on the most dominant time scales. We also reveal that the ratio between the two conductivities in the hydrodynamic regime shows a large deviation from the standard form so-called the magnonic WF law.