  The celebrated Wiedemann-Franz (WF) law which governs the relation between
charge and heat transport traces back to the experimental discovery in 1853 by
Wiedemann and Franz. Despite the fundamental difference of the
quantum-statistical properties between fermions and bosons, the linear-in-$T$
behavior of the WF law at low temperatures has recently been found to be the
universal property by the discovery of the WF law for magnon transport.
However, the WF law is for the linear response, and whether or not the
universal law is valid even in the nonlinear regime of Bose systems remains an
open issue. Here we provide a solution to this fundamental challenge. We show
that the ratio of the thermal to spin transport coefficient of magnons in
topologically trivial insulating magnets exhibits a different behavior from the
linear response and the universal law breaks down in the strong nonlinear
regime. This finding is within experimental reach with current device and
measurement technologies. Our discovery is the key ingredient in magnon-based
spintronics, in the evaluation of the figure of merit for thermomagnetic
conversion elements of spintronics devices.
