AC Wien effect in spin ice, manifest in non-linear non-equilibrium susceptibility

We predict the non-linear non-equilibrium response of a “magnetolyte”, the Coulomb fluid of magnetic monopoles in spin ice. This involves an increase of the monopole density due to the second Wien effect—a universal and robust enhancement for Coulomb systems in an external field—which in turn speeds up the magnetization dynamics, manifest in a non-linear susceptibility. Along the way, we gain new insights into the AC version of the classic Wien effect. One striking discovery is that of a frequency window where the Wien effect for magnetolyte and electrolyte are indistinguishable, with the former exhibiting perfect symmetry between the charges. In addition, we find a new low-frequency regime where the growing magnetization counteracts the Wien effect. We discuss for what parameters best to observe the AC Wien effect in Dy${}_2$Ti${}_2$O${}_7$.