Comment on "Reconsidering the nonlinear emergent inductance: time-varying Joule heating and its impact on the AC electrical response"

When non-collinear spin textures are driven by current, an emergent electric field arises due to the emergent electromagnetic induction. So far, this phenomenon has been reported in several materials, manifesting the current-nonlinear imaginary part of the complex impedance. Recently, Furuta et al. proposed a time-varying temperature increase due to Joule heating as an alternative explanation for these current-nonlinear complex impedances [arXiv:2407.00309v1]. In this study, we re-examine the nonlinear complex impedance in GdRuAl12 and YMn6Sn6, specifically addressing the impact of the time-varying temperature increase. Our findings reveal that the magnetic-field angle, frequency, and temperature dependence of nonlinear complex impedances in these two materials cannot be explained by the time-varying temperature increase. Instead, these dependencies of the imaginary part of the nonlinear impedance are consistent with the expected behaviour in the theory of emergent electromagnetic induction. Moreover, we observe a significant real part of the nonlinear complex impedance, likely resulting from the dissipation associated with the current-driven motion of helices and domain walls. Our findings highlight the diverse current-nonlinear transport phenomena of spin dynamical origin in helimagnets.