Reconsidering nonlinear emergent inductance: Time-varying Joule heating and its impact on AC electrical response

A nonlinearly enhanced electrical reactance Im⁡𝑍 under a large AC current was measured to explore emergent inductors, which constitute a new class of inductors based on the spin-transfer torque effect. A nonlinear Im⁡𝑍 was observed in conducting magnets that contain noncollinear magnetic textures and interpreted as the realization of an inductance due to current-induced spin dynamics. However, curious behavior was concomitantly observed. For instance, the nonlinear Im⁡𝑍 always has a cutoff frequency of 100−104Hz, which is much lower than the resonance frequency of a ferromagnetic domain wall, ∼107Hz. Furthermore, the magnitude of Im⁡𝑍 is much greater than that theoretically expected, and the temperature and magnetic field dependences are complicated. This behavior appears to be difficult to understand in terms of the current-induced spin dynamics, and therefore, the earlier interpretation of the nonlinear Im⁡𝑍 should be further verified. Here, we theoretically and experimentally show that time-varying Joule heating and its impact on the AC electrical response can naturally explain these observations. In the experimental approach, we investigate the nonlinear AC electrical response of two conducting materials that exhibit no magnetic order, CuIr2⁢S4 and 1⁢𝑇′−MoTe2. Under time-varying Joule heating, a nonlinearly enhanced Im⁡𝑍 is observed in both systems, verifying the concept of the Joule-heating-induced AC electrical response. We reconsider the nonlinear emergent inductance reported thus far and discover that the Joule-heating-induced AC electrical response approximately reproduces the temperature and magnetic field dependences, cutoff frequency, and magnitude of Im⁡𝑍. Our study implies that the nonlinear Im⁡𝑍 previously observed in conducting magnets that contain noncollinear magnetic textures includes a considerable contribution of the Joule-heating-induced apparent AC impedance.