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Spatially varying magnetic textures can exhibit electric-current-induceddynamics as a result of the spin-transfer torque effect. When such a magneticsystem is electrically driven, an electric field is generated, which is calledthe emergent electric field. In particular, when magnetic-texture dynamics areinduced under the application of an AC electric current, the emergent electricfield also appears in an AC manner, notably, with an out-of-phase time profile,thus exhibiting inductor behaviour, often called an emergent inductor. Here weshow that the emergent inductance exhibited by magnetic textures in the pinnedregime can be explained in terms of the current-induced energy stored in themagnetic system. We numerically find that the inductance values defined fromthe emergent electric field and the current-induced magnetization-distortionenergy, respectively, are in quantitative agreement in the so-called adiabaticlimit. Our findings indicate that emergent inductors retain the basic conceptof conventional inductors; that is, the energy is stored under the applicationof electric current.

Energetic perspective on emergent inductance exhibited by magnetic textures in the pinned regime