  Spatially varying magnetic textures can exhibit electric-current-induced
dynamics as a result of the spin-transfer torque effect. When such a magnetic
system is electrically driven, an electric field is generated, which is called
the emergent electric field. In particular, when magnetic-texture dynamics are
induced under the application of an AC electric current, the emergent electric
field also appears in an AC manner, notably, with an out-of-phase time profile,
thus exhibiting inductor behaviour, often called an emergent inductor. Here we
show that the emergent inductance exhibited by magnetic textures in the pinned
regime can be explained in terms of the current-induced energy stored in the
magnetic system. We numerically find that the inductance values defined from
the emergent electric field and the current-induced magnetization-distortion
energy, respectively, are in quantitative agreement in the so-called adiabatic
limit. Our findings indicate that emergent inductors retain the basic concept
of conventional inductors; that is, the energy is stored under the application
of electric current.
