Theory of emergent inductors with general magnetic structures

In recent years, a new concept of inductors employing quantum mechanics on helical magnets has been theoretically proposed [Nagaosa JJAP (2019)]. This concept, referred to as the emergent inductor, has been actively studied because the inductor following this concept can achieve significant miniaturization of electrical circuits.

However, the finite inductance has been experimentally observed not only in spiral phases but also in other phases [Yokouchi et al., Nature (2020), Kitaori et al., PNAS (2021)] and the origin of the inductance in these phases has not been understood. Here, we study the general formalism of the emergent induction arising from the dynamics of magnetization. We derive the linear response of the current density mediated by the dynamics of magnetization using a diagrammatic approach and formulate the impedance and inductance for general magnetic materials. We show that the inductance is composed of two components that contribute positively and negatively to the inductance. We also show that the positive inductance arises from Ohmic dissipation including the effect of the emergent electric field (Berry phase in real space), while the negative inductance arises from the polarization of the itinerant electrons.