Symmetry of the emergent inductance tensor exhibited by magnetic textures

TL;DR

This paper investigates the symmetry properties of the emergent inductance tensor in magnetic textures, revealing it is symmetric in the adiabatic limit and identifying conditions for transverse inductance responses.

Contribution

It analytically and numerically demonstrates that the emergent inductance tensor is symmetric in the adiabatic limit and characterizes magnetic textures capable of exhibiting transverse inductance responses.

Findings

Emergent inductance tensor is symmetric in the adiabatic limit.

Transverse inductance response depends on magnetic texture symmetries.

Provides a theoretical basis for exploring transverse responses in emergent inductors.

Abstract

Metals hosting gradually varying spatial magnetic textures are attracting attention as a new class of inductor. Under the application of an alternating current, the spin-transfer-torque effect induces oscillating dynamics of the magnetic texture, which subsequently yields the spin-motive force as a back action, resulting in an inductive voltage response. In general, a second-order tensor representing a material's response can have an off-diagonal component. However, it is unclear what symmetries the emergent inductance tensor has and also which magnetic textures can exhibit a transverse inductance response. Here we reveal both analytically and numerically that the emergent inductance tensor should be a symmetric tensor in the so-called adiabatic limit. By considering this symmetric tensor in terms of symmetry operations that a magnetic texture has, we further characterize the magnetic textures in which the transverse inductance response can appear. This finding provides a basis for exploring the transverse response of emergent inductors, which has yet to be discovered.