Nonlinear spin motive force driven by quantum geometry

Quantum geometry characterizes the geometric structures of the parameter space on which electronic states depend, and these structures are called the quantum metric and Berry curvature. Such a structure in electron momentum space is known to govern both linear and nonlinear electrical responses. Extending this concept, enlarged parameter space composed of momentum k and magnetization m, namely the (k, m)-space, is considered. In the linear response, the current generated by time-varying magnetization (j ∝ ∂_t m), known as the spin-motive force (SMF), is determined by the (k, m)-space Berry curvature.  Such a linear SMF, however, will vanish under the one cycle of magnetization dynamics. Its nonlinear counterpart will avoid such a disappearance and are expected to be expressed in terms of the quantum metric in (k, m)-space. However, such a nonlinear SMF has remained unexplored up to date.

In this talk, we propose a theory of nonlinear SMF induced by time-varying magnetization from the viewpoint of (k, m)-space quantum geometry [1]. Using the semiclassical wave-packet theory and the perturbation expansion in the exchange interaction, we find an intrinsic second-order SMF have both rectification and second-harmonic generation, and arises from the (k, m)-space quantum metric and Berry curvature. 

[1] T. Meguro, H. Ishizuka, K. Nomura, in preparation.