Spin-motive force, i.e., the electric current induced by magnetization dynamics, is theoretically studied beyond the Thouless-pump paradigm. In contrast to the linear-response regime, where the induced current is purely ac, we show that spin-motive force acquires both a dc component and a second-harmonic component at nonlinear order in magnetization dynamics. We further clarify that both contributions originate from the geometric properties of electronic bands—quantum geometry defined in the mixed parameter space $(\mathit{k},\mathit{m})$ spanned by electron momentum $\mathit{k}$ and magnetization $\mathit{m}$. By applying the theory to a Luttinger model, we demonstrate that our mechanism yields a finite nonlinear current even in the insulating regime, and the resulting electrical signal is measurable in a conventional current-measurement setup. Our findings offer an operating principle of ac-to-dc conversion with magnetic materials, highlighting the pivotal role of the $(\mathit{k},\mathit{m})$-mixed-space quantum geometry in magnetization-dynamics-induced electric currents.

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• Berry curvature
• Magnetization dynamics
• Quantum geometry
• Quantum metric
• Spintronics
• Magnetic semiconductors
• Boltzmann theory