Magnetic Bloch Oscillations in Odd-Wave Magnets and the Nonlinear Edelstein Effect

Abstract: Bloch oscillations (BOs) are a quantum phenomenon in which electrons subjected to an electric field in a periodic potential exhibit an oscillating current without a net drift. In real conductors, scattering reduces the coherence required for BOs driving the system toward a steady state with a DC current. While previous studies have focused on charge transport, charge carriers also possess spin, raising the question of whether BOs can emerge in magnetic observables. Here, we show that the magnetization of odd-wave magnets can undergo BOs before relaxing to the steady-state Edelstein value, a phenomenon we term $\textit{magnetic}$ BOs. Using analytical and numerical methods, we demonstrate this effect in a minimal one-dimensional model of a p-wave magnet and generalize it to two dimensions. Our analysis further reveals that the Edelstein magnetization is generically nonlinear in the applied electric field. Finally, we argue that magnetic BOs can be detected in materials through higher-harmonic generation in THz sub-cycle lightwave spectroscopy. Magnetic BOs provide a genuine non-equilibrium signature of spin-charge coupling in unconventional magnets.