False Vacuum Decay in Flat-Band Ferromagnets: Role of Quantum Geometry and Chiral Edge States

Dynamical control of quantum matter is a challenging, yet promising direction for probing strongly correlated states. Motivated by recent experiments in twisted MoTe₂ that demonstrated optical control of magnetization, we propose a protocol for probing magnetization dynamics in flat-band ferromagnets. We investigate the nucleation and dynamical growth of magnetic bubbles prepared on top of a false vaccum in both itinerant ferromagnets and spin-polarized Chern insulators. For ferromagnetic metals, we emphasize the crucial role of a nontrivial quantum geometry in the magnetization dynamics, which in turn also provides a probe for the quantum metric. Furthermore, for quantum Hall ferromagnets, we show how properties of chiral edge modes localized at domain-wall boundaries can be dynamically accessed. Our Letter demonstrates the potential for nonequilibrium protocols to control and probe strongly correlated phases, with particular relevance for twisted MoTe₂ and graphene-based flat-band ferromagnets.