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In this work, we introduce the theoretical framework of the phonon-mediated Migdal effect for neutrino-nucleus scattering in semiconductors, considering both the Standard Model and the presence of the neutrino magnetic moment. We calculate the rate of electron excitation resulting from the Migdal effect and observe a substantial coherent enhancement compared to ordinary neutrino-electron scattering. Furthermore, we provide numerical sensitivities for detecting the Migdal effect and constraints on the neutrino magnetic moment, utilizing an experimental setup with reactor neutrinos.