We show that magnetism in moir\'e Mott-Wigner crystals can be induced by the collective vibration of electrons around their equilibrium positions (i.e., electronic phonons), even without spin interactions between electrons. Due to a geometric valley-orbit coupling from the Berry phase effect, the zero-point energy of electronic phonons reaches minimum when electrons are fully valley polarized. This leads to a spontaneous magnetization when below a critical temperature. We also propose to engineer the magnetism through the photoexcitation of chiral electronic phonons.
Categories: cond-mat.mes-hall cond-mat.str-el