Spontaneous symmetry breaking of magnetostriction in metals with multi-valley band structure

We show that a first-order phase transition can take place in a metal in a strong magnetic field if an electron Landau level approaches the Fermi energy of the metal. This transition is due to the electron-phonon interaction and is characterized by a jump in magnetostriction of the metal. If there are several equivalent groups of charge carriers in the metal, a spontaneous symmetry breaking of the magnetostriction can occur when the Landau level crosses the Fermi energy, and this breaking manifests itself as a series of the structural phase transitions that change a crystal symmetry of the metal. With these results, we discuss unusual findings recently discovered in bismuth.[ In the new version more explanations and examples added.]