Elementary excitations in a ferroelectric antiferromagnet with Jahn–Teller excitations

The spectrum is obtained for elementary excitations of an axial ferroelectric antiferromagnet containing Jahn–Teller ions in a magnetic field H parallel and perpendicular to the equilibrium electric polarization P₀. It is shown that noncommutativity of operators of electric polarization and magnetic moment of a Jahn–Teller ion induces high-frequency oscillations of the magnetic moment (H⊥ P₀), splitting of the degenerate optical phonon branch in a magnetic field, and precession of the electric polarization vector (H|| P₀). These effects are also possible in a paramagnetic crystal in external electric and magnetic fields.