Competition of Structural Orderings in Presence of Magnetic Interactions

The competition of two types of structural phase transitions in crystals with triple degenerate ground electronic states of transition metal ions is considered in the framework of the cooperative Jahn-Teller effect. The signs of the spontaneous deformations are different for the two orderings under discussion: the ferroelastic ordering corresponds to the elongation of all octahedrons in the same z- direction, while the XY-ordering of the octahedrons forms the tetragonal compression around the ions with orbital degeneracy. It is shown that the magnetic interactions orienting the magnetic moments in the z-direction (external magnetic fields or molecular magnetic fields) support the XY type of ordering. As a result of that when the two structural interactions are of the same order, it is possible that the initial ferroelastic ordering is switched to the XY-ordering as a result of a phase transition induced by the magnetic interactions. On another hand, if the magnetic interactions are stronger than both Jahn-Teller interactions responsible for the structural transitions, the transition following the magnetic one is of XY-type. This is what could explain the experimental situation in the MnV$_{2}$O$_{4}$ crystals.