# Magnetic Properties and Spin Crossover in Transition Metal Oxides with d5 Ions at High Pressures

We analyze the influence of cooperative effects on the magnetic properties and spin crossover between the high-spin (HS) term S = 5/2 and low-spin (LS) term S = 1/2 in Mott–Hubbard dielectrics with 3d5 ions under high pressures. Two cooperation mechanisms (superexchange interaction and effective interaction via the elastic system) are considered. The sign of the exchange interaction changes because of the crossover from the antiferromagnetic in the HS state to the ferromagnetic in the LS state. In view of the large difference between the ionic radii of the HS and LS states, the systems with spin crossover acquire an additional strong coupling via the elastic system. Using the Hubbard operator representation and considering the electronic states of the two terms simultaneously, we obtain the effective Hamiltonian with allowance for the cooperative effects. The magnetic phase diagram and the spin crossover are investigated in the mean field approximation. It is shown that the inclusion of cooperative effects at low temperatures leads to a first-order phase transition between the antiferromagnetic HS state and the ferromagnetic LS state. At higher temperatures, more complicated sequences of phase transitions are possible upon an increase in pressure, including the HS paramagnet–HS antiferromagnet–LS paramagnet and HS antiferromagnet–LS paramagnet–LS ferromagnet transitions.