Magnetite Fe₃O₄ is a two-sublattice ferrimagnet in which magnetic ordering is determined by the exchange interaction between the A and B sublattices. Experimental data show that with increasing pressure the Curie temperature increases almost linearly [1, 2]. To provide a theoretical description of this effect, the method of random exchange interaction fields [3–5] is employed in this work. This method makes it possible to account for the distribution of effective exchange fields rather than their averaged value, as in molecular field theory. Within this approach, the magnetic state is described by a system of self-consistent equations for the relative magnetic moments of the sublattices. The critical temperature is determined by the degeneracy condition of the linear system, namely by setting the corresponding determinant equal to zero. The exchange integrals between ions are expressed in terms of model parameters previously obtained for compounds of the magnetite–titanomagnetite family [6]. The relationship between pressure and magnetic order is introduced through the dependence of the exchange integral on the crystal lattice volume. Compression reduces interatomic distances, enhancing the overlap of electronic orbitals and thereby increasing the magnitude of the exchange interaction. This dependence is written in terms of the magnetic Grüneisen parameter and the isothermal compressibility. In the region of moderate pressures, a linear approximation for the exchange integral is obtained, which leads to a linear variation of the critical temperature. The calculations performed show that:
• the increase of the Curie temperature with pressure is determined by the enhancement of inter-sublattice exchange;
• in the pressure range up to several GPa, the dependence remains linear;
• the calculated coefficient dTc/dP agrees in magnitude with experimental estimates [1, 2];
• the character of magnetic ordering does not change within the considered pressure range; only the stability of the ferrimagnetic state increases.
Thus, within this model, pressure acts as a parameter controlling the effective strength of the exchange interaction. The random field method makes it possible to trace this relationship without reducing the description to a simple mean-field approximation and ensures a proper account of fluctuations of the exchange integrals. The obtained result confirms that a change in the crystal lattice volume directly affects the critical temperature of magnetite and can be quantitatively described within the proposed framework.