Thermodynamic model of a solid with RKKY interaction and magnetoelastic coupling

•A model magnetic solid with magnetoelastic coupling and RKKY interaction was studied.•The self-consistent thermodynamic description based on Gibbs energy was constructed.•Existence of ferromagnetic and various antiferromagnetic phases was predicted.•Lattice and magnetic response functions were studied vs. pressure and magnetic field.•The vital consequences of the magnetoelastic coupling were discussed. Thermodynamic description of a model system with magnetoelastic coupling is presented. The elastic, vibrational, electronic and magnetic energy contributions are taken into account. The long-range RKKY interaction is considered together with the nearest-neighbour direct exchange. The generalized Gibbs potential and the set of equations of state are derived, from which all thermodynamic functions are self-consistently obtained. Thermodynamic properties are calculated numerically for FCC structure for arbitrary external pressure, magnetic field and temperature, and widely discussed. In particular, for some parameters of interaction potential and electron concentration corresponding to antiferromagnetic phase, the existence of negative thermal expansion coefficient is predicted.