Thermodynamics of spin ice on an antiperovskite lattice in the cluster approximation

Low-temperature thermodynamic properties of spin ice have been studied for compounds with the structure of antiperovskite containing rare-earth ions with the general chemical formula $ReMe\mathrm{O}$ (where $Re$ – is a rare-earth element, $Me$ – is a divalent metal). The calculations were carried out in the cluster approximation. The cases of undistorted and distorted $\mathrm{O}Re_6$ octahedron are discussed. In the case of an undistorted octahedron in the absence of an external magnetic field, the ground state of the system is infinitely degenerate. When an external magnetic field is applied, anomalies in the temperature dependences of heat capacity, entropy and magnetization are detected. In the case of a distorted octahedron and assuming that this distortion leads to the energy efficiency of two of the sixty-four configurations, it is obtained that there is a phase transition in the system of magnetic rare-earth ions.