Minimal model for the magnetic phase diagram of [formula omitted]Ge, [formula omitted]Si, and related materials

Abstract

We present a theoretical analysis of the magnetic phase diagram of CeTi1-xScxGe and GdFe1-xCoxSi as a function of the temperature and the Sc and Co concentration x, respectively. CeScGe and GdCoSi, as many other RTX (R = rare earth, T = transition metal, X = p-block element) compounds, present a tetragonal crystal structure where bilayers of R are separated by layers of T and X. While GdFeSi and CeTi0.75Sc0.25Ge are ferromagnetic, CeScGe and GdCoSi order antiferromagnetically with the R 4f magnetic moments on the same bilayer aligned ferromagnetically and magnetic moments in nearest neighbouring bilayers aligned antiferromagnetically. The antiferromagnetic transition temperature TN decreases with decreasing concentration x in both compounds and for low enough values of x the compounds show a ferromagnetic behavior. Based on these observations we construct a simplified model Hamiltonian that we solve numerically for the specific heat and the magnetization. We find a good qualitative agreement between the model and the experimental data. Our results show that the main magnetic effect of the Sc → Ti and Co → Fe substitution in these compounds is consistent with a change in the sign of the exchange coupling between magnetic moments in neighbouring bilayers. We expect a similar phenomenology for other magnetic RTX compounds with the same type of crystal structure.