Minimal model for the magnetic phase diagram of CeTi$_{1-x}$Sc$_{x}$Ge, GdFe$_{1-x}$Co$_{x}$Si, and related materials

TL;DR

This paper presents a theoretical model explaining the magnetic phase transitions in CeTi$_{1-x}$Sc$_{x}$Ge and GdFe$_{1-x}$Co$_{x}$Si, highlighting how element substitution affects interlayer exchange interactions and magnetic ordering.

Contribution

The authors develop a simplified Hamiltonian model that captures the impact of element substitution on magnetic phases, aligning well with experimental observations.

Findings

Antiferromagnetic transition temperature decreases with substitution.

Sign change in exchange coupling explains magnetic phase evolution.

Model agrees qualitatively with experimental data.

Abstract

We present a theoretical analysis of the magnetic phase diagram of CeTi$_{1-x}$Sc$_{x}$Ge and GdFe$_{1-x}$Co$_{x}$Si 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 CeTi$_{0.75}$Sc$_{0.25}$Ge 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 $T_N$ 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 $\to$ Ti and Co $\to$ 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.