Magnetic phase diagram of Eu1−xGdxS

Abstract

We propose a model to investigate the magnetic properties of Eu${}_{1\ensuremath{-}x}$Gd${}_{x}$S consisting of an s-f term with chemical disorder due to the separation of the atomic energy levels of the $s$ electrons $\ensuremath{\Delta}V$ and a disordered Heisenberg term. The model is solved by using a self-consistent modified Rudermann-Kittel-Kasuya-Yosida technique. Disorder is accounted for by the coherent potential approximation, and the electronic self-energy is obtained by using a suitable alloy analogy. By comparing with experimental data for the red-shift of the absorption edge at $x=0.01$, and considering the fact that an insulator-metal transition takes place at the same concentration, we are able to ascertain $\ensuremath{\Delta}V$ at about $0.58$ eV. We compute the critical temperatures in dependence on $x$ and obtain a transition from ferromagnetism to AFM-II type antiferromagnetism at $x\ensuremath{\approx}0.4$. The spin-glass phase is briefly discussed within the mean-field approximation. We also compute the critical temperatures for the pure s-f model including antiferromagnetism on the simple cubic and the face-centered-cubic lattices in dependence on the band occupation $n$, and obtain the following sequences of phases: ferromagnetism (FM) $\ensuremath{\rightarrow}$ AFM-A $\ensuremath{\rightarrow}$ AFM-C $\ensuremath{\rightarrow}$ AFM-G for the former, and FM $\ensuremath{\rightarrow}$ AFM-II $\ensuremath{\rightarrow}$ AFM-III $\ensuremath{\rightarrow}$ AFM-I for the latter.