First-principles investigations of the magnetic phase diagram of Gd$_{1-x}$Ca$_{x}$MnO$_{3}$

We studied for the first time the magnetic phase diagram of the rare-earth manganites series Gd$_{1-x}$Ca$_{x}$MnO$_{3}$ (GCMO) over the full concentration range based on density functional theory. GCMO has been shown to form solid solutions. We take into account this disordered character by adapting special quasi random structures at different concentration steps. The magnetic phase diagram is mainly described by means of the magnetic exchange interactions between the Mn sites and Monte Carlo simulations were performed to estimate the corresponding transition temperatures. They agree very well with recent experiments. The hole doped region $x<0.5$ shows a strong ferromagnetic ground state, which competes with A-type antiferromagnetism at higher Ca concentrations $x>0.6$.