The Effect of Applied Hydrostatic Pressures in Ferromagnetic Ordered HoM2 [M = (Al, Ni)] Laves Phases: A DFT Study

In this study, density functional theory (DFT) with Hubbard U correction calculations (DFT+U) was used to examine the ferromagnetic properties of HoM₂ Laves phases (M = {Al, Ni}) under external hydrostatic pressure from 0 GPa to 1.0 GPa. The resulting net magnetic moments of 8.61 µ_B/f.u. (HoAl₂) and 8.12 µ_B/f.u. (HoNi₂) align with values reported in experiments. Additionally, for both alloys, the ferromagnetic behavior remains unchanged under applied pressures from 0 GPa to 1.0 GPa. The study also confirms that the magnetic properties of the alloys are mainly influenced by the 4<i>f</i> electrons, with 3<i>d</i> electrons playing a slightly more significant role in HoNi₂ Laves phases compared to HoAl₂. The contribution of electrons in <i>d</i> and <i>f</i> orbitals to the net magnetic moment of each Laves phase alloy within the specified pressure range was examined. Furthermore, the crystal geometry optimization and electronic specific heat coefficient were calculated as functions of applied pressures up to 1.0 GPa for both ferromagnetically ordered Laves phases.