Prediction of magnetic moment collapse in ZrFe$_2$ under hydrostatic pressure

Electronic structure and magnetic properties of ZrFe$_2$ with a cubic Laves phase are investigated by calculations based on the density functional theory. The total magnetic moment (m) of 3.14 $\mu_B$ per formula unit (\emph{f.u.}) is obtained at the experimental lattice constant (7.06 \AA), which is larger than 3.06 $\mu_B$/\emph{f.u.} obtained at the theoretical equilibrium lattice constant (6.85 \AA). The localized $3d$ magnetic moment is in negative diffusive sp background moment. We predict a two-step magnetic collapse under pressure: one is from 3.06 $\mu_B$/\emph{f.u.} to 1.26 $\mu_B$/\emph{f.u.} at about 3.6 GPa, and the other is from 0.5 $\mu_B$/\emph{f.u.} to nonmagnetic state at about 15 GPa. We understand this process by the changes of density of states. The magnetic moment decreases under the pressure in the vicinity of the experimental lattice constant with $d\ln m/dp=-0.038$ GPa$^{-1}$. The spontaneous volume magnetostriction is 0.015. We suggest that the Invar effect of this alloy may be understood when considering the magnetic moment variation according to the Weiss $2\gamma$-model.