Abstract
An efficient scheme for evaluating the critical temperatures of ferromagnetic, antiferromagnetic, and ferrimagnetic crystals with multiple sublattices is presented. The approach is based on a pairwise Heisenberg Hamiltonian and a random-phase approximation (Tyablikov's decoupling) for magnon Green's functions. The pair exchange interactions are derived from self-consistent electronic structure calculations using a magnetic force theorem. The developed technique is applied to hexagonal gadolinium and its selected intermetallic compounds $\mathrm{Gd}X$ $(X=\mathrm{Mg},\mathrm{Rh},\mathrm{Ni},\mathrm{Pd})$ with CsCl and CrB structures. The calculated critical temperatures are quite sensitive to a neglect of the nonmagnetic $(X)$ element; their values are in a fair agreement with experiment.
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