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We develop a self-consistently renormalized spin-wave theory, within amean-field approximation, for the two-dimensional Heisenberg ferromagnet withperpendicular easy-axis anisotropy on the honeycomb lattice, as well as itsfew-layer and bulk extensions. In this method, the magnetization dependence ontemperature is found as the solution of the self-consistency equation.Furthermore, we account for the physical difference of surface and bulk layersby treating the layers as separate sublattices. Thus, the method can be readilygeneralized to study various magnetic phenomena in a broad range of systems,including those comprising magnetically inequivalent sublattices. Using ourtheory, we calculate the temperature-dependent magnetization for twochromium-based layered van der Waals insulating magnets, Cr$_2$Ge$_2$Te$_6$ andCrI$_3$, employing various sets of Heisenberg exchange and single-ionanisotropy values reported for these materials in the existing literature. Asexpected, we observe a strong dimensionality effect where the orderingtemperature is reduced and its sensitivity on the anisotropy is enhanced withthe decrease of dimensionality.

Self-consistently renormailzed spin-wave theory of layered ferromagnets on honeycomb lattice