Theoretical analysis of the anisotropy of the magnetization of the Ho³⁺ ion in holmium iron garnet single crystals

The spontaneous magnetization of the Ho^3+ ion in holmium iron garnet (HoIG) single crystals in the temperature range of 4.2--294 K along the directions 111, 110, and 100 are calculated, taking into account the effects of six magnetically inequivalent sites occupied by the Ho^3+ ions based on the quantum theory. The calculated results show that the magnetization of the Ho^3+ ion in HoIG is obviously anisotropic. The theoretical results are in agreement with those of experiments. A primary interpretation of the anisotropy of magnetization of the Ho^3+ ion in HoIG is put forward.