Anisotropy of the Magnetic Properties of Er³⁺ Ion in Erbium Iron Garnet Crystal at Low Temperature

With the consideration of crystal field (CF) and exchange interaction between the magnetic ions, we conduct a theoretical analysis to the anisotropy of the magnetization caused by Er³⁺ ions in erbium iron garnet (ErIG) in the temperature range from 4.2 to 150 K. It is found that the anisotropy of the magnetization caused by Er³⁺ ions originates mainly from the anisotropic Er³⁺–Fe³⁺ ion exchange interaction. In the course of research, a set of relatively suitable CF parameters are obtained by analyzing the influence of different CF parameters on the magnetization. The secular equation is solved by quantum theory after taking into account the coupling of the ⁴I_15/2 and ⁴I_13/2 multiplets, and the energy levels and wave functions of Er³⁺ ions are further obtained. Then, the magnetization of Er³⁺ ions at six inequivalent sublattices when magnetized along the [100], [110], and [111] directions are calculated, respectively. Following this, comparisons between the average value of the so-obtained six quantities and the experimental data are made in the [100], [110], and [111] magnetization directions. The calculated results coincide well with the experimental data and [100] is the easy magnetization direction.