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

• Published in: IEEE transactions on magnetics 2022-04, Vol.58 (4), p.1-6
• Main Authors: Xu, Youan, Cai, Wei, Yang, Biwu, Liang, Youwei, Yang, Zhiyong
• Format: Article
• Language: English
• Subjects: Anisotropic magnetoresistance; Anisotropy; crystal field (CF); Crystals; Elementary particle exchange interactions; Energy levels; Erbium; exchange interaction; Garnets; Ion exchange; Ions; Iron; Low temperature; Magnetic properties; Magnetism; Magnetization; Mathematical analysis; Parameters; Quantum theory; Wave functions
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/TMAG.2022.3142505

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 Er 3+ 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 Er 3+ ions originates mainly from the anisotropic Er 3+ -Fe 3+ 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 4 I 15/2 and 4 I 13/2 multiplets, and the energy levels and wave functions of Er 3+ ions are further obtained. Then, the magnetization of Er 3+ 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.