Energy Levels, Wavefunctions, and Relaxation Times of Tb3+ in Yttrium Iron Garnet

The energy levels, wavefunctions, and relaxation times of the Tb³⁺ ion in yttrium iron garnet are investigated with particular emphasis on the ``near‐crossing'' regions. The calculations are based on an extended point‐charge model for the crystal field parameters with an exchange integral equal to that of Gd³⁺. It is shown that the near crossing comes about through a two‐step process. First, the tetragonal component projects out a nearly degenerate $\text{|±6〉}$ doublet from the lower six cubic levels. Second, the exchange field splits this doublet and separates off a singlet from the remaining four levels. There is a near‐crossing when the singlet intersects the lower doublet level. The wavefunctions in the near‐crossing region are utilized in the calculation of the relaxation time. It is found that at low temperatures the spin‐magnon process is dominant and τ=10⁻¹⁰ sec (T=0°K) at the point of closest approach. A calculation of the FMR linewidth which is based on the slow relaxation model with parameters inferred from the energy level analysis is outlined and compared with experiment. Quantitative agreement is obtained with respect to the angular dependence, temperature dependence, and over‐all magnitude of the low‐temperature peaks reported by Solev'ev and Gurevich.