Crystal-field determination for trivalent thulium in yttrium orthoaluminate

The polarized absorption spectra of YAlO₃:Tm³⁺ were analyzed at 77^∘{}K. A free-ion calculation was performed by fitting the centers of gravity of the J manifolds. The coefficients which gave the best least-squares deviation of the calculated "free-ion" spectra from the observed "free-ion" spectra were E¹=7075.5, E²=33.8, E³=654.3, ζ=2631.8, α=8.0, β=-764.9; where all parameters have units of cm^-1. A crystal-field calculation was also carried out by fitting Stark splittings and irreducible representations to the observed spectra. In order to obtain good starting parameters for fitting a Cₛ (C₁ₕ) symmetry Hamiltonian, a descending symmetries technique was used. The results of a least-squares fit of the crystal-field Hamiltonian to the observed ³F₄, ³F₃, ¹G₄, and ¹D₂ Stark splittings gave the following parameters for the Cₛ Hamiltonian: B₀²=-434.9, ReB₂²=420.8, ImB₂²=199.4, B₀⁴=-691.6, ReB₂⁴=444.9, ImB₂⁴=114.2, ReB₄⁴=501.2, ImB₄⁴=-389.2, B₀⁶=-260.4, ReB₂⁶=175.6, ImB₂⁶=229.7, ReB₄⁶=92.7, ImB₄⁶=542.4, ReB₆⁶=410.5, ImB₆⁶=113.4; where all units are in cm^-1.