Crystal-field determination for trivalent erbium in yttrium orthoaluminate

A free-ion-model crystal-field calculation has been performed for YAlO₃:Er³⁺. A free-ion calculation was done by fitting a free-ion Hamiltonian, which included Coulomb, spin-orbit, configuration, spin-spin, and spin-other-orbit interactions. The coefficients which gave the best least-squares deviation of the calculated centers of gravity from the observed centers of gravity were E¹=6174.1, E²=32.836, E³=651.69, ξ=2350.5, α=27.825, β=-722.32, γ=3729.4, M⁰=3.525, M²=[1.974], M⁴=[1.339], P²=2.4779, P⁴=-0.0406, P⁶=0.1247, T²=157.04, T³=42.522, T⁴=62.23, T⁶=-259.93, T⁷=402.94, T⁸=66.377 with an rms deviation of 29.1; where all quantities have units of cm^-1. The intermediate-coupled free-ion vectors were then used to fit a Cₛ (C₁ₕ) Hamiltonian to the observed Stark splittings. The crystal-field parameters obtained from a previous calculation on YAlO₃:Tm³⁺ were used as starting parameters. The parameters which gave the best fit to the observed YAlO₃:Er³⁺ Stark spectra were B₀²=-183.2, ReB₂²=385.6, ImB₂²=185.2, B₀⁴=-816.2, ReB₂⁴=444.0, ImB₂⁴=39.7, ReB₄⁴=637.0, ImB₄⁴=-222.8, B₀⁶=-603.8, ReB₂⁶=-42.2, ImB₂⁶=305.4, ReB₄⁶=229.7, ImB₄⁶=523.8, ReB₆⁶=317.0, ImB₆⁶=87.0 with an rms deviation of 6.9; where all units are in cm^-1.