Spectroscopic and Magnetic Susceptibility Analyses of the $^{7}F_{J}$ and $^{5}$D$_{4}$ Multiplet Manifolds of Tb$^{3+}$(4f$^{8})$ in TbAlO$_{3}$

Detailed analyses of temperature-dependent spectroscopic and magnetic susceptibility data are reported for the crystal-field split energy levels of the $^{7}$F$_{J}$ and $^{5}$D$_{4}$ of Tb$^{3+}$ TbAlO$_{3}$. The spectroscopic data include absorption spectra obtained between 480 and 2940 nm from 8 to 300 K. High resolution fluorescence spectra are reported, representing transitions from $^{5}$D$_{4}$ to$^{ 7}$F$_{6,5,4}$, at a sample temperature of 85 K. Using crystal-field modeling techniques recently adapted for low symmetry systems, we have assigned all 58 experimental Stark levels within the $^{7}$F$_{J}$ and $^{5}$D$_{4}$ manifolds, with a fitting standard deviation of 4.5 cm$^{-1}$ (3.8 cm$^{-1}$ rms error). Furthermore, the theoretical Stark levels and calculated wavefunctions were used to determine the temperature dependence of the magnetic susceptibility along the $c$-axis of the TbAlO$_{3}$ crystal. Agreement is obtained between the calculated susceptibility and temperature-dependent magnetic data reported earlier. The susceptibility calculation also confirms the predicted ordering of states within the $^{7}$F$_{6}$ multiplet manifold.