Paramagnetic-Resonance Study of Crystal-Field and Exchange Effects in an Excited State of TmN

Abstract

Paramagnetic resonance has been observed in an excited ${\Gamma }_5$ triplet state 222°K above the singlet ${\Gamma }_1$ ground state of ${\mathrm{Tm}}^{3+}$ ($4f^{12}$) in cubic TmN (i.e., pure compound concentrated in ${\mathrm{Tm}}^{3+}$). The $g$ factor has a small temperature dependence that has been interpreted as a shift, caused by ferromagnetic exchange, from the crystal-field only value. For exchange small compared to crystal-field effects, theory predicts a $g$ shift proportional to a quantity differing only slightly from the susceptibility, i.e., going approximately as $\frac{1}{T}$ for the temperature range of interest. The over-all trend of the $g$ temperature dependence is consistent with this for small ferromagnetic exchange; however, there is an anomalous minimum in the $g$ temperature dependence centered about 120°K. The intensity reaches its maximum and the linewidth a minimum near the same temperature. The analysis of the behavior of $g$, ignoring the anomaly, gives the values $x=-0.990\mathrm{}$, $W=-3.47\mathrm{}°$K for the crystal-field parameters, and $\mathcal{I}\mathrm{}\left(0\right)J(J+1\mathrm{})\mathrm{}\equiv J(J+1\mathrm{})\mathrm{}\Sigma i^{}{\mathcal{I}}_{\mathrm{ij}}=11.4\mathrm{}°$K for the exchange energy per ion. These crystal-field parameters give a calculated temperature dependence of the resonant intensity in quite good agreement with experiment.