Zeeman interaction and Jahn-Teller effect in ${\mathrm{\Gamma }}_8$ multiplet

We present a thorough analysis of the interplay of magnetic moment and the Jahn-Teller effect in the ${\mathrm{\Gamma }}_8$ cubic multiplet. We find that in the presence of dynamical Jahn-Teller effect, the Zeeman interaction remains isotropic, whereas the $g$ and $G$ factors can change their signs. The static Jahn-Teller distortion also can change the sign of these $g$ factors as well as the nature of the magnetic anisotropy. Combining the theory with state-of-the-art {\it ab initio} calculations, we analyzed the magnetic properties of Np${}^{4+}$ and Ir${}^{4+}$ impurity ions in cubic environment. The calculated $g$ factors of Np${}^{4+}$ impurity agree well with experimental data. The {\it ab initio} calculation predicts strong Jahn-Teller effect in Ir${}^{4+}$ ion in cubic environment and the strong vibronic reduction of $g$ and $G$ factors.