Relevance of Jahn-Teller effect in strongly anisotropic metal sites

Recently, heavy transition metal compounds have been intensively investigated because of their unusual magnetic properties driven by strong spin-orbit coupling. In particular, the systems with highly degenerate local electronic states, as represented by the $d^1$ double perovskites containing Mo$^{5+}$, Re$^{6+}$, Os$^{7+}$, show enhanced anisotropy in exchange interactions. Despite the four-fold (quasi) degeneracy in the $d^1$ materials, the Jahn-Teller (JT) distortion has not been observed in many of them by x-ray and neutron diffraction down to a few Kelvin. This ``violation'' of JT theorem has been often reported, whereas no explanation for it has been given so far. Here, we address the nature of the JT effect in cubic double perovskites with $ab~initio$ based methodology. We calculated the local properties such as crystal field levels, vibronic coupling, and magnetic moments, by using state-of-the-art post Hartree-Fock method. The JT stabilization for these ions is obtained weak to intermediate compared to the frequency of the local active vibration. This implies either the absence or a dynamical character of JT effect, explaining the absence of static JT distortions. The influence of the dynamical JT effect on local magnetic properties will be presented.