6. Dynamic and Static Jahn-Teller Effect in Impurities: Determination of the Tunneling Splitting

In this paper we review the concepts of dynamic and static Jahn-Teller (JT) effects and study their influence in the electron paramagnetic resonance (EPR) spectra of transition metal impurities in wide gap insulators. We show that the key quantities involved in this problem are the tunneling splitting, usually denoted 3Γ, and the splitting, δ, between∼​3z ² −r ² and∼​ x ² −y ² energy levels due to the random strain field which is present in every real crystal. It is pointed out that in the E⊗e JT problem the kinetic energy of nuclei involved in the ground state plays a key role for understanding the actual value of 3Γ and thus the existence of dynamic JT effect. The results of ab initio calculations on a variety of JT systems show that 3Γ values span a much larger range than previously suggested. In particular, we find that 3Γ=235cm⁻¹ for MgO:Cu²⁺ while 3Γ=10⁻⁴cm⁻¹ for KCl:Ag²⁺. We also show that the dynamic JT effect can only appear for such large values of 3Γ as those found in MgO:Cu²⁺ since usual strain fields lead to δ values of the order of 10cm⁻¹ that would otherwise localize the system in only one of the JT wells. The present results explain satisfactorily why the JT effect for Cu²⁺ and Ag²⁺ impurities in MgO is dynamic while static for Ag²⁺-doped CaO and alkali chlorides. The origin of such a difference is discussed in detail.