Ultrasonic investigation of the Jahn-Teller effect in BaF₂:Cu crystal

Abstract

The present work is an ultrasonic study of the temperature dependence of the dynamic elastic moduli in the single crystal of BaF2 doped with Cu. Similar to the observation in CaF2:Cu2+, the temperature dependence of the real and imaginary parts of the elastic modulus c 44 manifest typical anomalies, which are induced by the Jahn-Teller effect in the T ⊗ (e + t 2) case with orthorhombic or trigonal stable structures. However, in BaF2:Cu, these anomalies are much smaller than in CaF2:Cu2+. We attribute this difference to the lower concentration of the Cu2+ dopants that isovalently replace Ba2+ in the BaF2 matrix. Our study of BaF2:Cu reveals the following relaxation mechanisms: thermal activation, tunneling through the potential energy barrier, and two-phonon relaxation.