Ultrasonic evaluation of the Jahn–Teller effect parameters. Application toZnSe:Cr2 +

Abstract

A method is constructed that uses ultrasonic experiments to evaluate theparameters of the Jahn–Teller (JT) effect in impurity centers in crystals. Themethod is based on measurements of temperature dependent attenuation andphase velocity and does not require assumptions about mechanisms of relaxation.The results are illustrated by measurements performed on the impurity systemZnSe:Cr2 + , in which theCr2 + ion has a threefolddegenerate T term in the ground state, subject to the JT problem. Ultrasound propagation anomalies show thatthe main JT distortions of the tetrahedral environment of theCr2 + ion are of tetragonal E type and hence the lowest branch of the adiabatic potential energysurface (APES) is formed in accordance with the problem. With dopant concentration3.8 × 1018 cm − 3 the modulus of the constant of linear vibronic coupling to tetragonalE type vibrations is determined by two independent experiments:|FE| = 5.49 × 10 − 5 dyn revealed from attenuation measurements, while a slightly different value|FE| = 5.57 × 10 − 5 dynemerges from phase velocity measurements. Contributions of other active vibronic modes to the elasticmodulus Cl = (C11 + C12 + 2C44)/2 are analyzed and it is shown that the influence of the totally symmetric mode isnegligible. Using additional information about this system obtained from independentsources, we also estimated the primary force constant in the E direction (KE≈(1.4–4.2) × 104 dyn cm − 1) and orthorhombic and trigonal saddle points of the APES in the five-dimensionalspace of the tetragonal and trigonal coordinates, their stabilization energies beingEJTO≈81–450 cm − 1 andEJTT≈48–417 cm − 1, respectively (thevariations of the KE, EJTO and EJTT values are due to different literature data forEJTE). With these data the APES of the JT linear problem for the Cr2 + ion in the ZnSe:Cr2 + system is revealed.