Effect of Linear Jahn-Teller Coupling on Paramagnetic Resonance in aE2State

The theory of the effect of a dynamic Jahn-Teller effect on the electron-paramagnetic-resonance spectrum of a ${}_{}{}^2{}_{}{}^{}E$ state is developed from the limit of weak Jahn-Teller coupling taking account only of linear coupling. The principal changes produced in the EPR spectrum of the vibronic ground state may be represented simply by introducing appropriate reduction factors into the spin Hamiltonian which describes the splitting of the electronic ${}_{}{}^2{}_{}{}^{}E$ state by a magnetic field, strain, or hyperfine interaction. These reduction factors affect the anisotropic part of the spin Hamiltonian but not the isotropic part; they are diminished from unity by the Jahn-Teller coupling; and they are analogous to the reduction factors introduced earlier in the theory of a triplet state. The theory is used to discuss Höchli's data for ${\mathrm{Sc}}^{2+}$ in Ca${\mathrm{F}}_2$ and Sr${\mathrm{F}}_2$ and Coffman's data for ${\mathrm{Cu}}^{2+}$ in MgO. While the latter case is consistent with either a moderately strong linear Jahn-Teller coupling or with the tunneling model, the present theory applied to ${\mathrm{Sc}}^{2+}$ in Ca${\mathrm{F}}_2$ and Sr${\mathrm{F}}_2$ indicates that in these cases the Jahn-Teller coupling is quite weak.