Effects of Vibronic Dynamics of Cu(H$\text{}_{2}$O)$\text{}_{6}$ Complexes and Electron Spin Relaxation in Temperature Dependence of EPR Linewidth in Diamagnetic Tutton Salt Single Crystals

EPR linewidth of Cu$\text{}^{2+}$ in the Tutton salt crystals weakly depends on temperature at low temperatures and then it rapidly grows above 60 K. We present detailed results of measurements and analysis for $\text{}^{63}$Cu$\text{}^{2+}$ in K$\text{}_{2}$Zn(SO$\text{}_{4}$)$\text{}_{2}$·6 H$\text{}_{2}$O, K$\text{}_{2}$ Zn(SO$\text{}_{4}$)$\text{}_{2}$·6D$\text{}_{2}$O, (NH$\text{}_{4}$)$\text{}_{2}$Mg(SO$\text{}_{4}$)$\text{}_{2}$·6H$\text{}_{2}$O and Cs$\text{}_{2}$Zn (SO$\text{}_{4}$)$\text{}_{2}$·6H$\text{}_{2}$O in a temperature range of 4.2-300 K and compare them with already published electron spin-lattice relaxation data. The relaxation contributes weakly to the linewidth which is dominated by molecular dynamics and grows exponentially with temperature. To describe this we are discussing the influence of jumps between two sites of Cu$\text{}^{2+}$ complexes in a slow motion region where the sites are differently thermally populated. This case has not been considered so far. We have derived appropriate expressions describing the contribution of jumps to the linewidth which allows the determination of the jump rate and energy difference δ$\text{}_{A,B}$ between the two sites being two Jahn-Teller distorted configurations of the vibronic Cu(H$\text{}_{2}$O)$\text{}_{6}$ complexes. The jump rate 1/τ strongly depends on temperature and reaches 10$\text{}^{9}$ s$\text{}^{-1}$ at room temperature, whereas theδ$\text{}_{A,B}$ varies from 117 cm$\text{}^{-1}$ for K$\text{}_{2}$Zn(SO$\text{}_{4}$)$\text{}_{2}$·6D$\text{}_{2}$O to 422 cm$\text{}^{-1}$ for Cs$\text{}_{2}$Zn(SO$\text{}_{4}$)$\text{}_{2}$·6 H$\text{}_{2}$O. The comparison with vibronic level splitting, which varies in the range of 67-102 cm$\text{}^{-1}$, indicates that the reorientation mechanism involves phonon induced tunnelling via excited vibronic levels. These reorientations do not contribute, however, to the spin-lattice relaxation which is governed by ordinary two-phonon relaxation processes in the whole temperature range. Thus, the reorientations and spin relaxation are two independent phenomena contributing to the total linewidth.