Temperature dependences of the CW-EPR spectrum as well as the electron spin−lattice relaxation time T 1 and phase memory time T M determined by electron spin echo were measured for Cu2+ ions in (NH4)2Mg(SO4)2·6H2O single crystal. The dependences are dominated by vibronic behavior of the Cu(H2O)6 2+ complex and connected to the dynamic Jahn−Teller effect producing reorientations between two lowest energy wells of the adiabatic potential surface. Below 70 K the static Jahn−Teller effect is observed, and the system is strongly localized, by the local strains, in the deepest potential well leaving higher wells not populated. Above this temperature the second well becomes progressively populated, and a rapid averaging of the g z and g y factors as well as corresponding hyperfine splittings appears. The Boltzmann population of these two wells is achieved at 160 K. Simultaneously with g factors averaging a continuous broadening of the hyperfine lines is observed with line shape transformed from Gaussian at 70 K to Lorentzian at 160 K. The averaging and broadening processes are thermally activated with energy barrier δ12 = 108 ± 3 cm-1 = 156 K = 1.26 kJ/mol being the energy difference between the two deepest potential wells. Electron spin relaxation was measured below 50 K where electron spin-echo signal was detectable. Spin−lattice relaxation is driven by the direct and Raman processes with relaxation rate 1/T 1 = aT + bT 5 as expected for dynamic Jahn−Teller systems. Spin−spin phase relaxation described by the phase memory time T M depends on temperature as 1/T M = a + bT + c exp(−Δ/kT) with Δ = 102 ± 2 cm-1. At low temperatures the higher energy well is not populated; thus, Δ can be assigned as the energy of the first excited vibronic level in the deepest well. The Δ and δ12 are temperature-independent, indicating that adiabatic potential surface is not affected by temperature. We suggest that the deviations of experimental data from theoretically predicted vibronic g-factors averaging observed for Cu2+ in many Tutton salt type crystals are not due to temperature variations of the local strains or barrier height but are due to the fact that Boltzmann population of the potential wells cannot exist at low temperatures. This effect is especially pronounced for Cu2+ ions in (NH4)2Mg(SO4)2·6H2O since the energy Δ of the first vibronic level is lower than the energy difference δ12 between adjacent wells. In such case the phonon-assisted tunneling jumps between the energy wells induced by two-phonon Raman processes via virtual state of energy δ12 become to be effective when kT ≥ δ12/2, and the Boltzmann population of the second well is achieved via direct phonon process when thermal phonons of energy kT ≥ δ12 are available.
X-band electron spin resonance (ESR) spectra of S(3)(-) radicals in ultramarine analog (pigment) prepared from zeolite A and maintaining the original structure of parent zeolite were recorded in the temperature range of 4.2-380 K. Electron spin echo experiments (echo detected ESR, electron spin-lattice relaxation, and spin echo dephasing) were performed in the temperature range of 4.2-50 K. The rigid lattice g factors are g(x) = 2.0016, g(y) = 2.0505, and g(z) = 2.0355, and they are gradually averaged with temperature to the final collapse into a single line with g = 2.028 above 300 K. This is due to reorientations of S(3)(-) molecule between 12 possible orientations in the sodalite cage through the energy barrier of 2.4 kJ/mol. The low-lying orbital states of the open form of S(3)(-) molecule having C(2v) symmetry are considered and molecular orbital (MO) theory of the g factors is presented. The orbital mixing coefficients were calculated from experimental g factors and available theoretical orbital splitting. They indicate that the unpaired electron spin density in the ground state is localized mainly (about 50%) on the central sulfur atom of S(3)(-) anion radical, whereas in the excited electronic state the density is localized mainly on the lateral sulfur atoms (90%). A strong broadening of the ESR lines in directions around the twofold symmetry axis of the radical S(3)(-) molecule (z-axis) is discovered below 10 K. It is due to a distribution of the S-S-S bond angle value influencing mainly the energy of the (2)B(2)-symmetry MO. This effect is smeared out by molecular dynamics at higher temperatures. A distribution of the g factors is confirmed by the recovery of the spin system magnetization during spin-lattice relaxation measurements, which is described by a stretched exponential function. Both the spin-lattice relaxation and electron spin echo dephasing are governed by localized phonon mode of energy of about 40 cm(-1). Thus, the anion-radical S(3)(-) molecules are weakly bonded to the zeolite framework, and they do not participate in the phonon motion of the host lattice because of their own local dynamics.
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