Hyperfine effects on spin-lattice relaxation rates of rare-earth salts: Theory and experimental data

A general approach to spin-lattice relaxation is given for salts to which a crystalline field theory is appropriate. In particular, the theory of Elliott & Stevens for the interaction of a rare-earth ion with static ionic surroundings is generalized phenomenologically to represent the interaction of the rare-earth ion with the lattice vibrational modes. Evaluation of the spin-lattice interaction in terms of a few constants is possible. One- and two-phonon processes are investigated and the relaxation times for non-Kramers and Kramers salts computed. For the one-phonon (or direct) process the non-Kramers salts exhibit the typical behaviour T 1 ∝ H -2 T -1 , and the Kramers salts T 1 ∝ H -4 T -1 . It is shown that, for a given Zeeman splitting of the ground doublet, the latter may exhibit an enormous anisotropy with respect to the direction of the external field, approximately proportional to the anisotropy of the temperature-independent part of the susceptibility. Application of the general theory is made to two salts, holmium and dysprosium ethyl sulphate; the former a non-Kramers, the latter a Kramers salt. It is shown that the dysprosium salt would be expected to show a relaxation time in the direct process region which will vary as sin -2 θ cos -2 θH -4 T -1 , where θ is the angle the external magnetic field makes with the crystallographic symmetry axis. For two-phonon processes, the additional distinction of whether the Debye energy ( Kθ D ) is less than or greater than the crystalline field splitting Δ between the ground state and the first excited state must be made. Non-Kramers salts to which the former condition apply ( Kθ D < Δ) are shown to possess two-phonon relaxation processes of the usual Raman type. The relaxation time is proportional to T -7 and is independent of magnetic field. When Kθ D > Δ, there is present in addition a term arising from a resonance process, analogous to the resonance radiation effect in gases. Phonons of energy ~ Δ are absorbed and emitted by the spin system preferentially because of a phonon resonance with the crystalline field splitting of the spin states. As normally KT is much less than Δ, this leads to a relaxation time proportional to exp (Δ/ KT ). This process will dominate the Raman process except at very high and low temperatures. It is shown to be significant right down to the liquid-helium range by comparison with the relaxation rate due to direct processes. Kramers salts, when Kθ D < Δ, owing to a cancellation in the rate equation, exhibit a Raman relaxation time proportional to T -9 and independent of field. This 'Van Vleck cancellation’ is shown to be a consequence of time reversal symmetry. When Kθ D > Δ, the resonance process is also present, the relaxation time again being proportional to exp (Δ/ KT ). The resonance process is now shown to be dominant down to 1 or 2 °K for many rare-earth salts. Experimental verification is found for the resonance relaxation process in the rare-earth ethyl sulphates. In general, it is expected that this mechanism will be significant for any magnetic salt in which Kθ D > Δ.

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Analysis of Spin Polarisation Transients in Periodically Photo-excited Triplet States

Zeitschrift für Naturforschung A ◽

10.1515/zna-1975-0501 ◽

1975 ◽

Vol 30 (5) ◽

pp. 571-582 ◽

Cited By ~ 9

Author(s):

C. J. Winscom

Keyword(s):

Lattice Relaxation ◽

Rectangular Pulse ◽

Decay Rates ◽

Spin Lattice Relaxation ◽

Pulse Excitation ◽

Triplet States ◽

Relaxation Rates ◽

Spin Sublevel ◽

Spin Lattice ◽

The Individual

Abstract The behaviour of spin sublevel populations with time following periodic photo-excitation is ex-amined. The treatment is limited to conditions of magnetic field strength and temperature for which the spin lattice relaxation rates dominate the individual spin sublevel decay rates. The response of the system to three modes of excitation is considered: (i) continuous excitation using a time-independent intensity (ii) periodic rectangular pulse excitation and (iii) periodic waveform excitation. A convenient correspondence between the various forms of solutions is pointed out. The requirements of an experiment to determine spin-lattice relaxation rates in organic triplets at 77 K are discussed.

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Anion reorientations and cation diffusion in a carbon-substituted sodium nido-borate Na-7,9-C2B9H12: 1H and 23Na NMR studies

Zeitschrift für Physikalische Chemie ◽

10.1515/zpch-2021-3108 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Alexander V. Skripov ◽

Olga A. Babanova ◽

Roman V. Skoryunov ◽

Alexei V. Soloninin ◽

Terrence J. Udovic

Keyword(s):

Lattice Relaxation ◽

Activation Energies ◽

Spin Lattice Relaxation ◽

Relaxation Rates ◽

Cation Diffusion ◽

Relaxation Data ◽

Nmr Studies ◽

Spin Lattice ◽

Jump Rate ◽

Disordered Phase

Abstract Polyhydroborate-based salts of lithium and sodium have attracted much recent interest as promising solid-state electrolytes for energy-related applications. A member of this family, sodium dicarba-nido-undecahydroborate Na-7,9-C2B9H12 exhibits superionic conductivity above its order-disorder phase transition temperature, ∼360 K. To investigate the dynamics of the anions and cations in this compound at the microscopic level, we have measured the 1H and 23Na nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation rates over the temperature range of 148–384 K. It has been found that the transition from the low-T ordered to the high-T disordered phase is accompanied by an abrupt, several-orders-of-magnitude acceleration of both the reorientational jump rate of the complex anions and the diffusive jump rate of Na+ cations. These results support the idea that reorientations of large [C2B9H12]− anions can facilitate cation diffusion and, thus, the ionic conductivity. The apparent activation energies for anion reorientations obtained from the 1H spin-lattice relaxation data are 314 meV for the ordered phase and 272 meV for the disordered phase. The activation energies for Na+ diffusive jumps derived from the 23Na spin-lattice relaxation data are 350 and 268 meV for the ordered and disordered phases, respectively.

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