Spin-Lattice Relaxation in Some Rare-Earth Salts. I. Temperature Dependence

1966 ◽  
Vol 141 (1) ◽  
pp. 461-478 ◽  
Author(s):  
G. H. Larson ◽  
C. D. Jeffries
Keyword(s):  
Rare Earth ◽  
Temperature Dependence ◽  
Lattice Relaxation ◽  
Spin Lattice Relaxation ◽  
Spin Lattice ◽  
Rare Earth Salts

Spin-lattice relaxation in rare-earth salts

1961 ◽  
Vol 264 (1319) ◽  
pp. 458-484 ◽  
Keyword(s):  
Relaxation Time ◽  
Rare Earth ◽  
Lattice Relaxation ◽  
Spin Lattice Relaxation ◽  
Direct Process ◽  
Rare Earth Ion ◽  
Crystalline Field ◽  
Spin Lattice ◽  
Rare Earth Salts ◽  
Resonance Process

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.

Bonded Hydrogen and Trapped H2 in a-Si1−xGex:H Alloys

1989 ◽  
Vol 149 ◽  
Author(s):  
E. J. Vanderheiden ◽  
G. A. Williams ◽  
P. C. Taylor ◽  
F. Finger ◽  
W. Fuhs
Keyword(s):  
Temperature Dependence ◽  
Molecular Hydrogen ◽  
Relaxation Times ◽  
Lattice Relaxation ◽  
Spin Lattice Relaxation ◽  
Spin Lattice ◽  
H Nmr ◽  
Local Environments

ABSTRACT1H NMR has been employed to study the local environments of bonded hydrogen and trapped molecular hydrogen (H2) in a series of a-Si1−xGex:H alloys. There is a monotonic decrease of bonded hydrogen with increasing x from ≈ 10 at. % at x = 0 (a-Si:H) to ≈ 1 at. % at x = 1 (a-Ge:H). The amplitude of the broad 1H NMR line, which is attributed to clustered bonded hydrogen, decreases continuously across the system. The amplitude of the narrow 1H NMR line, which is attributed to bonded hydrogen essentially randomly distributed in the films, decreases as x increases from 0 to ≈ 0.2. From x = 0.2 to x ≈ 0.6 the amplitude of the narrow 1H NMR line is essentially constant, and for x ≥ 0.6 the amplitude decreases once again. The existence of trapped H2 molecules is inferred indirectly by their influence on the temperature dependence of the spin-lattice relaxation times, T1. Through T1, measurements it is determined that the trapped H2 concentration drops precipitously between x = 0.1 and x = 0.2, but is fairly constant for 0.2 ≤ x ≤ 0.6. For a-Si:H (x = 0) the H2 concentration is ≈ 0.1 at. %, while for x ≥ 0.2 the concentration of H2 is ≤ 0.02 at. %.

Calculation of NQR v's and T1-1' s being proportional to T4 and T5 , respectively

1990 ◽  
Vol 45 (3-4) ◽  
pp. 536-540
Author(s):  
Mariusz Máckowiak ◽  
Costas Dimitropoulos
Keyword(s):  
Temperature Dependence ◽  
Relaxation Rate ◽  
Spin System ◽  
Low Frequency ◽  
Lattice Relaxation ◽  
Spin Lattice Relaxation ◽  
Lattice Vibrations ◽  
Spin Lattice ◽  
Simplifying Assumptions ◽  
The One

Abstract The second-order Raman phonon process for a multilevel spin system is shown to give a quadru-polar spin-lattice relaxation rate T1-1varying as T5 at very low temperatures. This relaxation rate for quadrupole spins is similar to the one discussed for a paramagnetic spin system having a multilevel ground state. The temperature dependence of T1 is discussed on the basis of some simplifying assumptions about the nature of the lattice vibrations in the Debye approximation. This type of relaxation process has been observed below 20 K in tetramethylammonium hydrogen bis-trichloroacetate for the 35Cl T1-1 . Below 20 K the NQR frequency in the same crystal reveals a T4 temperature dependence due to the induced modulations of the vibrational and librational coordinates by the low-frequency acoustic phonons.

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