Field Dependence of the Direct-Process Spin-Lattice Relaxation Time in Rare-Earth Salts

1963 ◽  
Vol 131 (1) ◽  
pp. 190-197 ◽  
Author(s):  
D. Huber
Keyword(s):  
Relaxation Time ◽  
Rare Earth ◽  
Field Dependence ◽  
Lattice Relaxation ◽  
Lattice Relaxation Time ◽  
Spin Lattice Relaxation ◽  
Direct Process ◽  
Spin Lattice Relaxation Time ◽  
Spin Lattice ◽  
Rare Earth Salts

SPIN–LATTICE RELAXATION TIME OF Fe3+ ION

1964 ◽  
Vol 42 (4) ◽  
pp. 583-594 ◽  
Author(s):  
M. P. Madan
Keyword(s):  
Relaxation Time ◽  
Lattice Relaxation ◽  
Lattice Relaxation Time ◽  
Spin Lattice Relaxation ◽  
Direct Process ◽  
Phonon Interaction ◽  
Crystal Axis ◽  
Spin Lattice Relaxation Time ◽  
Spin Lattice ◽  
Relaxation Effects

The spin–lattice relaxation time T1 of Fe3+ ions in iron–rubidium alum [RbAl(SO4)2∙12H2O], in rutile [TiO2], and in potassium cobalticyanide [K3CO(CN)6] has been measured in the temperature range 1.6 °K to 4.2 °K at a frequency of 9400 Mc by the pulse saturation technique. For Fe3+ in rubidium alum, it is found that for crystals having a nominal concentration of 1% and lower the variation of relaxation time with temperature is of the form [Formula: see text]; for higher concentrations the variation is of the form [Formula: see text]. Cross-relaxation effects are noticed for higher concentrations at all settings of crystal orientations. For Fe3+ in rutile on the average, the relaxation time is approximately inversely proportional to temperature, thus indicating the presence of a direct process. There is no significant change in the relaxation time, when the angle of the applied magnetic field with the crystal axis is varied. For Fe3+in K3Co(CN)6, above 2.8 °K, it is found that the relaxation time is proportional to T−8; this is consistent with a two-phonon interaction process (Raman). It is not believed that at the lowest temperature used in this experiment relaxation is taking place through a single-phonon process (direct).

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.

NUCLEAR SPIN-LATTICE RELAXATION TIME IN TIN

1978 ◽  
Vol 39 (C6) ◽  
pp. C6-1215-C6-1216
Author(s):  
H. Ahola ◽  
G.J. Ehnholm ◽  
S.T. Islander ◽  
B. Rantala
Keyword(s):  
Relaxation Time ◽  
Nuclear Spin ◽  
Lattice Relaxation ◽  
Lattice Relaxation Time ◽  
Spin Lattice Relaxation ◽  
Spin Lattice Relaxation Time ◽  
Spin Lattice ◽  
Nuclear Spin Lattice Relaxation
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