Magnetic Field Dependence of Paramagnetic Relaxation in a Kramers Salt

Abstract

Some time ago, Van Vleck 1 predicted that, under certain conditions, an ensemble of paramagnetic ions present in a nonmagnetic crystal and in a magnetic field H should attain thermal equilibrium with a characteristic time 7\ that is inversely proportional to H 4 and to the ambient temperature T. The linear variation of relaxation rate with temperature has been observed by many authors, 2 " 4 but the dependence on magnetic field does not appear to have been given a clear experimental test. 5 Since the fourth-power variation rests on assumptions that are rather basic, it seemed worthwhile to study the field dependence in detail.As discussed by Orbach, 6 the fourth power is expected when the paramagnetism arises from just one pair of Kramers conjugate states, when the thermalizing interaction occurs through thermal modulation of the local crystalline electric field at the site of the paramagnetic ion, and when the temperature is low enough that the "direct" relaxation process, viz. the absorption and emission of phonons resonant with the Zeeman transition, prevails. If the last condition is not satisfied, the direct process is augmented by a "Raman" process, which carries the temperature variation T 9 and is independent of magnetic field.It has been pointed out 2 that 3 Fe + present as a dilute substitutional impurity in KgCo(CN) 6 furnishes an almost ideal vehicle for a test. Several workers 2 ' 7 have reported a temperature dependence consistent with l/7\ =AT + BT 9 , but the variation of A and B with field was not measured. In the present study, the relaxation rate was measured as a function of H and T.Measurements were made at Zeeman frequencies between 3.9 and 12 kMc/sec, corresponding to fields between 1100 and 3700 gauss, and at temperatures between 2.16 and 1.38°K. A sample having an iron concentration of 0. 24 at. % was used. The data were taken with an electron paramagnetic resonance spectrometer that has been described elsewhere. 2 For the present work, the sample cavity was replaced by a multimode cavity that displayed three resonances across S-band (2-4 kMc/sec) and ten in the Xband region (8-12 kMc/sec), and in addition, the microwave spectrometer components were replaced by their S-band counterparts for the low-field measurements.The results are summarized in Fig. 1. Since we were interested in the direct relaxation rate AT, the Raman rate BT g was subtracted from the observed rate, the value B having been taken from the measurements of Rannestad and Wagner. 2 It is satisfying to note that this Raman rate, measured at an altogether different value of magnetic field (about 600 gauss), agreed with the values found in the present work. It is to be noted that the higher temperature relaxation rates observed at the lowest value of the Zeeman field and the Raman contribution to those rates were of comparable magnitude. As a consequence, the calculated direct rate showed sub-141

Field-dependent spin-lattice relaxation of Cr3+ in Al2O3

“…The former case has already been studied [2], and theory predicts a variation inversely proportional to the fourth power of the magnetic field. Close agreement wlth this was found by Davids and Wagner [5] for Fe 3+ in potassium colbalticyanide, a material possessing an isolated Kramers doublet. Although Cr 3+ (3d ~) in ruby has 9 a 4F3/2 ground state consisting of two Kramers doublets, transitions are possible between the doublets and these are not governed by Kramers' theorem.…”

Relaxation Times of Organic Radicals and Transition Metal Ions

“…This dependence on B04 has been demonstrated (Davids and Wagner, 1964) and exploited to use higher observe power at higher frequency to improve SIN of otherwise too-slowly relaxing species (Muller et aI., 1989). The firstorder Raman process can vary as B02 (longer relaxation time at lower field) (Marchand and Stapleton, 1974), but the more common Raman process is predicted to be independent of magnetic field.…”

Temperature Dependence of Electron Spin Relaxation of 2,2-Diphenyl-1-Picrylhydrazyl in Polystyrene

“…It has been proposed that the dependence of 1/T 1 on T for DPPH is due to the direct process [9] or to an Orbach process with energy less than 1 K [10]. Frequency dependence is predicted for the direct process [24], so the similarity in relaxation rates for the high concentration DPPH sample at X-band and Q-band (Fig. 2) is not consistent with assignment of a direct process.…”