Hyperfine field, magnetic fluctuations

F.6.4.1. Introduction. If the surface-related phenomena are negligible, the electronic spins in the particle will fluctuate in unison (see Section D.3.1), and the orientation of the hyperfine field will fluctuate like the orientation of the magnetic moment of the particle m. The Mossbauer nucleus senses the relaxation of m via the hyperfine interaction and thus the Mossbauer spectrum can, in principle, be influenced by all the trajectories of m. 

For fiB 2KV, there is only one energy minimum, i.e. there is no energy barrier between different magnetization directions [57], and the fluctuations of the magnetic hyperfine field can therefore be considered fast compared to Tm- The induced magnetic hyperfine field is then proportional to the induced magnetization. Using... 

Whereas the paramagnetic shift of the nuclear magnetic resonance frequency for a given applied field is related to the strength of the local hyperfine field at the nuclear site, induced by the electronic moments, the nuclear spin-lattice relaxation rate yields information about the low-frequency spectrum of thermally induced spin fluctuations. The influence of pair-correlation effects on the NMR relaxation in paramagnets was analysed experimentally and theoretically by... 

Pronounced spin fluctuations or spin waves occur in the ordered state down to and including absolute zero temperature. These fluctuations reduce the mean spin value of the Fe ions below S. This reduction is directly measurable from the Mossbauer spectra since the magnitude of the hyperfine field is proportional to <5>. Comparison of the saturated hyperfine field of 41.0 0.5 T for K2peF5 with that of 62.2 0.5 T for FeFj, the corresponding three-dimensional magnetic compound where virtually no spin fluctuations occur, shows that in K2FeFj there is considerable reduction of below S. 

The translational motions and spin dynamics of conduction electrons in metals produce fluctuating local magnetic hyperfine fields. These couple to the nuclear magnetic moments, inducing transitions between nuclear spin levels and causing nuclear spin relaxation. The translational motions of electrons occur on a very rapid time scale in metals (<10 s), so the frequency spectrum of hyperfine field fluctuations is spread over a wide range of w-values. Only a small fraction of the spectral intensity falls at the relatively low nuclear resonance frequency (ojq 10 s ). Nevertheless, the interaction is so strong that this process is usually the dominant mode of relaxation for nuclei in metallic systems, either solid or liquid. 

Another interesting spectroscopy performed on SmBg is nuclear magnetic resonance (NMR) where the temperature dependence of the B relaxation rate has been measured by Pena et al. (1981). Above 10 K the temperature dependence is exponential with a gap of 5.6 meV The authors interpret their results as the consequence of the fluctuations of 4f spins thus relating the measured line width to the contribution of the hyperfine field from these fluctuations. The NMR experiments thus measure directly a gap in the 4f spectrum, where the only other experiment, directly related to a gap in the 4f spectrum, was the IDS obtained by optical reflection by Travaglini and Wachter (1984a). Similar NMR results have been obtained by Takigawa et al. (1983). 

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