Fluctuating hyperfine fields

There are two main types of relaxation in Mossbauer studies paramagnetic and superpara-magnetic relaxation. As a rule, the observed spectra are quite complicated. The simple relaxation processes for electronic spin S = j can be analysed in terms of a fluctuating hyperfine field HJ t) which takes on the values - H and —H. If off-diagonal terms in the hyperfine Hamiltonian are absent, then... 

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... 

The collapse of a six-line hyperfine spectrum with decreasing relaxation time is illustrated by the calculated spectra in Fig. 3.8 [44] for a " Fe nucleus in a fluctuating magnetic field and a fixed electric field gradient for different values of the electronic relaxation time. If the fluctuation rate is very slow compared to the precession frequency of the nucleus in the field H, the full six-line hyperfine pattern is observed. If the fluctuation rate is extremely rapid the nucleus will see only the time-averaged field which is zero and a symmetric quadrupolar pattern will be seen. At intermediate frequencies the spectra reflect the fact that the 2> -> transitions which make up the low-velocity component of the quadrupole doublet relax at higher frequencies than do the I I i> and -]-> -> transitions which... 

Rotational motion exerts fluctuating magnetic fields on the electron spin and also averages the various tensor components (see Fig. 2). Nitro-xide EPR spectra are profoundly influenced by the rate of this motion relative to the range of electron spin precession frequencies within each hyperfine line. Thus, one can use EPR spectroscopy to determine tr accurately. There are distinct temporal regimes in which spin label spectra require different types of data collection methods and data analysis to achieve this. These regimes are discussed below. 

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... 

The NMR parameters in table 13 are given for liquid helium temperatures. As the temperature is raised, excited electronic states are populated, and the nucleus is subjected to the influence of different hyperfine fields, fluctuating due to the random processes of thermal activation and deactivation. Now, in place of a single precession frequency for... 

At sufficiently low temperatures, usually below 10 20 K for transition metal complexes with 5 = and below 50 K for free radicals, transverse relaxation of electron spins is dominated by fluctuation of dipolar hyperfine fields from distant protons. These fluctuations are driven by coupling among the protons,... 

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