Nuclear magnetic resonance local fluctuations

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... 

In solid-state physics, positive muons are used to measure the local magnetic induction at the site of the muon. Constant fields are measured via the (O 28.3) precession frequency, whereas fluctuating fields via relaxation. This makes xSR a method analogous to nuclear magnetic resonance (NMR) or electron paramagnetic resonance (EPR) with the advantages that no radioffequency field or macroscopic populations of the resonant species are needed. Muons are also easy to use in a cryogenic environment as both the fast muon and the decay positron easily traverse vacuum separation windows. 

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. 

The microdynamic behaviour of molecules in fluids is attributed to Brownian motion, and the frequency distribution of the components of the local fluctuating magnetic field is expressed by a power spectral density. The component of this spectral density at the resonance frequency is responsible for nuclear relaxation. The magnitude of this component, taken together with the energy of interaction between the nuclear spin system and the molecular motions, determines the value of T. ... 

Spin relaxation in a nucleus is induced by random fluctuations of local magnetic fields. These result from time-dependent modulation of the coupling energy of the resonating nuclear spin with nearby nuclear spins, electron spins, quadrupole moments, etc. Any time-dependent phenomenon able to modulate these couplings can contribute to nuclear relaxation. The distribution of the frequencies contained in these time-dependent phenomena is described by a correlation function, characterized by a parameter Tc, the correlation time. Its reciprocal can be considered as the maximum frequency produced by the fluctuations in the vicinity of the nuclear spin. If more than one process modulates the coupling between the nuclear spin and its surroundings, the reciprocal of the effective correlation time is the sum of the reciprocals of the various contributions... 

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