Fluctuating magnetic moment

Introducing the thermal average of the square of the fluctuating magnetic moment, (T), into eq. (29), one obtains the equation of state in the magnetic system with the bulk magnetization M and external field B at temperature T as... 

The relaxivity enhancement of water protons in the aqueous solutions of paramagnetic complexes arises from time fluctuation of the dipolar coupling between the electron magnetic moment of the metal ion and the nuclear magnetic moment of the solvent nuclei (13,14). The dipolar interaction... 

When the anisotropy energy is large enough it prevents any precession of the magnetic moment of super-paramagnetic crystals. The magnetic fluctuations then arise from the jumps of the moment between different easy directions. The precession prohibition is introduced into the Freed equations in order to meet that requirement every time the electron Larmor precession frequency appears in the equations, it is set to zero 12). 

The fluctuating part of the longitudinal magnetic moment was calculated as (14) ... 

However, no fingerprint such as a final state multiplet structure, as expected for fully localized 5 f electron and found in Am metal, is observed. The localization of 5 f-states is only weak (band-narrowing and widthdrawal from hybridization) in 6-Pu. This in fact is also consistent with the absence of a magnetic moment formation in 6-Pu (rather, a spin-fluctuation regime is observed ). 

Both Ti and T2 relaxations of water protons are mainly due to fluctuating dipole-dipole interactions between intra- and inter-molecular protons [62]. The fluctuating magnetic noise from all the magnetic moments in the sample (these moments are collectively tamed the lattice) includes a specific range of frequency components which depends on the rate of molecular motion. The molecular motion is usually represented by the correlation time, xc, i.e., the average lifetime staying in a certain state. A reciprocal of the correlation time corresponds to the relative frequency (or rate) of the molecular motion. The distribution of the motional frequencies is known as the spectral density function. 

Magnetic fields are generated by the rotation of a molecular magnetic moment and modulated by molecular collisions. Nuclear spin interacts with the fluctuating magnetic field. 

This is a so-called non-dispersive term. This effect can be viewed as transient increases or decreases of the precession frequency due to local field fluctuations along z (the Bq direction). These changes in the precession frequency do not appreciably affect the -projection of the nuclear magnetic moment but dephase its projection in the xy plane. In cases where two nuclear spins relax each other,... 

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