Magnetic moment fluctuation

Fig. 5.28 The 4/ shell of each Gd atom carries a local magnetic moment which remains constant with temperature. The relative axes of these magnetic moments fluctuate with rising temperature. This behavior can be modeled by spin waves being characterized by the angle a between nearest neighbors. From [127], copyright 1998, reproduced with permission from World Scientific Publishing Co. Pte. Ltd...

At temperatures much higher than T,t, the temporal fluctuations of the magnetic moment are slow compared to thermal fluctuations, and the susceptibility is expected to be strongly temperature dependent, behaving like a Curie-Weiss law with a Curie-Weiss temperature of the order of Tsf. At temperatures much lower than Tsf, the intrinsic magnetic moment fluctuations are rapid compared to thermal fluctuations, and the resultant dynamical magnetic moment averages to zero over the timescale of interest so that the susceptibility approaches a constant value in the limit T- 0. In this model, anomalies in other... 

The existence of interparticle interactions leads to an additional term to the local field. For dipolar interactions = /jlIcI = 4>o m< where d is the interparticle distance and is the volume fraction of particles. This also yields a contribution to linewidth = 4>o s C absence of magnetic moments fluctuations). 

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. 

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