Magnetic anisotropy relaxation

Some gadolinium-based MOF have also revealed the peculiar dynamics of the magnetization with the appearance of the out-of-phase component of the dynamic magnetization in presence of an applied static magnetic field. This behaviour, which is reminiscent of the field-induced slow relaxation that characterize many lanthanide-based SMMs, is however not related to the magnetic anisotropy, which is vanishingly small in most Gd3+ systems. 

Lipari G. and Szabo A. (1980) Effect of Vibrational Motion on Fluorescence Depolarization and Nuclear Magnetic Resonance Relaxation in Macromolecules and Membranes, Biophys. J. 30, 489—506. Steiner R. F. (1991) Fluorescence Anisotropy Theory and Applications, in Lakowicz J. R. (Ed.), Topics in Fluorescence Spectroscopy, Vol. 2, Principles, Plenum Press, New York, pp. 127-176. 

We remark that even at the same intuitive level the counterarguments turn up easily (1) Eq. (4.96) with i V from Eq. (4.97) yields an incorrect value for the static (co —> 0) susceptibility [cf. Eq. (4.88)] and (2) Eq. (4.96) ignores the fact that the magnetic anisotropy imparts the exponential evolution only in relaxation of (Pi), leaving the quadrupole one ((P2)) unchanged. 

When the superparamagnetic theory is applied for interpretation of any measured susceptibility line, it means that some model function x(V,a>,T) depending on several material parameters, is processed through averaging like such as Eq. (4.121) or (1.122). In our case the basic set of the material parameters comprises magnetization /, anisotropy energy density K, relaxation time To, and the particle volume fraction tp. Obviously, for nanosize-dispersed systems the effective values of /, K, and t0 do not coincide with those for a bulk material. The size/volume averaging itself introduces two independent... 

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