Slow spin dynamics

This approximation will only be valid for 7 —> 0, as fluctuations are often visible as the sample is warmed towards 7m. Little is understood, however, about slow spin dynamics (i.e., within the iSR, but below the neutron time window) in ordered magnets. A theoretical treatment of spin lattice relaxation and its relation to jxSR for a Heisenberg ferromagnet has been given by Dalmas de Rentier and Yaouanc (1995). 

A preliminary report (Amato et al. 1998) presents ZF- and LF-pSR data down to 0.1K. The ZF spectra are characterized by nuclear-electronic double relaxation. The nuclear part can be suppressed in LF = 20 G. No magnetic transition was observed. Below 10 K, the electronic relaxation rate increases monotonically with decreasing temperature. Application of LF = 200 G also suppresses electronic relaxation, indicating rather slow dynamics of the spin system. From the field dependence of relaxation rate the spin fluctuation frequency was found to be V4f(r —> 0) 2.7 MHz. It appears that this is another case where spin correlations develop at low temperatures, but persistent slow spin dynamics prevent the formation of an ordered magnetic state (see CeNiSn in sect. 9.2 for comparison). 

Abernathy and Sharp (130,145) treated the intermediate regime, when the reorientation of the paramagnetic species is in-between the slow- and fast-rotations limits. They applied the spin-dynamics method, described in Section VI, to the case of outer-sphere relaxation and interpreted NMRD profiles for non-aqueous solvents in the presence of complexes of Ni(II) (S = 1) and Mn(III) (S = 2). 

The quantum alternative for the description of the vibrational degrees of freedom has been commented by Westlund et al. (85). The comments indicate that, to get a reasonable description of the field-dependent electron spin relaxation caused by the quantum vibrations, one needs to consider the first as well as the second order coupling between the spin and the vibrational modes in the ZFS interaction, and to take into account the lifetime of a vibrational state, Tw, as well as the time constant,T2V, associated with a width of vibrational transitions. A model of nuclear spin relaxation, including the electron spin subsystem coupled to a quantum vibrational bath, has been proposed (7d5). The contributions of the T2V and Tw vibrational relaxation (associated with the linear and the quadratic term in the Taylor expansion of the ZFS tensor, respectively) to the electron spin relaxation was considered. The description of the electron spin dynamics was included in the calculations of the PRE by the SBM approach, as well as in the framework of the general slow-motion theory, with appropriate modifications. The theoretical predictions were compared once again with the experimental PRE values for the Ni(H20)g complex in aqueous solution. This work can be treated as a quantum-mechanical counterpart of the classical approach presented in the paper by Kruk and Kowalewski (161). 

In conclusion, the molecular motion seems to be well described, and the decomposition of the electron spin dynamics from the dipole-dipole interaction is a good approximation. However, the calculated electron spin relaxation was too slow to account for the paramagnetic relaxation, either because the ZFS was too small in magnitude or fluctuating too fast. The reorientation of the water could have a large effect on the ZFS, but unfortunately this was not included in the treatment due to the problems with describing it from symmetry modes. Also, non-linear terms in the property surface might be of importance for a proper description of the ZFS fluctuations. 

The development of new ID and 2D pulse sequences enables the spectroscopist to obtain structure and dynamic information about systems that were previously very hard to study. As an example is reported in Fig. 3.2.13 the 2D spectrum of erythromycin A measured with the FIREMAT (Five p Replicated Magic Angle Turning ) technique [30]. The slow spinning speed of 390 Hz produces a spinning sideband pattern for each peak in one dimension, whereas a multipulse sequence in combination with a special processing method produces isotropic lines in the second dimension. 

The tSR data are compatible with either dense spin glass freezing or with the sudden condensation of a coherent Kondo state (for a discussion see, for example, Grewe and Steglich 1991) with slow, but dynamic spin correlations at 2.5K. The latter interpretation ties in with the specific heat data, especially in applied fields. The former could be explained in terms of the magnetic polaron model formulated by Kasuya et al. (1993a,b). 

FIGURE 5.23 Mean spin-lattice relaxation time ( H NMR experiments) as a function of temperature of neat polystyrene PS-tij and with addition of 13% of benzene. (Adapted from J. Mol. Liquid., 86, Vogel, M., Medick, R, and Rbssler, E., Slow molecular dynamics in binary organic glass formers, 103-108, 2000, Copyright 2000, with permission from Elsevier.)... 

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