Dynamic magnetic susceptibility

Figure 4.32. Linear dynamic magnetic susceptibilities of a randomly oriented super-paramagnetic assembly (a, b) and of a magnetic fluid of the same particles (c, d) for all the graphs the ratio TdAb = 10-4. Vertical axes for % are scaled in the units of cp2/r so that at to —> 0 both % tend to 1/3.

Sadykov EK, Isavnin AG (1996) Theoiy of dynamic magnetic susceptibility in uniaxial superpaiamagnetic particles. Phys Solid State 38 1160-1164... 

D fermion system to a 2-D classical Coulomb gas is employed to calculate the dynamical magnetic susceptibility of the 1-D fermion system. The result points towards the existence of bound magnon states in a 1-D fermion system. 

In a completely analogous way to fig. 59 one obtains an RPA expression for the dynamic magnetic susceptibility... 

Fig. 33. (a) Dyson equation for the pseudofermion propagators of CEF states n, m (broken lines). Phonons are indicated by wavy lines. Open circles represent the magnetoelastic interaction vertex, (b) Bubble diagram for the dynamical magnetic susceptibility using renormalized propagators. Open squares represent the dipolar operator J. 

The pair scattering for two quasiparticles with opposite momenta at the Fermi surface is evaluated adopting the ladder approximation displayed in fig. 5. The problem is therefore reduced to finding the four-point vertex which is irreducible with respect to particle-particle scattering. The basic assumption is that the important structure in the scattering amplitudes comes from exchange of collective modes in the two particle-hole channels. The central quantity of these theories is the dynamic magnetic susceptibility x (fl ) which can be determined... 

Fig- 18. Dynamic magnetic susceptibility Im x(o3), normalized to its maximum value, as a function of frequency a>. Solid lines result from the NCA, the dashed line corresponds to the quasi-elastic line shape eq, (25), and the dots are experimental data for CePda (solid circles at 5 K, open circles at 280 K from Galera et al. (1985a,b)) (Bickers et al. 1987). 

Dynamic magnetic susceptibilities as measured by electron-spin resonance, nuclear-spin resonance and inelastic neutron scattering experiments... 

The second, more practical, expression is in terms of the dynamic magnetic susceptibility x iQ> T). Its connection to the correlation function described by eq. (2) is given via the fluctuation dissipation theorem,... 

Other parameters which have been used to provide a measure of a include physical dimensions (thermomechanical analysis, TMA) [126], magnetic susceptibility [178,179], light emission [180,181], reflectance spectra (dynamic reflectance spectroscopy, DRS) [182] and dielectric properties (dynamic scanning dielectrometry, DSD) [183,184], For completeness, we may make passing reference here to the extreme instances of non-isothermal behaviour which occur during self-sustained burning (studied from responses [185] of a thermocouple within the reactant) and detonation. Such behaviour is, however, beyond the scope of the present review. 

The structures and dynamic magnetic behaviours of 31-Dy4 and 31-Tb4 have been presented in Figure 3.22. Four lanthanide ions are aggregated in the grid-like metal core by a central p4-S and eight peripheral i2-S atoms from ethanethiol ligands [38]. The individual lanthanide centres occupy distorted six-coordinate [LnNS5] octahedral coordination environments. Ac susceptibilities measurements reveal pronounced temperature dependence with a series of maxima below 28 K, typical for SMM behaviour, in complex 31-Dy4. Furthermore, an... 

The convenient NMR observables depend on the characteristics of the system studied, but generally the protons of the liquid are readily detected. The apparent NMR linewidths are often determined by the magnetic susceptibility inhomogeneities in the sample and do not directly reflect the dynamics of the liquid. This report will focus largely on theoretical approaches to understand the spin-lattice relaxation rate constants for both classes of microporous materials. The magnetic held dependence of the spin-lattice relaxation rate constant generally provides a useful dynamical characterization of the liquid and often a structural characterization of the confining media. 

J. Furrer, K. Elbayed, M. Bourdonneau, J. Raya, D. Linial, A. Bianco and M. Piotto, Dynamic and magnetic susceptibility effects on the MAS NMR linewidth of a tetrapeptide bound to different resins, Magn. Reson. Chem., 2002, 40, 123-132. 

Observation of magnetic susceptibility relaxation after perturbation of a spin equilibrium would be the most direct way to measure the dynamics of the equilibrium. This does not appear to have been reported as measured in solution. In principle susceptibility relaxation as a function of frequency could be measured much as dielectric relaxation is examined. The requirement is for a sufficiently strong magnetic field with very sensitive detection. A nonequilibrium magnetic susceptibility has been generated by light at low temperatures in the solid state (39). 

Magnetic susceptibility, nickel 7]5-ligands, 8, 159—160 Magnetization, in dynamic NMR, 1, 409 Main-chain metallopolymers, with -coordinated metals and long spacers, characteristics, 12, 347... 

The results of numerical calculations of the dynamic nonlinear susceptibilities for a random assembly of monodisperse grains along formulas (4.99)-(4.111) are presented in Figure. 4.2. We show them as the functions of the temperature parameter a oc 1 /T, taking coio = 10-8 as the reference value. This choice seems reasonable since the low-frequency magnetic measurements are typically carried out at co about 102 — 103 Hz, and the customary reference value of To lies in the 10 10 — 10 s range. The curves obtained by the approximate formula (4.112) are plotted with thin dashed lines that visually almost coincide with the curves corresponding to the exact solution. 

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