Static susceptibility frequency dependence

Finally, we note that when band-structure (and wave function) calculations will be available for polymers in the presence of stationary and nonstationary magnetic fields, it will be possible to compute both the current induced by the magnetic field and the static and frequency-dependent magnetic susceptibilities. Since, however, no such calculations for polymers (even in a very approximate form) are available in the... 

Static charge-density susceptibilities have been computed ab initio by Li et al (38). The frequency-dependent susceptibility x(r, r cd) can be calculated within density functional theory, using methods developed by Ando (39 Zang-will and Soven (40 Gross and Kohn (4I and van Gisbergen, Snijders, and Baerends (42). In ab initio work, x(r, r co) can be determined by use of time-dependent perturbation techniques, pseudo-state methods (43-49), quantum Monte Carlo calculations (50-52), or by explicit construction of the linear response function in coupled cluster theory (53). Then the imaginary-frequency susceptibility can be obtained by analytic continuation from the susceptibility at real frequencies, or by a direct replacement co ico, where possible (for example, in pseudo-state expressions). 

This line has an important advantages over the Lorentz line, since in Eq. (385) (i) the static susceptibility does not depend unlike that in Eq. (355a) on the collision frequency y and (ii) the loss curve is asymmetric. However, in contrast to the formula (382) the integral absorption corresponding to (385) diverges ... 

Fig. 1.7 The temperature dependence of dynamic susceptibility measured on different frequencies. Curves 1-11 correspond to frequencies from 0.51 Hz till 51-10 Hz, xfc is static susceptibility measured in zero magnetic field [25]...

Fig.7 (a) Molecular structure of [Co(2,2 -bi1hiazoline)(N3)2]. (b) Helical chains along the a axis and the octahedrons of Co(ll) ions, (c) Temperature dependence of the real (top) and imaginary (bottom) components of the ac susceptibility in zero applied static field with an oscillating field of 3 Oe at a frequency of 111-9999 Hz. The lines are guides, (d) Arrhenius plot using r vs. data extracted from the ac susceptibility measurements. The red line is a fit to the Arrhenius equation. Reprinted with permission from [60]. Copyright 2003 American Chemical Society... 

Here Ar( ) isothermal susceptibility of eq. (36) and xA ) is the isolated susceptibility that is identical to the Van Vleck contribution Ar (T) in eq. (36). They differ by the Curie contributions of the degenerate CEF states. The latter are due to the thermal repopulation of those states when they are split by a static external strain. Eq. (A9) seems to suggest that even an arbitrary small sound frequency, ft) 0, is too high to allow for repopulation of states. Thus Curie terms would be absent and the isolated quadrupolar susceptibility would determine the T-dependence of the sound velocities at finite frequencies. However, this singular behaviour of t 7 (ft)) in eq. (A9) is an artifact of the RPA approximation used,... 

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