Polydisperse systems, dynamic susceptibility

The study that we describe below was inspired by our work on fitting the dynamic susceptibilities measurements for real assemblies of fine particles. Those data typically describe polydisperse systems in the low-frequency bandwidth a>/2% = 1 — 103 Hz. As To 10 s or smaller, then, using formula (4.132) for estimations, one concludes that the frequency interval mentioned becomes a dispersion range for the interwell (superparamagnetic) mode at coto< ct > 1, that is, a > 10. For temperatures up to 300 K, this condition holds for quite a number of nanomagnetic systems. 

In Section IV.B a procedure of numerical solution for Eq. (4.329) is described and enables us to obtain the linear and cubic dynamic susceptibilities for a solid system of uniaxial fine particles. Then, with allowance for the polydispersity of real samples, the model is applied for interpreting the magnetodynamic measurements done on Co-Cu composites [64], and a fairly good agreement is demonstrated. In our work we have proposed for the low-frequency cubic susceptibility of a randomly oriented particle assembly an interpolation (appropriate in the whole temperature range) formula... 

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