Superparamagnetic systems

To summarize this part of the chapter, we have constructed a consistent theory of linear and cubic dynamic susceptibilities of a noninteracting superparamagnetic system with uniaxial particle anisotropy. The scheme developed was specified for consideration of the assemblies with random axis distribution but may be easily extended for any other type of the orientational order imposed on the particle anisotropy axes. A proposed simple approximation is shown to be capable of successful replacement of the results of numerical calculations. 

To facilitate understanding, let us recall the main features of the linear longitudinal susceptibility of a superparamagnetic system. The general solution of the linear problem (4.263) can be formally presented as the spectral expansion... 

Figure 4.23. Signal (a) and noise (b) power densities, and SNR (c) for a superparamagnetic system in the linear response approximation. In the first two figures the vertical scales are chosen to retain only the susceptibility dependencies that really matter namely, in (a) (2T/Q)%" = Q /Vm [see Eq. (4.278)] in (b) rt x 2 = Qs/Vlflpo [see Eq. (4.279)]. In (c) the SNR is characterized by the function R [see Eq. (4.280)]. All the results are given for the low-frequency case fho = 10-4.

In Section IV.B.4 we have shown that the quadratic dynamic susceptibilities of a superparamagnetic system display temperature maxima that are sharper than those of the linear ones. If the maximum occurs as well at the temperature dependence of the signal-to-noise ratio, this should be called the nonlinear stochastic resonance. However, before discussing this phenomenon, one has to define what should be taken as the signal-to-noise ratio in a nonlinear case. 

A consistent study of the linear and lowest nonlinear (quadratic) susceptibilities of a superparamagnetic system subjected to a constant (bias) field is presented. The particles forming the assembly are assumed to be uniaxial and identical. The method of study is mainly the numerical solution (which may be carried out with any given accuracy) of the Fokker-Planck equation for the orientational distribution function of the particle magnetic moment. Besides that, a simple heuristic expression for the quadratic response based on the effective relaxation... 

---