Blocked superparamagnetism

In studies of superparamagnetic relaxation the blocking temperature is defined as the temperature at which the relaxation time equals the time scale of the experimental technique. Thus, the blocking temperature is not uniquely defined, but depends on the experimental technique that is used for the study of superparamagnetic relaxation. In Mossbauer spectroscopy studies of samples with a broad distribution of relaxation times, the average blocking temperature is commonly defined as the temperature where half of the spectral area is in a sextet and half of it is in a singlet or a doublet form. 

At high temperatures, a nanoparticle is in a superparamagnetic state with thermal equilibrium properties as described in the previous section. At low temperatures, the magnetic moment is blocked in one potential well with a small probability to overcome the energy barrier, while at intermediate temperatures, where the relaxation time of a spin is comparable to the observation time, dynamical properties can be observed, including magnetic relaxation and a frequency-dependent ac susceptibility. 

We are interested in knowing how the relaxation time of uniaxial spins is affected by a weak field at an arbitrary direction, since it will allow us to study how the superparamagnetic blocking is affected by a field. This field dependence of the relaxation time can be obtained by expanding the relaxation rate T = /x in powers of the field components. As the spins have inversion symmetry in the absence of a field, F should be an even function of the field components, and to third order it is given by... 

In order to determine the characteristics of the superparamagnetic blocking we use the equilibrium susceptibility Xeq calculated using the thermodynamic... 

Figure 3.21. Relaxation time t = co versus T(. For the 5 vol% and 17 vol% samples the lines are fits to the critical slowing down relation [Eq. (3.62)] with the parameters given in Table 111.1. The assumptions E = 0 and E = 500 yield exactly the same line. For the 0.06 vol% sample T is the superparamagnetic blocking temperature defined as the maximum of x".

Because the appearance of the superparamagnetic effect depends on the particle size and on the anisotropy constant, it is often displayed at room temperature by iron oxides <10 nm in size, for example, soil iron oxides. Superparamagnetic relaxation may be counteracted by lowering the temperature and thereby increasing x. Superparamagnetic particles will usually be ordered below a blocking temperature,Tb, which is ... 

Allen, P.D.,T.G. St. Pierre, R. Street (1998) Magnetic interactions in native horse spleen ferritin below the superparamagnetic blocking temperature. J. Magn. Mag. Mat. 177—181 1459-1460... 

The virtual presence of all the spectral terms in the effective time makes this approach more adequate than the superparamagnetic blocking model. In the latter, the effective relaxation time of magnetization is identified just with the inverse of the decrement X], which is the smallest at , 0. 

All the samples measured showed characteristic superparamagnetic behavior with a blocking temperature TB. An independent method of determining the parameters of the particle size distribution g(D) is by means of the analysis of magnetic measurements under equilibrium conditions, i.e. at temperatures above the superparamagnetic blocking temperature Tb- For this purpose we performed magnetization measurements as a function of field M(H) at different temperatures [4,5]. 

The temperature at the maximum in the zero field dc susceptibility measurement determines the blocking temperature TB (Fig. 3). It was found to increase with the average diameter of the clusters of a given sample. The simplest model to explain superparamagnetism assumes that each particle has a uniaxial anisotropy with a direction independent of that of the other particles. The energy that is needed to reverse the magnetization U, determines the relaxation time of this process,... 

Here, z0 10-10 -10 13s is the inverse attempt frequency that depends on the damping of the magnetic moments by the phonons. The superparamagnetic blocking occurs when r equals the measuring time of each experimental point, te, therefore TB = all / kB ln(/(, / r0 ), where a is a constant that depends on the width of the particle size distribution. 

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