Neel magnetic relaxation

Fig. 3. Illustration of the origin of proton nuclear magnetic relaxation induced by a super-paramagnetic crystal. The water molecule (symbolized by a bee) experiences a magnetic field which fluctuates because of the translational diffusion and because of Neel relaxation. The bottom curve represents a typical time evolution of this field.

Spinu L, Stancu A (1998) Modelling magnetic relaxation phenomena in fine particles systems with a Preisach-Neel model. J Magnet Magnetic Mater 189 106-114 Srivastava KKP, Jones DH (1988) Toward a microscope description of superparamagnetism. Hyperfine Interactions 42 1047-1050... 

More explicitly, the Neel (Tn) and Brownian (Xb) magnetic relaxation times of a magnetic partide are described as ... 

It should be noted that the Neel-Brown relaxation model, although widely employed throughout the literature for predicting and interpreting dilferent parameters of interest in colloids for magnetic hyperthermia such as optimum particle size, frequency or field amplitude, has been criticised due to the disagreements found in both qualitative and quantitative analyses. Some of these will be commented on in Sections 2.4.1 and 2.4.2. 

Another process responsible for a fluctuation of the local magnetic field is Neel relaxation. It corresponds to the flip of the crystal magnetization vector from one easy direction of anisotropy to another. The correlation time of this... 

Relaxation induced by super-paramagnetic crystals is moreover complicated by another feature the influence of the electron magnetic moment is modulated by Neel relaxation, which depends on the crystal anisotropy (see Fig. 4). 

Therefore, for the internal (Neel) relaxation the parameter, r m plays the same role as the fluid viscosity r in the mechanism of the external (Brownian) diffusion. Note that the density of the anisotropy energy K is not included in x. This means that xD can be considered as the internal relaxation time of the magnetic moment only for magnetically isotropic particles (where K = a = 0). The sum of the rotations—thus allowing for both the diffusion of the magnetic moment with respect to the particle and for the diffusion of the particle body relative to the liquid matrix—determines the angle ft of spontaneous rotation of the vector p at the time moment t ... 

The magnetization dynamics of ferrofluids is characterized by the distinction between Brownian and Neel relaxations. Brownian relaxation refers to the mechanical rotation... 

Magnetic particles in a solution undergo two types of relaxation Brownian relaxation, in which the entire particle rotates, and Neel relaxation, in which the moment rotates while the particle remains still. The Brownian relaxation time xB is... 

We have mentioned that the question posed above was answered in part by Shliomis and Stepanov [9]. They showed that for uniaxial particles, for weak applied magnetic fields, and in the noninertial limit, the equations of motion of the ferrofluid particle incorporating both the internal and the Brownian relaxation processes decouple from each other. Thus the reciprocal of the greatest relaxation time is the sum of the reciprocals of the Neel and Brownian relaxation times of both processes considered independently that is, those of a frozen Neel and a frozen Brownian mechanism In this instance the joint probability of the orientations of the magnetic moment and the particle in the fluid (i.e., the crystallographic axes) is the product of the individual probability distributions of the orientations of the axes and the particle so that the underlying Fokker Planck equation for the joint probability distribution also... 

The Shliomis Stepanov approach [9] to the ferrofluid relaxation problem, which is based on the Fokker Planck equation, has come to be known in the literature on magnetism as the egg model. Yet another treatment has recently been given by Scherer and Matuttis [42] using a generalized Lagrangian formalism however, in the discussion of the applications of their method, they limited themselves to a frozen Neel and a frozen Brownian mechanism, respectively. 

In order to illustrate how precession-aided relaxation effects may manifest themselves in a ferrofluid, it will be useful to briefly summarize the differences in the relaxation behavior for axially symmetric and nonaxially symmetric potentials of the magnetocrystalline anisotropy and apphed held, when the Brownian relaxation mode is frozen. Thus only the solid-state (Neel) mechanism is operative that is, the magnetic moment of the single-domain particle may reorientate only with respect to the crystalline axes. 

Here the ratio Xri/xb represents the coupling between the magnetic and mechanical motions arising from the nonseparable namre of the Langevin equations, Lqs. (121) and (122). Thus the correction to the solid-state result imposed by the fluid is once again of the order 10 Hence we may conclude, despite the iionseparability of the equations of motion, that the Neel relaxation time of the ferrofluid particle should still be accurately represented in the IHD and VLD limits by the solid-state relaxation time formulae, Eqs. (87) and (90). Furthermore, Eq. (122) should be closely approximated by the solid-state relaxation equation... 

In our study we treat the two mechanisms separately. For each we assume the dominance of that mechanism. This means that for Debye relaxation we assume that the magnetization vector is fixed to the particle, that is the Neel relaxation is blocked or frozen due to an insurmountable energy barrier preventing its operation. On the other hand for the Neel relaxation, we assume that the particle is fixed in space. 

The field-dependent expressions obtained in the previous sections for relaxation in an external magnetic field are applicable to both Neel and Debye relaxation and their specific application merely requires the use of the relevant time constant or t. ... 

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