Neel relaxation

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... 

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.

Relaxation is then generally governed by the equations of Freed (9). In the special case where the translational diffusion correlation time is much shorter than the Neel relaxation time, tq is dominated by diffusion and the equations of Freed reduce to the earlier equations of Ayant (10). 

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). 

Another effect of increasing the anisotropy is the lengthening of Neel relaxation time, which generally dominates xq. Since the zero-field relaxation rate is proportional to xq, this lengthening will increase the low field relax-ivity, a consequence opposed to the slackening due to the hidden transitions. 

These recent results are thus likely to have put an end to a previously controversial question ferritin is antiferromagnetic at room temperature (because T < T ) and the size of the ferrihydrite grains is small enough to observe super-paramagnetism with a Neel relaxation time of about 0.1 ns. 

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... 

The relaxation rates are affected differently by the immobilization of the nanoparticles. The Brownian relaxation time can be changed by changing the viscosity of the carrier while the Neel relaxation should be independent of the carrier liquid. The relaxation rates also are affected differently by phenomena such as immobilization of a nanoparticle due to endocytosis. 

Equation (80) will be the key equation in our discussion of precession aided Neel relaxation. 

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... 

ON THE THEORY OF DEBYE AND NEEL RELAXATION OF SINGLE DOMAIN FERROMAGNETIC PARTICLES... 

We may summarize the contents of this chapter in more detail as follows. In Section I we demonstrate how the explicit form of Gilbert s equation describing Neel relaxation may be written down from the gyromagnetic equation and how, in the limit of low damping, this becomes the Landau-Lifshitz equation. Next the application of this equation to ferrofluid relaxation is discussed together with the analogy to dielectric relaxation. 

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