Magnetic viscosity

Besides this advection, there is also a diffusion mechanism with a small coefficient of magnetic viscosity D. Thus, the final equation of the evolution of the magnetic field B has the form... 

The increment 7 depends on the magnetic viscosity D. The dynamo is called fast (this concept was introduced by Ya.B.) if the increment remains positive (and greater than a certain positive number) for arbitrarily small values of the magnetic viscosity D. 

However, if the electric resistivity is taken into account, there appears in general a new, very fundamental circumstance the normal component of the Laplacian of an arbitrary vector also depends on the tangential components of the vector. The magnetic viscosity creates feedback, due to which the tangential components are able to modify (in particular, to amplify) the normal component. Therefore, in principle, exponential, coordinated amplification of all fields also becomes possible, i.e., a dynamo But this is a peculiar kind of dynamo that depends on the magnetic viscosity. 

We note that, even if at the initial instant the component Hz were to depend only on x and y, and not on z, a dependence on z would appear because the motion along x and y is accompanied by a translational deformation, dvx/dz 0, dvy/dz 0. Therefore, for dHz/dz = 0 at the initial moment (in the absence of magnetic viscosity)... 

We shall make some remarks regarding the cases when the magnetic viscosity and the density of the medium are functions of the coordinates. It is obvious that no anti-dynamo theorems are possible if vm depends on all three space coordinates. In such a medium solutions are possible which simulate the functioning of dynamo-machines constructed by means of insulated conductors. However, in the simplest case vm = um(z) or vm — vm r) we can prove the impossibility of a dynamo. The equation for Hz in this case, as may be easily verified, again has the form (4), but relation (5) will no longer hold. In its place we must multiply (4) by Hzlvm and then, making use of the relation vVvm = 0, we obtain... 

Figure 15. Dynamic hysteresis-loop effects (a) magnetic viscosity and (b) sweep-rate dependence. The sweep-rate dependence amounts to a fluctuation-field [165] or sweep-rate correction to the static coercivity Hco.

An important aspect of magnetic viscosity is its field dependence. For example, S(H) tends to exhibit a maximum near the coercivity. This reflects the close relationship between the energy-barrier distribution and the irreversible part x>n of the susceptibility, and leads to S = x where the viscosity parameter Sv is only weakly field-dependent [5, 133, 159, 167, 169-172],... 

An effect closely related to magnetic viscosity is the dependence of the coercivity on the sweep rate rj = dH/dt Hc is largest for high sweep rates, that is, for fast hysteresis-loop measurements (Fig. 15). Sweep-rate and magnetic-viscosity dynamics have the same origin, but there is a very simple way of deriving a relation for the sweep-rate dependence. Let us assume that the energy barriers exhibit a power-law dependence... 

Barbara B, Sampaio LC, Marchand A, Kubo O, Takeuchi H (1994) Two-variables scaling of the magnetic viscosity in Ba-ferrite nano-particles. J Magnet Magnetic Mater 136 183-188 Barra A-L, Debrunner P, Gatteschi D, Schulz ChE, Sessoh R (1996) Superparamagnetic-like behavior in an octanuclear iron cluster. EuroPhys Lett 35 133-138... 

Street R, Woolley JC (1949) A study of magnetic viscosity. Proc Phys Soc A 62 562-572 Suber L, Fiorani D, Imperatori P, Foglia S, Montone A, Zysler R (1999) Effects of thermal treatments on stmctural and magnetic properties of acicular a-Fe20s nanoparticles. NanoStractured Mater 11 797-803... 

Figure 10. The egg model of Stepanov and Shliomis a>, is angular velocity of yolk, to, is angular velocity of eggshell, ft is local angular velocity of the surrounding fluid, IX = magnetic viscosity represented by the viscosity of the white, r is the viscosity of the surrounding fluid, v is the volume of the yolk. V is the hydrodynamic volume.

IRM isothermal remanence magnetization S(H) magnetic viscosity at the applied field H... 

The magnetic viscosity is related to the irreversible susceptibility XaiiH) by O Grady et al. (1993, 1994). 

The magnetic viscosity S(H) can be determined from the slope of the Af(t)-ln(f) curve and is foimd to vary with tiie field, generally going through a m udmum in the vicinity of the coercivity. The activation volume v is also determined experimentally because both S(H) and Xm(H) can be obtained from the time decay curves and remanence curves, respectively. O Grady et al. (1994) used the above analysis to study the magnetization reversal in (14.3 ATb/85 AFe) as a fimction of the number of bilayers. The time decay curves for a sample with 32 bilayers is shown in fig. 45 and the activation volumes as a function of bilayer number in fig. 46. 

Lu, P.-L., and S.H. Charap. 1994. Magnetic viscosity in high-density recording. Journal of AppUed Physics 75(10) 5768-5770. 

As already mentioned above, Tj(H) is also predicted to be seen by the disappearance of irreversibility. Salamon and Tholence (1982) explore this possibility by examining the relaxation of the magnetization of zero-field-cooled samples (CwMn 0.24% and a-FejoNi pPjo) following the application of a step increase in magnetic field. They show that the magnetic viscosity S(H, T) = dM(t)/d In t first increases with field at a fixed temperature, reaches a maximum at H (T) and then tends toward zero at large fields. The values of H (T) vary similar to the AT line, with 17 = 0.66 and 0.55 for CwMn and a-FeNiP,... 

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