Magnetic anisotropy magnetization vectors

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. 4. Constraints exerted by the anisotropy field upon the orientation of the magnetization vector. (I) High anisotropy magnetization is almost locked onto the easy axis. (II) Low anisotropy thermal energy is sufficient to move the magnetization vector aside from the easy axis.

If, after the material has been magnetically saturated to the value Bs, the field is reduced to zero, the magnetization vectors rotate out of line with the field towards the nearest preferred direction which is determined in part by magnetocrystalline anisotropy. The magnetization is thus prevented from complete relaxation to the virgin curve and hence, for zero field, there is a remanent induction Bx. In order to reduce the induction to zero a reverse field II,. has to be applied. The coercive field or coercivity II,. depends in part on crystalline anisotropy, as might be expected. 

When excited by an applied alternating magnetic field the magnetization vector will precess around the anisotropy field as discussed more fully later (Section 9.3.4). Resonance occurs when the frequency of the applied field coincides with the natural precessional frequency, i.e. the Larmor frequency coL = yfi0HA, with the result that the permeability falls and losses increase, as shown for a family of NiZn ferrites in Fig. 9.29. The onset of such ferrimagnetic resonances restricts the use of MnZn ferrites to frequencies of less than about 2 MHz. At higher frequencies, up to about 200 MHz, compositions from the NiZn family are used. 

In a single-domain particle of a-Fe203 the magnetization vector is held in the c-plane perpendicular to the c-axis by the magnetocrystalline field. Mossbauer studies use the 57Fe nucleus as the "observer to record when the relaxation time t becomes shorter than the period for precession of the nuclear spin about the direction of the effective field. Substitution into the equation for the Larmor frequency, or observer relaxation time, with an expression for the frequency factor proportional to the specific volume and anisotropy constant of the oxide gave (26, 27) the relationship ... 

Such a tunnel switching of the magnetization can be described by the so-called one-domain approximation, when the total magnetization vector M is taken as a main dynamic variable with fixed absolute value M. Then the total energy density, or the anisotropy energy E, is obtained from the spin-Hamiltonian H using a spin coherent state n) chosen along the direction n [332,333] ... 

The analysis which we have just given ignores the internal anisotropy of the ferrofluid particle. It is instructive to review a calculation of Shliomis [16-18] which considers the static susceptibility in a monodis-persed colloid taking account of the internal anisotropy of the particles. The direction of the magnetization vector will be represented by r = Ml and the direction of the internal anisotropy axis by n. The equilibrium distribution function of the orientations taking account of the internal anisotropy and the applied DC field is... 

K is the anisotropy constant t, and Tj are constants independent of u. Kv is, as in Section VI and [17], the barrier to rotation of the magnetic vector. The value V always differs from u, the magnetic volume of the particle, because [80] of the surfactant layer coating the particle and the thin non-magnetic layer which is often created on the particle surface owing to the interaction with the surfactant molecules. 

Figure 1 The principal sources of structural data are the NOEs, which give information on the spatial proximity d of protons coupling constants, which give information on dihedral angles < i and residual dipolar couplings, which give information on the relative orientation 0 of a bond vector with respect to the molecule (to the magnetic anisotropy tensor or an alignment tensor). Protons are shown as spheres. The dashed line indicates a coordinate system rigidly attached to the molecule.

It is clear that an ah initio calculation of the ground state of AF Cr, based on actual experimental data on the magnetic structure, would be at the moment absolutely unfeasible. That is why most calculations are performed for a vector Q = 2ir/a (1,0,0). In this case Cr has a CsCl unit cell. The local magnetic moments at different atoms are equal in magnitude but opposite in direction. Such an approach is used, in particular, in papers [2, 3, 4], in which the electronic structure of Cr is calculated within the framework of spin density functional theory. Our paper [6] is devoted to the study of the influence of relativistic effects on the electronic structure of chromium. The results of calculations demonstrate that the relativistic effects completely change the structure of the Or electron spectrum, which leads to its anisotropy for the directions being identical in the non-relativistic approach. 

Here, 0 is the angle between the magnetic field vector and the unique symmetry axis. Any anisotropy in the g value is assumed to be small compared to the zero field splitting effects. For Cr3+, which is characterized by S = , and mB = f, , — J, — the polycrystalline spectrum has the shape indicated in Fig. 18 (39). An example of the polycrystalline spectrum for the S = 1 case in which both D and E are nonzero is shown in Fig. 19 (40). A numerical evaluation of D and E may be made from the structure indicated in the spectrum. 

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