Cubic anisotropy

This indicates that even in amorphous samples, in which the uniaxial Ki terms are expected to dominate due to the local distortions from cubic symmetry, there is still a significant contribution from the K4 cubic anisotropy terms. It is interesting to contrast this with the numerical simulations for a-TbFe2 which have shown that the fourth-order anisotropy eneigy per atom was an order of magnitude smaller than the second-order anisotropy energy per atom, albeit that the fourth-order term was of the same order of magnitude... 

Figure 4 shows the calculated effective anisotropy energy density of a particle consisting of three crystallites with volume fractions 0.1, 0.2, and 0.7. The three crystallites have perpendicular easy axis and are strongly exchange coupled. Note if the three volumes are the same, no anisotropy occurs. For comparison, Fig. 4. gives the energy density surface for cubic anisotropy. 

As discussed by Ham [32], for each interaction two parameters are required, the isotropic terms gi, Am and a cubic anisotropy g2, Ahi- The angular dependent spectrum in Fig. 11 disappears above the relatively low temperatures of 6K, being replaced by an isotropic spectrum characterised by the gi,Ahi values alone which are the same as the low temperature gi, Am values. The parameters used to reproduce the spectra in Fig. 11 are given in Table 5 together with those found for Cu(II)/CaO. 

In this case, there is a symmetry against the change of sign of 0 (fig. 10 shows that this simply corresponds to an interchange of sublattices) and hence a term 03 cannot occur. The fourth order term, however, now contains two cubic invariants rather than a single term [(02)2 =

rotational invariance in the order parameter space (0i, 02), since all directions in the (01, 02) plane are equivalent. No such rotational symmetry applies to the (2x1) structure, of course. So the expansion eq. (26) results, which defines the universality class of the X Y model with cubic anisotropy . Of course, in this approach not much can he said on the phenomenological coefficients r, u, u, R in eq. (26). 

Universality class and critical exponents Ising XY with cubic anisotropy 3-state Potts 4-state Potts... 

Similarly it is concluded that the transition of interest for comer-cubic anisotropy can either be first order or continuous. In the latter case the critical behavior has to be that of the two-dimensional Ising model up to logarithmic corrections [308]. However, the triciitical and critical behaviors are identical up to logarithmic corrections in other words, no distinct tiicritical behavior is expected to occur [308]. 

This behavior of cubic anisotropy is equivalent to the corresponding component for /3-A PbCu(N02)6 in Eq. (31), but not restricted to one plane in this case. Similar isotropic signals ich also could not be frozen in at 4.2 K are found for mixed crystals Sr2Zni xCuxW(Te)06 in the range 0.05 [Pg.36]

Alpha-iron (a-Fe). Between room temperature and a transition temperature of 769°C, pure iron exhibits a body-centered cubic (bcc) crystal lattice (a = 286.645 pm at 25°C). Alpha-iron is a soft, ductile metal with a density of 7875 kg.m l Alpha-iron is also ferromagnetic, with a saturation magnetization at room temperature of 220 A-m -kg , and the cubic anisotropy constants are = 4.7 x 10 J-m and = 1.5 - 3.0 x 10 J m Carbon exhibits a poor solubility in alpha-iron with a maximum content of 0.025 wt.% C at 723°C. It is important to note that the word ferrite describes a solid solution of carbon into alpha-iron, though it is sometimes improperly used to describe alpha-iron (Section 2.1.9) ... 

Let us consider the mixing of uniaxial anisotropy with a constant first with simple cubic anisotropy with /Cj > 0 and /C2 = 0 and second with... 

C.3.2.2. Cubic Symmetry with [llOJ-Type Easy Axis and Uniaxial Symmetry. For uniaxial anisotropy adding to cubic anisotropy with /C, < 0 and /C2 ( ) i such that [110]-type directions correspond to easy axes, the determination of the m relaxation paths is not easy because it depends on three parameters and for y-Fe Oj, the K2 value is unknown. 

These interactions with cubic anisotropy can be well approximated by an isotropic Gaussian form... 

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