Anisotropy, basal plane

Fig. 18. Temperature dependence of the magnetization of a LuNi2B2C single crystal in a field of 3 T applied along the crystallographic directions c, a and (110), clearly showing an out-of-(tetragonal basal) plane anisotropy as well as an in-plane anisotropy of Hc2 where Hc2(T) is determined by the indicated linear extrapolation (after...

Fig. 10. Applied field dependence of the = 0 magnon energy gap in Tb—10%Ho demonstrating the validity of the frozen-lattice strain approximation as manifested by the minimum, but non-vanishing, of the gap energy at a held corresponding to the basal plane anisotropy held. Data taken with the field along the hard basal plane direction, except for the curves marked easy (axis) which show a linear increase of gap energy with field. The lines are theoretical curves. Different symbols are used to distinguish data taken at different temperatures. (After Nielsen et al. 1970b.)...

Lounasmaa and Sundstrom (1966), in view of the strong basal plane anisotropy of Tb at low temperatures, favoured introduction of a spin-wave energy gap as against a simple power law for Cm. They found a reasonable fit with Cm = 36 r exp(-23.5/T) from 8 to 20 K, based on the assumption Ce+Cl = Cp (Lu). In their analysis, Wells et al. (1976) used a theoretical expression... 

Fig. 6.28. The basal plane anisotropy of terbium, expressed as a critical field, plotted as a function of the reduced magnetization. Closed circles denote the neutron scattering results of Houmann et al. (1975) triangles and squares correspond to the macroscopic measurements of Rhyne (1965) and Feron et al. (1970), respectively.

Following the /-dependence of the appropriate Stevens factor, Dy exhibits a crystal field contribution to the basal plane anisotropy considerably larger than Tb and, as already noted (section 2.2.2), the a-axis is the easy direction so that If is negative. Although Feron et al. estimated kI from 1.7 to 105 K, below 50 K the available magnetic field was insufficient to pull the magnetization completely into the hard direction. Thus the extrapolations used to calculate K6(0) = -1.1 0.1 X 10 Jm should be treated with caution. 

Fig. 6.29. The basal plane anisotropy of dysprosium as a function of reduced magnetization. The results of Martin s, re-analysis of Rhyne s (1%5) magnetostriction measurements are shown. (Me.rhn and Rhynt, imj.

Both Rhyne and Feron estimated kKO) as 2.7 0.3 x 10 Jm whilst Cock (1976) deduced a value of 3.4 0.3 x 10 Jm The basal plane anisotropy in Ho is thus larger than in any other lanthanide, a result of the 4f charge distribution associated with the large orbital moment (L = 6). As in the case of k , the temperature dependence of kI cannot be readily parameterized and requires further investigation. 

Appropriately combined changes in these parameters of the order of 10% also fit the magnetization data. The substantial basal plane anisotropy thus has a magnitude second only to that of holmium. 

V = seniority quantum number V = axial anisotropy coefficients in SKci = basal plane anisotropy coefficient in... 

Expansion of the function Bj in a Fourier series in q R-,) and applications of the Bloch theorem to the sum over i in eq. (7.24) leads to peaks in x whenever qm is a sub-multiple of a c-axis reciprocal lattice vector. The same argument can be made in the case of a spiral structure. The reasons for the incommensurate-to-commensurate q transition are to be found in (a) the single-ion anisotropy terms in the hamiltonian, including magnetoelastic effects. For CAM-type structures the axial anisotropy favors maximum ordered moment at each site which can only develop in a commensurate structure. For spiral-type structures the basal plane anisotropy will also favor a commensurate structure, as will the nagnetoelastic anisotropy (b) the exchange will also favor a maximum ordered... 

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