Stevens factors

According to a two-sublattice mean field model, the EMD of inter-metallic compounds is determined by the competition between the EMDs of the rare earth sublattice and the transition metal sublattice. In the Th2Zn]7-type crystal lattice, the Sm sublattice prefers c-axis anisotropy to others because of the positive Stevens factor (aj) of Sm, and the Fe sublattice contributes to the c-plane anisotropy. Both Co and carbon in Sm2(Fe1 xCox)17C>. help to enhance the contribution of the Sm sublattice dominant to the EMD, but the effect of carbon is larger than that of Co. 

Second-order Stevens factor for different R elements and preferred magnetization direction observed in various R2Fe14B and R2Co17 compounds. (After Buschow et al. 

The quantities 6 are the Stevens factors (a, fir, y, for n = 2, 4 and 6, respectively), (rn) are Hartree-Fock radial integrals and A are crystal-field potentials. The quantities O are Stevens operators and Hm in the last term of eq. (11) represents the molecular-field acting on the rare earth moment. 

Here ay is the second-order Stevens factor, is the Sternheimer antishielding factor and a2 is a screening constant. 

In the majority of lanthanide cases, with the ground J multiplet (often referred to as the Hund s rule state) so isolated, the CEF analysis is simplified. When /=constant, I= X) j,jz), and the action of each r Z/ term on any such state can be expressed as a dimensionless Stevens factor (Stevens 1967) 0/ = /, yj, for / = 2,4,6, respectively... 

Pi — direction cosines of strain measurement direction Pj = fourth-order Stevens factor P = exponents characterizing temperature dependence of a and P sixth-order Stevens factor... 

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. 6.30. Crystal field parameters, divided by appropriate Stevens factors, for dilute alloys of Tb, Ho, Er and Tm in the hosts Y( ), Lu(D) and Sc(0), as deduced from magnetization and susceptibility measurements (after Touborg 1977).

So spin value of Iron obtained Stevens factor... 

Estimated values of anisotropy fields in RjCoj B compound are 0.6 T for R = La and 7.5 T for R = Pr (Buschow et al. 1985c). The cobalt sublattice anisotropy favours an easy magnetization direction perpendicular to c-axis, whereas the crystal field induced anisotropy of the 4f sublattice corresponds to the second order Stevens factor Uj of R component. 

As can be seen from table 33.6 there is generally a rather marked difference between the effective Z4 values derived for the nitrides compared with those for the remaining pnictides. As Yuan (1977) pointed out this difference is due to the extremely small Ln-Ln distances in the nitrides which are virtually the same as in the trivalent metals. In the nitrides, therefore, the 12 nearest Ln neighbors will have a nonnegligible influence on the crystal-field potential as they will alter the form of the f-electron cloud and hence the Stevens factors p and y which were calculated for free rare earth ions. 

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