Magnetism: axial anisotropy

Cj is the second-order magnetic axial anisotropy value for the free ion... 

FIGURE 5.3 Axial anisotropy in an S = 1/2 system. A simplified representation is drawn of the porphyrin prosthetic group in low-spin ferricytochrome c in a magnet (Hagen 2006). (Reproduced by permission of The Royal Society of Chemistry.)... 

Fig. 2. Magnetic energy of a spm crystal as a function of the tilt angle between the magnetization and the easy axis of uni-axial anisotropy.

In these sperimagnetic structures, the subnetwork magnetisations are reduced. The influence of the exchange interactions and a random axial anisotropy on the average magnetic moment can be described using the Hamiltonian (Harris et al. 1973)... 

By contrast, in the strong-field limit Ty saturates and becomes field independent due to Zeeman quenching of magnetic anisotropy. For axial anisotropy along z and no g-anisotropy, the molecular torque follows the simple law... 

Lebech and Rainford (1971) found that a field applied along the hexagonal axis easily pulls the cubic moments out of the basal plane, whereas a larger axial anisotropy constrains the hexagonal moments in the plane. This anisotropy is also apparent from the high field magnetization the moment at 34 T is only l-S/ie/atom. 

As we have already noted, Tb and Dy have such large axial anisotropies that at low temperatures their moments can only be pulled a few degrees out of the basal plane. Conventional torque magnetometry techniques are thus unsuitable, but estimates of the axial anisotropy coefficients have been made from analyses of the magnetization measurements (Feron et al., 1970 Rhyne et al., 1968) and also from measurements of the zero torque position of a torque magnetometer with uncoupled servo (Rhyne and Clark, 1967). All of these experiments were actually interpreted with the aid of an expression for the macroscopic anisotropy energy of the form ... 

We now discuss the question of possible anisotropy in the two-ion exchange terms in the hamiltonian. It may be shown (Mackintosh and Bjerrum-M0ller, 1972 Nicklow, 1971 Nicklow et al., 1971) that tu, is not a symmetric function of q for wave vectors along the c-axis of a cone-shaped magnetic structure. It may also be shown (Nicklow et al., 1971) that both single-ion and two ion (pure axial) anisotropy terms cancel in the expression for the difference in the spin-wave frequencies for +q and -q,... 

The construction of a numerical effective Hamiltonian from accurate electronic structure calculations permits us to determine the complete Z9-tensor and therewith the orientation of the magnetic axes frame of the system with its easy axis or easy plane, depending on the relative energies of the different Ms components of the triplet. When the magnetic axes frame coincides with the cartesian axes frame, D is diagonal and the energy levels of the triplet can be described with two parameters the axial anisotropy D and the rhombic anisotropy E as defined in Eq.2.16. Hence, the symmetric anisotropic interaction of the 5 = 1/2 spin moments, which by themselves are isotropic by definition, makes that the total spin moment of the system is no longer fully isotropic. 

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