By E.P. Wohlfarth, K.H.J. Buschow
Because the booklet of quantity three in 1982 there was a revival of study on magnetism and a reported raise in curiosity from either the medical and the technological part. quantity five consequently includes chapters that supply the reader with an perception into sleek developments in magnetism and new achievements during this zone. the themes handled the following contain the elevated task and investigations of the magnetism of magnetic superconductors and investigations of the magnetic homes of hydrides, the certainty of first-order magnetic strategies and of quadrupolar interactions in 4f platforms and their function in magnetic ordering and magneto-elastic results, and the magnetism of strongly better itinerant alloys and compounds and the magnetism of Invar alloys.
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Additional info for Handbook of Magnetic Materials: Volume 5
The study of the quadrupolar properties in the cubic phase leads to G r = 150 inK. 85 K (Morin 1988). This difference is consistent with the weak softening of the Cll - C12 elastic mode (Takke et al. e. the anharmonic elastic coupling of the Cll - C12 mode with a zone-boundary phonon, which softens at the M point of the Brillouin zone (Knorr et al. 1980). 10). 38 E MORIN and D. 2. Antiferroquadrupolar ordering Several types of AFQ structures may exist. First, the lifting of the degeneracy of the cubic ground state may lead to wave functions different from one site to the other (Sivardi~re and Blume 1972).
3. 0 T(*K) Fig. 15. 0 K (from Bucher et al. 1972a). cerium ions. In TmGa 3 the temperature range of the AFQ phase is much too narrow. 35 K, a temperature characteristic of very weak AFQ interactions, which may easily be broken by the application of a magnetic field. From a theoretical point of view, the existence of many inter- and intralattice pair coefficients complicates the analysis of the data. 3. Structural transitions possibly of quadrupolar origin A few other structural transitions have been reported in the literature, which may be evidence for quadrupolar interactions.
1). However, the detailed expressions for most terms are different from those of cubic symmetry and are given below (see Morin et al. 1988). The CEF Hamiltonian The CEF Hamiltonian may be written, in terms of the Stevens operators (Hutchings 1964) and in the axes system where the z-axis is parallel to the c-axis of the hexagonal or tetragonal unit cell, as, ~Hex CEF = ~a'et CEF = 0 0 0 0 0 0 6 (60) 6 B2 0 2 + B404 + B606 + B606 , 0 0 0 0 4 4 0 0 4 4 B2 02 + B 404 + B404 + B606 q- B606 • (61) The bilinear Hamiltonian For hexagonal and tetragonal symmetries, the existence of one privileged direction, namely , dictates that there are two invariants in the full bilinear exchange coupling.