By S. Halilov (auth.), Dr. David J. Singh, Dr. Dimitrios A. Papaconstantopoulos (eds.)
Recent advancements in digital constitution conception have ended in a brand new knowing of magnetic fabrics on the microscopic point. this permits a really first-principles method of investigations of technologically vital magnetic fabrics. between those advances were useful schemes for dealing with non-collinear magnetic platforms, together with relativity, realizing of the origins and position of orbital magnetism inside band constitution formalisms, density practical methods for magnons and low-lying spin excitations, realizing of the interaction of orbital, spin and lattice orderings in complicated oxides, delivery theories for layered platforms, and the speculation of magnetic interactions in doped semiconductors. The booklet covers those contemporary advancements with overview articles via many of the major originators of those advances.
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MK r A L H A Fig. 25. Theoretical magnon spectrum of Tm, ferromagnetic phase adjustment of the crystal-field anisotropy, which appears as ascale factor in the dispersion relation. 73) is not complete and the two-ion anisotropy terms, not included in the present treatment, could improve the situation. The most complicated situation is met in Tm, since no spiral configuration seems to satisfy the equilibrium condition for the given exchange and crystal-field parameters. As is known, the ground state of Tm is ferrimagnetic, with 3 subsequent moments along the c-axis aligned parallel, and 4 furt her moments in the opposite direction.
20. 85) if there is no effect of spin-orbit coupling. 86) J(q)-S . s+ The lowest-order correction in 111 leads to q 8 ] nWq = nW_q [1- InW s(8+s) . 87) Clearly, the effect of softening the f-d exchange (I < 00) vanishes for W -+ 0, and reduces the frequencies in the higher region, where the f-spin 8 does not follow the fast motion of the conduction electron site spin moments any longer. At least part of the persisting discrepancy between the experimental and the calculated magnon spectra, in particular along the hexagonal axis r A, should be attributed to the neglect of intersite spin correlations in the adiabatic approach, which is less justified for the more extended conduction states of the REMs as compared to the 3d-states of Fe, Co, and Ni  .
It shows again that this latter intraatomic energy balance contributes little to the interatomic magnetic interaction as long as q and 0 are not both large. 34). 2 Gd Through Tm: Specific Choice of the Basic Variables and the Hamiltonian The radial distributions of the charge and spin densities are nearly the same in all heavy rare-earth metals, which is clear from Fig. 6. In constrast to the partly filled orbitals of 3d metals, the 4f orbitals centered on the nearest sites are significantly less overlapped, which makes the indirect exchange between them a dominant mechanism for the low-lying excitations, along with the anisotropie terms of the relativistic plus electrostatics nature.