Anti-ferromagnetic structure

FIGURE 5.1 Left the anti-ferromagnetic structure CoO right the band structure and the density of state (DOS) in LSDA and GGA approximations, respectively the upper and down arrows are associated with the spin orbital projections after Dufek et al. (1994). 

The occurence of the magnetic structure of the A-type also demands a 3-dimensional linking of octahedra in corners. The magnetic coupling, however, is of a different kind in the 3 directions The A-type is a magnetic layer structure, in which ferromagnetic sheets are coupled anti-ferromagnetically in the third direction. 

The principal types of interaction of a substance with a magnetic field are called diamagnetism, paramagnetism, ferromagnetism, anti-ferromagnetism, and ferrimagnetism. They are useful in providing information about the electronic structures of the substances, especially as discussed in Chapters 5 and 11. 

V.G. Bar yachtar, A.E. Borovik, V.A. Popov,, E.L. Stefanovsky, About anti-ferromagnet domain structure, arising with the change of magnetic anisotropy. Sov. Phys.-JETP, 59, No 10, 1299-1306 (1970)... 

Thereafter, crystals were brought back to the aerobic 25% MPD solution, buffered with 50 mAf sodium phosphate, pH 5.5. This procedure is based on Avigliano et al. s (157) method of preparing T2D ascorbate oxidase in solution and was modified by Merli et al. (159) for use with ascorbate oxidase crystals. The 2.5-A-resolution X-ray structure analysis by difference-Fourier techniques and crystallographic refinement shows that about 1.3 copper ions per ascorbate oxidase monomer are removed. The copper is lost from all three copper sites of the trinuclear copper species, whereby the EPR-active type-2 copper is the most depleted (see Fig. 10). Type-1 copper is not affected. The EPR spectra from polycrystalline samples of the respective native and T2D ascorbate oxidase were recorded. The native spectrum exhibits the type-1 and type-2 EPR signals in a ratio of about 1 1, as expected from the crystal structure. The T2D spectrum reveals the characteristic resonances of the type-1 copper center, also observed for T2D ascorbate oxidase in frozen solution, and the complete disappearance of the spectroscopic type-2 copper. This observation indicates preferential formation of a Cu-depleted form with the holes equally distributed over all three copper sites. Each of these Cu-depleted species may represent an anti-ferromagnetically coupled copper pair that is EPR-silent and that could explain the disappearance of the type-2 EPR signal. 

Classic spin structures corresponding to ferromagnetic (FM) anti-ferromagnetic (AF) ferrimagnetic (FI) weak ferromagnetic (WF) noncollinear antiferromagnetic (NC-AF) spin glass (SG)... 

In Fig. (7.8) are shown direct calculations of the planar spin spirals as a function of moment and of volume, the moment is seen to increase monotonically with the volume. One can see that the spin spiral qxw is stable for low volumes and moments, while the spin spiral qrx is stable at higher volumes and moments. Now, we calculate the spin spirals for fixed moments, both with the BGFM and with with the Heisenberg model with both FM and DLM interactions, just as described above for bcc Fe, fee Ni, and fee Co. We also calculate the spin spirals directly with the force theorem without the Heisenberg expansion by doing one calculation with the potentials from either the ferromagnetic or anti-ferromagnetic solution and the new spin spiral structure. The results can be seen in Fig.(7.9). 

Prior to the work of Ref [84], a series of LMTO calculations had studied UO2. A full-potential, non-spin-polarized LMTO treatment with a gradient-corrected XC model gave a lattice constant (fluorite structure) of 9.81 au, well below the experimental 10.34 au (see [84] for references to the other literature). An approximate LMTO (LMTO-ASA) non-spin-polarized treatment with LDA XC gave 9.92 au and a bulk modulus of 5 = 291 GPa versus the experimental value 207 GPa. Spin-polarized LDA calculations did give anti-ferromagnetic ordering (foimd experimentally) at the experimental lattice constant but the moment vanished at the LDA equilibrium value. All the results were metallic. 

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