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By Professor Vladimir A. Gubanov, Dr. Alexandr I. Liechtenstein, Dr. Andrei V. Postnikov (auth.)

The quantum idea of magnetism is a well-developed a part of modern solid-state physics. the elemental innovations of this thought can be utilized to explain such vital results as ferromagnetic ordering oflocalized magnetic moments in crystals and ferromagnetism of metals produced via basically delocalized electrons, in addition to numerous sorts of mutual orientation of atomic magnetic moments in solids owning diverse crystal lattices and compositions. In contemporary years,the spin-fluctuational method has been built, which could triumph over a few contradictions among "localized" and "itinerant" types within the quantum mechanics of magnetic crystals. those are just many of the central achievements of quantum magnetic idea. just about all of the recognized magnetic houses of solids may be qualitat­ ively defined at the foundation of its thoughts. extra advancements should still open up the potential of trustworthy quantitative description of magnetic homes of solids. regrettably, such calculations in accordance with version options seem to be very complex and, commonly, now not certain sufficient. The really small variety of parameters of qualitative versions aren't in a position to keep in mind the very kinds of magnetic interactions that seem in crystals. extra improvement of magnetic thought calls for quantitative details on digital wave functionality within the crystal thought of. this is often proved by way of digital band­ constitution and cluster calculations. in lots of instances the latter could be a place to begin for quantitative calculations of parameters utilized in magnetic theory.

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43]. 38] that the total energy of the spin spiral at low angles becomes very sensitive to the choice of tight-binding calculation parameters. Therefore, the calculated value of D can be considered only as an order-of-magnitude estimate. The parameter-free method of calculating the spin-wave stiffness constant is discussed in Chap. 4. 30) ij For the AT configuration, it would result in a linear dependence of excitation energy on (1 - cos (), where the slope of the line is a combination of various interatomic exchange integrals.

4). e. they behave as the rigid bands of an itinerant ferromagnet. 51) is still valid. The more complex situation of a pair of parallel, or antiparallel magnetic moments appearing at two impurity sites can be treated in a similar way, but with potential perturbation introduced at the two sites. --i-;I7 (- r ) . 5 Criteria for the Existence of Magnetic Moments 39 each block being, in tum, a submatrix in the basis of partial states. 54) g21;g22 where 1 and 2 label the sites, and the IX indices are omitted for brevity.

6 shows the evolution of the magnetic moment per atom with the e angle. Note that the value of the local magnetic moment in iron remains practically unchanged up to e = 90°, and after a rapid decrease at e> 120° it does not drop to zero even at e = 180°. For Ni, the magnetic moment is considerably reduced at e > 30° and tends to zero as e-+ 180°. This reveals the more itinerant nature of magnetic moments in Ni, in contrast to those of Fe. 47].

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