Topic

# Exchange interaction

About: Exchange interaction is a research topic. Over the lifetime, 8325 publications have been published within this topic receiving 162805 citations. The topic is also known as: exchange energy & exchange term.

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TL;DR: In this paper, it is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-S$ Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic.

Abstract: It is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-$S$ Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic. The method of proof is capable of excluding a variety of types of ordering in one and two dimensions.

6,236 citations

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TL;DR: In this article, it was shown that electronic orbital ordering is a necessary condition to obtain the correct crystal structure and parameters of the exchange interaction for the Mott-Hubbard insulator.

Abstract: Evidence is presented that within the density-functional theory orbital polarization has to be treated on an equal footing with spin polarization and charge density for strongly interacting electron systems. Using a basis-set independent generalization of the LDA+U functional, we show that electronic orbital ordering is a necessary condition to obtain the correct crystal structure and parameters of the exchange interaction for the Mott-Hubbard insulator ${\mathrm{KCuF}}_{3}$.

3,523 citations

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TL;DR: In this article, the intrinsic domain magnetization of a ferromagnetic with the external magnetic field was obtained, and an approximation to low temperatures and equivalent to those used by Bloch in his derivation of the ${T}^{1}$ law, were introduced.

Abstract: In this paper, the variation of the intrinsic domain magnetization of a ferromagnetic with the external magnetic field, is obtained. The basis of the treatment is the exchange interaction model amplified by explicit consideration of the dipole-dipole interaction between the atomic magnets. Approximations appropriate to low temperatures and equivalent to those used by Bloch in his derivation of the ${T}^{1}$ law, are introduced. The resultant expression for the intrinsic volume susceptibility decreases slowly with increasing field; at high fields the functional dependence is as the inverse square root of the field. The variation with temperature is linear; at room temperature and for fields of about 4000 gauss, the order of magnitude of the (volume) susceptibility is ${10}^{\ensuremath{-}4}$. The results are compared with experiment and satisfactory agreement is found.

2,884 citations

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TL;DR: In this article, the T3/2 law for the temperature dependence of the magnetization of ferromagnetism is shown to be applicable up to very high temperatures, and this result is in good agreement with the results of experiments on metallic ferromagnetic magnetization.

Abstract: The importance to the mechanism of ferromagnetim of exchange interaction between conduction electrons and unfilled inner shell electrons (called s-d interaction) has been pointed out by Zener. Especially for rare earth metals, this interaction seems to be the only mechanism which can cause ferroand antiferromagnetism. However Zener's works are unsatistisfactory because his model is phenomenological and moreover does not involve antiferromagnetism and spin wave mode. Our paper considers this s-d interaction on a more rigorous basis. By a certain approximation, there appear long range eychange type interactions between d-electron spins and, in certain conditions both ferroand antiferromagnetism appear. The excitations of spin wave modes are the same as those in the ordinary modes of the short range exchange force, viz, the energy of the spin wave excitations is proportional to q2 for ferromagnetism and q for antiferromagnetism in the region of small wave vector q. The T3/2 law for the temperature dependence of the magnetization of ferromagnetism is applicable up to very high temperatures, and this result is in good agreement with the results of experiments on metallic ferromagnetism.

1,988 citations

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TL;DR: In this paper, it is shown that the spin coupling between the incomplete $d$ shells and the conduction electrons leads to a tendency for a ferromagnetic alignment of $d $ spins.

Abstract: It is assumed (1) that the interaction between the incomplete $d$ shells of the transition elements is insufficient to disrupt the coupling between the $d$ electrons in the same shells, and (2) that the exchange interaction between adjacent $d$ shells always has the same sign irrespective of distance of separation. The direct interaction between adjacent $d$ shells then invariably leads to a tendency for an antiferromagnetic alignment of $d$ spins. The body-centered cubic structure of the transition metals V, Cr, Cb, Mo, Ta, and W is thereby interpreted, as well as more complex lattices of certain alloys. It is demonstrated that the spin coupling between the incomplete $d$ shells and the conduction electrons leads to a tendency for a ferromagnetic alignment of $d$ spins. The occurrence of ferromagnetism is thereby interpreted in a much more straightforward manner than through the ad hoc assumption of a reversal in sign of the exchange integral. The occurrence of antiferromagnetism and of ferromagnetism in various systems is readily understood, and certain simple rules are deduced for deciding which type of magnetism will occur in particular alloys.

1,660 citations