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Ferromagnetic State and Phase Transitions Ferromagnetic state and phase transitions Yuri Mnyukh 76 Peggy Lane, Farmington, CT, USA, e-mail: [email protected] (Dated: June 20, 2011) Evidence is summarized attesting that the standard exchange field theory of ferromagnetism by Heisenberg has not been successful. It is replaced by the crystal field and a simple assumption that spin orientation is inexorably associated with the orientation of its carrier. It follows at once that both ferromagnetic phase transitions and magnetization must involve a structural rearrangement. The mechanism of structural rearrangements in solids is nucleation and interface propagation. The new approach accounts coherently for ferromagnetic state and its manifestations. 1. Weiss' molecular and Heisenberg's electron Its positive sign led to a collinear ferromagnetism, and exchange fields negative to a collinear antiferromagnetism. Since then it has become accepted that Heisenberg gave a quantum- Generally, ferromagnetics are spin-containing materials mechanical explanation for Weiss' "molecular field": that are (or can be) magnetized and remain magnetized "Only quantum mechanics has brought about in the absence of magnetic field. This definition also explanation of the true nature of ferromagnetism" includes ferrimagnetics, antiferromagnetics, and (Tamm [2]). "Heisenberg has shown that the Weiss' practically unlimited variety of magnetic structures. theory of molecular field can get a simple and The classical Weiss / Heisenberg theory of straightforward explanation in terms of quantum ferromagnetism, taught in the universities and presented mechanics" (Seitz [1]). in many textbooks (e. g., [1-4]), deals basically with the special case of a collinear (parallel and antiparallel) spin arrangement. 2. Inconsistence with the reality The logic behind the theory in question is as follows. General acceptance of the Heisenberg's theory of There is a spontaneously magnetized crystal (e. g., of ferromagnetism remains unshakable to the present Fe or Ni) due to a parallel alignment of the elementary days. Judging from the textbooks on physics, one may magnetic dipoles. It remains stable up to its critical conclude that it is rather successful [6]. In these books (Curie) temperature point when the thermal agitation and other concise presentations every effort was made suddenly destroys that alignment. It needed to be to portray it as basically valid and a great achievement, explained how the ferromagnetic state can be while contradictions, blank areas, and vast thermodynamically stable up to the really observed disagreements with experiment are either omitted as temperatures so high as 1042 K in Fe. It seemed "details" or only vaguely mentioned. As a result, a new unavoidable to suggest that the force holding the student gets wrong impression about the real status of dipoles in parallel is the dipole interaction. Setting aside the theory. In general, the theory remains basically the probability that such interaction in Fe would rather unchallenged. But the more detailed the source is, the cause mutual dipole repulsion than attraction, how more drawbacks are exposed. There are experts who strong must this interaction be? It followed from the pointed out to its essential shortcomings. Weiss' theory that it had to be about 104 times stronger than the magnetic dipole interaction alone. The Bleaney & Bleaney [7]: "There is no doubt that conclusion seemed undeniable: besides the magnetic ferromagnetism is due to the exchange forces first dipole interaction, there is also interaction due to a discovered by Heisenberg, but the quantitative theory of much more powerful "molecular field" of unknown ferromagnetism contains many difficulties". physical nature. "We have a broad understanding of the outlines of ferromagnetic theory, but not of the details. The Heisenberg [5] accepted the Weiss' theory and exchange interaction between two electrons cannot be developed its quantum-mechanical interpretation. His calculated a priori ... We cannot even be certain of its theory maintains that overlapping of the electron shells sign." results in extremely strong electron exchange interaction responsible for collinear orientation of the Belov [8]: "...Many important questions connected magnetic moments. The main parameter in the with the behavior of materials in the region [of quantum-mechanical formula was exchange integral. ferromagnetic transition] remain unsettled or in dispute 1 to the present time. These include ...the actual materials". Tamm [2] noted that "it is the usual temperature behavior of the spontaneous magnetization magnetic interaction of atoms [rather than exchange near the Curie point, the causes of the 'smearing out' of interaction] that is responsible for such, for example, the magnetic transition... the existence of 'residual' phenomena as magnetic anisotropy and spontaneous magnetization above the Curie magnetostriction". In this respect many other temperature, and the nature of the temperature phenomena could also be mentioned: domain structure, dependence of elastic, electric, thermal, and other magnetic hysteresis, magnetocaloric effect, Barkhausen properties near the Curie point. It even remains effect, first-order magnetic phase transitions, unsettled what we should take to be the Curie magnetization kinetics, and more. Remarkably, the temperature, and how to determine it". question why the exchange forces do not exhibit "The theory of Weiss and Heisenberg cannot be themselves in those phenomena has never been raised. applied to the quantitative description of phenomena in the neighborhood of the Curie point... Even for such a There are also other phenomena and facts the 'simple' ferromagnetic substance as nickel it is not exchange interaction offers no reasonable explanation, possible to 'squeeze' the experimental results into the if at all. Among them: Weiss-Heisenberg theory". (A) The value of the exchange integral for Ni was found lower by about two orders of magnitude needed Bozorth [3]: "The data for iron and for nickel [at low to account for its Curie temperature. temperatures] show that the Weiss theory in either its (B) A collinear order of the atomic magnetic original or modified form is quite inadequate". moments in ferro-, antiferro- and ferrimagnetics "The Curie point is not always defined in accordance represents only particular cases, while there is, in fact, a with the Weiss theory but in other more empirical great variety of non-collinear magnetic structures as ways..." well. The exchange field was unable to provide a parallel alignment in those innumerable magnetic Crangle [9]: "It seems difficult to be convinced that structures. direct exchange between localized electrons can be the (C) There are materials where magnetic moments are main origin of the ferromagnetism in metals of the iron too far apart to make any direct exchange possible. The group". appropriate electron shells in the ferromagnetic rare-earth metals do not overlap. The „exchange field‟ Kittel [6]: "The Neel temperatures TN often vary theory was expanded to those cases anyway, to become considerably between samples, and in some cases there "superexchange". is large thermal hysteresis". (D) The actual speed of magnetization is well below of the theoretically expected. Feynman [10]: "Even the quantum theory deviates (E) The exchange forces have the wrong sign. from the observed behavior at both high and low temperatures". "The exact behavior near the Curie point has never 3. The sign problem been thoroughly figured out". "The theory of the sudden transition at the Curie point Even the initial verifications of the Heisenberg's still needs to be completed." theory had to prevent its acceptance. The verifications "We still have the question: why is a piece of have produced a wrong sign of the exchange forces. lodestone in the ground magnetized?" Feynman [10] was skeptical at least, as seen from these "To the theoretical physicists, ferromagnetism statements: "When it was clear that quantum mechanics presents a number of very interesting, unsolved, and could supply a tremendous spin-oriented force - even if, beautiful challenges. One challenge is to understand apparently, of the wrong sign - it was suggested that why it exists at all". ferromagnetism might have its origin in this same force", and "The most recent calculations of the energy The last statement is especially indicative, between the two electron spins in iron still give the considering that it was the primary purpose of the wrong sign", and even "This physics of ours is a lot of Weiss' and Heisenberg's theories to explain why fakery." The sign problem was later carefully examined ferromagnetism exists at all. Moreover, it turned out in a special review [11] and found fundamentally that the exchange forces, as powerful as they assumed unavoidable in the Heisenberg model. It was suggested to be, do not physically participate in the actual that the "neglect of the sign may hide important ferromagnetic phenomena. Thus, Seitz [1] maintained physics." that the "Heisenberg's model…is too simple to be used for quantitative investigation of the real ferromagnetic 2 4. Ferromagnetic phase transitions: from The number of recognized first-order ferromagnetic cooperative to magnetostructural phase transitions continued growing. They were found to be of the fist order even in the basic ferromagnetics - In order to present a coherent picture of Fe, Ni and Co [12-14]. This process was accompanied ferromagnetism, which is the purpose of this article, the by the increasing
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