Itinerant Magnetism The Transition Metals

Like in molecular quantum chemistry, the localized-delocalized antagonism is omnipresent in the theoretical literature on itinerant magnetism. On the one hand, the Hubbard model [292] and related theories for strongly correlated systems have been employed to study rare-earth and also transition metals. Since the latter do not have flat bands, extensions to the Hubbard theory are required [293-295] also, to make the model Hamiltonians (almost) exactly solvable, simplifications are introduced. On the other hand, density-functional theory is able to extract Stoner s parameters [296,297] for a self-consistent description of itinerant magnetism [298]. As has been illustrated before, the theoretical limits of the LDA became apparent from Fe phase stability problems (see Section 2.12.1) and were solved by using gradient corrections. The present status of DFT in the treatment of cooperative magnetism has also been reviewed [299]. 

In general, metallic ferro- and antiferromagnetism is a rare phenomenon because, among the transition metals, only Fe, Co, and Ni are ferromagnetic. 

The 4/ orbitals are only slightly perturbed by the neighboring atoms and give rise to very narrow bands. Thus, the bands are filled with electrons in a marmer analogous to Hund s rules for the fillings of atomic energy levels. This results in unpaired spins and magnetic moments. 

The solid and dashed lines correspond to the a and spins, respectively. 

The spontaneous spin-polarization also results in a rearrangement of the electron density in a-Fe, and the different energetic shifts of the a and jS spin 

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It would not be appropriate here to discuss the many points at issue in the intense international debate which has been going on for some time in this area. The comments of the discussion panel at the international conference on magnetism in Kyoto, ICM 82, provide a convenient summary (Kanamori 1983) and a book dedicated to itinerant magnetism is now available (CapeUmann 1987). We shall therefore give only a brief outline of the expectations of those theories which are currently used by the majority of experimentalists in attempting to explain the observed ferromagnetic behaviour of the transition metal intermetallic compounds. 

A more complex magnetic behaviour is expected for RI compounds in which the second component is a 3d transition metal such as Mn, Fe, or Co. The magnetic behaviour of the transition metal component is now based on the magnetic polarization of the electronic d-bands. Consequently, in this section we summarize the theory of itinerant or band magnetism and its application to transport properties. We begin with the Stoner-Wohlfarth model and include a summary of recent works. 

There are no direct Fermi surface studies of the transition metal Laves phases -which is unfortunate in light of the part they have played, and continue to play, in our understanding of f electron behavior. The Np Laves phases have played a special role because they appear to span the critical separation between localized and itinerant behavior (Aldred et al. 1974). The U and Ce transition metal Laves phases occur on the itinerant side of the Hill (1970) plots, but some do approach, and just cross, the critical separation. The transition to magnetic behavior can be very closely approached by considering NpRu Osz-x alloys (Aldred et al. 1975). Because their properties are consistent with the Hill correlation, it would initially appear that one has a nice simple picture based on a direct f-f overlap analysis. Certainly, a Hill plot analysis was part of the motivation for the extensive studies of the Np materials. However, it appears that these materials heavily involve interaction with the ligands. 

In the Introduction the problem of construction of a theoretical model of the metal surface was briefly discussed. If a model that would permit the theoretical description of the chemisorption complex is to be constructed, one must decide which type of the theoretical description of the metal should be used. Two basic approaches exist in the theory of transition metals (48). The first one is based on the assumption that the d-elec-trons are localized either on atoms or in bonds (which is particularly attractive for the discussion of the surface problems). The other is the itinerant approach, based on the collective model of metals (which was particularly successful in explaining the bulk properties of metals). The choice between these two is not easy. Even in contemporary solid state literature the possibility of d-electron localization is still being discussed (49-51). Examples can be found in the literature that discuss the following problems high cohesion energy of transition metals (52), their crystallographic structure (53), magnetic moments of the constituent atoms in alloys (54), optical and photoemission properties (48, 49), and plasma oscillation losses (55). 

Transitions from a localized to an itinerant state of an unfilled shell are not a special property of actinides they can, for instance, be induced by pressure as they rue in Ce and in other lanthanides or heavy actinides under pressure (see Chap. C). The uniqueness for the actinide metals series lies in the fact that the transition occurs naturally almost as a pure consequence of the increase of the magnetic moment due to unpaired spins, which is maximum at the half-filled shell. The concept has resulted in re-writing the Periodic Chart in such a way as to make the onset of an atomic magnetic moment the ordering rule (see Fig. 1 of Chap. E). Whether the spin-polarisation model is the only way to explain the transition remains an open question. In a very recent article by Harrison an Ander-... 

Another example of this kind of transition is shown in table 11.1, taken from the work of Smith and Kmetko [601]. It is a quasiperiodic table of all the transition elements and lanthanides in the periodic table, arranged in order of mean localised radius in the vertical direction, and adjusted horizontally so that filled and empty d and / subshells coincide. What Smith and Kmetko discovered is that a broad diagonal sweep across this table separates metals with localised electron properties (magnets) from those with itinerant electron properties (conductors). This boundary (shown as a shaded curve in the figure) is the locus of the Mott transition. Metals lying along this curve are sensitive to pressure effects (Ce has an isomorphic phase transition from the a to the 7 phase at about 1 kbar, U becomes... 

Few materials show up the limitations of the two extreme viewpoints of magnetic moment formation in transition metal systems ( localized or itinerant ) more than do their intermetallic compounds. In some compounds, e.g., the (non-integral) magnetic moment may vary from one type of site to another and the moment associated with a particular transition metal atom is often different in its different compounds. The interest in the wide variety of properties exhibited by intermetallic compounds stems as much from the opportunity they offer for the understanding of magnetism in metallic systems at a fundamental level as from the possibility of producing materials of technological importance. 

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