Mott-Hubbard transitions

A concept related to the localization vs. itineracy problem of electron states, and which has been very useful in providing a frame for the understanding of the actinide metallic bond, is the Mott-Hubbard transition. By this name one calls the transition from an itinerant, electrically conducting, metallic state to a localized, insulator s state in solids, under the effect of external, thermodynamic variables, such as temperature or pressure, the effect of which is to change the interatomic distances in the lattice. 

This transition has been emphasized by Mott for the case of localized impurity states in a semiconductor, forming a metallic band at some concentration of impurities (i.e. at some average distance between the impurities). It is referred to very often as the Mott (or Mott-Hubbard) transition. 

When the cores are approached, the sub-bands split, acquiring a bandwidth, and decreasing the gap between them (Fig. 14 a). At a definite inter-core distance, the subbands cross and merge into the non-polarized narrow band. At this critical distance a, the narrow band has a metallic behaviour. At the system transits from insulator to metallic (Mott-Hubbard transition). Since some electrons may acquire the energies of the higher sub-band, in the solid there will be excessively filled cores containing two antiparallel spins and excessively depleted cores without any spins (polar states). 

The Case of Americium the Mott-Hubbard Transition and the Effects of 102... 

It is perhaps useful to distinguish the two ways in which the concept of a Mott-Hubbard transition is introduced in the discussion of actinide metals. 

Evidence from Photoemission Spectroscopy for the Mott-Hubbard Transition. . . 230... 

Fig. 7 a-c. Schematic representation of final state screening models for lanthanide and d-metal core level responses (a) and c)) (c.b. means conduction band). In part b), the possible situations for light and heavy actinides (before and after the Mott-Hubbard transition) are also represented... 

Figure 17 is a clear illustration of the Mott-Hubbard transition in the actinide series the 5f emission occurs, for a-Pu, at Ep, indicating a high 5f-density of states pinned at the Fermi-level, whereas the 5 f emission occurs at lower energy for americium metal. In this case, therefore, a theoretical concept deduced indirectly from the physical properties of the two metals, finds direct (one might even say photographic ) confirmation in the photoemission spectra. 

These effects have not been observed in band-crossing transitions, but have in the so-called Mott-Hubbard transitions described in the next section. 

A fundamental question is whether the transition between localized and itinerant electronic behavior is continuous or discontinuous. Mott (1949) was the first to point out that an on-site electrostatic energy Ua > Wr, is needed to account for the fact that NiO is an antiferromagnetic insulator rather than a metal. Hubbard (1963) subsequently introduced U formally as a parameter into the Hamiltonian for band electrons his model predicted a smooth transition from a Pauli paramagnetic metal to an antiferromagnetic insulator as the ratio W/U decreased to below a critical value of order unity. This metal-insulator transition is known as the Mott-Hubbard transition. 

It is, however, not the JTD that turn these systems into insulators but strong correlations. The nature of metal-insulator transitions in these systems is one of the most debated points at present. Experimentally, a metal-insulator transition can be induced by relatively modest pressure in Rb4C60 and in the compound with the smallest lattice parameters (Na2C60) a residual metallic character can be detected. These behaviors support the idea that these compounds lie on the border of a Mott-Hubbard transition. We still observe typical molecular excitations of JT-distorted C60 on the metallic side of the transition, suggesting a possible coexistence. 

Note that what is today known as a Mott-Hubbard transition pertains to a half-filled s band. The situation for Hg clusters is very different. The overlap of the full s band with the empty p band drives the transition. The low-lying d electrons make the problem no easier. 

The effects of electron-phonon interactions alone were described in Chapter 4. We showed that these interactions lead to a dimerized, semiconducting ground state and to solitonic structures in the excited states. On the other hand, the effects of electron-electron interactions in a polymer with a fixed geometry were described in Chapters 5 and 6. There it was shown that the electronic interactions cause a metal-insulator (or Mott-Hubbard) transition in undimerized chains. Electron-electron interactions also cause Mott-Wannier excitons in the weak-coupling limit of dimerized chains, and to both Mott-Hubbard excitons and spin density wave excitations in the strong coupling limit. 

The ability to adjust to a t < 1 allows for extensive cation substitutions on both the A and M sites the structure is also tolerant of large concentrations of both oxygen and cation vacancies. The perovskites considered in this volume are stoichiometric with MO3 arrays containing a single transition-metal atom M. Emphasis is given to the peculiar physical properties that occur at the transition from localized to itinerant electronic behavior and from Curie-Weiss to Pauli paramagnetism at a Mott-Hubbard transition on the MO3 array. The transition from localized to itinerant electronic behavior can be approached from either the itinerant-electron side or the localized-electron side in single-valent MO3 arrays by isovalent substitutions on the A sites that vary the tolerance factor t. It can also be crossed in mixed-valent... 

MO3 arrays by aliovalent substitutions on the A sites. In all cases, the crossover is marked by lattice instabilities. The Mott-Hubbard transition occurs on the itinerant-electron side, and this transition is also marked by lattice instabilities. 

Finally, a a band on the itinerant-electron side of the Mott-Hubbard transition in the presence of localized t spins S = 3/2 signals covalent-mixing parameters X and therefore a cubic-field splitting (Eq. 5 of Goodenough, this volume) that approaches Aex- To test this deduction, hydrostatic pressure was used to induce a transition from the high-spin to the low-spin states in CaFeOs the transition was observed to occur at a pressure Pc 30 GPa [50]. 

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