Mott-Hubbard compounds

First we consider the origin of band gaps and characters of the valence and conduction electron states in 3d transition-metal compounds [104]. Band structure calculations using effective one-particle potentials predict often either metallic behavior or gaps which are much too small. This is due to the fact that the electron-electron interactions are underestimated. In the Mott-Hubbard theory excited states which are essentially MMCT states are taken into account dfd -y The subscripts i and] label the transition-metal sites. These... 

A somewhat different interpretation has been given by Johansson who applied the Mott-Hubbard theory of localized versus itinerant electron behaviour also to compounds. This interpretation differs from the above one mainly in that it assumes complete localization for magnetic compounds, and that at a certain critical inter-atomic distance we have to switch our description from a metallic state to an insulating one for the 5 f electrons (see Eq. (42)). In Eq. (42), an is substituted by a convenient measure of the spatial extension of the 5 f orbital, the expectation values (analogous to (of Fig. 10) and Xmoh is calculated from the R j radii of actinide metals (Fig. 3). The result is given in Table 6. 

Figure 6.52 Schematic electron addition and removal spectra representing the electronic structure of transition-metal compounds for different regimes of the parameter values (a) charge-transfer insulator with U > A (b) Mott-Hubbard insulator A> U (From Rao et al, 1992).

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. 

Figure 6 (a) Resistivity [after Ref. 47] and (b) EPR spin susceptibility of (TMTTF)2X compounds [after Ref. 46] undergoing a one-dimensional Mott-Hubbard localization below 7p (c) electron spin susceptibility of (TMTSF)2PF6 [after Ref. 38] (d) plot of the l3C spin lattice relaxation rate versus 7xf(7) for three compounds in the TM2X series. The temperature below which the charges are localized is indicated by 7p. No localization is observed for Se compounds (dashed line) above the SDW or SC ordering. (From Ref. 41b.)... 

Correlation effects are likely to be quite important in the compound 0(ET)2I3 since they also are narrowband conductors. However, the reason why these strong interactions do not materialize in a Mott-Hubbard insulator could be attributed to the absence of one-dimensional character for this system, which precludes establishment of a Mott-Hubbard localized state. 

A systematic semiempirical study of the core-level photoemission spectra of a wide range of 3d transition-metal compounds has been carried out (Bocquet et al., 1992,1996). The values for U and A obtained from a simplified Cl cluster model analysis are demonstrated in Figure 7.2. As can be inferred from the graphs, the heavier 3d transition metal compounds shown in the figure are expected to be charge-transfer insulators, whereas the compounds of the fighter metals are generally expected to be of the Mott-Hubbard type. 

It has been seen in the previous section that the ratio of the onsite electron-electron Coulomb repulsion and the one-electron bandwidth is a critical parameter. The Mott-Hubbard insulating state is observed when U > W, that is, with narrow-band systems like transition metal compounds. Disorder is another condition that localizes charge carriers. In crystalline solids, there are several possible types of disorder. One kind arises from the random placement of impurity atoms in lattice sites or interstitial sites. The term Anderson localization is applied to systems in which the charge carriers are localized by this type of disorder. Anderson localization is important in a wide range of materials, from phosphorus-doped silicon to the perovskite oxide strontium-doped lanthanum vanadate, Lai cSr t V03. 

The ARPES spectra signal for the sulfur compound (TMTTF)2PF,5, displays a rigid shift of the leading edge near the Fermi energy to about 100 meV. This value is consistent with the charge gap of 900 K obtained from transport experiments DC or 800 cm from optical conductivity of (TMTTF)2PF6, Within a onedimensional frame of interpretation, this gap has been ascribed to a Mott-Hubbard localization gap [99],... 

Despite the success of this simple picture, not all B-site cations with partially filled d orbitals give rise to metallic perovskites, and many are antiferromagnetic (AFM) insulators. This dilemma was resolved in the middle of the twentieth century with respect to transition metal oxides by assuming that electron correlation, taking the form of Coulomb repulsion between electrons, split the partly filled 3d band into a filled and an empty sub-band, with a band gap between the two. This gap is the Hubbard or Mott-Hubbard gap, denoted by U, and the compounds that display this type of behaviour are called Mott insulators. 

It was realized quite early that the parent, undoped, compounds should be viewed as Mott insulators. More recent studies of the doping dependence have revealed the generic features between cuprates and other classes of Mott insulators. The principal trends in the evolution of the in-plane electronic conductivity with doping are in accord with the results of the calculations performed for Mott-Hubbard systems as will be described in sect. 3. 

The AM4Q8 (A = Ga, Ge M = V, Nb, Ta Q = S, Se) compounds exhibit a lacunar spinel structure [8] with tetrahedral transition metal clusters M4 (see Figure la). These compounds are Mott insulators exhibiting a very small Mott-Hubbard gap (0.2 0.1 eV) due to the presence of the M4 clusters [9]. A direct consequence of this low gap value is a high sensitivity to external perturbations such as doping or external pressure which can induce an insulator to metal transition in these compounds [10,11,12,13]. We have recently shown that these compounds are also very sensitive to electric pulses [3,4,14,15]. The AM4Q8 (A = Ga, Ge M = V, Nb, Ta Q = S, Se) Mott insulator compounds exhibit indeed an unprecedented type of resistive switching (RS) of interest for... 

A) simple radical-ion salts with low conductivity and semiconducting behavior ff(T) = oq exp —EJkT) with the activation energy 0.1 < "a < 0.4 eV. A complete charge transfer (p = 1) is evidenced from X-ray structural data and from infrared spectroscopy results these compounds are Mott—Hubbard insulators as already defined a few examples are KTCNQ and some 1 1 salts based on tetrachalcogenafiilvalenes [336]. 

---