Theory of mott transition : Applications to transition metal oxides

2014 We study the metal-insulator transition due to correlations between electrons using a Hubbard model. Neglecting fluctuations in charge, we only take into account fluctuations in spin density which build up magnetic moments on each site. A close analogy with binary alloys follows from this. At zero temperature, with increasing value of the ratio of the interaction between electrons U to the bandwidth W, we obtain successively a non magnetic metal, an antiferromagnetic one and an antiferromagnetic insulator. This is due, as in Slater’s idea, to the exchange part of the self consistent potential which cannot have the full periodicity of the lattice. As it is possible to find a solution with lower energy and with antiferromagnetism to Hubbard hamiltonian, one can construct a self consistent solution with random but non zero moments on each site. The alloy analog of the metal insulator transition is band splitting. For large values of the ratio U/W, the material remains insulating through the Néel temperature. For intermediate values, the line boundary between a Pauli metal and a paramagnetic insulator shows that the insulating phase is favoured at high temperature because of the entropy disorder. We draw a general schematic phase diagram for the Hubbard model and we discuss the relevance of the theory to transition metal oxides. The main qualitative features are consistent with our theory. LE JOURNAL DE PHYSIQUE TOME 33, JANVIER 1972, Classification Physics Abstracts : 17.26 Insulator metal transitions are a phenomenon which have been known for quite a while in a wide variety of systems : metal vapour liquid system (mercury) metal ammonia solutions, disordered systems (impurity bands), transition metal chalcogenides. In the last few years there has been considerable interest in transition metal oxides. These oxides form a very interesting class of materials [1]. Their electrical properties range from very good insulator to very good metal. Some of them have an intermediate behaviour and can exhibit a metal-insulator transition with temperature, pressure, or doping. Besides pratical interest due to possible applications to switches these oxides are of fundamental interest. This stems from the fact they prove to be a striking failure for the elementary Bloch-Wilson theory. It is well known that a metal whose band are either completely full or entirely empty must be an insulator. While it is possible on the basis of the Bloch-Wilson theory to account for metallic behaviour in systems with an even number of electrons per unit cell through band overlap, it is not possible to explain an insulating behaviour when the number of electrons per unit cell is odd. Among the insulating oxides are compounds which on these basis should be metallic. Mott [2] was the first to observe these facts on nickel oxide. For these materials he proposed to abandon Bloch model. The starting point would be a localized ground state wave function or Heitler London one which has the immediate advantage of explaining the insulating behaviour. The reason lies on the fact that if the band is very narrow you do not lose a lot of kinetic energy by localizing the electrons, so an insulating ground state is then favourable. However, as the atoms are brought together the cost in kinetic energy in confining electrons to the atomic sites Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01972003301012500