Theory of mott transition : Applications to transition metal oxides

M. Cyrot

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.

Mots clés: band structure; transition metal compounds

Domaines: Articles anciens

M. Cyrot. Theory of mott transition : Applications to transition metal oxides. Journal de Physique, 1972, 33 (1), pp.125-134. ⟨10.1051/jphys:01972003301012500⟩. ⟨jpa-00207204⟩