Magnetic correlations and quantum criticality in the insulating antiferromagnetic, insulating spin liquid, renormalized Fermi liquid, and metallic antiferromagnetic phases of the Mott system V₂O₃

Magnetic correlations in all four phases of pure and doped vanadium sesquioxide (V₂O₃) have been examined by magnetic thermal-neutron scattering. Specifically, we have studied the antiferromagnetic and paramagnetic phases of metallic V_2-yO₃, the antiferromagnetic insulating and paramagnetic metallic phases of stoichiometric V₂O₃, and the antiferromagnetic and paramagnetic phases of insulating V_1.944Cr_0.056O₃. While the antiferromagnetic insulator can be accounted for by a localized Heisenberg spin model, the long-range order in the antiferromagnetic metal is an incommensurate spin-density wave, resulting from a Fermi surface nesting instability. Spin dynamics in the strongly correlated metal are dominated by spin fluctuations with a “single lobe” spectrum in the Stoner electron-hole continuum. Furthermore, our results in metallic V₂O₃ represent an unprecedentedly complete characterization of the spin fluctuations near a metallic quantum critical point, and provide quantitative support for the self-consistent renormalization theory for itinerant antiferromagnets in the small moment limit. Dynamic magnetic correlations for ħω<k_BT in the paramagnetic insulator carry substantial magnetic spectral weight. However, they are extremely short-ranged, extending only to the nearest neighbors. The phase transition to the antiferromagnetic insulator, from the paramagnetic metal and the paramagnetic insulator, introduces a sudden switching of magnetic correlations to a different spatial periodicity which indicates a sudden change in the underlying spin Hamiltonian. To describe this phase transition and also the unusual short-range order in the paramagnetic state, it seems necessary to take into account the orbital degrees of freedom associated with the degenerate d orbitals at the Fermi level in V₂O₃.