Magnetic correlations and quantum criticality in the insulating antiferromagnetic, insulating spin liquid, renormalized Fermi liquid, and metallic antiferromagnetic phases of the Mott system ${\mathrm{V}}_2{\mathrm{O}}_3$

Magnetic correlations in all four phases of pure and doped vanadium sesquioxide $\left({\mathrm{V}}_2{\mathrm{O}}_3\right)$ have been examined by magnetic thermal-neutron scattering. Specifically, we have studied the antiferromagnetic and paramagnetic phases of metallic ${\mathrm{V}}_{2-y}{\mathrm{O}}_3,$ the antiferromagnetic insulating and paramagnetic metallic phases of stoichiometric ${\mathrm{V}}_2{\mathrm{O}}_3,$ and the antiferromagnetic and paramagnetic phases of insulating ${\mathrm{V}}_{1.944}{\mathrm{Cr}}_{0.056}{\mathrm{O}}_3.$ 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 ${\mathrm{V}}_2{\mathrm{O}}_3$ 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 $ħ\omega <k_{B}T$ 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 ${\mathrm{V}}_2{\mathrm{O}}_3.$