Spin-orbital fluctuations in the paramagnetic Mott insulator (V$_{1-x}$Cr$_x$)$_2$O$_3$*

The phase diagram of rhombohedral V$_2$O$_3$ features several distinct strongly correlated phases as a function of doping, pressure and temperature. When doped with chromium for 180 K$<$T$<$450 K the material undergoes a Mott metal to insulator transition. Using the modern time-of-flight neutron scattering spectrometer SEQUOIA at the SNS, we have probed the excitation spectrum of (V$_{0.96}$Cr$_{0.04}$)$_2$O$_3$ in the PI phase and in the monoclinic commensurate anti-ferromagnet for T$<$180 K. An effective exchange Hamiltonian that accounts for the low T spin waves indicates alternating FM and AFM interactions for nearest neighbor spin pairs that are equivalent in the PI. We argue that the corresponding spin-orbital fluctuations are responsible for the extremely short-range dynamic spin correlations that we document in the PI phase.