Paramagnetic Spin Correlations in Colossal Magnetoresistive La$_{0.7}$Ca$_{0.3}$MnO$_{3}$

Inelastic neutron scattering measurements, taken on the ARCS time-of-flight spectrometer, reveal dynamic spin correlations throughout the Brillouin zone in the colossal magnetoresistive system La$_{0.7}$Ca$_{0.3}$MnO$_{3}$ at 265~K ($\approx$1.03~$T_{C}$). Well defined correlations are observed in constant-$E$ scans. The long-wavelength behavior can be attributed to spin diffusion, qualitatively consistent with dynamical scaling theory, with a correlation length of $\approx$10~{\AA}. Dynamic correlations are observed at energies up to at least 28~meV, suggesting persistent short range spin correlations in the paramagnetic phase. An additional and unexpected component of the scattering is observed at lower energies which takes the form of ridges of strong scattering running along ($H$~0~0) and equivalent directions.