  We have utilized the resonant x-ray diffraction technique at the Mn L-edge in
order to directly compare magnetic and orbital correlations in the Mn
sub-lattice of Pr0.6Ca0.4MnO3. The resonant line shape is measured below T_OO ~
240 K at the orbital ordering wave vector (0,1/2,0), and below T_N ~ 175 K at
the antiferromagnetic wave vector (1/2,0,0). Comparing the width of the
super-lattice peaks at the two wavevectors, we find that the correlation length
of the magnetism exceeds that of the orbital order by nearly a factor of two.
Furthermore, we observe a large (~ 3 eV) shift in spectral weight between the
magnetic and orbital line shapes, which cannot be explained within the classic
Goodenough picture of a charge-ordered ground state. To explain the large
shift, we calculate the resonant line shapes for orbital and magnetic
diffraction based on a relaxed charge-ordered model.
