  We found that the conventional model of orbital ordering of 3x^2-r^2/3y^2-r^2
type in the eg states of La_0.5Sr_1.5MnO_4 is incompatible with measurements of
linear dichroism in the Mn 2p-edge x-ray absorption, whereas these eg states
exhibit predominantly cross-type orbital ordering of x^2-z^2/y^2-z^2. LDA+U
band-structure calculations reveal that such a cross-type orbital ordering
results from a combined effect of antiferromagnetic structure, Jahn-Teller
distortion, and on-site Coulomb interactions.
