  Density waves are inherent to the phase diagrams of materials that exhibit
unusual, and sometimes extraordinarily useful properties, such as
superconductivity and colossal magnetoresistance. While the pure charge density
waves (CDW) are well described by an itinerant approach, where electrons are
treated as waves propagating through the crystal, the charge-orbital ordering
(COO) is usually explained by a local approach, where the electrons are treated
as localized on the atomic sites. Here we show that in the half-doped manganite
La0.5Sr1.5MnO4 (LSMO) the electronic susceptibility, calculated from the
angle-resolved photoemission spectra (ARPES), exhibits a prominent
nesting-driven peak at one quarter of the Brillouin zone diagonal, that is
equal to the reciprocal lattice vector of the charge-orbital pattern. Our
results demonstrate that the Fermi surface geometry determines the propensity
of the system to form a COO state which, in turn, implies the applicability of
the itinerant approach also to the COO.
