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.
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