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Density waves are inherent to the phase diagrams of materials that exhibitunusual, and sometimes extraordinarily useful properties, such assuperconductivity and colossal magnetoresistance. While the pure charge densitywaves (CDW) are well described by an itinerant approach, where electrons aretreated as waves propagating through the crystal, the charge-orbital ordering(COO) is usually explained by a local approach, where the electrons are treatedas localized on the atomic sites. Here we show that in the half-doped manganiteLa0.5Sr1.5MnO4 (LSMO) the electronic susceptibility, calculated from theangle-resolved photoemission spectra (ARPES), exhibits a prominentnesting-driven peak at one quarter of the Brillouin zone diagonal, that isequal to the reciprocal lattice vector of the charge-orbital pattern. Ourresults demonstrate that the Fermi surface geometry determines the propensityof the system to form a COO state which, in turn, implies the applicability ofthe itinerant approach also to the COO.

Bridging charge-orbital ordering and Fermi surface instabilities in half-doped single-layered manganite La_0.5Sr_1.5MnO_4