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In this sample series, Fe was continuously substituted by Cr over the full composition range. The lattice parameter in the [001] growth direction steadily increases from L1(0) -FePt toward L1(0) -CrPt, confirming the incorporation of Cr in the lattice occupying Fe sites. With the observed high degree of chemical ordering and (001) orientation, strong perpendicular magnetic anisotropy is associated, which persists up to a Cr content of x = 20 at % Similarly, the coercive field in the easy-axis direction is strongly reduced, which is, however, further attributed to a strong alteration of the film morphology with Cr substitution. The latter changes from a well-separated island microstructure to a more continuous film morphology. In the dilute alloy with low Cr content, isolated Cr magnetic moments couple antiferromagnetically to the ferromagnetic Fe matrix. In this case, all Cr moments are aligned parallel, thus forming a ferrimagnetic FeCrPt system. With increasing Cr concentration, nearest-neighbor Cr-Cr pairs start to appear, thereby increasing magnetic frustration and disorder, which lead to canting of neighboring magnetic moments, as revealed by atomistic spin-model simulations with model parameters based on first principles. At higher Cr concentrations, a frustrated ferrimagnetic order is established. With Cr substitution of up to 20 at. %, no pronounced change in Curie temperature, which is in the range of 700 K, was noticed. But with further addition the Curie temperature drops down substantially even down to room temperature at 47 at. % Cr. Furthermore, x-ray magnetic circular dichroism studies on dilute alloys containing up to 20 at. % of Cr revealed similar spin moments for Fe and Cr in the range between 2.1-2.5 mu B but rather large orbital moments of up to 0.50 +/- 0.10 mu B for Cr. 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