We investigate the origin of the abundance ratios and scatter of the neutron-capture elements Sr, Ba, and Eu in the stellar halo of a Milky Way-mass galaxy formed in a hydrodynamical cosmological simulation, and compare them with those of α elements. For this, we implement a novel treatment for chemical enrichment of Type II supernovae that considers the effects of the rotation of massive stars on the chemical yields and differential enrichment according to the life-times of progenitor stars. We find that differential enrichment has a significant impact on the early enrichment of the interstellar medium which is translated into broader element ratio distributions, particularly in the case of the oldest, most metal-poor stars. We find that the [element/Fe] ratios of the α-elements O, Mg, and Si have systematically lower scatter compared to the neutron-capture elements ratios Sr, Ba, and Eu at [Fe/H] < -2, which is ~0.1-0.4 dex for the former and between ~0.5 and 1 dex for the latter. The different scatter levels found for the neutron-capture and α-elements is consistent with observations of old stars in the Milky Way. Our model also predicts a high scatter for the [Sr/Ba] ratio, which results from the treatment of the fast-rotating stars and the dependence of the chemical yields on the metallicity, mass, and rotational velocities. Such chemical patterns appear naturally if the different ejection times associated with stars of different mass are properly described, without the need to invoke for additional mixing mechanisms or a distinct treatment of the α- and neutron-capture elements.
