We present a comprehensive study of the chemical properties of the stellar haloes of Milky-Way mass galaxies, analysing the transition between the inner to the outer haloes. We find the transition radius between the relative dominance of the inner-halo and outer-halo stellar populations to be ~15-20 kpc for most of our haloes, similar to that inferred for the Milky Way from recent observations. While the number density of stars in the simulated inner-halo populations decreases rapidly with distance, the outer-halo populations contribute about 20-40 per cent in the fiducial solar neighborhood, in particular at the lowest metallicities. We have determined [Fe/H] profiles for our simulated haloes; they exhibit flat or mild gradients, in the range [-0.002, -0.01 ] dex/kpc. The metallicity distribution functions exhibit different features, reflecting the different assembly history of the individual stellar haloes. We find that stellar haloes formed with larger contributions from massive subgalactic systems have steeper metallicity gradients. Very metal-poor stars are mainly contributed to the halo systems by lower-mass satellites. There is a clear trend among the predicted metallicity distribution functions that a higher fraction of low-metallicity stars are found with increasing radius. These properties are consistent with the range of behaviours observed for stellar haloes of nearby galaxies.
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