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Abstract Spatial patterns of stellar elemental abundances encode rich information about a galaxy’s formation history. We analyze the radial, vertical, and azimuthal variations of metals in stars, both today and at formation, in the FIRE-2 cosmological simulations of Milky Way (MW)-mass galaxies, and we compare them with the MW. The radial gradient today is steeper (more negative) for younger stars, which agrees with the MW, although radial gradients are shallower in FIRE-2. Importantly, this age dependence was present already at birth: radial gradients today are only modestly (≲0.01 dex kpc⁻¹) shallower than at birth. Disk vertical settling gives rise to negative vertical gradients across all stars, but vertical gradients of mono-age stellar populations are weak. Similar to the MW, vertical gradients in FIRE-2 are shallower at larger radii, but they are overall shallower in FIRE-2. This vertical dependence was present already at birth: vertical gradients today are only modestly (≲0.1 dex kpc⁻¹) shallower than at birth. Azimuthal scatter is nearly constant with radius, and it is nearly constant with age ≲8 Gyr ago but increases for older stars. Azimuthal scatter is slightly larger (≲0.04 dex) today than at formation. Galaxies with larger azimuthal scatter have a stronger radial gradient, implying that azimuthal scatter today arises primarily from the radial redistribution of gas and stars. Overall, spatial variations of stellar metallicities show only modest differences between formation and today; spatial variations today primarily reflect the conditions of stars at birth, with spatial redistribution of stars after birth contributing secondarily. 

Abstract Using the FIRE-2 cosmological zoom-in simulations, we investigate the temporal evolution of gas-phase metallicity radial gradients of Milky Way–mass progenitors in the redshift range of 0.4 <z< 3. We pay special attention to the occurrence of positive (i.e., inverted) metallicity gradients—where metallicity increases with galactocentric radius. This trend, contrary to the more commonly observed negative radial gradients, has been frequently seen in recent spatially resolved grism observations. The rate of occurrence of positive gradients in FIRE-2 is about ∼7% for 0.4 <z< 3 and ∼13% at higher redshifts (1.5 <z< 3), broadly consistent with observations. Moreover, we investigate the correlations among galaxy metallicity gradient, stellar mass, star formation rate (SFR), and degree of rotational support. Metallicity gradients show a strong correlation with both sSFR and the rotational-to-dispersion velocity ratio (v_c/σ), implying that starbursts and kinematic morphology of galaxies play significant roles in shaping these gradients. The FIRE-2 simulations indicate that galaxies with high sSFR ( $\log \left(\mathrm{sSFR}\right[{\mathrm{yr}}^{-1}\left]\right)\gtrsim -9.2$) and weak rotational support (v_c/σ≲ 1) are more likely—by ∼15%—to develop positive metallicity gradients. This trend is attributed to galaxy-scale gas flows driven by stellar feedback, which effectively redistribute metals within the interstellar medium. Our results support the important role of stellar feedback in governing the chemo-structural evolution and disk formation of Milky Way–mass galaxies at the cosmic noon epoch.