The Milky Ways stellar disk exhibits a bimodality in the [Fe/H] vs. [$alpha$/Fe] plane, showing a distinct high-$alpha$ and low-$alpha$ sequence whose origin is still under debate. We examine the [Fe/H]-[$alpha$/Fe] abundance plane in cosmological hydrodynamical simulations of Milky Way like galaxies from the NIHAO-UHD project and show that the bimodal $alpha$-sequence is a generic consequence of a gas-rich merger at some time in the Galaxys evolution. The high-$alpha$ sequence evolves first in the early galaxies, extending to high metallicities, while it is the low-$alpha$ sequence that is formed after the gas-rich merger. The merger brings in fresh metal-poor gas diluting the interstellar mediums metallicity while keeping the [$alpha$/Fe] abundance almost unchanged. The kinematic, structural and spatial properties of the bimodal $alpha$-sequence in our simulations reproduces that of observations. In all simulations, the high-$alpha$ disk is old, radially concentrated towards the galaxys center and shows large scale heights. In contrast, the low-$alpha$ disk is younger, more radially extended and concentrated to the disk mid-plane. Our results show that the abundance plane is well described by these two populations that have been distributed radially across the disk by migration: at present-day in the solar neighbourhood, low-$alpha$ stars originate from both the inner and outer disk while most of the high-$alpha$ stars have migrated from the inner disk. We show that age dating the stars in the [Fe/H]-[$alpha$/Fe] plane can constrain the time of the low-$alpha$ sequence forming merger and conclude that $alpha$-bimodality is likely a not uncommon feature of disk galaxies.
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