Using idealised N-body simulations of a Milky Way-sized disc galaxy, we qualitatively study how the metallicity distributions of the thin disc star particles are modified by the formation of the bar and spiral arm structures. The thin disc in our numerical experiments initially has a tight negative radial metallicity gradient and a constant vertical scale-height. We show that the radial mixing of stars drives a positive vertical metallicity gradient in the thin disc. On the other hand, if the initial thin disc is flared, with vertical scale-height increasing with galactocentric radius, the metal poor stars originally in the outer disc become dominant in regions above the disc plane at every radii. This process can drive a negative vertical metallicity gradient, which is consistent with the current observed trend. This model mimics a scenario where the star-forming thin disc was flared in the outer region at earlier epochs. Our numerical experiment with an initial flared disc predicts that the negative vertical metallicity gradient of the mono-age relatively young thin disc population should be steeper in the inner disc, and the radial metallicity gradient of the mono-age population should be shallower at greater heights above the disc plane. We also predict that the metallicity distribution function of mono-age young thin disc populations above the disc plane would be more positively skewed in the inner disc compared to the outer disc.
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