  Aims. Using a suite of cosmological chemodynamical disc galaxy simulations,
we assess how (a) radial metallicity gradients evolve with scaleheight; (b) the
vertical metallicity gradients change through the thick disc; and (c) the
vertical gradient of the stellar rotation velocity varies through the disc. We
compare with the Milky Way to search for analogous trends. Methods. We analyse
five simulated spiral galaxies with masses comparable to the Milky Way. The
simulations span a range of star formation and energy feedback strengths and
prescriptions, particle- and grid-based hydrodynamical implementations, as well
as initial conditions/assembly history. Results. Consistently, we find that the
steeper, negative, radial metallicity gradients seen in the mid-plane flatten
with increasing height away from the plane. In simulations with stronger
(and/or more spatially-extended) feedback, the negative radial gradients
invert, becoming positive for heights in excess of 1 kpc. Such behaviour is
consistent with that inferred from recent observations. Our measurements of the
vertical metallicity gradients show no clear correlation with galactocentric
radius, and are in good agreement with those observed in the Milky Way's thick
disc (locally). Conclusions. Simulations employing stronger/more extended
feedback prescriptions possess radial and vertical metallicity and kinematic
gradients more in line with recent observations. The inverted, positive, radial
metallicity gradients seen in the simulated thick stellar discs originate from
a population of younger, more metal-rich, stars formed in-situ, superimposed
upon a background population of older migrators from the inner disc; the
contrast provided by the former increases radially, due to the inside-out
growth of the disc. A similar behaviour may be responsible for the same
flattening seen in the radial gradients with scaleheight in the Milky Way.
