The metal-rich halo component extended in z: a characterization with
  Gaia DR2 and APOGEE
  We report an analysis of the metal-rich tail ([Fe/H] $> -0.75$) of halo stars
located at distances from the Galactic plane $z$ up to $|z| \sim 10$ kpc,
observed by the Apache Point Observatory Galactic Evolution Experiment
(APOGEE). We examine the chemistry, kinematics, and dynamics of this metal-rich
halo sample using chemical abundances and radial velocities provided by the
fourteenth APOGEE data release (DR14) and proper motions from the second Gaia
data release (DR2). The analysis reveals three chemically different stellar
populations in the [Mg/Fe] vs. [Fe/H] space -- the two distinct halo
populations already reported in the literature, and a third group with
intermediate [Mg/Fe] $\sim$+0.1. We derive the $U$, $V$ and $W$ velocity
components with respect to the Local Standard of Rest, as well as orbits for
the three stellar groups, and find that they differ also in their kinematical
and dynamical properties. The high-[Mg/Fe] population exhibits a mean prograde
rotation, as well as orbits that are more bound and closer to the plane,
whereas the low-[Mg/Fe] population has $<V>$ closer to 0, and stars that move
in less-bound orbits reaching larger distances from the centre and the Galactic
plane. The intermediate-Mg stars exhibit different orbital characteristics,
moving with a strong prograde rotation and low excentricity, but in less-bound
orbits. This stellar population resembles the two stellar overdensities lying
about $|z| \sim 5$ kpc recently reported in the literature, for which a disc
origin has been claimed.
