  We report the spectroscopic analysis of 20 halo ab-type RR Lyrae stars with
heliocentric distances between 15 and 165 kpc, conducted using
medium-resolution spectra from the Magellan Inamori Kyocera Echelle (MIKE)
spectrograph. We obtain the systemic line-of-sight velocities of our targets
with typical uncertainties of 5-10 km s$^{-1}$, and compute orbital parameters
for a subsample out to 50 kpc from the Galactic centre, including proper motion
data from Gaia DR3. The orientation of our stars' orbits, determined for an
isolated Milky Way and for a model perturbed by the Large Magellanic Cloud,
appears to suggest an accreted origin for at least half of the sample. In
addition, we derive atmospheric parameters and chemical abundance ratios for
seven stars beyond 20 kpc. The derived $\alpha$-abundances of five of these
stars follow a Milky Way halo-like trend, while the other two display an
underabundance of $\alpha$-elements for their [Fe/H], indicating an association
with accretion events. Furthermore, based on the [Sr/Ba] ratio, we can
speculate about the conditions for the formation of a potential chemically
peculiar carbon-enhanced metal-poor (CEMP) RR Lyrae star. By analysing the
stars' orbital parameters and abundance ratios, we find hints of association of
two of our stars with two massive satellites, namely the Large Magellanic Cloud
and Sagittarius. Overall, our results are in line with the suggestion that the
accretion of sub-haloes largely contributes to the outer halo stellar
populations.
