  We numerically examine the dynamics of a skyrmion interacting with a
two-dimensional periodic substrate under dc and biharmonic ac drives. We show
that the Magnus force of the skyrmion produces circular orbits that can
resonate with the ac drive and the periodicity of the substrate to create
quantized motion both parallel and perpendicular to the dc drive. The skyrmion
Hall angle exhibits a series of increasing and/or decreasing steps along with
strongly fluctuating regimes. In the phase locked regimes, the skyrmion Hall
angle is constant and the skyrmion motion consists of periodic orbits
encircling an integer number of obstacles per every or every other ac drive
cycle. We also observe phases in which the skyrmion moves at $90^\circ$ with
respect to the driving direction even in the presence of damping, a phenomenon
called absolute transverse mobility that can exhibit reentrance as a function
of dc drive. When the biharmonic ac drives have different amplitudes, in the
two directions we find regimes in which the skyrmion Hall angle shows a sign
reversal from positive to negative, as well as a reentrant pinning effect in
which the skyrmion is mobile at low drives but becomes pinned at higher drives.
These behaviors arise due to the combination of the Magnus force with the
periodic motion of the skyrmions, which produce Shapiro steps, directional
locking, and ratchet effects.
