  We report exotic orbital phenomena of spinning test particles orbiting around
a Kerr black hole, i.e., some orbits of spinning particles are asymmetrical
about the equatorial plane. When a nonspinning test particle orbits around a
Kerr black hole in a strong field region, due to relativistic orbital
precessions, the pattern of trajectories is symmetrical about the equatorial
plane of the Kerr black hole. However, the patterns of the spinning particles'
orbit are no longer symmetrical about the equatorial plane for some orbital
configurations and large spins. We argue that these asymmetrical patterns come
from the spin-spin interactions between spinning particles and Kerr black
holes, because the directions of spin-spin forces can be arbitrary, and
distribute asymmetrically about the equatorial plane.
