  We investigate the collective motion of magnetic rotors suspended in a
viscous fluid under an uniform rotating magnetic field. The rotors are
positioned on a square lattice, and low Reynolds hydrodynamics is assumed. For
a $3 \times 3$ array of magnets, we observe three characteristic dynamical
patterns as the external field strength is varied: a synchronized pattern, an
oscillating pattern, and a chessboard pattern. The relative stability of these
depends on the competition between the energy due to the external magnetic
field and the energy of the magnetic dipole-dipole interactions among the
rotors. We argue that the chessboard pattern can be understood as an
alternation in the stability of two degenerate states, characterized by striped
and spin-ice configurations, as the applied magnetic field rotates. For larger
arrays, we observe propagation of slip waves that are similar to metachronal
waves. The rotor arrays have potential as microfluidic devices that can mix
fluids and create vortices of different sizes.
