  Understanding the motion of particles on an air-liquid interface can impact a
wide range of scientific fields and applications. Diamagnetic particles
floating on an air-paramagnetic-liquid interface are previously known to have a
repulsive motion from a magnet. Here, we show a motion mechanism where the
diamagnetic particles floating on the air-paramagnetic-liquid interface are
attracted and eventually trapped at an off-center distance from the magnet. The
behavior of magnetic particles has been also studied and the motion mechanisms
are theorized in a unified framework, revealing that the motion of particles on
an air-paramagnetic-liquid interface is governed not only by magnetic energy,
but as an interplay of the curvature of the interface deformation created by
the nonuniform magnetic field, the gravitational potential, and the magnetic
energy from the particle and the liquid. The attractive motion mechanism has
been applied in directed self-assembly and robotic particle guiding.
