  Designing and constructing model systems that embody the statistical
mechanics of frustration is now possible using nanotechnology. We have arranged
nanomagnets on a two-dimensional square lattice to form an artificial spin ice,
and studied its fractional excitations, emergent magnetic monopoles, and how
they respond to a driving field using X-ray magnetic microscopy. We observe a
regime in which the monopole drift velocity is linear in field above a critical
field for the onset of motion. The temperature dependence of the critical field
can be described by introducing an interaction term into the Bean-Livingston
model of field-assisted barrier hopping. By analogy with electrical charge
drift motion, we define and measure a monopole mobility that is larger both for
higher temperatures and stronger interactions between nanomagnets. The mobility
in this linear regime is described by a creep model of zero-dimensional charges
moving within a network of quasi-one-dimensional objects.
