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

Thermally and field-driven mobility of emergent magnetic charges in square artificial spin ice