Magnetic monopole and string excitations in two-dimensional spin ice

We study the magnetic excitations of a square lattice spin ice recently produced in an artificial form as an array of nanoscale magnets. Our analysis, based on the dipolar interaction between the nanomagnetic islands, correctly reproduces the ground state observed experimentally. In addition, we find magnetic monopolelike excitations effectively interacting by means of the usual Coulombic plus a linear confining potential, the latter being related to a stringlike excitation binding the monopoles pairs, which indicates that the fractionalization of magnetic dipoles may not be so easy in two dimensions. These findings contrast this material with the three-dimensional analog, where such monopoles experience only the Coulombic interaction. We discuss, however, two entropic effects that affect the monopole interactions. First, the string configurational entropy may lose the string tension and then free magnetic monopoles should also be found in lower dimensional spin ices; second, in contrast to the string configurational entropy, an entropically driven Coulomb force, which increases with temperature, has the opposite effect of confining the magnetic defects.