  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 upon the dipolar interaction between the nanomagnetic islands, correctly
reproduces the ground-state observed experimentally. In addition, we find
magnetic monopole-like excitations effectively interacting by means of the
usual Coulombic plus a linear confining potential, the latter being related to
a string-like excitation binding the monopoles pairs, what indicates that the
fractionalization of magnetic dipoles may not be so easy in two dimensions.
These findings contrast this material with the three-dimensional analogue,
where such monopoles experience only the Coulombic interaction. We discuss,
however, two entropic effects that affect the monopole interactions: firstly,
the string configurational entropy may loose the string tension and then, free
magnetic monopoles should also be found in lower dimensional spin ices;
secondly, 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.
