  We investigate numerically the micromagnetic properties and the low-energy
physics of an artificial square spin system in which the nanomagnets are
physically connected at the lattice vertices. Micromagnetic simulations reveal
that the energy stored at the vertex sites strongly depends on the type of
magnetic domain wall formed by the four connected nanomagnets. As a
consequence, the energy gap between the vertex types can be partially modified
by varying the geometrical parameters of the nanomagnets, such as their width
and thickness. Based on the energy levels given by the micromagnetic
simulations, we compute the thermodynamic properties of the corresponding spin
models using Monte Carlo simulations. We found two regimes, both being
characterized by an extensive ground state manifold, in sharp contrast with
similar lattices with disconnected nanomagnets. For narrow and thin
nanomagnets, low-energy spin configurations consist of independent
ferromagnetic straight lines crossing the whole lattice. The ground state
manifold is thus highly degenerate, although this degeneracy is subdominant. In
the limit of thick and wide nanomagnets, our findings suggest that the
celebrated square ice model may be fabricated experimentally from a simple
square lattice of connected elements. These results show that the micromagnetic
nature of artificial spin systems involves another degree of freedom that can
be finely tuned to explore strongly correlated disordered magnetic states of
matter.
