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Analyzing the magnetic structure factor of a field demagnetized artificial square ice, qualitative deviations from what would predict the square ice model are observed. Combining micromagnetic and Monte Carlo simulations, we demonstrate that these deviations signal the presence of interactions between nanomagnets that extend beyond nearest neighbors. Including further neighbor, dipolar-like couplings in the square ice model, we find that the first seven or eight coupling strengths are needed to reproduce semi-quantitatively the main features of the magnetic structure factor measured experimentally. An alternative, more realistic numerical scenario is also proposed in which the ice condition is slightly detuned. In that case as well, the features evidenced in the experimental magnetic structure factor are only well-described when further neighbor couplings are taken into account. Our results show that long range dipolar interactions are not totally washed out in a field demagnetized artificial square ice, and cannot be neglected as they impact the magnetic correlations within or at the vicinity of the ice manifold., Comment: 9 pages, 8 figures

Arrays of interacting magnetic nanostructures were introduced recently as a powerful approach to investigate experimentally the exotic many-body physics of frustrated spin models. Following a similar strategy based on lithographically-patterned magnetic lattices, we provide a first attempt to fabricate a lab-on-chip platform to explore the physics of vertex models. The central idea of this work is to replace the spin degree of freedom of artificial frustrated spin systems by a local micromagnetic knob, which can be finely tuned by a proper design of the vertex geometry. This concept is demonstrated both numerically and experimentally on the celebrated six vertex model, and we show how all variants of this model can be apprehended through the engineering of magnetic square lattices. Our results open new avenues to design arrays of magnetic nanostructures not only to study a wide range of frustrated spin models, but to explore vertex models as well.

The low-energy magnetic configurations of artificial frustrated spin chains are investigated using magnetic force microscopy and micromagnetic simulations. Contrary to most studies on two-dimensional artificial spin systems where frustration arises from the lattice geometry, here magnetic frustration originates from competing interactions between neighboring spins. By tuning continuously the strength and sign of these interactions, we show that different magnetic phases can be stabilized. Comparison between our experimental findings and predictions from the one-dimensional Anisotropic Next-Nearest-Neighbor Ising (ANNNI) model reveals that artificial frustrated spin chains have a richer phase diagram than initially expected. Besides the observation of several magnetic orders and the potential extension of this work to highly-degenerated artificial spin chains, our results suggest that the micromagnetic nature of the individual magnetic elements allows observation of metastable spin configurations., Comment: 5 pages, 4 figures