Magnetic metamaterials such as artificial spin ice offer a route to tailor magnetic properties. Such materials can be fabricated by lithographically defining arrays of nanoscale magnetic islands. The magnetostatic interactions between the elements are influenced by their shape and geometric arrangement and can lead to long-range ordering. We demonstrate how the magnetic order in a two-dimensional periodic array of circular disks is controlled by the lattice symmetry. Antiferromagnetic and ferromagnetic order extending through the entire array is observed for the square and hexagonal lattice, respectively. Furthermore, we show that a minute deviation from perfect circularity of the elements along a preferred direction results in room-temperature blocking and favors collinear spin textures.

We have studied the impact of lattice geometry on the dynamic properties of close-spaced arrays of circular nanomagnets, also known as magnonic crystals. To this end, we prepared 2D nanomagnet arrays with both square and hexagonal lattice symmetries (300 nm disc diameter, 400 nm center-tocenter distance) and performed broadband ferromagnetic resonance (FMR) measurements. Micromagnetic simulations were used to interpret distinct features of the measured resonance spectra. The FMR bias field was applied along two distinct principle directions for each lattice, and a sample with well-separated, decoupled discs was measured for reference. We found that the interdisc dipolar coupling has a strong impact on the FMR for these 2D magnonic crystals. Distinctly different oscillation modes were found for the individual nanomagnets, dependent on lattice symmetry and direction of the bias field. Moreover, we find that spectral peak splitting from excitation of edge and center modes, as well as the damping, depend on the lattice symmetry and the orientation of the bias field. These findings demonstrate that lattice geometry has a strong influence on the excited spin-wave spectrum and is a relevant design parameter for novel spintronic devices.

Long-range magnetic ordering can be stabilized in arrays of single-domain nanomagnets through dipolar interactions. In these metamaterials, the magnetic properties are determined by geometric parameters such as the nanomagnet shape and lattice symmetry. Here, we demonstrate engineering of the anisotropy in a dipolar magnetic metamaterial by tuning of the lattice parameters. Furthermore, we show how a modified Kittel's law explains the resulting domain configurations of the dipolar ferromagnetic arrays.

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