Figure 1

SEM and MFM images of perpendicular moment nanomagnet arrays in kagome and honeycomb geometries with 600 nm lattice spacing. Each island in MFM shows either black or white, indicating that it consists of a single magnetic domain with moment pointing either up or down.Reuse & Permissions

Figure 2

(a),(b),(c) Correlations as a function of pair order after ac demagnetization for a perpendicular honeycomb lattice at 500 nm spacing, a perpendicular kagome lattice at 500 nm spacing and an in-plane hexagonal lattice at 750 nm spacing (from [11]). Simulated results that constrain the nearest neighbor correlations in a quasiequilibrium Gibbsian model (model $G$: Red circles) and a kinetic zero-temperature quenched model (model $Z$: Green triangles) agree well with the experiment. (d),(e),(f) Corresponding pair energies from micromagnetic simulations [25] as a function of pair order, using black points for antiferromagnetic interactions and red points for ferromagnetic interactions. Note that AF/FM interactions are indicated only for the in-plane lattice because the interactions are purely antiferromagnetic in the perpendicular lattice material. The insets label the neighbor pairs for each lattice.Reuse & Permissions

Figure 3

(a),(b) Ground state domains in perpendicular honeycomb lattices at 500 nm and 800 nm spacing in the same image scale ($18\times 18\mu {\mathrm{m}}^2$). Red and blue areas indicate the twofold ground state degeneracy.Reuse & Permissions

Figure 4

(a) Nearest-neighbor correlations as a function of nearest-neighbor interaction energies for all inter-island spacings of the perpendicular kagome lattices and in-plane hexagonal lattices. Marks at the top are the field-step Zeeman energy $M\Delta H$. (b) Monte Carlo simulation results for the ideal Ising kagome antiferromagnet and data from the main figure scaled to match. $E$ is the nearest-neighbor interaction energy, and $k_B$ is Boltzmann constant.Reuse & Permissions