Magneto-optical Kerr effect studies of square artificial spin ice

We report a magneto-optical Kerr effect study of the collective magnetic response of artificial square spin ice, a lithographically defined array of single-domain ferromagnetic islands. We find that the anisotropic interisland interactions lead to a nonmonotonic angular dependence of the array coercive field. Comparisons with micromagnetic simulations indicate that the two perpendicular sublattices exhibit distinct responses to island edge roughness, which clearly influence the magnetization reversal process. Furthermore, such comparisons demonstrate that disorder associated with roughness in the island edges plays a hitherto unrecognized but essential role in the collective behavior of these systems.

Figure 1

A SEM image of a square array at $a=320$ nm lattice spacing with the magnetic field at an angle $\theta$ to an array axis, compared to an array of 24 ideal stadium-shaped islands, also at a 320-nm spacing.

Figure 2

(a)–(e) Hysteresis loops comparing MOKE measurements (red dotted line) to simulations at $\theta =0^{\circ },{10}^{\circ },{15}^{\circ },{30}^{\circ },{45}^{\circ }$ for square arrays with 320-nm lattice spacing. The green (light gray) and blue (dark gray) lines show simulations for ideal and experimental island shapes, respectively. Note the significant changes with angle that are summarized in Fig. 3.

Figure 3

Coercivity as a function of angle for a square array with 320-nm lattice spacing. Simulations were run on a 24-island cluster similar to that of Fig. 1 for both ideal (green hourglass symbols) and SEM-derived (blue squares, purple diamonds) island shapes. Sim1 and Sim2 refer to two different simulations run for SEM images of different islands.

Figure 4

(a) Variation of coercivity at $\theta =0$ as a function of lattice spacing for square arrays. Measurements on various samples (arrays 1–4) are compared with micromagnetic simulations (black squares), comparing simulations of the same island outlines but with different spacing. Error bars for experiment are smaller than the data points. (b) Experiment and simulation for square arrays as a function of angle for the largest lattice spacing of 880 nm. The local maximum in $H_c$ near $\theta =5^{\circ }$ that appeared for 320 nm is missing for the larger lattice spacing. Simulations were run on a 12-island array as indicated in the inset, with an appropriately dilated lattice spacing between the SEM islands.