Crystallizing Kagome Artificial Spin Ice

Artificial spin ices are engineered arrays of dipolarly coupled nanobar magnets. They enable direct investigations of fascinating collective phenomena from their diverse microstates. However, experimental access to ground states in the geometrically frustrated systems has proven difficult, limiting studies and applications of novel properties and functionalities from the low energy states. Here, we introduce a convenient approach to control the competing diploar interactions between the neighboring nanomagnets, allowing us to tailor the vertex degeneracy of the ground states. We achieve this by tuning the length of selected nanobar magnets in the spin ice lattice. We demonstrate the effectiveness of our method by realizing multiple low energy microstates in a kagome artificial spin ice, particularly the hardly accessible long range ordered ground state—the spin crystal state. Our strategy can be directly applied to other artificial spin systems to achieve exotic phases and explore new emergent collective behaviors.

Figure 1

Tunable kagome artificial spin ice. (a) Design of tunable kagome artificial spin ice with extended length $L_{\alpha }$ of $\alpha$ magnets and fixed length $L_{\beta }$ of $\beta$ nanomagnets. (b) Six low energy vertex configurations satisfying the kagome ice rule are separated into two groups based on energies. $J_1$ and $J_2$ are the coupling strengths of frustrated magnet pairs. (c) Evolution of the vertex energies as a function of $L_{\alpha }$. (d) and (e) SEM images of kagome artificial spin ices with $L_{\alpha }=220\mathrm{nm}$ (d) and $L_{\alpha }=420\mathrm{nm}$ (e), respectively. Scale bar, 500 nm. (f) and (g) MFM images corresponding to (d) and (e), respectively. Arrows indicate spin configurations. Scale bar, 500 nm.

Figure 2

Transition from liquid to crystal. (a)–(f) MFM images for samples with various $L_{\alpha }$ values, respectively. Scale bar, $2\mu \mathrm{m}$. (g)–(l) spin configurations and vertex distributions extracted from (a)–(f). Type $K$-I and $K$-II vertices are shown in blue and red, respectively. (m)–(r) corresponding maps of magnetic structure factors calculated respectively from the spin configurations in (g)–(l). Insets of (o)–(r) show expanded views of the split Bragg peaks. r.l.u.: reciprocal lattice unit.

Figure 3

Magnetic charge ordering. (a)–(f) magnetic charge distributions corresponding to MFM images in Figs. 2, respectively. Green and yellow denote two phases of magnetic charge ordering. Scale bar, $2\mu \mathrm{m}$. (g)–(l) maps of magnetic charge structure factors associated with (a)–(f). Insets show expanded views of the split Bragg peaks. r.l.u.: reciprocal lattice unit.