Fig. 3.

Annealing of magnetic carpet. a Experimental images showing an initial polycrystalline carpet (t = 0s, top) realized with an in-plane rotating field (B₀ = 2.5 mT, f = 40 Hz), and a monocrystalline carpet obtained after t = 2 min of propulsion (B₀ = 2.5 mT, B_z = 2.7 mT, f = 40 Hz). The scale bar is 20 μm, see Supplementary Movie 5 in the Supplementary Information. b Bond-orientational correlation functions g₆(r) of the two carpets with superimposed corresponding peaks as solid disks and fits to an algebraic dependence $g_6\left(r\right)~r^{-{\eta }_6}$ as dashed lines. The exponent η₆ can be used to distinguish the crystalline phase (η₆ > 1/4) from the hexatic one³. c Average carpet speed 〈v_c〉 vs. field amplitude B₀ for different values of B_z. The continuous black line is a fit to the data using Eq. (16), with fixed parameters l = 3.2 μm, χ = 0.4, ω = 251.3 rads⁻¹ and h = 2.6 μm. The small inset indicates the corresponding location of the experimental points in the diagram in Fig. 1g (B₀∼B_z is taken). Error bars are obtained from the statistical average of different experiments. d Bond-orientational order parameter Ψ(t) vs. time t for different values of B₀ (thus carpet speed v_c). In the continuous lines in the graph is obtained by averaging the experimental data over a discrete time window. All experiments are conducted for carpets having a similar size of ~1000 particles. e Annealing time τ_c vs. field amplitude B₀, with continuous black line is a fit to the data using Eq. (6)