Competing Symmetries and Broken Bonds in Superconducting Vortex-Antivortex Molecular Crystals

Hall probe microscopy has been used to image vortex-antivortex molecules induced in superconducting Pb films by the stray fields from square arrays of magnetic dots. We have directly observed spontaneous vortex-antivortex pairs and studied how they interact with added free (anti)fluxons in an applied magnetic field. We observe a variety of phenomena arising from competing symmetries which either drive added antivortices to join antivortex shells around dots or stabilize the translationally symmetric antivortex lattice between the dots. Added vortices annihilate antivortex shells, leading first to a stable “nulling state” with no free fluxons and then, at high densities, to vortex shells around the dots stabilized by the asymmetric antipinning potential. Our experimental findings are in good agreement with Ginzburg-Landau calculations.

Figure 1

Atomic force microscope image of the magnetic disk array (left) and (i)–(vi) SHPM images of magnetization reversal (scan range is $\sim 17\mu \mathrm{m}\times 17\mu \mathrm{m}$ at 20 K). The gray scale of images (i) and (ii) spans 2.66 G and 2.63 G, respectively (see text).

Figure 2

SHPM image of spontaneous VAV configurations at $H_a=3.5\mathrm{Oe}$ ($H_{\mathrm{eff}}\approx 0$) and $T=5\mathrm{K}$ (a) and a schematic depiction of the AV locations (b) (dashed circles indicate the locations of magnetic disks). (c) Map of magnetic induction across theoretically predicted VAV configurations. (d), (e) Magnetic induction map across dot $B$, experiment (d) vs theory (e). (f), (g) Induction profiles across one AV along the lines indicated in (d).

Figure 3

(a) SHPM images obtained at two different effective applied fields imaged at $T=5\mathrm{K}$ and their difference image (see text). (b)-(e) Cooper-pair density plots obtained theoretically for applied fields $H_{\mathrm{eff}}=0$, $-0.6$, $-1$, and $-1.8\mathrm{Oe}$, respectively.

Figure 4

Number of experimentally observed free (anti)vortices vs applied magnetic field (open dots) at $T=5\mathrm{K}$. Solid line shows the predictions of GL theory (shifted by $+4\mathrm{Oe}$ on the field axis to simulate flux trapping in solenoid). (i)-(iv) Experimental SHPM difference images constructed between the indicated fields (see text). $\Delta H=0.5\mathrm{Oe}$ corresponds to $\sim 3{\varphi }_0$ per field-of-view on average. (v) Experimental SHPM image of the “nulling” state ($H_a=5.5\mathrm{Oe}$).

Figure 5

SHPM images at $T=5\mathrm{K}$ and corresponding Cooper-pair density plots illustrating formation of (a) an interstitial vortex lattice ($H_{\mathrm{eff}}\approx 4.5\mathrm{Oe}$) and (b) interstitial vortex shells for high vortex densities ($H_{\mathrm{eff}}\approx 7.5\mathrm{Oe}$).