Magneto-optical imaging of flux penetration into arrays of ${\text{Bi}}_2{\text{Sr}}_2{\text{CaCu}}_2{\text{O}}_8$ microdisks

We have used differential magneto-optical (MO) imaging to investigate the mixed state of superconducting ${\text{Bi}}_2{\text{Sr}}_2{\text{CaCu}}_2{\text{O}}_{8+\delta }$ (BSCCO) microdisks fabricated on a single-crystal sample. MO difference images of the stray field distribution over a range of out-of-plane fields allow us to distinguish between flux that is penetrating the disks and that entering the underlying BSCCO platelet. We find that flux preferentially flows along linear defects into the interstitial platelet regions up to a characteristic field $H_p$, above which flux enters the disks. We identify this as the field of first penetration of pancake vortices over the Bean-Livingston barrier around the disks, where $H_p\left(T\right)$ at intermediate temperatures is well described by an exponentially decaying function with a characteristic temperature $T_0=19\text{K}$. At a given temperature, a minority of the disks exhibit a lower penetration field and we correlate the location of these disks with the linear defects in the BSCCO crystal.

Figure 1

(Color online) Optical micrograph of the disk array showing the orientation of the $40\mu \text{m}\times 40\mu \text{m}$ square unit cell (dashed outline) and the directions of the crystallographic $a$ and $b$ axes.

Figure 2

(Color online) MO difference images $\left(100\mu \text{m}\times 100\mu \text{m}\right)$ at $T=45\text{K}$: (a) below $H_p$ (disks in Meissner state), (b) above $H_p$ for the $20\mu \text{m}$ disks, and (c) above $H_p$ for the $15\mu \text{m}$ disks. (d) Plot of $\text{log}\left(H_p/\left[1-{\left(T/T_c\right)}^2\right]\right)$ vs $T$ of the experimental data for the $15\mu \text{m}$ (◇) and $20\mu \text{m}$ (◯) diameter disks and the theoretical fit (dashed lines) using Eq. (1).

Figure 3

(Color online) MO difference images $\left(0.4\text{mm}\times 0.3\text{mm},T=72\text{K}\right)$ constructed by subtracting the reference state in zero field from the images captured at applied fields of (a) 7.5 Oe and (b) 11.6 Oe. Arrows indicate the location of linear flux channels and the dashed outline in (a) indicates the unit cell of the array with corners on the $20\mu \text{m}$ disks (cf. Fig. 1).

Figure 4

(Color online) MO difference images $\left(0.4\text{mm}\times 0.3\text{mm},T=45\text{K}\right)$: (a) 32–27 Oe and (b) 50–49 Oe. Arrows in both images indicate the location of disks lying at the interface between the regions of differing vortex mobility. The dashed lines in (b) trace the edge of the channels observed in (a).