Two-dimensional vortex behavior in highly underdoped $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ observed by scanning Hall probe microscopy

We report scanning Hall probe microscopy of highly underdoped superconducting $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ with $T_c$ ranging from $5\text{to}15\mathrm{K}$, which showed distinct flux bundles with less than one superconducting flux quantum $\left({\Phi }_0\right)$ through the sample surface. The sub-${\Phi }_0$ features occurred more frequently for lower $T_c$, were more mobile than conventional vortices, and occurred more readily when the sample was cooled with an in-plane field component. We show that these features are consistent with kinked stacks of pancake vortices.

Figure 1

Superconducting transitions in the $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.375}$ crystal measured by in situ magnetic susceptibility with the Hall probe in an applied $8.3\mathrm{mHz}$ field of amplitude $0.25\mathrm{Oe}$ for stages 1 and 2 and $0.20\mathrm{Oe}$ for stages 3–8. Stages offset by $0.15\Omega ∕\mathrm{G}$. Filled symbols are second measurements at different locations. A Hall probe response of $R_H=0.115\pm 0.015\Omega ∕\mathrm{G}$ indicates no measurable Meissner response, while $0\Omega ∕\mathrm{G}$ indicates full shielding. Inset: Midpoint transition temperature $\left(T_c\right)$ versus cumulative room temperature annealing time for the $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.375}$ crystal. Vertical bars indicate the full transition width, limited by our measurement resolution.

Figure 2

(Color) Hall probe images of magnetic flux in the $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.375}$ crystal for increasing $T_c$ (stages 1–6). The probe’s size was nominally $0.5\mu \mathrm{m}$. The circular features with largest $B_z$ are likely straight pancake vortex stacks (full vortices), while the dimmer and sometimes noncircular features are identified as segments of kinked pancake vortex stacks (partial vortices). The applied field $H_z$ while cooling through $T_c$ and the temperature $T$ at which each image was acquired were (a) $0.15\mathrm{Oe}$ and $2.0\mathrm{K}$, (b) $0.21\mathrm{Oe}$ and $2.3\mathrm{K}$, (c) $0.21\mathrm{Oe}$ and $2.4\mathrm{K}$, (d) $0.21\mathrm{Oe}$ and $2.2\mathrm{K}$, (e) $0.43\mathrm{Oe}$ and $4.3\mathrm{K}$, and (f) $0.20\mathrm{Oe}$ and $4.1\mathrm{K}$. A constant background has been subtracted from each image. For (f), low frequency telegraph noise in the Hall probe signal was subtracted from the raw images before averaging.

Figure 3

Histogram of partial vortex peak field as a fraction of full vortex peak field in the $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.375}$ crystal. Sample was cooled to low temperature in a perpendicular field before each image was acquired. Total bar heights show data from all anneal stages (all $T_c$ values).

Figure 4

(Color) Fit to a kinked pancake vortex stack in the $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.375}$ at anneal stage 6 $(T_c=14.0\mathrm{K})$ at $T=4\mathrm{K}$. (a) Hall probe image containing partial vortices labeled 1 and 2. The three brightest features are full vortices. (b) Horizontal cross sections through the partial vortices, the sum of the partial vortices, and the full vortex labeled FV in (a). The solid line is from a 2D fit to the FV with $z=1.0\mu \mathrm{m}$ as a fixed parameter and ${\lambda }_{ab}=0.65\mu \mathrm{m}$ as a fit parameter. (c) Sketch of the assumed geometry of the kinked pancake stack, not to scale. (d) Zoom in of image (a) with the color scale adapted to the signal range of the partial vortices. (e) Fit to the partial vortices within the white oval in (d) as discussed in the text. $d=0.36\mu \mathrm{m}$ and kink length is $5.3\mu \mathrm{m}$. (f) Cross sections through the data (circles) and fit (line) along the dashed lines in (d) and (e).

Figure 5

(Color) Partial vortices coalesced during the sample coarse motion $(T=2.4\mathrm{K})$. (a) Hall probe image after cooling through $T_c=8.6\mathrm{K}$ in the $H_z=0.21\mathrm{Oe}$ applied field. White circles identify two partial vortices. (b) After a slight $z$ coarse motion of the sample. A comparison of the images suggests that the partial vortices in (a) collapsed to one full vortex in (b).

Figure 6

(Color) Effect of an in-plane field on partial vortex formation in $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.375}$. $T_c=14.4\mathrm{K}$ and $T=4\mathrm{K}$ for all the images. Field cooled through $T_c$ in $H_z=0.50\mathrm{Oe}$ and (a) $H_x=0$ and (b) $H_x=2.3\mathrm{Oe}$. Field cooled through $T_c$ in $H_z=0.20\mathrm{Oe}$ and (c) $H_x=0$, (d) $H_x=1.2\mathrm{Oe}$, and (e) $H_x=2.3\mathrm{Oe}$. Images acquired in zero applied field. The $x$ direction is horizontal, and $z$ is out of the page.

Figure 7

(Color) Comparison of vortex movement after elevating the temperature for the $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.375}$ crystal cooled in tilted and perpendicular fields. $T_c=14.4\mathrm{K}$. (a) Field cooled in $H_x=2.0\mathrm{Oe}$ and $H_z=0.25\mathrm{Oe}\text{to}T=3\mathrm{K}$. Image (i) was taken after the field was turned off. After thermal cycling sequentially to (ii) $6.6\mathrm{K}$, (iii) $8.0\mathrm{K}$, (iv) $9.8\mathrm{K}$, and (v) $12.2\mathrm{K}$. (b) The sample was field cooled in $H_x=0$ and $H_z=0.25\mathrm{Oe}\text{to}T=3\mathrm{K}$. Image (i) was taken after the field was turned off. (ii) After thermal cycling to $11.8\mathrm{K}$. $T=3.0\mathrm{K}$ for all images.

Figure 8

Fit results for low-temperature ${\lambda }_{ab}$ versus $T_c$ for the $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.375}$ crystal, obtained from fits to scanning Hall probe images of 40 different vortices at eight $T_c$ stages of a room temperature annealing. The fitted ${\lambda }_{ab}$ is an upper bound on the true ${\lambda }_{ab}\left(0\right)$. Horizontal bars indicate the resolution-limited full width of the superconducting transition for each $T_c$. Vertical error bars (shown only for the extreme data points) are from uncertainty in the probe calibration. A systematic error from uncertainty in the minimum sample-probe distance $z_0$ could shift the full data set by the extent indicated by the double arrow at $T_c=4\mathrm{K}$. Data points shown are with $z_0=0.8\mu \mathrm{m}$. For comparison, the dotted curve is from the fit to $H_{c1}\left(T_c\right)$ from Ref. 17, as discussed in the text. Inset: Temperature dependence of the ${\lambda }_{ab}$ results for two $T_c$ values. For each data set shown, ${\lambda }_{ab}$ was obtained from fits to scanning Hall probe images of an individual vortex as $T$ increased. The vortices disappeared before $T_c$. The dashed lines indicate the maximum extent the data sets could be shifted due to systematic errors.