Spatially modulated susceptibility in thin film ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$

The high critical temperature superconductor lanthanum barium copper oxide (${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$) exhibits a strong anomaly in critical temperature at 1/8th doping, nematicity, and other interesting properties. We report here scanning superconducting quantum interference device imaging of the magnetic fields and susceptibility in a number of thin film ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ samples with doping in the vicinity of the 1/8th anomaly. Spatially resolved measurements of the critical temperatures of these samples do not show a pronounced depression at 1/8th doping. They do, however, exhibit strong, nearly linear modulations of the susceptibility (“striae”) of multiple samples with surprisingly long periods of 1–4 $\mu \mathrm{m}$. Counterintuitively, vortices trap in positions of largest diamagnetic susceptibility in these striae. Given the rich interplay of different orders in this material system and its known sensitivity to epitaxial strain, we propose phase separation as a possible origin of these features and discuss scenarios in which that might arise.

Figure 1

SQUID Susceptometer with $0.1\mu \mathrm{m}$ radius pickup loop. (a) Schematic layout. The current leads, modulation coil, and field coil are labeled by $I$, $M$, and $F.C.$, respectively. All but the pickup loop/field coil regions are shielded from external magnetic fields by superconducting layers. (b) Layout of the pickup loop (purple), field coil (blue), and shields (red and purple) region. (c) Layout of the entire $2\mathrm{mm}\times 2\mathrm{mm}$ chip.

Figure 2

Sample geometry. (a) Schematic of 20-nm-thick LBCO film on a ${\mathrm{LaSrAlO}}_4$ substrate. (b) AFM image of AC 174, a 20-nm-thick film of ${\mathrm{La}}_x{\mathrm{Ba}}_{2-x}{\mathrm{CuO}}_4$ with nominal doping of ${\mathrm{x}}_{\mathrm{nom}}=0.125$.

Figure 3

Susceptibility touchdowns vs temperature. Measurements of the change in the mutual inductance $\varphi =\mathrm{\Phi }/I$ (in units of ${\mathrm{\Phi }}_0=h/2e$) between the field coil and the pickup loop in our SQUID susceptometers for sample AC 174 as a function of the z-piezo voltage. The sample comes into mechanical contact with the SQUID substrate at a z-piezo voltage of $V_z=70\mathrm{V}$. The dots are data, with selective temperatures labeled. The solid lines are fits to Eq. (1). For these fits, we took the measured value ${\varphi }_s=54{\mathrm{\Phi }}_0/\mathrm{A}$, the effective field coil radius $R=0.79\mu \mathrm{m}$ [12], the spacing $\delta z=0.5\mu \mathrm{m}$, with ${\varphi }_{\mathrm{offset}}$, $c_2$, $\alpha$ and $R/\mathrm{\Lambda }$ as fitting parameters. The inset replots the 6 K data, with best fits for $\delta \mathrm{z}=0.35\mu \mathrm{m}$ (blue solid line) and $0.65\mu \mathrm{m}$ (green dashed line).

Figure 4

Pearl length vs temperature. The symbols are fit values for $\mathrm{R}/\mathrm{\Lambda }$ from touchdown data as illustrated in Fig. 3, assuming the sample surface to pickup loop distance at contact $\delta z=0.50\mu \mathrm{m}$. The error bars on the data for AC174 represent systematic errors due to uncertainty in $\delta z$, with the lower and upper bars corresponding to $\delta \mathrm{z}=0.35\mu \mathrm{m}$ and $0.65\mu \mathrm{m}$, respectively.

Figure 5

Striae are observed in four of the five superconducting samples imaged. Magnetic susceptibility images of thin-film LBCO for distinct samples with nominal dopings of $0.090<x_{\mathrm{nom}}<0.135$. The “striae” are the periodic modulations in susceptibility shown in (a), (b), (d), and (e). Note the different scale bars: Striae periods between one and four microns were observed in these samples. An average background susceptibility was subtracted from each of these images. The amplitudes of the striae are approximately 1%, 8%, 4%, and 1% of the total susceptibility of scans (a), (b), (d), and (e), respectively.

Figure 6

Striae persist, with little change in period, to close to ${\mathrm{T}}_c$. Magnetometry (left column) and susceptibility (right column) images of a $10\mu \mathrm{m}$ wide by $9\mu \mathrm{m}$ high area of sample AC174, cooled and imaged in a field of $33\mu \mathrm{T}$ at the temperatures labeled, with a field coil modulation of 10 mA at 2.204 kHz. The false color variations are 4 $\mathrm{m}{\mathrm{\Phi }}_0$ for the magnetometry images, and $0.4{\mathrm{\Phi }}_0/\mathrm{A}$ for the susceptibility images. The white dashed lines represent the cross-sections through the data displayed in Fig. 7.

Figure 7

Temperature dependence of the striae. (a) Cross-sections through the susceptibility data of Fig. 6 at the temperatures labeled. (b) Two-dimensional Fourier transform of the 5.8 K data: the sharp peaks represent the susceptibility striae, with $1\mu \mathrm{m}$ period, amplitude $10m{\mathrm{\Phi }}_0/\mathrm{A}$, and angle of $-0.22$ radians. (c) Plot of the stripe amplitude, from such Fourier transforms as in (b), as a function of temperature T. (d) Plot of the stripe period vs T.

Figure 8

Stripe period varies with low temperature Pearl length. (a) Fit values from susceptibility touchdown curves for AC174 at two positions separated by 1 mm. (b) Plot of striae period vs fit values for $R/\mathrm{\Lambda }\left(5K\right)$ at several positions in sample AC174. The dots are data and the dashed lines connect the dots.

Figure 9

Superconducting vortices trap at positions of largest diamagnetic susceptibility. Simultaneously acquired magnetometry (upper) and susceptibility (lower) images of sample AC 174, cooled in a field of $23\mu \mathrm{T}$ and imaged in field at 5 K. Superposed on the susceptibility image are five equally spaced contours of magnetic flux (in black).

Figure 10

Vortices trap in regions of largest diamagnetic susceptibility, independent of cooling field. Magnetometry (left column) and susceptibility (right column) images of a $10\mu \mathrm{m}$ wide by $9\mu \mathrm{m}$ high area of sample AC 174, imaged at $T=5$ K with a field coil modulation of 10 mA at 2.204 kHz. The samples were cooled and imaged in the fields as labeled. The false color scales are 3 $\mathrm{m}{\mathrm{\Phi }}_0$ for the magnetometry images, and $0.1{\mathrm{\Phi }}_0/\mathrm{A}$ for the susceptibility images. The white dots represent the centers of the vortices, offset by $-0.25\mu \mathrm{m}$ in the susceptibility images to compensate for the displacement between the maximum magnetometry and susceptibility sensitivities for our SQUID sensor.