# Real-Space Probing of the Local Magnetic Response of Thin-Film Superconductors Using Single Spin Magnetometry

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## Abstract

**:**

_{2}Cu

_{3}O

_{7−δ}(YBCO) using scanning single spin magnetometry. Our experiments yield a direct measurement of the sample’s London penetration depth and allow for a quantitative reconstruction of the supercurrents flowing in the sample as a result of Meissner screening. These results show the potential of scanning single spin magnetometry for studies of the nanoscale magnetic properties of thin-film superconductors, which could be readily extended to elevated temperatures or magnetic fields.

## 1. Introduction

## 2. Experiment

_{2}Cu

_{3}O

_{7−δ}(YBCO) [24] (Figure 1d). The c-axis-oriented YBCO film was grown to a thickness ${d}_{\mathrm{YBCO}}$ of ∼119 nm on top of a (001)-oriented single-crystal SrTiO

_{3}(STO) substrate using pulsed laser deposition and was covered with ∼16 nm of STO to avoid oxygen diffusion out of the sample [25]. Patterning was performed by optical lithography and Ar ion milling 5 nm into the substrate yielding step size ${z}_{\mathrm{Step}}\sim $ 140 nm at the edge of the disk. The film shows a ${T}_{c}\approx 90$ K as measured in-situ by a four-probe conductance measurement. The data presented in this work were taken on the 6 μm diameter disk highlighted in Figure 1d.

## 3. Results and Discussion

## 4. Conclusions and Summary

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Nitrogen-Vacancy (NV) centre ground state spin levels with zero-field frequency splitting ${D}_{0}$ and Zeeman splitting $2{\gamma}_{\mathrm{NV}}{B}_{\mathrm{NV}}$ (with ${\gamma}_{\mathrm{NV}}=28$ GHz/T and ${B}_{\mathrm{NV}}$ the magnetic field along the NV axis). As indicated by the red circles, the |${m}_{s}=0\rangle $ spin sub-level exhibits a higher fluorescence rate than |${m}_{s}=\pm 1\rangle $. (

**b**) Optically detected electron spin resonance (ESR) of a single scanning NV centrer. (

**c**) Schematic cross-section of the sample and the scanning probe hosting the NV centrer. The NV is stabilised at a distance ${z}_{\mathrm{NV}}$ from the superconductor surface using atomic-force distance control. (

**d**) Top view of the micro-structured YBCO sample. Blue (grey) represents regions of YBCO (substrate), respectively. The highlighted disk with 6 μm diameter is used here to study Meissner screening and a nearby four-point bridge to determine sample resistance. The projection of the NV centre axis onto the sample plane is denoted by ${\overrightarrow{e}}_{\mathrm{NV}}$.

**Figure 2.**(

**a**) Quantitative map of the magnetic field ${B}_{\mathrm{NV}}$, measured with the scanning NV spin above the YBCO disk in an external magnetic field of 1.7 mT applied perpendicular to the sample. Low magnetic fields are observed in the centre of the disk due to Meissner screening in the superconductor and maximal fields at the edges of the disk due to compression of the field lines expelled from the disk. The observed absence of rotational symmetry of ${B}_{\mathrm{NV}}$ around the disk centre is a result of the NV orientation being away from the sample normal. The data were acquired with a pixel dwell-time of 12 s resulting in a scan time of 8 h for the entire scan. The green readout laser was set to a power of 350 μW with a microwave power of ∼15 dBm sent into the cryostat. The dashed line indicates the position of the line scan in Figure 3. (

**b**) Calculation of ${B}_{\mathrm{NV}}$ using the numerical model described in the text, with $\lambda =250$ nm and ${z}_{\mathrm{NV}}=100$ nm as manually set input parameters.

**Figure 3.**(

**a**) Measurement of ${B}_{\mathrm{NV}}$ across the YBCO disk along the trajectory indicated in Figure 2a. The black line in (

**a**) shows the fit with the numerical model which yields a penetration depth of $\lambda =249\pm 5$ nm. Data points marked in blue were excluded from the fit (see text). The data integration time was 24 s per point resulting in 80 min for the entire scan. A laser power of 470 W and a microwave power of ∼15 dBm were applied to the NV spin. (

**b**) Magnetic field lines around the YBCO disk in the Meissner state, along with a sketch of the experimental setup. The field lines together with the NV spin quantisation direction (purple arrows) highlighted for various positions illustrate the asymmetry in ${B}_{\mathrm{NV}}$ observed in the data. The dashed line illustrates the topography of the scan which is taken into account in the calculation of ${B}_{\mathrm{NV}}$.

**Figure 4.**(

**a**) Current density ${j}_{s}$ reconstructed by magnetic field reverse-propagation from the data in Figure 2a. The circular currents generate a magnetic field counteracting the external magnetic field. (

**b**) Azimuthal average of the current density ${j}_{s}\left(r\right)$ as a function of distance to the disk centre, along with the current density calculated in the numerical model.

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**MDPI and ACS Style**

Rohner, D.; Thiel, L.; Müller, B.; Kasperczyk, M.; Kleiner, R.; Koelle, D.; Maletinsky, P.
Real-Space Probing of the Local Magnetic Response of Thin-Film Superconductors Using Single Spin Magnetometry. *Sensors* **2018**, *18*, 3790.
https://doi.org/10.3390/s18113790

**AMA Style**

Rohner D, Thiel L, Müller B, Kasperczyk M, Kleiner R, Koelle D, Maletinsky P.
Real-Space Probing of the Local Magnetic Response of Thin-Film Superconductors Using Single Spin Magnetometry. *Sensors*. 2018; 18(11):3790.
https://doi.org/10.3390/s18113790

**Chicago/Turabian Style**

Rohner, Dominik, Lucas Thiel, Benedikt Müller, Mark Kasperczyk, Reinhold Kleiner, Dieter Koelle, and Patrick Maletinsky.
2018. "Real-Space Probing of the Local Magnetic Response of Thin-Film Superconductors Using Single Spin Magnetometry" *Sensors* 18, no. 11: 3790.
https://doi.org/10.3390/s18113790