Widefield NV Magnetic Field Reconstruction for Probing the Meissner Effect and Critical Current Density under Pressure

TL;DR

This work demonstrates a quantitative, widefield NV-based reconstruction of the Meissner effect in a Hg-1223 superconducting microcrystal under 4 GPa. By fitting ODMR spectra with a Hamiltonian that incorporates NV stress and Zeeman terms, the authors map the local magnetic field magnitude and direction across the sample as a function of temperature. They use Brandt's model to extract the temperature-dependent critical current density $j_c$, finding $j_c \,\approx\,1.5\times10^4$ A cm$^{-2}$ at 120 K, in line with ambient-pressure reports, and show how pressure variations influence the measurement. Overall, the study provides a fully optical approach to characterize $H_{c1}$, $H_{c2}$, and $j_c$ under pressure, highlighting NV magnetometry as a powerful tool for high-pressure superconductivity research.

Abstract

The spatial distribution of a magnetic field can be determined with micrometer resolution using widefield nitrogen vacancy (NV) center magnetic imaging. Nevertheless, reconstructing the magnetic field from the raw data can be challenging due to the degeneracy of the four possible NV axes and the tremendous amount of data. While a qualitative approach is sufficient for most analyses, a quantitative analysis offers deeper insight into the physical system. Here, we apply NV widefield magnetic imaging to a HgBa$_{2}$Ca$_{2}$Cu$_{3}$O$_{8+δ}$ (Hg-1223) superconducting microcrystal at a pressure of 4 GPa. We fit the results with solutions from the Hamiltonian describing the NV center ground state and take into account the relative intensities of the resonances to determine the local magnetic field magnitude and angle. Thus, we reconstruct the temperature-dependent expulsion of the magnetic field due to the Meissner effect around the superconductor. By comparing the resulting parameters to Brandt's model, which describes the magnetic behavior of a type-II superconductor, we extract the critical current density $j_c$. Overall, this work showcases the first widefield quantitative reconstruction of the Meissner effect under pressure and an optical method to study critical current density. Thus, it provides new insights into the application of NV magnetometry to superconductivity research at high pressures.

Figures (4)

• Figure 1: (a) Definition of the fitting parameters with respect to the crystallographic axes of the diamond (see text). The brownish arrows represent the four NV axes. The red arrow at $T>T_{c}$ represents the applied magnetic field $\vec{B_{0}}$ along the $[001]$, while the blue arrow $\vec{B^{'}}$ at $T<T_{c}$ illustrates the bending of the magnetic field angle (shortening of the vector is not shown). This only describes one point on the NV ensemble and is spatially dependent. (b) Illustration of the magnetic field expulsion around a superconducting cylindrical disk with a crystallographic axis $c$. The arrows show both the bending of the magnetic field vector and the decrease of its magnitude. Note that $B_{0}\parallel c\parallel[001]$.
• Figure 2: (a-c) Maps of the magnetic field magnitude $\lVert\vec{B}\rVert$ and (d-f) maps of the polar angle $\theta_{B}$ obtained at temperatures of 120.8 K, 135.2 K, and 149.9 K, respectively. The Meissner effect results in a higher magnetic field magnitude surrounding the sample, and a lower magnetic field and a larger polar angle towards the center of the superconducting Hg-1223 microcrystal. The inner and outer contours outline the sample geometry and the pressure chamber, respectively. The scale bar is 25 $\mu m$.
• Figure 3: Magnetic field reconstruction of the Meissner effect at different temperatures for (a) horizontal and (b) vertical line cuts. We focus on the results near the critical temperature $\sim 138$ K, otherwise, the data show negligible variation. Each arrow represents the magnitude $\lVert\vec{B}\rVert$ and the polar angle $\theta_{B}$ of the magnetic field. Due to the strong expulsion of the magnetic field around the center of the Hg-1223 sample in its superconducting state, no magnetic field vectors could be drawn at low temperatures in the corresponding parts of the graphs. When approaching the $T_{c}$, from 135.2 K to 137.6 K, the change in the magnetic field is rapid. A reference magnetic field vector with an amplitude 3 mT along the $c$-axis of the sample is drawn for each graph. The dashed black lines on the background roughly outline the width of the sample.
• Figure 4: (a) Model of a semi-infinite superconducting slab, with a width $2w$ in the transverse direction $x$ and a thickness $t$. Brandt's model is used to calculate the magnetic field profile along the dashed-gray line cut $B(x)$ in order to determine the critical current density $j_{c}$. (b) Temperature-dependent critical current density $j_{c}$ of Hg-1223 obtained using Brandt's model. The critical current density value is approximately $1.5\times10^4\, {\rm A} \cdot {\rm cm} ^{-2}$ at 120 K and 4 GPa. Inset: Fits of the magnitude of the magnetic field along the transverse $x$ direction, for three temperatures below $T_c$: 124.4 K, 129.5 K, and 136.8 K. The sharpest edge on the positive $x$-side (blue markers) is used to obtain the best fit, shown by the green line. The corresponding values obtained from this best fit are then plotted for the negative $x$-side (black markers). Due to the finite spatial resolution and the absence of sharp sample edges, changes in the magnetic field on the edges are smoothed out. The dashed black lines on the background indicate the width of the sample.