Flux Trapping Characterization for Superconducting Electronics Using a Cryogenic Widefield NV-Diamond Microscope

Abstract

Magnetic flux trapping is a significant hurdle limiting the reliability and scalability of superconducting electronics, yet tools for imaging flux vortices remain slow or insensitive. We present a cryogenic widefield NV-diamond magnetic microscope capable of rapid, micrometer-scale imaging of flux trapping in superconducting devices. Using this technique, we measure vortex expulsion fields in Nb thin films and patterned strips, revealing a crossover in expulsion behavior between $10$ and $20~μ$m strip widths. The observed scaling agrees with theoretical models and suggests the influence of film defects on vortex expulsion dynamics. This instrument enables high-throughput magnetic characterization of superconducting materials and circuits, providing new insight for flux mitigation strategies in scalable superconducting electronics.

Figures (5)

• Figure 1: (a) Schematic of the NV cryo-microscope. (b) NV ground-state energy levels as a function of on-axis magnetic field $B_z$. (c) Example single-pixel ODMR spectra measured at a vortex location. The vortex magnetic field below $T_c$ results in an observed increase in the ODMR linewidth $\Gamma$. The increased fluorescence contrast observed can be attributed to temperature-dependent effects low_temp_NV_effects. (d) Cross-section view showing the diamond optical coatings and overall diamond/sample stackup. (e) A photograph of the sensor head showing the various hardware components used for sample positioning, MW delivery, and thermal management.
• Figure 2: (a)-(b) Magnetic field images showing flux vortices in a bare superconducting Nb film in background fields $B_r=$ 0.38 $\upmu$T and 0.64 $\upmu$T. (c) Measured vortex areal density over a range of $B_r$. (d)-(e) Magnetic field images of the film at $B_r=$ 13.11 $\upmu$T and 32.35 $\upmu$T. (f) Map of vortex pinning sites observed across ten temperature cycles at $B_r=$ 0.64 $\upmu$T, where dot color indicates the frequency with which vortices appeared. An example image from this dataset is shown in (b).
• Figure 3: A video showing flux trapping in a Nb film across ten cooldowns, with $B_r=$ 0.64 $\upmu$T.
• Figure 4: (a) Test chip layout with 20 $\upmu$m strip test structure highlighted. The blue regions are Nb, while in the white regions the superconductor has been etched away. The outlined red-dashed region is the strip region, where all strip expulsion field measurements were performed, while the outlined solid-magenta region is the moat-array region. (b) 20 $\upmu$m strips for $B_r=B_{1}<B_2$, where the first vortices in strips are observed (circled in white). (c) 20 $\upmu$m strips for $B_r>B_{2}>B_1$, with many vortices observed in the strips.
• Figure 5: (a) Vortex areal density $n_v$ vs. applied field $B_r$ for selected strip widths, showing the extracted expulsion fields $B_1$ and $B_2$ (in $\mu$T). Each $n_v$ value represents the number of vortices counted across multiple strips in a single cooldown (see Supplementary Table S2 suppl). (b) Expulsion field vs. strip width, expected to scale as $\beta \Phi_0/W^2$ with different predictions for the dimensionless factor $\beta$washington1982observation. Data for $W \leq 10~\upmu\text{m}$ and $W \geq 20~\upmu\text{m}$ agree well with $\beta = 3.43 \pm 0.12$ and $1.89 \pm 0.09$, respectively. The narrow-strip ($W \leq 10~\upmu\text{m}$) data match the theoretical $B_{c1}$ (Eq. \ref{['eq:Bc1']}) for $\xi = 18 \pm 4$ nm, corresponding to Nb films at 4 K. The data deviate from $B_{c1}$ calculated using $\xi \approx 380$ nm near $T_c$. At all strip widths, the data exceed the vortex stability field $B_0 = \pi \Phi_0 / 4 W^2$ (Eq. \ref{['eq:eq1']}).