Single-spin scanning magnetic microscopy with radial basis function reconstruction algorithm
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-05-04 |
| Journal | Applied Physics Letters |
| Authors | Cheng-Jie Wang, Rui Li, Bei Ding, Pengfei Wang, Wenhong Wang |
| Institutions | Hefei National Center for Physical Sciences at Nanoscale, University of Science and Technology of China |
| Citations | 4 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research presents a novel, robust scheme for single-spin scanning magnetic microscopy using Nitrogen-Vacancy (NV) centers, specifically designed to overcome the dynamic range limitations imposed by the linewidth of standard Optically Detected Magnetic Resonance (ODMR).
- Core Value Proposition: Enables efficient, high-acutance imaging of magnetic fields fluctuating up to several milliteslas (mT), which are common in exotic magnetic structures (e.g., skyrmions).
- Methodology: Implements a magnetic field tracking mechanism that dynamically adjusts three Microwave (MW) excitation frequencies (f0, f-, f+) based on real-time photoluminescence (PL) feedback, mapping multiple magnetic resonance contour lines.
- Reconstruction Algorithm: Utilizes a Radial Basis Function (RBF) algorithm, specifically the Thin Plate Spline (TPS), to reconstruct the continuous magnetic field map from the scattered contour line data, incorporating a smoothness constraint for noise resilience.
- Performance Metrics: Achieved a maximum detectable magnetic field gradient of 0.86 mT per pixel, significantly exceeding the limitations of conventional ODMR spectroscopy.
- Dynamic Range: Simulations confirmed a high dynamic range capability, successfully tracking field fluctuations up to 10 mT.
- Efficiency: The scanning scheme is fast, acquiring a 4096-pixel image in approximately 5 minutes, compared to an estimated 34 minutes for a full ODMR spectrum method.
- Validation: The scheme was experimentally validated by imaging the stray field of the frustrated magnetic material Fe3Sn2.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Maximum Detectable Gradient | 0.86 | mT per pixel | Acutance limit, twice the frequency offset (d) per pixel. |
| Magnetic Field Dynamic Range | 10 | mT | Achieved in simulations (fluctuation range). |
| Scanning Speed (4096 pixels) | ~5 | minutes | Total acquisition time for the image. |
| Integration Time per Pixel | 25 | ms | Integration time per frequency measurement. |
| Pulsed ODMR Sensitivity | 1.6 | ”T/âHz | Measured sensitivity of the NV sensor. |
| Bias Magnetic Field (Bz) | 5.5 | mT | Applied along the NV axis for measurement. |
| MW Frequency Offset (d) | 12 | MHz | Fixed offset used for tracking (assigned as FWHM). |
| Reconstruction Parameter (λ) | 1 x 10-9 | N/A | Smoothness constraint parameter for RBF-TPS. |
| Simulated Mean Photon Count | 5000 | N/A | Used to introduce shot noise in simulations. |
| Sample Material | Fe3Sn2 | N/A | Frustrated magnetic thin film used for experimental validation. |
Key Methodologies
Section titled âKey MethodologiesâThe imaging process relies on a dynamic frequency tracking loop combined with a sophisticated RBF reconstruction algorithm.
-
Experimental Setup:
- A diamond sensor containing a near-surface NV center is used.
- The sample (Fe3Sn2 thin film on a resin platform) is scanned over the NV center using an Atomic Force Microscope (AFM) tuning fork tip.
- A 5.5 mT bias field is applied along the NV axis. MWs are delivered via a copper wire antenna.
-
Dynamic Frequency Tracking (Three-Frequency Measurement):
- Initial Step: The resonance frequency (f0) is determined at the first pixel using a full ODMR spectrum.
- Measurement: At each pixel, PL is recorded at three frequencies: f0, f- = f0 - d, and f+ = f0 + d (where d = 12 MHz is the fixed offset). This yields PL signals C0, C-, and C+.
- Tracking Logic: The system compares C0 to the minimum of C- and C+, using a threshold k (k = 0.96) to suppress noise.
- Adjustment: If the signal indicates the resonance has shifted beyond the tracking range (e.g., C- is significantly lower than C0), the entire set of frequencies (f0, f±) is shifted (e.g., by 8 MHz) for the next pixel to re-center the measurement on the new resonance peak.
-
Fringe Image and Data Preparation:
- The magnetic resonance fringe image (S) is calculated as the normalized PL: S = C0 / max{C-, C+}.
- The tracking procedure generates two maps: the normalized PL fringe image (S) and the map of the central excitation frequency (f0).
-
Magnetic Field Reconstruction (RBF-TPS Algorithm):
- Model: The resonance frequency map is approximated using the Thin Plate Spline (TPS) function, a type of Radial Basis Function (RBF).
- Minimization: The coefficients of the TPS function are determined by minimizing a weighted energy function E(f). This function balances the fidelity of the fit to the measured data (Si) against the smoothness of the reconstructed surface (bending energy), controlled by the parameter λ (1 x 10-9).
- Output: The reconstructed frequency map is converted into the final magnetic field map (B) along the NV axis.
Commercial Applications
Section titled âCommercial ApplicationsâThis high-efficiency, high-dynamic-range NV magnetometry technique is critical for advancing research and development in several high-tech sectors.
-
Advanced Data Storage (Spintronics):
- Efficient imaging of complex, high-gradient magnetic textures like magnetic skyrmions and domain walls, which are foundational elements in next-generation memory and logic devices.
- Characterization of magnetic switching dynamics in MRAM and racetrack memory prototypes.
-
Quantum Sensing and Metrology:
- Development of robust, high-speed magnetic field sensors capable of operating in environments with high magnetic noise and large field fluctuations (millitesla range).
- Enables faster screening and characterization of quantum materials and devices.
-
Materials Science and Condensed Matter Physics:
- High-resolution study of magnetism in novel materials, including frustrated magnets (like Fe3Sn2) and two-dimensional (2D) magnetic systems, where stray fields are often complex and localized.
-
Micro- and Nano-Electronics:
- Non-destructive testing (NDT) and failure analysis by mapping current distributions and localized magnetic anomalies in integrated circuits and microfabricated components.
-
NV Center System Integration:
- The RBF-TPS reconstruction algorithm can be integrated into commercial NV scanning microscope software packages, significantly enhancing their operational efficiency and dynamic range without requiring hardware modifications.
View Original Abstract
Exotic magnetic structures, such as magnetic skyrmions and domain walls, are becoming more important in nitrogen-vacancy center scanning magnetometry. However, a systematic imaging approach to mapping stray fields with fluctuations of several milliteslas generated by such structures is not yet available. Here, we present a scheme to image a millitesla magnetic field by tracking the magnetic resonance frequency, which can record multiple contour lines for a magnetic field. The radial basis function algorithm is employed to reconstruct the magnetic field from the contour lines. Simulations with shot noise quantitatively confirm the high quality of the reconstruction algorithm. The method was validated by imaging the stray field of a frustrated magnet. Our scheme had a maximum detectable magnetic field gradient of 0.86 mT per pixel, which enables the efficient imaging of millitesla magnetic fields.