Magnetometry of neurons using a superconducting qubit

Iron is a key trace element whose spatial distribution and valence state in tissues inform cellular mechanisms of toxicity, metabolism, and disease. Conventional single-cell analytical methods (e.g., ICP-MS, MALDI-MS) require homogenization and are not in situ, while optical methods (e.g., Raman) cannot resolve metal valence or coordination. ESR spectroscopy can identify oxidation and coordination states via spectroscopic fingerprints, but conventional ESR lacks the sensitivity and spatial resolution for in situ, single-cell measurements. Microscale magnetometers (Hall probes, MFM, NV centers, SQUIDs) can detect ESR-related magnetization, yet face a trade-off between spatial resolution and sensitivity. Superconducting devices allow tunable detector size, matching cellular dimensions and enabling arrays for imaging. Prior work showed superconducting flux-qubit ESR with tens of spins/√Hz sensitivity over micrometer areas. The present study asks whether a superconducting flux qubit can detect the magnetization from electron spins in iron-rich cultured neurons at cellular scales, thereby paving a route to single-cell ESR and spin imaging for studying iron metabolism in neurons and tissues.

• Conventional mass spectrometry methods (ICP-MS, MALDI-MS) achieve quantitative single-cell analysis but are destructive and not in situ.
• Optical techniques (Raman/SERS) enable in situ cellular imaging but do not provide detailed metal valence/coordination information.
• ESR spectroscopy offers fingerprints for oxidation/coordination states, yet conventional ESR has limited spatial resolution/sensitivity for single cells.
• Alternative microscale magnetometers used for ESR detection include scanning Hall probes, MFM, NV centers, and superconducting devices (SQUIDs, flux qubits), each balancing resolution versus sensitivity differently.
• Superconducting resonators and magnetometers have advanced ESR sensitivity; prior flux qubit work reached sensitivity down to ~tens of spins/√Hz over micrometer-scale areas, suggesting suitability for cellular-scale measurements.

Principle and device: A superconducting flux qubit on a silicon substrate is used as a sensitive magnetometer. The qubit state is read out inductively via a DC SQUID whose switching probability reflects the qubit state. A microwave excitation tone drives the qubit through an on-chip line. An in-plane magnetic field B|| polarizes electron spins in the sample (neurons), while a perpendicular field B⊥ sets the qubit’s operation point on its flux-dependent spectrum where the frequency has finite slope, converting sample magnetization changes into measurable qubit resonance shifts.

Sample preparation and insulation: Cultured neurons are prepared on a 2 µm thick poly(chloro-p-xylylene) (parylene-C) film to provide electrical insulation and mechanical support. Neurons are dissected from hippocampi of 18-day-old Wistar rat embryos, cultured per prior protocols, fixed with glutaraldehyde, freeze-dried, and the neuron-laden parylene-C film is detached from glass and transferred onto the qubit chip. Dense seeding (5000 cells/mm²) aids alignment. Neurons are cultured in Fe³⁺-rich medium to increase intracellular Fe³⁺ content (validated by staining and supplementary analyses). Without insulation, qubit readout is disrupted; parylene-C provides necessary electrical isolation while maintaining proximity.

Assembly and spacing: After transfer, ethanol is applied to promote film adhesion by surface tension. Optical interference patterns indicate a qubit–neuron separation of several micrometers, within the flux qubit’s sensing volume.

Cryogenic measurement: Experiments are conducted in a dilution refrigerator. Temperatures are varied between 12.5 mK and 200 mK; B|| is varied from 2.5 mT to 12.5 mT. Qubit spectra are recorded as switching probability maps versus applied flux and microwave frequency. Sufficient wait times (>45 min) after temperature changes ensure thermalization. Magnetometry of pure parylene-C film without neurons is performed as a control to quantify background magnetization from substrate/insulator spins.

Modeling: Electron spins associated with cellular Fe³⁺ ions are modeled with spin S=5/2 and Hamiltonian H = μB g·B·S + D S_z^2 + E(S_x^2 − S_y^2), using literature parameters gx=1.83, gy=1.998, gz=2.0151, D=20.96 GHz, E=6.967 GHz. Energy levels E_n(B) and thermal populations are computed to simulate magnetization versus B||/T under experimental conditions.

Conventional ESR: X-band ESR spectroscopy (Bruker E500, TE011 cavity, Q~8000) at 9.38 GHz, 8 mW, with ~0.3 T field and 0.9 mT, 100 kHz field modulation is used to measure neurons prepared under the same conditions. Samples are in 5 mm quartz tubes at 10 K to identify spin species via g′-factor peaks.

• Flux-qubit spectra shift with temperature at fixed B||=10 mT, indicating decreasing neuron magnetization with increasing temperature. Clear qubit spectra observed above ~16 GHz due to parasitic resonances.
• Magnetization versus inverse temperature shows near-linear increase at higher temperatures and saturation at low temperatures; warmup and cooldown curves overlap (no hysteresis). Thermalization requires >45 min after temperature changes.
• Magnetization versus B|| at various T collapses approximately onto a B||/T scaling trend. Simulations using S=5/2, gx=1.83, gy=1.998, gz=2.0151, D=20.96 GHz, E=6.967 GHz predict linear dependence in the explored range (consistent with a two-level approximation since E2−E1 ~70 GHz >> experimental energy scale ~4 GHz).
• Experimental magnetization saturates earlier than simulations assuming the refrigerator temperature; attributed to elevated effective spin temperature due to limited thermal conductivity of parylene-C. Effective spin temperature saturates around 40–90 mK (field-dependent) despite colder base temperature.
• Control measurements on pure parylene-C show much smaller magnetization than neuron-laden films, confirming neuron-originated signal.
• Conventional ESR at 10 K shows peaks at g′≈4.3 (dominant; high-spin Fe³⁺, ±3/2 transition), g′≈9.8 (Fe³⁺, ±1/2 transition), and g′≈2.0 (likely Cu or radicals). The dominance of Fe³⁺ features confirms iron spins are the main contributors to magnetization detected by the qubit.
• Spatial resolution: Qubit loop size (24×6 µm) matches neuron size (10–20 µm); neuron seeding yields ~14 µm average spacing, implying sensing area typically interrogates approximately one neuron.
• Estimated spin count and density: Assuming conversion factors from prior solid-state calibrations, detected spins ~9×10^6 within ~100 µm³ sensing volume → ~9×10^13 spins/mm³. Conventional ESR yields ~2×10^12–2×10^13 spins/mm³; order-of-magnitude agreement supports common origin.
• Estimated iron mass in cells ~8 µg/g, consistent with literature for human brain tissue (2–34 µg/g).

The study demonstrates that a superconducting flux qubit can sensitively detect magnetization from electron spins in cultured neurons, addressing the key limitation of conventional ESR for single-cell analysis. The observed temperature and field dependencies are consistent with Fe³⁺ spin physics (S=5/2 with zero-field splitting), and independent ESR spectra confirm iron as the dominant spin species. The flux qubit’s micrometer-scale loop area confers cellular-level spatial resolution, indicating feasibility for single-neuron magnetometry and, with excitation tones, ESR spectroscopy at the single-cell level. These capabilities would enable mapping of iron distribution and redox states across heterogeneous cell populations, advancing the study of metal metabolism in neural tissues. Disparities between simulated and measured magnetization curves highlight the role of effective spin temperature and thermal coupling, suggesting that improved thermal pathways and extended field ranges are needed to reach full saturation and extract intrinsic spin parameters (e.g., g-tensor, spin number) directly. Arrays of flux qubits or controlled motion of cell-laden films could enable spatial imaging of spin distributions in tissues.

This work establishes superconducting flux qubits as microscale magnetometers capable of detecting electron spins in cultured neurons, with evidence pointing to Fe³⁺ as the dominant contributor, validated by conventional ESR. The qubit’s sensing area matches single-cell dimensions, opening a pathway to single-cell ESR spectroscopy and imaging of spin species in biological systems. Future directions include: improving thermal coupling (e.g., alternative insulating materials with higher thermal conductivity) to align spin and fridge temperatures; extending in-plane field compatibility (e.g., niobium-based devices or thin superconducting films) to reach saturation regimes; establishing quantitative calibration from magnetization to spin number via reference samples and full-saturation measurements; integrating ESR excitation to disentangle multiple spin species by their g-factors; and developing qubit arrays or scanning approaches for spatial mapping of spin distributions in tissues.

• Thermal coupling: Effective spin temperature saturates at ~40–90 mK due to limited thermal conductivity of parylene-C, leading to earlier-than-expected magnetization saturation and deviations from model predictions.
• Magnetic field range: Aluminum flux qubit becomes inoperational for in-plane fields >~20 mT, limiting access to full magnetization saturation and parameter extraction.
• Quantification: Exact conversion from measured magnetization to absolute spin number is not directly known without a calibrated conversion factor; current spin number estimates rely on assumptions from solid-state calibrations.
• Spectral range: Parasitic circuit resonances limited clear qubit spectra to >~16 GHz.
• Sample preparation constraints: Necessity of an insulating layer increases qubit–sample spacing; maintaining minimal distance while ensuring electrical isolation is required. Long thermalization times (>45 min) are needed after temperature changes.
• Control materials: Background spins from substrate/insulator are small but nonzero and require separate control measurements.