Magnetic field noise analyses generated by the interactions between a nitrogen vacancy center diamond and surface and bulk impurities

At a Glance

Metadata	Details
Publication Date	2021-01-11
Journal	Physica B Condensed Matter
Authors	Philip Chrostoski, Bruce Barrios, D. H. Santamore
Institutions	Missouri University of Science and Technology, Delaware State University
Citations	13
Analysis	Full AI Review Included

Executive Summary

This research investigates the fundamental mechanisms of magnetic field noise in Nitrogen Vacancy (NV) center diamonds, crucial for improving the sensitivity and spectral resolution of nanoscale sensors.

Dominant Noise Source Identified: The primary source of magnetic field noise is spin precession fluctuation noise, which is found to be more than five orders of magnitude larger than spin flip fluctuation noise.
Optimal Surface Termination: Oxygen (O)-terminated surfaces yield the lowest noise floor, achieving a 5 to 6 orders of magnitude reduction in noise density compared to Hydrogen (H)- and Fluorine (F)-terminated systems at low frequencies (< 10⁴ Hz).
Mechanism of Reduction: The superior performance of O-terminated surfaces is attributed to the extremely short spin-lattice relaxation time of the impurity electron spins (~7.5 ps), which limits the impurity-impurity spin correlation time, suppressing the dominant spin precession noise.
Bulk Impurity Dominance: In the bulk diamond, Carbon-13 nuclear spins generate noise roughly two orders of magnitude greater than nitrogen impurities, primarily due to the higher number density of ¹³C atoms.
Approximation Warning: The commonly used secular approximation (rotating wave approximation) significantly underestimates the magnetic noise by a factor of 2.7 when the applied magnetic field is low (B < 1 G).
Controlling Factor: For H- and F-terminated surfaces, noise is controlled by the impurity hopping rate at low impurity concentrations (N < 10⁶) and transitions to being controlled by the spin flip rate at high concentrations (N > 10⁶).

Technical Specifications

Parameter	Value	Unit	Context
Noise Reduction (O- vs H/F)	5 to 6	Orders of Magnitude	Low frequency (< 10⁴ Hz) surface noise reduction.
Spin Precession vs Spin Flip Noise Ratio	> 5	Orders of Magnitude	Overall comparison of dominant noise mechanisms.
O-terminated T₁ Relaxation Time	~7.5	ps	Impurity electron spin-lattice relaxation time (T₁).
H-terminated T₁ Relaxation Time	13	µs	Impurity electron spin-lattice relaxation time (T₁).
F-terminated T₁ Relaxation Time	300	µs	Impurity electron spin-lattice relaxation time (T₁).
Carbon-13 vs Nitrogen Bulk Noise Ratio	~2	Orders of Magnitude	Carbon-13 noise is higher due to density.
Secular Approximation Error Factor	2.7	Factor	Noise underestimation at low applied magnetic fields.
Low Applied Magnetic Field Threshold	< 1	G	Field strength where secular approximation is inaccurate.
High Applied Magnetic Field Threshold	> 100	G	Field strength where secular approximation is valid.
Assumed Carbon-13 Number Density	10¹⁹	atoms/cm³	Typical experimental density for bulk noise calculation.
Assumed Nitrogen Number Density	10¹⁸	atoms/cm³	Typical experimental density for bulk noise calculation.

Key Methodologies

The study employed advanced theoretical and numerical methods to model the stochastic dynamics of spin fluctuations arising from impurities.

Surface Noise Modeling (Langevin Method):
- The magnetic noise generated by paramagnetic surface impurities (H-, O-, F-terminated systems absorbed in a thin water layer) was calculated using the Langevin method applied to the Bloch equation.
- The model incorporates two noise mechanisms: fluctuations due to spin precession and fluctuations due to spin flips (hopping).
- The overall effective frequency (Ω) is defined as a linear superposition of the NV electron spin precession (Ω_B) and the impurity interaction term (Ω_imp).
Bulk Noise Modeling (Correlated-Cluster Expansion):
- Noise from bulk impurities (Carbon-13 and Nitrogen nuclear spins) was calculated using the correlated-cluster expansion method, which is suited for dense systems of interacting particles.
- The Hamiltonian includes the free NV center term (H₀), the impurity-impurity dipole-dipole interactions (H_II), and the NV-impurity hyperfine interactions (H_SI).
- A cluster size of k = 2 spins was used, as larger clusters exhibit identical properties due to the rapid falloff of dipole-dipole coupling strength.
Approximation Comparison:
- The noise spectrum for bulk impurities was calculated using both the simplified secular approximation (neglecting off-diagonal terms of the nuclear dipole-dipole Hamiltonian) and the non-secular (exact) method.
- This comparison validated that the secular approximation is only accurate at high applied magnetic fields (B > 100 G).
Probability Distribution:
- The spatial distribution of impurity clusters was modeled using a Poisson probability density function to generalize the single-cluster results to the full N-cluster system.

Commercial Applications

The findings directly impact the design and performance optimization of devices utilizing NV center diamonds, particularly in fields requiring high sensitivity and coherence.

Quantum Sensing and Metrology:
- Development of high-sensitivity magnetic and electric field sensors.
- Optimization of surface treatments (O-termination) for near-surface NV centers used in nanoscale sensing applications.
Quantum Information Processing (QIP):
- Improving quantum coherence times by minimizing noise from both surface and bulk spin baths.
Magnetic Imaging:
- High spatial resolution devices and magnetic imaging systems (e.g., optical magnetic imaging of living cells).
Life Sciences and Biomedicine:
- Use of NV centers as biomarkers and nanometre-scale temperature sensors in biological environments.
Materials Science:
- Guidance for diamond synthesis (e.g., isotopic enrichment) to minimize ¹³C concentration and reduce bulk noise.

Tech Support

Original Source

DOI: https://doi.org/10.1016/j.physb.2020.412767

References

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