Microwave-free magnetometry with nitrogen-vacancy centers in diamond

The negatively charged nitrogen-vacancy (NV) center in diamond has emerged as a unique nanoscale sensor full of interesting applications and has been extensively researched in the past years resulting in numerous technological breakthroughs. It forms the basis for sensors to detect magnetic fields¹ (MFs), temperature,^2,3 strain,⁴ rotation,^5,6 electric fields,⁷ and quantum geometrical phases.⁸ In particular, the use of the optically detected magnetic resonance (ODMR) technique⁹ to probe the magnetically sensitive ground state of the NV center has proven to be a successful tool for sensitive MF measurements, both with single and ensembles of NV centers.^1,10,11 Realization of ODMR sensing protocols typically involves green pump light for optical polarization of the NV centers, the application of microwave (MW) fields for the manipulation of their spin state, and an optical readout step involving either detection of NV-photoluminescence (PL)¹ or absorption of 1042 nm radiation resonant with the singlet transition.^12–15 The relevant energy levels can be seen in Fig. 1.¹ When the applied MW fields are resonant with the splitting of the Zeeman sub-levels of the NV center, the transfer of spin populations results in an observable change in PL or absorption.

There are cases where the use of strong MW fields proves to be detrimental to the sensing protocol and therefore can prohibit the employment of an NV-based sensor. An example is the detection of MFs generated by eddy currents in conductive materials in the context of magnetic induction tomography^16,17 (MIT), a research application currently undertaken in our laboratory,¹⁸ where the presence of a conductive structure under examination will heavily affect the application of MW to the diamond. Another example is MF mapping of conductive, magnetic structures.¹⁹ 

There have been several demonstrations of MW-free, and all-optical, diamond-based magnetic sensors, initially implemented with single NV centers attached to scanning atomic force microscopes,^20–22 and more recently with ensembles of NV centers.¹⁹ These MW-free magnetometric protocols have been realized by exploiting either the properties of the NV centers' PL or their decoherence properties under the influence of external MFs. So far, these protocols remain either qualitative, requiring complicated setups to achieve high spatial resolution, or lack high magnetic-field sensitivities and bandwidth.

In this letter, we demonstrate the principles of a sensitive MW-free magnetometer by exploiting the properties of the ground-state level anti-crossing (GSLAC) of the NV center in diamond. We note that the presented technique can be extended to other magnetically sensitive features in the NV-PL or absorption, as discussed later, as well as features associated with other spin defects in solid-state systems. In particular, for the NV center, a ∼102.4 mT background MF causes ground-state Zeeman-sublevel degeneracy and mixing (the anti-crossing), which is visible as a drop in NV-PL under optical pumping. Any additional external MF will perturb the anti-crossing condition and, thus, result in a PL change that can be monitored and used for sensitive detection of the perturbing MF.

Using this technique, we demonstrate a MW-free magnetometer with a 6 nT/$Hz$ MF sensitivity, a bandwidth exceeding 300 kHz, and a projected 0.43 nT/$Hz$ sensitivity limited by the photon shot noise of the PL detection.²³ 

A schematic of the experimental setup is shown in Fig. 1. We used a single-crystal (111)-cut $(2.1×2.3×0.6)mm3$ diamond, synthesized using a high-temperature high-pressure (HPHT) method (Element 6). The diamond with an initial nitrogen concentration of <200 ppm was electron-irradiated at 14 MeV (dose: $1018 cm−2$⁠) and then annealed at 700 °C for 3 h. The resulting NV centers are randomly oriented along all four <111> crystallographic axes of the diamond.

The diamond is placed within a custom-made electromagnet (EM) [Fig. 1(a)] and can be rotated around the z-axis. The EM produces 11.2 mT/A; the current is provided by a computer-controlled power supply (Statron Typ 3257.1). The EM can be moved with a computer-controlled 3D translation stage (Thorlabs PT3-Z8) to align the MF with the respect to the diamond. Additionally, it can be rotated around the y-axis. Therefore, all degrees of freedom to place the diamond in the center of the magnet and to align the [111] NV-axis parallel to the MF can be addressed and optimized.

A secondary coil with four turns is wound around the diamond mount to apply small modulation of the MF. The additional oscillating component $Bm$ is produced with the power amplified output (amplifier: AE Techron 7224-P) of a function generator (Tektronix AFG2021) that is also used as the local oscillator (LO) for the lock-in amplifier (LIA, SRS 865).

The NV centers in diamond are optically spin-polarized with 220 mW of 532 nm light taken from a 12 W laser (Coherent Verdi). The power is adjusted with a half-wave plate (HWP) and a polarizing beam-splitter (PBS) cube. Before the diamond, the light is sent trough an acousto-optical modulator (AOM, AA Electronics MT350-A0) to enable power modulation. Part of the laser light is split-off and measured on a photodiode (PD, Thorlabs PDA36A). The signal is input into a proportional–integral–derivative controller (PID, SRS SIM960) to stabilize the beam power. After the AOM, the beam is focused with a 40 mm focal-length lens into the diamond. The red/near-infrared NV-PL is collected with a 30 mm focal-length lens (numerical aperture $∼0.5$⁠). The collimated PL is separated from the green transmission with a dichroic mirror and a band-stop filter for 532 nm light before being focused onto a PD (Thorlabs PDA36A). The PD signal is sent to the LIA and demodulated at the LO frequency or measured at dc. After initial alignment and calibration of the magnet, the field was scanned from 0 mT to 120 mT in 5 s and the PL was monitored. Figure 2(a) shows the PL measured with the PD as a function of the MF. Figure 2(b) shows the corresponding LIA signal. The modulation frequency of the field was 100 kHz, the modulation depth ∼0.1 mT, and the LIA time constant 30 μs; 64 scans were averaged.

Both plots contain several features previously discussed in the literature. The initial gradual decrease in PL is associated with a reduction in emission of the non-aligned NV centers due to spin-mixing.²⁴ Around 51.4 mT, the observed features [1–7 in Fig. 2(c)] correspond to cross-relaxation events between the NV center and single substitutional nitrogen (P1) centers.^24–26 The feature at 60 mT [9 in Fig. 2(c)] is attributed to cross relaxation with NV centers that are not aligned along the MF.²⁴ At ∼102.4 mT [6 in Fig. 2(d)] is the GSLAC. Several additional features are visible. They can be associated with cross-relaxation events with either the nuclear spins of nearby P1 centers [2–5 and 7–10 in Fig. 2(d)]^24–26 or nuclear spins of ¹³C atoms [1 in Fig. 2(d)].

The angles α and β between the NV-axis and the applied MF need to be precisely controlled [Fig. 1(a)] within ∼1 mrad.²⁷ Misalignment causes a transverse field component which couples the $mS=−1$ and the m_S = 0 magnetic sublevels, broadens the observed GSLAC feature, and therefore leads to a reduction in magnetometric sensitivity. To optimize the GSLAC feature parameters, the angles and the position of the magnet were aligned until a minimum full width at half maximum of 1.2 mT and an optimal contrast of 4.5% was observed [Figs. 2(b) and 2(c)].

An important characteristic of any magnetometer is the sensitivity to ac MFs. For example, in eddy current sensing experiments, oscillating MFs need to be detected. To document the capacity of the MW-free magnetometer to detect these fields, the background MF is scanned around the GSLAC feature while a small oscillating MF (⁠$Bm≈0.09$ mT) is applied at a given frequency. The frequency is then stepped from 300 Hz to 300 kHz (limited by the bandwidth of the power amplifier). The PL is measured with a PD and its oscillating component is read-out with the LIA. On the slopes of the GSLAC feature, the magnetometer is most sensitive to oscillating MFs. An example of such scan is shown in Fig. 3(a). For each frequency, the peak-to-peak response signal of the LIA amplitude output (R) is recorded and normalized with the oscillating current through the driving coil. This current is measured via its voltage drop over a 8 Ω resistor. Initially, the transfer function of the amplifier was measured, and during the experiment coarsely compensated for by adjusting the drive amplitude voltage. This way the current amplitude through the driving coil was effectively the same for all frequencies.

Figure 3(b) shows the peak lock-in amplitude as a function of the modulation frequency. After an initial drop in the response to oscillating fields, the spectrum appears basically flat between 60 kHz and 300 kHz. The initial drop in the response and the slight increase for higher frequencies can be attributed to mutual inductance of the driving coil and the surrounding background field magnet as well as induction in the aluminum magnet mount. Observation of the induced current in the EM is consistent with the frequency characteristic of this feature.

Around the GSLAC feature, the derivative fluorescence signal as detected in the properly phased LIA X output depends linearly on the MF and can therefore be used for precise MF measurements. The calibration signal is shown in Fig. 4(a); the modulation frequency (100 kHz), modulation depth (∼0.1 mT), alignment, and laser power were optimized to maximize the slope, and therefore, the sensitivity of the magnetometer. The data near the zero-crossing are fitted with a straight line to translate the LIA output signal amplitude into MF. Then, the background MF is set to the center of the GSLAC feature (102.4 mT) where the magnetometer is maximally sensitive to external MFs. Figure 4(b) shows a time trace of the magnetometer response to a square-wave-modulated MF of ∼45 μT peak-to-peak amplitude applied with an additional external coil. The standard deviation of the data for a single step level is 1.8 μT (∼80 ms, 4800 samples), so that the steps in the MF can be observed with a signal-to-noise ratio of 25. For noise measurements, the LIA voltage output is recorded for 1 s and translated into MF variations. A fast-Fourier transform is performed to extract information of the MF noise. The data are displayed in Fig. 4(c) with the green pump-power stabilization (red) and without it (green). For comparison, similar data are collected at a MF of around 80 mT (blue). At this field, the setup is insensitive to MF variations and the data can be used to understand the technical noise level of the magnetometer. The noise floor is flat and around 6 nT/$Hz$⁠. The electronic noise floor without green pump light and therefore without PL (black) is about 0.25 nT/$Hz$⁠.

Fundamentally, the magnetometer is limited by the shot-noise of the collected PL. For the given setup, the photon shot-noise limit is calculated to be 0.43 nT/$Hz$ (Ref. 23) (resulting from 300 μW collected PL). However, this limit could be reduced by orders of magnitude by maximizing the amount of emitted and collected PL, possible by saturating the NV-PL and increasing the numerical aperture of the collection optics. The 1/f MF noise in Fig. 4(b) is attributed to the main field power supply. In an actual device, however, scanning of the MF would not be necessary, so that a small permanent magnet with less MF noise could be used. The frequency spikes at the line voltage frequency and its higher harmonics are also attributed to the power supply. They are the dominating noise component in Fig. 4(b). The roll-off for frequencies above 3.5 kHz is a result of filtering by the LIA. The time-constant for the measurements in Fig. 4(c) was 300 μs and the filter slope 24 dB/octave.

In conclusion, we demonstrated a MW-free, NV-center based magnetometer with a 6 nT/$Hz$ noise floor and a bandwidth exceeding 300 kHz. This device can be useful in applications where MW spectroscopy cannot be performed on the NV centers. This is the case where the diamond-based sensor is placed in proximity to conductive objects, and as such, is of particular relevance for spatially resolved conductivity measurements in the context of MIT. The ability of the present technique to detect nuclear spins (seen as side-features near the GSLAC peak) with high signal-to-noise ratio indicates a possibility of applications in sensing spins external to the NV centers. If a layer of shallow-implanted NV-centers is used, spins external to diamond can be probed.

Future investigations will involve a thorough study of the lineshape and width of the signal near the GSLAC, as well as of the additional features around it, with the aim of understanding the fundamental sensitivity and bandwidth limitations²⁸ of our sensing protocol. In addition, combination of the presented MW-free magnetometer with an absorption-based protocol will allow for MF sensing with a sensitivity exceeding the PL shot noise limit.^14,15

We acknowledge support by the DFG through the DIP Program (FO 703/2-1). H.Z. is a recipient of a fellowship through GRK Symmetry Breaking (DFG/GRK 1581). N.L. acknowledges support from a Marie Curie International Incoming Fellowship within the 7th European Community Framework Programme. L.B. is supported by a Marie Curie Individual Fellowship within the second Horizon 2020 Work Programme. D.B. and A.J. acknowledge support from the AFOSR/DARPA QuASAR Program. V.M.A. acknowledges support from NSF Grant No. IIP-1549836. We thank P. R. Nelson, J. W. Blanchard, and D. Twitchen for useful discussions.