Zero-field magnetometry using hyperfine-biased nitrogen-vacancy centers near diamond surfaces

Shallow nitrogen-vacancy (NV) centers in diamond are promising for nanomagnetometry, for they can be placed proximate to targets. To study the intrinsic magnetic properties, zero-field magnetometry is desirable. However, for shallow NV centers under zero field, the strain near diamond surfaces would cause level anticrossing between the spin states, leading to clock transitions whose frequencies are insensitive to magnetic signals. Furthermore, the charge noises from the surfaces would induce extra spin decoherence and hence reduce the magnetic sensitivity. Here, we demonstrate that the relatively strong hyperfine coupling (130 MHz) from a first-shell ${}^{13}\mathrm{C}$ nuclear spin can provide an effective bias field to an NV center spin so that the clock-transition condition is broken and the charge noises are suppressed. The hyperfine bias enhances the dc magnetic sensitivity by a factor of 22 in our setup. With the charge noises suppressed by the strong hyperfine field, the ac magnetometry under zero field also reaches the limit set by decoherence due to the nuclear spin bath. In addition, the 130 MHz splitting of the NV center spin transitions allows relaxometry of magnetic noises simultaneously at two well-separated frequencies (∼2.870 ± 0.065 GHz), providing (low-resolution) spectral information of high-frequency noises under zero field. The hyperfine-bias-enhanced zero-field magnetometry can be combined with dynamical decoupling to enhance single-molecule magnetic resonance spectroscopy and to improve the frequency resolution in nanoscale magnetic resonance imaging.

Figure 1

Hyperfine spin resonances of nitrogen-vacancy (NV) centers. (a) Structure of an NV center with a host ${}^{15}\mathrm{N}$ nuclear spin and a first-shell ${}^{13}\mathrm{C}$ nuclear spin. The external magnetic field $\mathbf{B}$ is applied along the NV axis (the $z$ axis), and the $x$ axis is defined by the strain. (b) Spin resonance frequencies of an NV center without a strongly coupled ${}^{13}\mathrm{C}$ (NV1) as functions of the magnetic field. The red dots and blue diamonds are for the ${}^{15}\mathrm{N}$ nuclear spin states with ${\mu }_{\mathrm{N}}=+\frac{1}{2}$ and $-\frac{1}{2}$, respectively. The corresponding lines are calculated results with strains ${\mathrm{\Pi }}_x=3.16\mathrm{MHz}$ and ${\mathrm{\Pi }}_z=3.96\mathrm{MHz}$. (c) Spin resonance frequencies of an NV center with a first-shell ${}^{13}\mathrm{C}$ (NV2-C13). The black dots and purple diamonds are for the ${}^{15}\mathrm{N}$ nuclear spin states ${\mu }_{\mathrm{N}}=+\frac{1}{2}$ and $-\frac{1}{2}$, respectively. The inset shows results at fields close to the level anticrossing (LAC) at $B_z\approx 2.3$ mT. The corresponding lines are calculated results with ${\mathrm{\Pi }}_x=2.20\mathrm{MHz}$ and ${\mathrm{\Pi }}_z=1.10\mathrm{MHz}$. (d) Susceptibilities of spin resonance frequencies to the magnetic field $|\partial f/\partial B_z|$ near zero magnetic field for NV1 (red and blue) and NV2-C13 (black).

Figure 2

Zero-field dc magnetometry by a nitrogen-vacancy (NV) center without or with a first-shell ${}^{13}\mathrm{C}$. (a) and (b) Spin coherence time ($T_2^{*}$) of NV1 and NV2-C13, respectively. The dots are measured data, and the lines are fitting curves. Inset in (b) shows results near the level anticrossing (LAC). (c) Sensitivity of NV1 (orange) and NV2-C13 (blue), estimated with Eq. (4) using the parameters extracted from the experimental data. (d) Real-time magnetic field measurement using NV1 and NV2-C13. The two microwave frequencies $f_{1/2}$ are indicated by red dots in the inset of the upper panel. The acquisition time is 0.2 s per frequency. An electromagnet is used to generate magnetic field as shown in the upper panel. The middle and lower panels show the measured results by NV2-C13 and NV1, respectively.

Figure 3

Echo coherence time and sensitivity of ac magnetometry by a nitrogen-vacancy (NV) center without or with a first-shell ${}^{13}\mathrm{C}$. (a) and (b) Spin coherence time ($T_2$) of NV1 and NV2-C13, respectively. Inset in (a) zooms in the field dependence near the level anticrossing (LAC). (c) Sensitivities of NV1 (orange) and NV2-C13 (blue) using the parameters extracted from the experimental data as functions of magnetic field.

Figure 4

Two-frequency zero-field relaxometry enabled by hyperfine coupling to a first-shell ${}^{13}\mathrm{C}$ nuclear spin. (a) Optically detected magnetic resonance (ODMR) spectrum of NV3-C13 with a magnetic nanoparticle placed in the proximity. (b) Populations in the states $|m_s=-1,{\mu }_{\mathrm{C}}=+\frac{1}{2}\rangle$ (red), $|m_s=-1,{\mu }_{\mathrm{C}}=-\frac{1}{2}\rangle$ (navy), and $|m_s=0,{\mu }_{\mathrm{C}}=+\frac{1}{2}\rangle$ (gray) as functions of time after the initialization.

Figure 5

Optically detected magnetic resonance (ODMR) spectra of NV1 and NV2-C13 under $B=33.2$ mT.

Figure 6

Optically detected magnetic resonance (ODMR) spectra of NV1 and NV2-C13 under various weak magnetic fields.

Figure 7

Ramsey interference signals of NV1 and NV2-13C under different magnetic fields.

Figure 8

Relaxation dynamics and pulse sequences for $T_1$ measurement. (a) Relaxation rates between different states. The transition rate (${\gamma }_{\alpha /\beta }$) between $|m_s=+1\rangle$ and $|m_s=-1\rangle$ is much smaller than ${\mathrm{\Gamma }}_i$ when the noise is mainly from the magnetic nanoparticle. (b) Pulse sequences to measure the $T_1$ time. (c) Pulse sequences to measure double-quantum relaxations.

Figure 9

Populations of the spin states and the double-quantum (DQ) signals between $|m_s=+1;{\mu }_C\rangle$ and $|m_s=-1;{\mu }_C\rangle$. (a) Upper: populations of the states $|m_s;{\mu }_C=-\frac{1}{2}\rangle$; lower: DQ relaxation between $|m_s=+1,{\mu }_C=-\frac{1}{2}\rangle$ and $|m_s=-1,{\mu }_C=-\frac{1}{2}\rangle$. (b) Upper: populations of the states $|m_s;{\mu }_C=+\frac{1}{2}\rangle$; lower: DQ relaxation between $|m_s=+1,{\mu }_C=+\frac{1}{2}\rangle$ and $|m_s=-1,{\mu }_C=+\frac{1}{2}\rangle$. The dots are measured spin populations and DQ relaxations, and the curves are fitting results from Eq. (C1).