Magnetic field orientation dependence of continuous-wave optically detected magnetic resonance with nitrogen-vacancy ensembles

Abstract

Continuous-wave optically detected magnetic resonance (CW-ODMR) measurements with nitrogen-vacancy (NV) spins in diamond are used for sensing DC magnetic fields from nearby magnetic targets. However, this technique suffers from ambiguities in the extraction of the magnetic field components when resonances due to different NV orientation classes overlap with each other. Here, we perform detailed experimental and theoretical studies of such effects on NV ensembles experiencing low bias magnetic fields. In particular, through symmetry considerations, we systematically examine the ODMR response of different NV orientation classes as a function of the orientation of the magnetic field vector. Our studies are of importance for performing a careful and detailed analysis of the ODMR spectra in order to infer the vector magnetic field information. Our results find application in the studies of magnetic samples that require a low applied bias field and also can be potentially adapted to defect spins in other solid-state systems.

Figures (11)

• Figure 1: (a) The diamond lattice hosts four possible NV center orientations, labeled as NV$_\kappa$, NV$_\varphi$, NV$_\lambda$, and NV$_\chi$. For the case of dense NV center ensembles in a single-crystal diamond, the NV centers are equally distributed among the four orientations. For small static magnetic fields (<4 mT), the spin quantization axis of the NV center is along one of the four possible $\langle 111 \rangle$ crystallographic directions. (b) ODMR spectrum corresponding to a magnetic field $\vb*{B}$ that results in distinct projections on all four NV orientations. As a result, the Zeeman splitting $\Delta{f_{i}} = |f_{i+} - f_{i-}|$ varies for each NV orientation, leading to the appearance of eight dips in the spectrum. (c) Schematic representation of the diamond lattice illustrating how the magnetic field $\vb*{B}$ projects onto the four NV orientations. The projections depend on the polar ($\theta$) and azimuthal ($\phi$) angles of $\vb*{B}$ relative to the diamond crystal coordinate system ($x, y, z$). (d) The energy level splittings corresponding to the magnetic field configuration in Fig. 1 (c). Transition frequencies correspond to the dips visible in the ODMR spectrum.
• Figure 2: (a) Schematic of the experimental setup, illustrating the optical, electronic, and microwave components. The NV magnetometer setup makes use of a 30 mm cage mount that integrates all essential optics for fluorescence collection and filtering. A photo-diode converts the NV fluorescence into a voltage signal, which is then processed using a data acquisition (DAQ) system. The electromagnetic coils used for applying a DC magnetic field, labeled "Coil 1" and "Coil 2", are aligned along the Y and Z axes of the laboratory coordinate system, respectively, allowing controlled field application. (b) A zoomed-in view of the diamond sample and the PCB which transmits the microwave field. The applied magnetic field $\vb*{B}$ is depicted with respect to both the laboratory coordinate system (X, Y, Z) and the diamond crystal coordinate system $(x,y,z)$, illustrating its orientation in both coordinate systems. The inset provides a top-down view of the diamond crystal, highlighting the projections of the $\langle111\rangle$ NV axes and their direction relative to the applied magnetic field. (c) Heat-map depicting the number of observable ODMR dips as a function of the orientation angles $\theta$ and $\phi$ for an applied magnetic field of magnitude $|\vb*{B}| = 3$ mT. Here, any two resonance dips are considered distinct if the separation between them $\geq 12$ MHz. This is done to account for the power-broadening effects we experimentally observe in the CW-ODMR spectrum. We note the eight-fold symmetry in the heat-map, which can be attributed to the three-fold mirror symmetry and the three-fold rotational symmetry about the NV axes.
• Figure 3: (a) Illustration of the experimental setup for Case 1, where the current flowing through both the coils is zero, i.e., $|\vb*{B}|$ = 0. (b) The projection of the magnetic field onto the NV orientations is zero. (c) A single dip corresponding to the ZFS is observed in the ODMR spectrum. However, a splitting within this ZFS dip is also observed and a two-peak Lorentzian fit is performed by considering the intrinsic effective field present in the diamond lattice.
• Figure 4: (a) Illustration of the experimental setup for Case 2, where the magnetic field is applied along the Z-axis using Coil 1 only. (b) The applied field $\vb*{B}$ is perpendicular to the green-shaded plane. Due to the tetrahedral symmetry of diamond lattice, the field projections on all four NV orientations share the same magnitude equal to $\frac{B}{\sqrt{3}}$. (c) Consequently, the Zeeman-split resonances of all NV orientations overlap, producing only two distinct dips in the ODMR spectrum.
• Figure 5: (a) Schematic of the experimental setup for Case 3, where the magnetic field is applied along the $Y$-axis using Coil 2. The resulting field orientation satisfies $B_x = B_y$, as also illustrated in the inset. (b) The applied field lies along the intersection of the green and purple planes, ensuring that the projections onto NV$_{\varphi}$ and NV$_{\lambda}$ are zero, while NV$_{\kappa}$ and NV$_{\chi}$ experience equal and opposite projections. (c) Consequently, three distinct dips appear in the ODMR spectrum due to the overlapping resonances of NV$_{\varphi}$ and NV$_{\lambda}$.