All-Optical dc Nanotesla Magnetometry Using Silicon Vacancy Fine Structure in Isotopically Purified Silicon Carbide

We uncover the fine structure of a silicon vacancy in isotopically purified silicon carbide (4H-${}^{28}\mathrm{SiC}$) and reveal not yet considered terms in the spin Hamiltonian, originated from the trigonal pyramidal symmetry of this spin-$3/2$ color center. These terms give rise to additional spin transitions, which would be otherwise forbidden, and lead to a level anticrossing in an external magnetic field. We observe a sharp variation of the photoluminescence intensity in the vicinity of this level anticrossing, which can be used for a purely all-optical sensing of the magnetic field. We achieve dc magnetic field sensitivity better than $100\mathrm{nT}/\sqrt{\mathrm{Hz}}$ within a volume of $3\times {10}^{-7}\mathrm{m}{\mathrm{m}}^3$ at room temperature and demonstrate that this contactless method is robust at high temperatures up to at least 500 K. As our approach does not require application of radio-frequency fields, it is scalable to much larger volumes. For an optimized light-trapping waveguide of $3{\mathrm{mm}}^3$, the projection noise limit is below $100\mathrm{fT}/\sqrt{\mathrm{Hz}}$.

Popular Summary

Precise measurements of magnetic fields are required in many applications from space science to medicine and nanotechnology. One of the standard approaches to realize highly sensitive chip-scale magnetometry is based on the optically detected magnetic resonance of color centers in solids. In this technique, intense radio-frequency pulses are applied to manipulate spin states subject to the external magnetic field, which are then read out optically. Here, we demonstrate an alternative method for magnetic-field sensing that does not require radio-frequency fields. This method is based on sharp variations in the photoluminescence intensity with magnetic field, associated with atom-size defects in silicon carbide. Using this straightforward approach, we achieve 100-nT dc magnetic-field resolution within a $1000\mu {\mathrm{m}}^3$ detection volume for an integration time of 1 s.

The pronounced variations in the photoluminescence intensity that we observe are caused by level anticrossings and are related to additional terms in the spin Hamiltonian associated with the trigonal pyramidal symmetry of the silicon vacancy defects in silicon carbide. These terms have not been considered thus far, and they also explain the puzzling observation of the spin transitions with the change of the spin projection quantum number equal to $\pm 2$ (i.e., the transitions that are typically forbidden). We show that since these effects are a basic property of any spin-$3/2$ system possessing low symmetry, our approach can be applied to many other similar defect centers in wide-band-gap materials as well as to quantum dots. The demonstrated method is robust up to at least 500 K, which suggests that it is a simple, contactless method to monitor weak magnetic fields over a broad temperature range, particularly when radio-frequency fields cannot or should not be applied. For an optimized light-trapping waveguide of $1\mathrm{m}{\mathrm{m}}^3$, we expect that magnetic fields in the subpicotesla range can be detected within 1 s.

We anticipate that our findings will pave the way for experimental applications in detecting magnetic fields in biomedicine and geophysics.

Figure 1

(a) The GS ($2D=70\mathrm{MHz}$) and ES ($2D^{\prime }=410\mathrm{MHz}$) spin sublevels of the $V_{\mathrm{Si}}$ point defect in external magnetic field $B_z\parallel c$, assuming a weak perpendicular component $B_{\perp }\ll B_z$. The vertical arrows indicate rf-driven spin transitions, their thicknesses mirroring the contrasts of the corresponding ODMR lines. The magnetic field evolutions of the GS and ES are shown schematically, i.e., not to scale. (b) Magnetic field versus frequency evolution of the $V_{\mathrm{Si}}$ ODMR signal recorded at room temperature and at low rf power. The solid and dashed lines are the positions of the ODMR peaks calculated for the $\mathrm{\Delta }{m}_S=\pm 2$ transitions in the GS and $\mathrm{\Delta }{m}_S=\pm 1$ transitions in the ES, respectively. (c) Low-rf-power (9 dBm) and high-rf-power (40 dBm) ODMR spectra in zero magnetic field.

Figure 2

(a) Relative strength of the ${\nu }_1$ and ${\nu }_2$ ODMR transitions ($\mathrm{\Delta }{\mathrm{PL}}_1/\mathrm{\Delta }{\mathrm{PL}}_2$) as a function of the magnetic field $\mathbf{B}$ applied parallel to the $c$ axis of 4H-SiC. The arrows indicate the positions of GSLAC-1 (2.5 mT) and ESLAC-1 (15 mT). The vertical dashed lines correspond to the expected positions of GSLAC-2 (lower field) and ESLAC-2 (higher field). (b) Lock-in detection of the PL variation $\mathrm{\Delta }\mathrm{PL}/\mathrm{PL}$ as a function of the dc magnetic field $B_z$, where $\mathrm{\Delta }\mathrm{PL}$ is caused by the application of an additional weak oscillating magnetic field $\mathrm{\Delta }B$; i.e., $B_z+\mathrm{\Delta }B\cos \omega t$ with $\mathrm{\Delta }B=83\mu \mathrm{T}$ and $\omega /2\pi =5\mathrm{kHz}$. The sharp resonancelike signal at 1.25 mT corresponds to GSLAC-2. Resonant rf field is not applied. Upper inset: A scheme of the experiment. Lower inset: A detailed measurement in the magnetic field range corresponding to ESLAC-2.

Figure 3

(a) Evolution of the ${\nu }_1$ and ${\nu }_3$ ODMR lines in the vicinity of GSLACs as a function of the magnetic field $B_z$. The perpendicular components of the geomagnetic field are compensated. (b) Same as (a), but measured for nonzero $B_x$. The vertical arrows indicate the positions of the turning points ${\nu }_1^{\mathrm{AC}}$ and ${\nu }_3^{\mathrm{AC}}$, which are a direct measure of the level splittings at GSLAC-1 and GSLAC-2, respectively. (c) The GSLAC splittings as a function of $B_x$. The solid lines are calculations as explained in the text.

Figure 4

(a) Lock-in detection of the PL variation in the vicinity of GSLAC-2 ($B_{G2}=1.25\mathrm{mT}$) under application of a weak oscillating magnetic field, recorded at different temperatures. (b) The in-phase $U_X$ and quadrature $U_Y$ components of the lock-in photovoltage (left axis) for different magnetic fields (right axis), increased in sub-$\mu \mathrm{T}$ steps every 125 s. The horizontal line is the $U_Y$ mean value. The maximum field sensitivity is obtained for the modulation depth $\mathrm{\Delta }B=200\mu \mathrm{T}$ and modulation frequency $\omega /2\pi =511\mathrm{Hz}$. Temperature in (b) is $T=300\mathrm{K}$.

Figure 5

(a) Lock-in detection of the PL variation in the vicinity of GSLAC-2 ($B_{G2}=1.25\mathrm{mT}$), performed in 4H-SiC with natural isotope abundance. Satellite resonances are due to the hyperfine interaction with ${}^{29}\mathrm{Si}$ nuclei. Inset: Variation of the peak-to-peak width as a function of the magnetic field orientation. (b) PL variations at GSLAC-1 (at $B_{G1}$) and GSLAC-2 (at $B_{G2}$) for different magnetic field orientations with respect to the $c$-axis (polar angle $\theta$). $T=300\mathrm{K}$. The nonzero peak-to-peak width for $\theta =0°$ is ascribed to magnetic fluctuations of the environment (nuclear spins and paramagnetic impurities) and magnetic field alignment uncertainty (1°).

Figure 6

(a) Evolution of the ODMR spectrum as a function of the perpendicular magnetic field $B_{\perp }=B_x$ ($B_y=0$). (b) Points represent the quadratic shift $({\nu }_2+{\nu }_1)/2-{\nu }_0$ versus the Zeeman splitting in terms of $3({\nu }_2-{\nu }_1{)}^2/8{\nu }_0$. Solid line is a linear fit to Eq. (d5) with a slope of $0.995\pm 0.01$.