Spin defects in hBN as promising temperature, pressure and magnetic field quantum sensors

Spin defects in solid-state materials are strong candidate systems for quantum information technology and sensing applications. Here we explore in details the recently discovered negatively charged boron vacancies (VB−) in hexagonal boron nitride (hBN) and demonstrate their use as atomic scale sensors for temperature, magnetic fields and externally applied pressure. These applications are possible due to the high-spin triplet ground state and bright spin-dependent photoluminescence of the VB−. Specifically, we find that the frequency shift in optically detected magnetic resonance measurements is not only sensitive to static magnetic fields, but also to temperature and pressure changes which we relate to crystal lattice parameters. We show that spin-rich hBN films are potentially applicable as intrinsic sensors in heterostructures made of functionalized 2D materials.


Calculation of polynomial coefficients of Table 1 for temperature measurements
In the main text we derive a relationship between the ZFS $% ( , -) and the relative changes , -of the temperature-dependent lattice parameters ( ) and ( ) (see Eq. (2) in the main text). In the following, we will extend this and derive an expression to compute $% ( ) directly. First, the temperature-dependent lattice parameters ( ) and ( ) are required. We use the mathematical description in terms of a third-order polynomial as described in Ref. [24].
2 and 2 are the polynomial coefficients given in Table 3 of Ref.
[24] and is an integer. The relative changes of the lattice parameters with respect to room temperature are: for k= 1,2,3 Next, we will implement ( ) and -( ) into Eq.
for k= 1,2,3 To assess the heating effect induced by the laser, we measured ODMR spectra at different laser powers between 200 and 1000 mW. An overall shift of <10 MHz due to laser heating is observed. The data is shown in Supplementary Figure 2. Supplementary Figure 2 Influence of laser power on the ODMR signal. a cw-ODMR signals for different laser powers. b Change of the ZFS parameter Dgs/h as a function of the applied laser power. A total shift of <10 MHz due to laser heating is observed. This effect can be neglected for other measurements, since all other measurements presented in this work were performed with laser power <100 mW.
To estimate the heating induced by the microwaves, we measured ODMR spectra at different microwave power between 0.03 and 3 W at room temperature (ambient laboratory conditions). We summarize this data in Supplementary Figure 3. We do observe a change of the ZFS of about 5 MHz, which corresponds to a heating of 10K (red symbols). However, we tend to assign the main effect to the resistive heating of the stripline and not to the power absorbed by the spin system in resonance. The two effects can be separated by a precise measurement in a stabilized cryo-system (shown in purple). The local sample temperature is constant within the error bars, which means that the resonant absorbed microwaves have very little or no influence on the temperature dependent ZFS in this microwave power range.
Supplementary Figure 3 Influence of microwave power on the ODMR signal at room temperature (red) and for temperature stabilized stripline at 300 K (purple). a cw-ODMR signals for different microwave powers. The spectra without temperature stabilization (red) are shifted towards lower frequencies for higher microwave powers. b Change of the ZFS parameter Dgs/h as a function of the applied microwave power. A total shift of 5 MHz due to the resistive heating of the stripline is observed (red spheres). However, the local sample temperature (purple spheres) remains unaffected. The error bars of the Dgs value represent the standard deviation of fits to spectrum.
For pressure sensing, we applied sinusoidal modulation to the B-field about a fixed value. To optimize sensitivity, we measured the influence of modulating the amplitude of the magnetic field onto the ODMR signal to select the one with best S/N ratio. This is shown in Supplementary Figure 4. It is interesting to note, that this modulation scheme also allows us to resolve the hyperfine structure resulting from having 3 equivalent nitrogen nuclei surrounding the boron vacancy.
Supplementary Figure 4 Influence of the magnetic field modulation on the ODMR spectra. a Magnetic field modulation leads to the first derivative of the standard cw-ODMR signal. b Peak-to-peak amplitude can be enhanced by increasing the magnetic field modulation. c ODMR linewidth vs. modulation amplitude. The overmodulation results in line broadening of the signal.
To address possible influence of local strains, we performed ODMR experiments at different sites on the sample and at different temperatures. The parameter we monitored was the off-axis ZFS Egs, sometimes called strain parameter, which we show in Supplementary Figure 5. As can be seen, Egs/h does not depend on the local spot on the sample, but scatters around Egs/h=49 MHz at different temperatures.

Supplementary Figure 5
Off-axis zero-field splitting term Egs/h measured at different sites on the sample a and at different temperatures (110-350K) b for a selected site. The Egs/h values are scattered around 49 MHz, but without a clear trend. The error bars are the same as defined in Supplementary Fig. 3b.