Magnetic criticality-enhanced hybrid nanodiamond-thermometer under ambient conditions

Nitrogen vacancy (NV) centres in diamond are attractive as quantum sensors owing to their superb coherence under ambient conditions. However, the NV centre spin resonances are relatively insensitive to some important parameters such as temperature. Here we design and experimentally demonstrate a hybrid nano-thermometer composed of NV centres and a magnetic nanoparticle (MNP), in which the temperature sensitivity is enhanced by the critical magnetization of the MNP near the ferromagnetic-paramagnetic transition temperature. The temperature susceptibility of the NV center spin resonance reached 14 MHz/K, enhanced from the value without the MNP by two orders of magnitude. The sensitivity of a hybrid nano-thermometer composed of a Cu_{1-x}Ni_{x} MNP and a nanodiamond was measured to be 11 mK/Hz^{1/2} under ambient conditions. With such high-sensitivity, we monitored nanometer-scale temperature variation of 0.3 degree with a time resolution of 60 msec. This hybrid nano-thermometer provides a novel approach to studying a broad range of thermal processes at nanoscales such as nano-plasmonics, sub-cellular heat-stimulated processes, thermodynamics of nanostructures, and thermal remanent magnetization of nanoparticles.

earth nanoparticles 12 , nanogels 13 , dyes 14 or proteins 15 . However, these techniques are limited by various factors, such as low sensitivity (rare-earth nanoparticles), contactrelated artefacts (SThM), fluorescence instability (dyes), or the requirement of extreme working conditions (SQUID based nano-thermometer). Nitrogen-vacancy (NV) centres in diamond are a promising nano-sensor 16 owing to their atomic size and long spin coherence time 17,18 under ambient conditions. The spin resonances of NV centres shift with temperature, providing a mechanism for atomic scale temperature sensors 19 .
However, the temperature dependence of NV centre spin resonances, which results from the shift of the zero-field splitting D, is a small effect (dD/dT≈ −74 kHz/K) 19 .
Therefore, even with single NV centres in ultra-high pure bulk diamond sample and advanced pulse control techniques, the sensitivity for temperature sensing is limited to a level of several mK/Hz 1/2 (Refs. [20][21][22]. Here we demonstrate the strategy of hybridization 23 to improve the sensitivity of diamond nano-thermometers by converting the temperature variation to a magnetic field change. NV centres have been demonstrated to be ultra-sensitive to external magnetic field [24][25][26][27][28] . The magnetization of a magnetic nanoparticle (MNP) can be used to monitor its local temperature, and this mechanism becomes ultra-sensitive when temperature is close to the magnetic phase transition point (i.e., critical point) of the 3 MNP. The sensitivity of a hybrid nano-thermometer composed of a Cu1-xNix MNP and a nanodiamond under ambient was measured to be 11 mK/Hz 1/2 under ambient conditions. The temperature range in which the hybrid sensor has high sensitivity can be setting different critical temperatures of the materials (e.g., via tuning the chemical composition of the Cu1-xNix MNP). This hybrid nano-thermometer provides a novel approach to studying a broad range of thermal processes at nanoscales such as nanoplasmonics, sub-cellular heat-stimulated processes, thermodynamics of nanostructures, and thermal remanent magnetization of nanoparticles.

Scheme of the hybrid sensor and theoretical sensitivity estimation
The hybrid nano-thermometer is composed of a fluorescent nanodiamond (FND) and an MNP, as shown in Fig. 1a. The ground state of the NV centre is a spin triplet (S = 1) with a zero-field splitting D ≈ 2.87 GHz between the m s = 0 state and the m s = ±1 states. The spin transitions of NV centres in the FND are shifted by the magnetic field from the MNP, B MNP (T). The Hamiltonian of an NV centre can be written 16 as where E is the lattice strain effect and γ = 28 MHz/mT is the electron gyromagnetic ratio. The field from the MNP BMNP(T) is determined by its magnetization (T), which depends sensitively on the temperature when the temperature is below and close to the ferromagnetic-paramagnetic transition point (Fig. 1b). Therefore the spin resonance of the NV centres in the FND presents abrupt dependence on temperature near the transition point of the MNP. Previously, the temperature shift of zero filed splitting dD/dT≈74 kHz/K is measured to extract the temperature change [19][20][21][22] . Here the transition frequencies ± (for |0〉 ↔ |±1〉) of the NV centre spins are measured to extract the magnetization properties of the adjacent MNP (Fig. 1c), which serves as a transducer and amplifier of the local temperature variation. The critical behavior of the MNP enhances the temperature sensitivity of the NV centres. 4 The sensitivity of the hybrid sensor is determined by the magnetization of MNP, the number and coherence of NV centres, and the relative position and orientation between the two nanoparticles. FNDs with size ~100 nm containing 500 NV centres were used in experiments.  32,33 , the hybrid sensor can be designed to fulfil a wide range of applications. In Fig. 1d, we present the composition (and thus temperature) dependence of the sensitivity of the Cu1-xNix MNP based hybrid sensor. The optimized temperature sensitivity is better than 10 mK for the whole range (0 K to 637 K), which has considered the contrast change of optically detected magnetic resonance (ODMR) with temperature 32 .

Proof-of-the-principle experiment -Gd particle and bulk diamond
As a proof-of-the-principle demonstration of the magnetic criticality-enhanced quantum sensing, we tested a hybrid sensor composed of a gadolinium (Gd) particle (with size ~2 mm and mass ≈30 mg) and a single NV centre in a bulk diamond (3 mm 5 x 3 mm x 1 mm). The distance between the NV center and the Gd particle is about 2 mm. Such a distance is chosen to approximately simulate the configuration of an MNP coupled to an FND since the field from a magnetic particle, in the dipole approximation, is proportional to the total volume and inversely proportional to the cubic distance. Gd has the ferromagnetic-paramagnetic transition near room temperature (TC≈19℃) 34 .
Continuous-wave ODMR measurement was carried out in a temperature range between 11 ℃ and 37 ℃ under a uniform external magnetic field ( B ≈ 100 Gauss).  The induced magnetic moment can be deduced from the ODMR spectrum, which is consistent with the magnetic moment of the same Gd particle measured by vibrating sample magnetometer (VSM, Quantum Design). For comparison, the ODMR spectral shift of the same NV centre (with Gd removed) is shown in Fig. 2c, which presents only a weak dependence on temperature, dD/dT = −71 ± 2 kHz/K (Fig. 2d), consistent with previous reports 19 . The magnetic criticality of the Gd particle induces an enhancement of spectral susceptibility to temperature by a factor of 200. The magnetically enhanced temperature sensitivity of the NV centre is evaluated with Eq.
(3) in Method using the experimentally measured d/dT, the spin resonance width, the contrast, and the photon counts. We realized a sensitivity of 45 mK Hz −1/2 . While this sensitivity was limited by the weak photon counts (8×10 4 sec −1 per NV center) in our system, it is already 200 times better than the bare NV centre in the same setup.

Sensitivity enhancement by ensemble NV centres -Gd particle and FND
To achieve a better temperature sensitivity of the hybrid sensor, we replaced the single-NV bulk diamond with an FND containing ensemble NV centers (from Admas, claimed of about 500 NV centres per FND) to enhance the photon counts of the hybrid 6 sensor. The FND was placed about 2 mm away from the Gd particle. The distance between the FND and the Gd particle was chosen comparable to the size of the Gd particle so as to simulate the field strength from an MNP. To show that the dependence of the sensitivity on temperature, we measured the sensitivity at different temperatures with a photon count rate of 6×10 6 sec −1 . The resonant frequency ω − as a function of temperature is shown as an inset in Fig. 3a (with a sharp change near TC). The sensitivity, as determined by equation (3) in Method using experimentally measured photon counts, spin resonance width, contrast and d/dT, is shown in Fig. 3a  The temperature range was chosen near the optimal value (T≈19℃, close to TC of Gd).

Nano-thermometer -CuNi MNP and FND
Finally, we demonstrate that the criticality-enhanced sensing works at nanoscale. The frequency shift induced by the magnetization of the MNP is reversible when the temperature was scanned back and forth between below and above the critical temperature of the material, as in Fig. 4c. The reversibility is ascribed to the large anisotropy energy of CuNi nanoparticles. Meanwhile, this hybrid sensor is very robust and stable. In measurements over more than one month, its temperature response showed negligible change. From the frequencies resonance, the magnetization of the CuNi MNP at different temperatures can be determined by numerical simulation, which agrees well with the critical behavior of CuNi (Fig. 4d). The Curie temperature is determined to be about 340 K, consistent with the composition of the MNP Cu0.26Ni0.74 measured by the energy-dispersive X-ray spectroscopy (EDX) in TEM 31 . The 8 consistency verifies that the heating within the 300 nm laser spot is uniform and the temperatures of the MNP and the FND are close.
Then we measured the sensitivity of the hybrid nano-sensor. In the nano-sensor, due to the magnetic field gradient and NV centre distribution in the FND, the line shape changes (both line width and contrast) much more significant than the frequency shift with temperature, especially for temperatures close to the critical point. As illustrated in Fig. 4b, in the 1 ℃ temperature change close to TC (67 ℃), the ODMR line shape changes significantly. From the difference between the two spectra, we find that the most sensitive frequency is close to the center of the dip (Fig.4b lower panel). Thus we use the contrast change dS/dT for the microwave frequency fixed at the dip position to measure the sensitivity. According to equation (2) in Method, a sensitivity of 11 mK/Hz 1/2 was realized at the most sensitive point (the temperature-induced variation of the normalized signal dS/dT=0.025 /K at ω = 2866 MHz, with photon counts L= 12 Mcps). This sensitivity is close the the optimal temperature sensitivity of 3 mK/Hz 1/2 (Fig. 1d).
We tested the real-time temperature monitoring using the hybrid nano-sensor.
With the modified three-point method (choosing two of the most sensitive frequencies, at the dip of the ODMR spectrum, one far from the resonance, as reference to cancel laser fluctuation), we carried out the real time measurement at 63℃, the shot-noise limited sensitivity for three-point method could be 23 (2)  The temperature sensitivity can be further improved by using NV centre spins of longer coherence times and employing pulse control protocols for high-sensitivity d.c.
magnetic field sensing 26 . Figure 6a shows

Sensitivity -theoretical estimation and experimental measurements
Magnetizations of Cu 0.3 Ni 0.7 alloy NMP are calculated with a mean-field theory.
Transitions frequencies of the NV centre spins are obtained by diagonalizing the effective Hamiltonian in equation (1). For ensemble NV centres in an FND, continuous wave ODMR is utilized for thermal sensing. Thus sensitivity 28 becomes where (ω) is the normalized ODMR spectrum and L is the photon count rates. If the ODMR spectrum is Lorentz shape. The sensitivity can be optimized by choosing the frequency at the half-height of the resonance. The result is where ∆ω is the linewidth and C is the contrast of the resonance.
To test whether the sensitivity of our system is shot noise limited, we kept the system at a stable temperature and different integration times were used to carry out three-point ODMR measurements. One point was chosen as the reference frequency to normalize the laser fluctuation for long term measurement. The sensitivity evaluated from three-point method is larger by √1.5 than the sensitivities evaluated from Equation (2) and (3). The standard deviation of temperature δT as a function of the square root of integration time √∆ determines the temperature sensitivity, η = δ • √∆ .

Sample preparation
The bulk diamond (from Element Six) is a high-purity type-IIa sample with a natural 1.1% 13

Experimental setup
We used a home-built confocal microscope for imaging and ODMR measurement.
NV centre spins are optically pumped by a 532 nm laser, manipulated by resonant microwave fields applied through a 25 m diameter gold wire, and detected via spinstate-dependent fluorescence measurements. The power of the microwave is adjusted to maximize the ODMR contrast but without extra heating effect and is kept unchanged through the experiments. For FNDs, the width of ODMR spectra is mainly determined by the inhomogeneous broadening of ensemble NV centres (which is much greater than the power broadening induced by the laser excitation). For the CuNi-FND hybrid sensor, the nanoscale magnetic field gradient causes extra broadening to the ODMR spectra.
An incubator from INSTEC was used in the Gd-related experiments to control the temperature with the stability of sub 10 mK. A Pt thermocouple was placed near the Gd particle to monitor the local temperature. The heating and cooling rate of the incubator is 0.5 º C/min, and ODMR measurements were carried out after the sample reached its thermal equilibrium state (in about 20 minutes). In the real time temperature monitor experiments (Fig. 3c), the heater of the incubator generates a periodical temperature variation (with square-wave of 0.2 º C amplitude and 400 sec period), and induces a smooth temperature oscillation at the sample position (with 0.1 º C amplitude and 400 sec period, due to the thermal gradient from the heater to sample). In