11.2.1 Ultrahigh Precision Temperature Measurement

The NV⁻ center in diamond is an artificial solid‐state atom with optically addressable spin states. It has a crystal field splitting of D = 2.87 GHz between m_s = 0 and ±1, which can be optically read out under ambient conditions even at the single spin level with the optically detected magnetic resonance (ODMR) technique [7], as described in Section 3.4. Remarkably, the spin states have an exceptionally long coherence time (e.g. T₂), capable of remaining coherent for more than 1 ms in isotope‐free bulk diamond at room temperature [8]. Both the spin resonance and coherence time of the NV⁻ center are sensitive to the variations of temperature, magnetic field, electric field, and mechanical stress present in its environment [3]. This renders NV⁻ a useful tool for ultra‐sensitive measurements of these physical parameters at the nanoscale, provided that the centers are implanted in nanoscale diamonds or near the surface of bulk diamonds.

Acosta et al. [9] were the first to investigate the effects of temperature on the spin resonance of the NV⁻ centers. Using ODMR, they measured the temperature‐dependent shift of the zero field splitting from 280 to 330 K for an ensemble (10 ppb–15 ppm) of NV⁻ in bulk diamond. A thermal shift of ΔD/ΔT = −75 kHz K⁻¹ was determined at around 300 K and the red‐shift was attributed to thermal expansion of the diamond crystal lattice [9, 10]. Later studies over a wider temperature range for a single NV⁻ center found that the frequency shifting is actually nonlinear with respect to temperature; for example, it may change to ΔD/ΔT = −150 kHz K⁻¹ at 600 K [11]. A polynomial that can properly describe the temperature dependence of the spin resonance frequency over 300–700 K is [11]

(11.12)

where D(T) is in unit of gigahertz and T in Kelvin. While the magnitude of the thermal shift is not substantial at room temperature, it can be measured with high precision due to the exceptional stability of the ODMR spectra. Another distinctive feature of the ODMR spectra is that the widths of the spin resonance peaks show little or almost no dependence on temperature up to 600 K due to the long spin coherence time. It has an important implication for the application of single NV⁻ centers as nanoscale thermometers over a broad temperature range, as discussed in the next section.

The concept of using FND for nanothermometry was initially disclosed in a study of thermal effects on the fluorescence lifetimes of NV⁻ centers. With 30‐nm FNDs heated in an oven, Plakhotnik and Gruber [12] observed a 2.7‐fold decrease in the fluorescence lifetime from 300 to 670 K. The heating–cooling cycle was reversible, suggesting the potential use of this nanomaterial as a luminescence thermometer with nanometric spatial resolution. Further studies of the thermal shifts of D for FNDs showed results in good agreement with that of bulk diamond [13]. Compared with other known luminescence thermometers composed of nanoparticles such as semiconductor quantum dots, rare earth doped oxides, and gold nanoparticles (GNPs) [14, 15], FNDs stand out for having a wider range of working temperature and single‐particle detection sensitivity.

Kucsko et al. [16] reported the first application of FNDs as nanoscale thermometers in 2013. They obtained the ODMR spectra of single 100‐nm FNDs spin‐coated on a glass slide using a green laser for excitation (Figure 11.1a and b) and were able to determine the temperatures with a precision of 0.1 K or better within a measurement time of four seconds (Figure 11.1c). To induce local temperature changes, GNPs were introduced into the samples and subsequently irradiated by a separate laser to serve as the heat source (denoted in Figure 11.1b). A spatial resolution of 200 nm was achieved by measuring the separations of the nanoparticles in fluorescence images (Figure 11.1d). The results, along with other similar studies [17], showed that it is possible to detect the temperature variations at the nanoscale with a sensitivity of 0.1 K Hz^−1/2 if the FNDs contain up to 1000 NV^– centers per particle. Further improvement of the temperature sensing sensitivity to the 1 mK Hz^−1/2 regime is achievable by utilizing the quantum coherence of single NV^– spins in bulk diamonds (Figure 11.2) [16–18]. These characteristics place FND in a category of the most sensitive and stable temperature probes known to date.

In light of its excellent biocompatibility, a natural (and logical) application of the FND nanosensor is to measure local temperatures in living cells. Kucsko et al. [16] demonstrated this applicability by introducing FNDs and GNPs (both ~100 nm in diameter) into human embryonic fibroblast cells through nanowire‐assisted delivery. They then monitored the temperature changes of a FND particle, while locally heating a nearby GNP by a separate laser. At the laser power of 12 μW, a temperature increase of 0.5 K was measured at the FND location, corresponding to a change of approximately 10 K at the GNP location, and the cell was still alive. However, cell death occurred when the laser power was increased to 120 μW, which resulted in a temperature change of 3.9 K for the FND and 80 K at the GNP position. The results demonstrated that the technique could actively control cell viability at the nanoscale, enabling the optimization of nanoparticle‐based photothermal therapy at the single‐cell or subcellular level (cf., Section 12.2 for further discussion).

11.2.2 Time‐Resolved Nanothermometry

The plot in Figure 11.2 compares sensor sizes and temperature accuracies between the NV‐based quantum thermometer and other techniques reported in the literature [16]. The comparison clearly shows that FND outperforms other nanothermometers (such as quantum dots and green fluorescent proteins) in terms of its precision in the temperature measurement. However, a nanothermometer is far from ideal if it cannot provide information on the dynamics of underlying heat transfer phenomena. The commonly used luminescence nanothermometers, such as the lanthanide complexes [19], typically have a response time in the range of seconds. This temporal resolution by no means is sufficient to follow the time evolution of any systems under investigation at the nanoscale. Similarly for FNDs, it is a time‐consuming process (in minutes) to acquire the whole ODMR spectrum of the NV⁻ centers. Moreover, additional data processing after the measurements is required to determine the peak positions and thus the temperature changes.

To speed up the process, Tzeng et al. [20] have developed a three‐point sampling method to determine the temperature of a system, which may or may not be necessarily in equilibrium with its surroundings, with a temporal resolution better than 10 μs. The method is based on the experimental finding that the widths of the ODMR peaks of the NV⁻ centers are nearly invariant with temperature changes. For 100‐nm FNDs, the full width at half maximum (FWHM) of the ODMR peaks is typically 20 MHz in observation. Over the temperature range of 300–700 K, the width changes less than 10%, while the peak positions are shifted by more than 20 MHz [11]. By assuming a Lorentzian profile of constant width (γ) and measuring the intensity changes of the fluorescence dip at three preselected frequencies (Figure 11.3), the researchers have been able to determine the temperature shift (δ) without scanning the whole ODMR spectrum according to the following equations [20]:

(11.13)

where

(11.14)

and I₁, I₂, and I₃ are the fluorescence intensities measured at points f₁, f₂, and f₃, respectively. The method enables real‐time measurement of the temperature changes over ±100 K and, more importantly, the studies of nanoscale heat transfer dynamics in a pump‐probe configuration with a pulsed heating source.

Exploiting this unique spin resonance feature, Chang and coworkers [20] conducted time‐resolved temperature measurement for a gold nanorod solution heated by a tightly focused 808 nm laser using 100‐nm FNDs as the single‐particle temperature sensors (Figure 11.4a). With the FNDs submerged in the medium and positioned near the 808 nm laser focus, they first observed superheating of the aqueous solution near the water–glass interface from the measured ODMR spectra (Figure 11.4b) and demonstrated a measurement precision of better than ±1 K over a temperature variation range of 100 K with a spatial resolution of approximately 0.5 μm. Later, by pulsing the heating laser (808 nm), the probing laser (532 nm), as well as the microwave radiation (Figure 11.4c), a temporal resolution of 10 μs was achieved through a pump‐probe type measurement using the three‐point method (Figure 11.4d). The validity of the measurements was finally verified with finite‐element numerical simulations in this proof‐of‐principle experiment. Compared with the time‐resolved temperature measurement with dye molecules in water [21], the results represent a significant improvement of both spatial and temporal resolution by 1 and 3 orders of magnitude, respectively.

11.2.3 All‐Optical Luminescence Nanothermometry

The thermal shifts of the spin resonances of NV⁻ centers, as illustrated above, provide an effective means for nanoscale temperature sensing with both high temporal and spatial resolutions. However, the method is technically demanding because microwave excitation is required to deplete the fluorescence emission. Additionally, the microwave has to be delivered through a metal wire or nanostructure placed close to the systems under investigation (typically within 10 μm). The requirement of such close proximity severely limits the practical use of the OMDR technique in the life science research. Alternatively, one may focus on the thermal shift of the zero‐phonon line (ZPL) of the NV⁻ centers. Chen et al. [10] have reported that the trend of the thermal shifting of the ZPL at 638 nm matches closely with that of the spin transitions at 2.87 GHz. At room temperature, the magnitude of the thermal shift is ΔZPL/ΔT = +0.015 nm K⁻¹ with a FWHM approximately 5 nm for the ZPL [10, 22]. Small as it may seem, the shift is sufficient for practical temperature measurement because both the position and width of the ZPL in the fluorescence spectra are highly stable. In comparison to the temperature sensing by ODMR, this all‐optical method has the advantages of being simple, straightforward, and readily implementable by any confocal microscope equipped with a CCD‐based monochromator.

Tsai et al. [23] tried out the above idea with 100‐nm FNDs containing about 900 NV⁻ centers per particle. Specifically, they used a 594 nm laser as the light source to avoid exciting the NV⁰ centers whose fluorescence emission band is partially overlapped with that of NV⁻ at 638 nm and thus can complicate the spectral analysis. Using FNDs dispersed in water as an example, while the overall feature of the emission band does not change much with temperature over 28–75 °C, its ZPL is significantly broadened and shifted to the red as the solution temperature increases (Figure 11.5a). To determine the sensitivity of this all‐optical method, the research team spin‐coated 100‐nm FNDs on a glass coverslip and obtained their fluorescence spectra at 25 °C for the individual particles (Figure 11.5b). The ZPL centers (λ₀) were then determined by fitting the spectra over 610–660 nm to a Lorentzian function along with an exponential function for the baseline correction as [24]

(11.15)

where I(λ) is the fluorescence intensity, λ is the wavelength, Γ is the Lorentzian half‐width, λ₀ is the ZPL center, and B, b, and A are constants. Signal averaging over 6 seconds by curve‐fitting of 60 independent spectra yielded λ₀ = 638.519 ± 0.013 nm at a 95% confidence interval (inset in Figure 11.5b), suggesting a temperature measurement sensitivity of ±2 K Hz^−1/2. Although the effective working range of this method is limited to be less than 100 °C due to the significant band broadening as temperature increases, it is well suitable for biological applications (cf., Section 12.2).

In a separate study, Plakhotnik et al. [24] demonstrated an all‐optical ratiometric temperature sensor consisting of a 50‐nm FND hosting more than 100 NV⁻ centers in the crystal matrix. Instead of detecting the thermal shift, they characterized the amplitude of the ZPL by fitting the fluorescence spectra with Eq. (11.15) and achieved a temperature measurement sensitivity of 0.3 K Hz^−1/2 using a 590 nm laser for the excitation. In addition to that, a long‐term stability was attained within 0.6 K (peak‐to‐peak value) for a single 50‐nm FND spin‐coated on a glass substrate and imaged with a home‐built microscope system. Although the method is intrinsically more sensitive than the detection of the ZPL shift, it is more susceptible to the interference from background (or baseline) signals. Fortunately, the background interference can be properly removed by conducting either fluorescence lifetime gating or magnetic modulation as discussed in Section 6.2.

11.2.4 Scanning Thermal Imaging

Thermal mapping is a process by which the spatial variation of the temperature of an object is measured. While feasible, it remains a challenge to apply the single‐particle FND nanothermometry for any practical thermal mapping at the nanoscale. In particular, to conduct the mapping, the FND probe must be scanned through the sample in order to obtain information about the spatial temperature distribution. To meet the challenge, Tetienne et al. [25] grafted a single FND particle (~100 nm in diameter) as a thermal probe onto the tip of an atomic force microscope (AFM). Hosting an ensemble of spins (~100 NV⁻ centers), the FND provided a significantly improved acquisition time by as much as an order of magnitude. Additionally, the combination of these two techniques preserved the sub‐100‐nm spatial resolution inherited from the scanning probe microscope for both temperature sensing and topographic imaging. The researchers applied this method, in conjunction with ODMR, to map the local temperature rise due to laser irradiation of a single 40‐nm GNP submerged in aqueous solution (cf., captions in Figure 11.6 for details). The results pave the way toward new applications of the FND nanothermometry in areas such as thermal imaging of material processing and microelectronic devices in operation.

Besides mapping nanoscale temperature changes, the FND nanothermometry is also capable of imaging the thermal conductivity (k) of a nanostructure. With this perspective, Laraoui et al. [26] attached a FND to the apex of a silicon tip of an AFM as a local temperature sensor. They then applied an electrical current to heat up the tip and brought the FND in contact with a surface of varying thermal conductivities with nanometer precision. The fast response time (<200 μs) of the sensor, due to its small size and high thermal conductivity, made it possible to study the nanoscale heat transfer dynamics triggered by an electrical pulse. By combining AFM and confocal fluorescence microscopy, the researchers attained excellent matching between thermal conductivity and topographic maps for a phantom microstructure made of a gold grid (k = 314 W m⁻¹K⁻¹) on a sapphire substrate (k = 30 W m⁻¹K⁻¹) with distinct thermal conductivities between these two materials. Such an integrated method promises multiple applications, ranging from the investigation of phonon dynamics in nanostructures to the characterization of heterogeneous phase transitions and chemical reactions in various solid‐state systems.

11.3.1 Continuous‐Wave Detection

In 1997, Wrachtrup and coworkers [7] demonstrated for the first time that the electron spin resonance spectra of a single NV⁻ center in a bulk diamond could be optically read out at the single‐molecule level by using the ODMR technique. In the absence of crystal strain, the spin resonance spectrum showed a single peak at 2.87 GHz, which would split into two if an external magnetic field was applied to the NV⁻ center, as verified by experiments (Figure 3.9) [27]. Mathematically, it has been shown that at B << D/γ_e, the two components of the splitting have the frequencies of [28]

(11.16)

where γ_e = g_eμ_B/h= 28.03 MHz mT⁻¹ and θ_B is the angle between the magnetic field and the NV⁻ center’s major symmetry axis. Using this equation, one can accurately determine the strength of the external magnetic field based on the observed Zeeman splittings with the NV⁻ center as a highly sensitive magnetic sensor. However, as pointed out by Schirhagl et al. [3], while the method is direct, the detection sensitivity is compromised by the significant broadening of the spin resonance bands. Much enhancement of the sensitivity can be gained by changing the detection to the pulsed modes, which take advantage of the NV⁻ center’s long coherence time in bulk diamond as well as the many refined microwave sequences that have been developed over the past few decades for magnetic resonance spectroscopy [29]. The combination of this unique spin system and the ODMR technique has enabled ultrasensitive and rapid detection of single electronic spin states under ambient conditions for nanoscale magnetic resonance imaging [30].

Some research groups have applied FNDs as a nanoscale imaging magnetometer to detect weak magnetic fields using the continuous‐wave approach [27, 31]. Specifically, Balasubramanian et al. [27] incorporated a 40‐nm FND hosting a single NV⁻ center into the cantilever of an AFM (Figure 11.7a and b) and applied the cantilever with the ODMR setup as a scanning probe microscope to achieve subwavelength imaging resolution of a nickel nanostructure. Additionally, by applying microwaves resonant at 2.750 GHz to the NV⁻ center, they observed a narrow dark line close to the corner of the triangular structure (Figure 11.7c). The width of the line was about 20 nm, corresponding to a measurement resolution of 0.5 mT.

Using a similar setup, Rondin et al. [31] conducted nanoscale magnetic imaging with a FND‐attached AFM tip to measure large off‐axis magnetic fields, which could induce spin level mixing and thus change the fluorescence intensity (Section 3.4). The method was all‐optical, requiring no microwave control, and hence expanding the operation range of the NV‐based magnetometry. The performance of the FND‐scanning probe magnetometer was demonstrated by mapping the magnetic field distribution created by a commercial magnetic hard disk. A sensitivity of 10 μT Hz^−1/2 was reported by the researchers in this study. The ultimate accuracy of these magnetic field measurements is about 20 μT, limited by the couplings of the NV⁻ centers with paramagnetic entities such as other NV centers, ¹³C, and ¹⁴N nuclei in the FNDs [32].

To demonstrate the chemical sensing capability of the FND‐based luminescence magnetometry, Lim et al. [33] integrated the NV‐based magnetic sensor with a microfluidic system. They manipulated a single magnetic particle in three dimensions in a microfluidic device with a combination of planar electro‐osmotic flow control and vertical magnetic actuation, and then applied a fixed FND hosting a single NV⁻ center to measure the strength of the magnetic field generated by the magnetic particle at a separation distance of 7.25 μm (Figure 11.8a), 3.62 μm (Figure 11.8b), and 1.50 μm (Figure 11.8c). From the peak shifts in the ODMR spectra, the magnetic field distribution was mapped out with nanometer accuracy. Their result compared favorably with the calculated magnetic field intensity of a model magnetic dipole as a function of distance from the FNDs.

Taking a different approach, Horowitz et al. [34] applied an infrared laser as an optical tweezer for the three‐dimensional control of a single 100‐nm FND particle in solution. Despite the motion and random orientation of the FND in the trap, they were able to observe distinct peaks in the ODMR spectra of an ensemble of NV⁻ centers in the particle. Similarly, Kayci et al. [35] employed an anti‐Brownian electro‐kinetic trap to manipulate a single FND particle under ambient and aqueous conditions for magneto‐optical spin detection. Furthermore, Geiselmann et al. [36] developed a deterministic optical trapping technique and demonstrated the three‐dimensional manipulation of individual FNDs hosting multiple NV⁻ centers to measure the local magnetic field in a glycerol–water mixture. The development of all these techniques has opened new opportunities to probe the magnetic fields in complex environments such as the interiors of microfluidic channels and live cells that are inaccessible by the scanning probe techniques existing today.

Developed originally to study condensed‐phase phenomena, the magnetic sensing techniques discussed above have also been applied to using the NV⁻ centers as nanoprobes in the gas phase [37–39]. For example, Hoang et al. [38] optically levitated a 100‐nm FND particle for electron spin control of its built‐in NV⁻ centers in low vacuum. Measuring the absolute internal temperature of the levitated FNDs by ODMR, the researchers observed an enhancement in the strength of the spin resonance signal as the air pressure was reduced, suggesting that oxygen gases could exert an effect on both the fluorescence intensity and the ODMR contrast. The study implies a potential application of NV⁻ for sensing gaseous oxygen, which has two unpaired electrons and is paramagnetic.

11.3.2 Relaxometry

Now we turn to the pulsed operations. As discussed in the previous section, the pulsed operations may provide a more sensitive means for magnetic sensing. Relaxometry is one of such techniques, which are traditionally used in nuclear magnetic resonance spectroscopy to measure nuclear spin relaxation rates that depend strongly on the fluctuations of the magnetic fields in microscopic environments. The technique is adopted here to monitor the relaxation of NV⁻ centers by optically polarizing its m_s = 0 state and then measuring the probability of finding the spins recovered in the same state at a later time, T₁, i.e. the spin–lattice relaxation time [40–44]. Time‐resolved measurements with a temporal resolution in the range of one minute are readily achievable with this technique [44].

With the relaxometry, Ermakova et al. [42] demonstrated the detection of a few ferritin molecules loaded on a single FND particle hosting multiple NV⁻ centers. Ferritin is an iron storage protein capable of transporting as many as 4500 atoms of Fe with a magnetic moment of 300 μ_B. The researchers first attached ferritin to the surface of a 40‐nm FND by noncovalent conjugation to form ferritin–FND complexes. From a comparison of the measured T₁ relaxation times between free FNDs and the ferritin–FND complexes for more than 30 particles in each group, a significant reduction of the T₁ time (from 41.8 μs of free FNDs to 5.7 μs of the ferritin–FND complexes) due to the protein conjugation was found. Compared with existing magnetic force microscopy techniques, the method has an unmatched advantage in that it does not require cryogenic temperature or vacuum, a major improvement in a practical sense.

In a proof‐of‐principle experiment for biological sensing with the relaxometry, Kaufmann et al. [43] applied the single NV⁻ centers in FNDs to detect gadolinium (Gd) spin labels in an artificial cell membrane under ambient conditions (cf., captions in Figure 11.9 for details). The Gd³⁺ ion is a common magnetic resonance imaging contrast agent with spin 7/2 and it can bind with the negatively charged head of the lipid molecule in a supported lipid bilayer by electrostatic forces. The Gd‐labeled lipids can thus produce considerable magnetic fluctuations in the artificial membrane by a combined effect of Gd–Gd spin dipole interactions, motional diffusion, and intrinsic Gd spin relaxation. The researchers found that the T₁ relaxation times of the membrane‐bound FNDs were significantly shortened when the artificial membrane was labeled with 10% Gd spin‐labeled lipids, suggesting a sensitivity of approximately 5 Gd spins Hz^−1/2. The ability to detect such a small number of spins in a model biological setting has established a new avenue for in situ nanoscale investigation of the dynamical processes in a single living cell.