Simultaneous detection of position and temperature of micromagnet using a quantum microscope

Zhenrong Shi; Zhonghao Li; Huanfei Wen; Hao Guo; Zongmin Ma; Jun Tang; Jun Liu

doi:10.3788/COL202422.101202

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Abstract

Micromagnets, as a promising technology for microscale manipulation and detection, have been the subject of extensive study. However, providing real-time, noninvasive feedback on the position and temperature of micromagnets in complex operational environments continues to pose a significant challenge. This paper presents a quantum imaging device utilizing diamond nitrogen-vacancy (NV) centers capable of providing simultaneous feedback on both the position and temperature of a micromagnet. The device achieves a temporal resolution of 2 s and a spatial resolution of 1.3 µm. Through flux localization analysis, we have determined a positioning accuracy within 50 µm and a temperature accuracy within 0.4 K.

Keywords

diamond nitrogen-vacancy centers micromagnet position simultaneous detection temperature

1. Introduction

With the rapid development of fine processing technology, integrated intelligent magnetic microstructures have emerged and found widespread applications in microelectromechanical systems (MEMS), medical applications, and scientific research^[1–4]. Noninvasive feedback techniques for these microstructures have attracted extensive attention over the past few decades^[5,6]. Among various position detection methods, capacitive and voltage-based techniques require contact between the sensor and the microstructure, which fails to meet the requirements for noncontact operation. In contrast, magnetic position detection offers distinct advantages, such as enhanced penetration through magnetic field structures, high controllability, and rapid response speed^[7,8]. Concurrently, temperature is a critical parameter that reflects the functionality and performance of microstructures. It plays a pivotal role in the magnetic thermal effects and targeted therapy within integrated microstructures^[9,10]. However, commonly used optical cameras and ultrasound methods fall short of providing adequate temperature feedback in complex environments, let alone dual feedback on both position and temperature^[11,12].

The magnetic field, inherent to micromagnets, remains unaffected by biological tissues and bodily fluids^[13]. Consequently, utilizing magnetic field information for micromagnet positioning offers significant advantages. Simultaneous imaging of magnetic fields and temperature is crucial for the effective application of micromagnets. Traditional magnetic microscopes, such as superconducting quantum interference devices (SQUIDs) and Hall magnetic microscopes, are widely used for magnetic field detection^[14,15]. Meanwhile, infrared microscopes and Raman spectroscopy are employed for imaging temperature fields^[16,17]. However, these techniques cannot simultaneously detect magnetic and temperature fields. Here, we exploit the high sensitivity of diamond nitrogen-vacancy (NV) centers to both magnetic fields and temperature^[18,19], enabling the simultaneous tracking of the position and temperature of a micromagnet. Besides their high sensitivity to magnetic fields and temperature, diamond NV centers are nontoxic to living organisms and operate at room temperature, making them an increasingly popular choice for magnetic and temperature-sensitive applications^[20].

In this paper, leveraging the outstanding magnetic field and temperature-sensing capabilities of diamond NV centers, we integrate these centers with camera sensors to develop a wide-field quantum imaging system for magnetic and temperature fields. This system exhibits high sensitivity to both magnetic fields and temperatures and can image these parameters simultaneously. Initially, we investigate the properties of diamond NV centers and elucidate the principles underlying the imaging of magnetic fields and temperatures. Subsequently, we explore the theoretical foundations and perform error analysis for using vector magnetic fields to locate micromagnets. Finally, we present experimental results that demonstrate the simultaneous imaging of positions and temperatures of micromagnets within simulated biological tissues.

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2. Principles and Experimental Setup

2.1. Experimental principles

The diamond NV center possesses a cubic crystal structure with C3v symmetry. The NV center is a crystal defect formed by replacing two carbon atoms in the diamond lattice with a nitrogen atom (N) and an adjacent vacancy^[21]. The NV center has two different fluorescent charge states, ${NV}^{0}$ and ${NV}^{-}$ ; the latter has higher detection sensitivity^[22]. In this paper, NV denotes ${NV}^{-}$ . Utilizing the unique level structure of NV centers at room temperature, magnetic field and temperature detection are facilitated through the optically detected magnetic resonance (ODMR) technique^[23]. Figure 1(a) illustrates that when the NV center is irradiated with a 532 nm green laser, its levels are excited from the ground state ( ${{}^{3}A}_{2}$ ) to the first excited state ( ${}^{3}E$ ). During relaxation, two types of spontaneous emission occur: one is the red fluorescence emission from the excited state to the ground state, which accounts for much of the radiation; the other is the nonradiative transition, where the singlet states ( ${{}^{1}A}_{1}$ and ${}^{1}E$ ) return to the ground state through spin-orbit coupling. Therefore, the system relaxes mostly to the ground state without emitting photons. For the excited states with $m_{s} = \pm 1$ , the transition probability to the metastable state is much higher than that of the $m_{s} = 0$ excited state. When the microwave frequency is resonant with the transition frequency between the excited state and the ground state, the fluorescence intensity is significantly reduced. Therefore, the fluorescence intensity is plotted as an ODMR signal curve by scanning the microwave frequency.

Figure 1.Schematic of the experimental principle. (a) Energy-level diagram of the NV center; (b) ODMR (black) and Lorentz-fitted curve (red) for one pixel; (c) NV symmetry axes and laboratory frame directions X, Y, and Z, defined in terms of diamond lattice vectors.

According to the Hamiltonian of the NV center, the transition frequency $f$ can be obtained from Eq. (1)^[23], $f = D + β_{T} δ_{T} \pm γ B_{NV} .$ (1)

Among them, $f$ corresponds to the NV resonant frequency for the transition from $m_{s} = 0$ to $m_{s} = + 1$ and $m_{s} = - 1$ . At room temperature, $β_{T} = - 74 kHz / K$ , $δ_{T}$ is the temperature variation relative to 300 K during the measurement, and $γ = g_{e} μ_{B} / h = 28 Hz / nT$ is the NV gyromagnetic ratio. $B_{NV}$ is the projection of the applied magnetic field along the NV symmetry axis. By simultaneously measuring the frequency shift of all four possible NV axes’ resonance frequencies, it is possible to decouple the effects of temperature and magnetic field, thus enabling simultaneous measurement of both the magnetic field and the temperature.

Due to the Zeeman effect, changes in the magnetic field cause a displacement of the sublevels with $m_{s} = \pm 1$ . A magnetic field B is projected onto the four NV orientations, causing the Zeeman shifts shown in Fig. 1(b). These four pairs of peaks correspond to the magnetic field intensities along the four axes, and the vector magnetic field can be obtained from these intensities using Eqs. (2 )–(4). Additionally, changes in temperature cause a shift in the microwave frequency of the transition between the $m_{s} = \pm 1$ and $m_{s} = 0$ sublevels, resulting in an overall shift of the entire ODMR curve with temperature. The temperature can be detected by measuring changes in $m_{s} = 0$ , and Eq. (5) provides the calculation method.

Figure 1(c) shows the unit vectors along the four axes of the diamond NV center defined in our laboratory reference frame as follows: ${\begin{matrix} u_{1} = \frac{1}{\sqrt{3}} (- \sqrt{2}, 0, 1); & u_{2} = \frac{1}{\sqrt{3}} (0, \sqrt{2}, 1) \\ u_{3} = \frac{1}{\sqrt{3}} (\sqrt{2}, 0, 1); & u_{4} = \frac{1}{\sqrt{3}} (0, - \sqrt{2}, 1) \end{matrix} .$ (2)

The $B_{X}$ , $B_{Y}$ , and $B_{Z}$ in the laboratory reference frame are as follows: ${\begin{matrix} B_{X} = \frac{\sqrt{6}}{4} (B_{2} - B_{1}) i \\ B_{Y} = \frac{\sqrt{6}}{4} (B_{3} - B_{4}) j \\ B_{Z} = \frac{\sqrt{3}}{4} (B_{1} + B_{2} + B_{3} + B_{4}) k \end{matrix} .$ (3)

Here, $B_{1}$ , $B_{2}$ , $B_{3}$ , and $B_{4}$ are the components of the magnetic field $B$ projected onto four NV axes. And $i$ , $j$ , $k$ are unit vectors in the $X$ , $Y$ , and $Z$ directions, respectively.

For temperatures $δ_{1}$ to $δ_{4}$ , ${\begin{matrix} δ_{1} = \frac{1}{2} (f_{1}^{+} - f_{1}^{-}); & δ_{2} = \frac{1}{2} (f_{2}^{+} - f_{2}^{-}) \\ δ_{3} = \frac{1}{2} (f_{3}^{+} - f_{3}^{-}); & δ_{4} = \frac{1}{2} (f_{4}^{+} - f_{4}^{-}) \end{matrix} .$ (4)

The temperature can be calculated using the following formula: $T = \frac{1}{4} (δ_{1} + δ_{2} + δ_{3} + δ_{4}) .$ (5)

2.2. Experimental setup

Figure 2(a) illustrates the experimental setup. The diamond NV centers are central to the entire imaging system. Ultrathin diamonds with a (110) crystal phase and a thickness of 200 nm are employed. These diamond NV center chips are bonded to a quartz substrate using crystal bonding wax, thereby serving as the sensitive units of the imaging system^[24]. The system comprises five subsystems: the laser excitation system, the microwave scanning system, the fluorescence collection system, the bias magnetic field system, and the control system. The laser excitation system primarily consists of an MGL-FN-532 laser (Changchun New Industrial Optoelectronic Technology Co., Ltd.) and a series of lenses that ensure a uniform laser power density of $0.5 {W/ mm}^{2}$ for exciting the diamond NV centers. The microwave scanning system includes a microwave source and an antenna, which deliver a resonant microwave field with a power of 30 dBm to the diamond NV centers. The fluorescence collection system features an objective lens, a CCD camera, and a computer that converts the fluorescence signal into an ODMR signal and calculates magnetic field and temperature data. The bias magnetic field system comprises a custom-made adjuster and two symmetrically positioned permanent magnets at the ends of the adjuster, generating an external magnetic field of approximately 3 mT near the NV centers. The control system consists of arbitrary signal generators that provide TTL pulse signals, coordinating the operation of the other four systems to facilitate pulse ODMR data acquisition.

Figure 2.Schematic diagram of the NV center quantum microscope experimental setup and imaging method. (a) Schematic diagram of the wide-field diamond NV center quantum microscope experimental setup; (b) schematic diagram of the ODMR scanning imaging method, where the camera’s shooting speed is synchronized with the microwave frequency sweep rate, meaning each image captured by the camera corresponds to the fluorescence image of the NV center at a microwave frequency point. By correlating the fluorescence intensity of all the images with the swept microwave frequency points, a complete ODMR spectrum is composed.

The NV center in diamond images on the focal plane of the CCD, with a resolution of $1920 pixels \times 1080 pixels$ and a size of $5 {μm}^{2}$ . The CCD exposure frequency is 200 frames per second (FPS). The system uses a $10 \times$ , $NA = 0.25$ objective lens, with a spatial resolution of approximately 1.3 µm (primarily influenced by the NA parameter of the microscope). The control system synchronizes the camera with the microwave source, which scans from 2.5 to 3.1 GHz with a step frequency of 0.3 MHz using the pulse-scan technique. The temporal resolution of the imaging system is 2 s^[25]. As shown in Fig. 2(b), we obtain a set of images, with each image representing a microwave frequency. The computer processes and analyzes many gray-scale images transmitted by the CCD. The gray-scale value of each pixel can be used to plot an ODMR and determine the peak position using Lorentzian fitting. The peak position is then used to estimate the magnetic field and temperature and ultimately generate magnetic field and temperature maps. The magnetic sensitivity is $η_{mag}$ , $η_{mag} = (h / g_{e} μ_{B}) \cdot [Δ V / C {(I_{0})}^{1 / 2}]$ ^[22], approximately $30 μT / {Hz}^{1 / 2}$ , where $h$ is the Planck constant, $g_{e}$ is the Lande factor, $μ_{B}$ is the Bohr magneton, $I_{0} = 1 \times 10^{8} s^{- 1}$ is the photon count per detection volume, $V = 15 MHz$ is the line width of the ODMR, and $C = 1.2 %$ is the contrast of the ODMR. The temperature sensitivity is $η_{tem}$ , $η_{tem} = V / (C \cdot {(I_{0})}^{1 / 2} \cdot β_{T})$ ^[24], at room temperature, $β_{T}$ is equal to $- 74 kHz / K$ , and thus $η_{tem}$ is $0.5 K / {Hz}^{1 / 2}$ . Upon analyzing the $η_{mag}$ and $η_{tem}$ calculation formulas, we found that the key factors affecting sensitivity include $I_{0}$ , $V$ , and $C$ . In our experiments, the primary factors influencing sensitivity were the laser pumping rate (LPR), microwave manipulation intensity (MMI), and physical field nonuniformity (PFNU). The values of LPR and MMI directly impact $V$ and $C$ , and neither excessively high nor excessively low LPR and MMI can achieve optimal sensitivity^[26,27]. In our experiments, we simultaneously optimized the laser pumping rate and microwave manipulation intensity to achieve the best sensitivity. PFNU can involve laser, microwave, bias magnetic field, electric field, and temperature, among others. In our experiments, we improved laser uniformity by optimizing the confocal laser system. We enhanced microwave uniformity by designing a high-uniformity radiation antenna, achieving 94% microwave radiation uniformity. To increase bias magnetic field uniformity, we created a high-precision magnetic field regulation device, reaching a uniformity of 95%. Additionally, we applied a strong bias magnetic field to reduce the impact of temperature and electric field nonuniformity.

3. Results

As shown in Fig. 3(a), we can assess the approximate position of the micromagnet visually through a magnetic field map. However, to estimate the position of the micromagnet more accurately, we need to employ more precise estimation methods. Here, we utilize the magnetic flux-based position estimation method for estimating the position of the micromagnet.

Figure 3.Multidipole magnetic model and localization algorithm. (a) The multidipole model in the reference system. The coordinate system is defined by the symmetry axis of the NV centers from Fig. 1(c) and the laboratory frame directions X, Y, and Z. (b) Algorithm for estimating the positions of magnetic flux, where the stage in the yellow box corresponds to data import and preprocessing; the stage in the green box corresponds to rough estimates of the positions of B_max and B_min; the stage in the blue box corresponds to precise estimates of the positions of B_max and B_min.

A cylindrical permanent magnet with a height of $2 L$ , radius of $R$ , and magnetization strength of $M$ is placed in the O-XYZ coordinate system. The geometric center of the magnet is at point $P$ with coordinates $(x_{0}, y_{0}, z_{0})$ . To ensure the accuracy of the magnetic dipole model, the observation distance $r$ should be at least 20 times the half height $L$ of the magnet and 10 times the radius $R$ of the magnet. To extend the effectiveness of the observation distance, we introduce a multidipole model. When the number of dipoles is $n$ , the observation distance $r$ can be calculated as $n$ times. This constraint is more relaxed than the constraint of the original single magnetic dipole model, thus expanding the effective range.

We consider the cylindrical magnet as being composed of $n$ smaller magnets of the same size, which are closely connected along the axis. Due to the constant and equal magnetic field strength of each smaller magnet, according to Maxwell’s equations, their magnetic field distributions do not affect each other. The $n$ magnets numbered along the axis as $P_{1}, P_{2}, \dots, P_{n}$ all have the same axial direction, corresponding to the direction vector $e$ , $e = (e_{x}, e_{y}, e_{z}) .$ (6)

The geometric center of the $k$ th submagnet [ $k \in (1, 2, \dots, n)$ ] can be represented as $(x_{k}, y_{k}, z_{k})$ , ${\begin{matrix} x_{k} = x_{0} + \frac{L}{n} (2 k - 1 - N) e_{x} \\ y_{k} = y_{0} + \frac{L}{n} (2 k - 1 - N) e_{y} \\ z_{k} = z_{0} + \frac{L}{n} (2 k - 1 - N) e_{z} \end{matrix} .$ (7)

We approximate each individual submagnet as a magnetic dipole, with its geometric center being the center of the dipole. Then, the magnetic induction intensity $B_{k} = {(B_{k - x}, B_{k - y}, B_{k - z})}^{T}$ of the $k$ th magnetic dipole at the observation point $S (x, y, z)$ on the diamond microscope observation surface is $B_{k} = [\begin{matrix} B_{k - x} \\ B_{k - y} \\ B_{k - z} \end{matrix}] = \frac{μ_{0} R^{3} L M}{2 n r^{5}} \cdot A .$ (8)

Here, $r = \sqrt{{(x - x_{k})}^{2} + {(y - y_{k})}^{2} + {(z - z_{k})}^{2}},$ (9) $A = [\begin{array}{l} \begin{matrix} {\begin{cases} e_{x} [2 {(x - x_{k})}^{2} - {(y - y_{k})}^{2} - {(z - z_{k})}^{2}] \\ + 3 e_{y} (x - x_{k}) (y - y_{k}) + 3 e_{z} (x - x_{k}) (z - z_{k}) \end{cases}} \end{matrix} \\ \begin{matrix} {\begin{cases} e_{y} [2 {(y - y_{k})}^{2} - {(x - x_{k})}^{2} - {(z - z_{k})}^{2}] \\ + 3 e_{x} (x - x_{k}) (y - y_{k}) + 3 e_{z} (x - x_{k}) (z - z_{k}) \end{cases}} \end{matrix} \\ \begin{matrix} {\begin{cases} e_{z} [2 {(z - z_{k})}^{2} - {(y - y_{k})}^{2} - {(x - x_{k})}^{2}] \\ + 3 e_{z} (x - x_{k}) (z - z_{k}) + 3 e_{y} (y - y_{k}) (z - z_{k}) \end{cases}} \end{matrix} \end{array}] .$ (10)

By integrating Eqs. (6) and (7), the magnetic induction intensity $B_{k}$ at the observation point of a submagnetic dipole can be expressed as a function of the geometric center $(x_{k}, y_{k}, z_{k})$ of the submagnet and the direction vector $e$ , as follows: $[\begin{matrix} B_{k - x} \\ B_{k - y} \\ B_{k - z} \end{matrix}] = [\begin{matrix} f_{1} (x_{k}, y_{k}, z_{k}, e_{x}, e_{y}, e_{z}) \\ f_{2} (x_{k}, y_{k}, z_{k}, e_{x}, e_{y}, e_{z}) \\ f_{3} (x_{k}, y_{k}, z_{k}, e_{x}, e_{y}, e_{z}) \end{matrix}] .$ (11)

Among these, $f_{1}$ , $f_{2}$ , and $f_{3}$ are functions of the nine parameters $[μ_{0}, R, L, M, n, r, x, y, z]$ .

As shown in Fig. 3(a), the positions of $x_{0}$ and $y_{0}$ on the O-XY plane (observation plane) can be determined by the characteristic positions of the magnetic field, $B_{\max}$ and $B_{\min}$ , on the magnetic field map of the bar magnet, where $Q_{1} (x_{Q 1}, y_{Q 1})$ and $Q_{2} (x_{Q 2}, y_{Q 2})$ represent the positions of $B_{\max}$ and $B_{\min}$ on the O-XY plane, respectively, ${\begin{matrix} e_{x} = \frac{x_{Q 1} - x_{Q 2}}{‖ Q_{1} Q_{2} ‖} = \sin θ \cdot \cos φ \\ e_{y} = \frac{y_{Q 1} - y_{Q 2}}{‖ Q_{1} Q_{2} ‖} = \sin θ \cdot \sin φ \\ e_{z} = \cos θ \\ x_{0} = \frac{x_{Q 1} - x_{Q 2}}{2}; y_{0} = \frac{y_{Q 1} - y_{Q 2}}{2} \end{matrix},$ (12) $[\begin{matrix} B_{k - x} \\ B_{k - y} \\ B_{k - z} \end{matrix}] = [\begin{matrix} F_{1} (z_{k}) \\ F_{2} (z_{k}) \\ F_{3} (z_{k}) \end{matrix}] .$ (13)

$F_{1}$ , $F_{2}$ , and $F_{3}$ are functions of the 14 parameters of $[μ_{0}, R, L, M, n, r, x, y, z, e_{x}, e_{y}, e_{z}, x_{0}, y_{0}]$ .

The total magnetic induction intensity, $B$ $(B_{x}, B_{y}, B_{z})$ , generated by the array of magnetic elements at the observation point, is the sum of the magnetic induction intensities of each individual submagnet, which is $B = [\begin{matrix} B_{x} \\ B_{y} \\ B_{z} \end{matrix}] = [\begin{matrix} \sum_{i = 1}^{k} F_{1} (z_{k}) \\ \sum_{i = 1}^{k} F_{2} (z_{k}) \\ \sum_{i = 1}^{k} F_{3} (z_{k}) \end{matrix}] .$ (14)

For the magnetic vector corresponding to a group of $k$ sensors, the $Z$ coordinate of the magnetic body can be obtained. These $k$ magnetic vectors can be provided by $B_{x}$ , $B_{y}$ , or $B_{z}$ , or a combination of them. In this case, we choose the $B_{z}$ magnetic vector as the reference.

The magnetic flux position estimation method only requires determining the positions of two magnetic poles and the magnitude of the magnetic flux in the magnetic field map of the micromagnet, which can then determine the position and attitude of the micromagnet. Therefore, the accuracy of the $B_{\max}$ position estimation is crucial. This method requires locating two specific positions representing the magnetic poles in the magnetic field map, which can be easily obtained through the magnetic flux method to determine the position and attitude of the micromagnet. The interval between these two positions and the average magnetic field of all the pixels in the magnetic field map have significant differences, making them easy to select.

As shown in Fig. 3(a), the optimal range of the magnetic poles is first determined. This range is used to roughly filter out the areas where $B_{\max}$ and $B_{\min}$ are most likely to appear, in preparation for subsequent accurate positioning. Then, within the optimal range, the positions of $B_{\max}$ and $B_{\min}$ are accurately determined using linear magnetic chain analysis. The specific operation of linear magnetic chain is as follows. First, the $X$ -axis and $Y$ -axis pixels at the positions within this range are taken as the horizontal coordinates, and the corresponding magnetic field values of the pixels are taken as the vertical coordinates. Through the analysis of a single-variable linear regression, the maximum peak value $(B_{\max - x}, B_{\max - y})$ and minimum peak value $(B_{\min - x}, B_{\min - y})$ are selected. Finally, the accurate positions of $B_{\max}$ and $B_{\min}$ are determined based on the positions of $B_{\max - x}$ , $B_{\max - y}$ , $B_{\min - x}$ , and $B_{\min - y}$ . Figure 3(b) shows the procedure for determining the positions of $B_{\max}$ and $B_{\min}$ .

4. Experimental Verification

To evaluate the performance of positioning, we tested a cylindrical permanent magnet at predetermined locations. The height of the permanent magnet is 130 µm, with a radius of 10 µm. Table 1 shows the positioning error of the cylindrical permanent magnet at 10 different positions, with each test repeated 10 times. The results indicate that the maximum positioning error is 78.12 µm, and the average positioning error is 48.52 µm. As shown in Figs. 4(a) and 4(b), when comparing the positioning error results, we found that the 10 sets of planar positioning errors ( $X$ axis and $Y$ axis) are similar, around 25 µm. However, the depth positioning error is larger than the planar positioning error, averaging around 40 µm, and it increases with the increasing detection depth, as shown in Fig. 4(c); hence, the overall positional error is approximately 50 µm.

Test Node	Positioning			Temperature
Test Node	Preset (µm)	Test (µm)	Error (µm)	Preset (K)	Test (K)	Error (K)
1	(80,30,1500)	(103,53,1536)	48.52	353.15	352.72	0.43
2	(160,80,1550)	(183,105,1588)	50.97	348.15	347.76	0.39
3	(240,130,1600)	(264,154,1639)	51.70	343.15	342.77	0.38
4	(320,180,1650)	(345,204,1691)	53.69	338.15	337.79	0.36
5	(400,230,1700)	(375,253,1743)	54.80	333.15	332.80	0.35
6	(480,280,1750)	(503,307,1796)	58.09	328.15	327.79	0.36
7	(560,330,1800)	(584,354,1850)	60.42	323.15	322.72	0.43
8	(640,380,1850)	(616,356,1905)	64.63	318.15	317.68	0.47
9	(720,430,1900)	(743,455,1964)	74.46	313.15	312.71	0.44
10	(800,480,1950)	(824,505,2020)	78.12	308.15	307.70	0.45

Table 1. Positioning and Temperature Performance Evaluation

View all Tables

Figure 4.Position and temperature error. (a)–(c) Position and error of the X axis, Y axis, and Z axis at 10 test nodes; (d) temperature and error at 10 test nodes.

In addition, to evaluate the performance of temperature detection, we tested the predetermined temperatures. Table 1 also shows the temperature errors in the 10 sets of repeated tests conducted at different temperatures. As shown in Fig. 4(d), the results indicate an average temperature error of approximately 0.4 K.

To simulate the dual imaging process of positioning and temperature of the micromagnet, the permanent magnet is heated to 353.15 K and placed in a transparent glass tank filled with silicone oil. Through optical means, we can conveniently obtain the position of the micromagnet at O-XY plane (gray-scale image). Figure 5 presents the gray-scale image and position and temperature feedback diagram. There is strong consistency between the gray-scale image and the displacement image. This indicates that the accuracy of the magnetic tracking method in real-time position tracking is stable. We noticed that as the measurement progressed, the temperature of the permanent magnet gradually decreased, which we attributed to the effect of temperature diffusion. Since it was not possible to perform real-time calibration of the temperature of the permanent magnet during the real-time testing, we were unable to obtain the real-time tracking error of the temperature. However, we could clearly observe the thermal diffusion phenomenon of the permanent magnet. The experimental results demonstrate that the NV center imaging technology can monitor the position and temperature of the micromagnet in real time.

Figure 5.Feedback of the position and temperature of micromagnets in complex environments.

5. Conclusion

This article introduces a new system for simultaneously tracking the position and temperature of a micromagnet. The positioning error of the system is 50 µm, and the average temperature error is 0.4 K. The magnetic field sensitivity of the diamond microscope is $30 μT / {Hz}^{1 / 2}$ , and the temperature sensitivity is $0.5 K / {Hz}^{1 / 2}$ . During the tracking process, the system demonstrates good sensitivity to both position and temperature. Therefore, our tracking method is highly suitable for imaging the position and temperature of a micromagnet. Furthermore, by improving the control strategy, it is possible to further enhance the localization accuracy. For example, combining technologies such as high-speed cameras and deep learning can unlock even greater potential for this technique.

Future improvements can be made to this method through a series of technological advancements. For instance, sensitivity to magnetic fields and temperature can be further enhanced using pulse-shaping techniques^[28]; spatial resolution and field of view can be improved by integration with scanning confocal systems^[29]; and detection speed can be increased by combining with high-speed ODMR detection methods^[30].

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