Magnetic microscopic imaging with an optically pumped magnetometer and flux guides

Many fields, such as neuroscience, biomedical research, and material science, are in need of high-sensitivity, high-spatial-resolution magnetometry. In order to meet demanding requirements for various applications, we have recently combined a cm-size spin-exchange relaxation-free (SERF) optically pumped magnetometer (OPM)^1,2 with high permeability ferrite flux guides (FGs) to realize a simple yet highly competitive approach for magnetic micro-imaging.³ Among various possible applications of this approach in neuroscience is the detection of a small number of neurons to improve understanding the human brain function and to record Magnetoencephalography signals in small animals, widely used in neuroscience research. For example, it can be applied to animal nerve impulse detection:⁴ FG-OPM can be placed at a stand-off distance of a few microns to nerve samples to improve both sensitivity and spatial resolution. The capability of microscopic magnetic imaging will be crucial for neurosurgery planning, developing diagnostic methods and treatments, and studying cognitive and perceptual responses.⁵ Beyond neuroscience, the FG-OPM approach can be applied to the detection of nano-particles, which will be valuable in many fields of medicine and biophysics. Specially, magnetic imaging of tagged nano-particles to cancerous cells will greatly improve diagnostics and treatment of cancer at an early stage.⁶ In addition to bio-applications, the approach can be also used for non-destructive testing and authentication of integrated circuits to uncover counterfeit parts.

To explore one specific aspect for applications via magnetic particles, in this paper, we apply the FG-OPM device to microscopic magnetic imaging of micron-size magnetic particles. Our previous work³ was focused on the proof-of-principle demonstrations with coils, which were operated at sufficiently high frequency for easy detection and were limited in size by our ability to construct them from available wire. Also, the tests of spatial resolution were done by manual scanning in one direction. In general, the experimental techniques developed in the previous work were not applicable for imaging DC magnetic objects such as micro- or nano-particles with good spatial resolution, sensitivity, and measurement speed. First of all, the sensitivity to DC magnetic fields was quite low owing to the much larger noise in the OPM (1/f noise) and FGs (domain-fluctuation noise). To address this, we introduced a modulation generated by a translation stage, which converts the DC field signal to a monochromatic signal of ∼0.6 Hz. Second, we implemented an automated 2D surface scanning system to eliminate the need for long-term manual scanning. Third, we have made target samples with magnetic micro-particles for more practical measurement and developed methods for their imaging and analysis. Finally, we performed numerical simulations that allow relating experimental measurements to the magnetization and localization of micro-particles and their magnetization orientation for a given FG tip configuration and stand-off distance. The modeling is essential for the analysis of the magnetization of a sample and for prediction of the performance of the device and its optimization.

The experimental setup for microscopic magnetic imaging consists of the FG-OPM device (a cm-size QuSpin OPM with $3×3×3$ mm³ Rb vapor cell and FGs with the $50 μ$m tips’ gap; the cell is located in the center of the larger gap of the FGs), magnetic shields, field and gradient compensation coils, a 3D position scanning system, and a sample holder (Fig. 1). In tests with coils, this FG-OPM achieved the spatial resolution of 250 μm (limited by the tip geometry of the manufactured ferrite FGs³) and the sensitivity of 23 pT/$Hz$ with the OPM operating at 20 fT/$Hz$ intrinsic sensitivity at a frequency larger than its 1/f corner frequency. An automatic scanning system is based on a three-axis translation stage and precision positioning motorized actuators providing a 2.5 cm travel distance (Thorlabs Z825B). It served to increase the measurement speed as well as to make the measurements more precise. The three-axis translation of the scanning system was entirely controlled by our LabView program. The FG-OPM was located inside a cylindrical ferrite shield with end-caps (18 cm diameter and 38 cm height) inserted into a two-layer open mu-metal concentric cylindrical shield (26 cm inner diameter, 29 cm outer diameter, and 69 cm height) to remove the ambient DC field and magnetic noise. The residual fields and linear gradients from the ferrite shield were cancelled by three orthogonal coils and a complete set of five first-order gradient coils placed inside the shield. A target magnetic sample, attached to a plastic sample holder connected to the scanning system through a rigid plastic bar, was located near the FG tips and moved with respect to the tips. The scanning system was located outside the mu-metal shield to reduce its effect on sensitive magnetic measurements. For data acquisition, a 24-bit analog-to-digital converter (NI PXIe-4497) was employed.

Magnetic particles of micron-size were prepared by fragmenting and grinding a 1 cm-diameter neodymium (NdFeB) magnet disk with the surface field of 0.2 T. Because neodymium is easily oxidized once the external coating of the magnet is broken and because of mechanical shock, the magnetic particles produced in this way were significantly demagnetized^7,8 as we observed in our experiments. Target flat samples of mm-size containing home-made micron-size magnetic particles shown in Figs. 2–4 were shortly magnetized by a “shim-a-ring” magnet⁹ generating a uniform 0.5 T magnetic field in order to orient the magnetization of the magnetic particles along the most sensitive direction of the FG-OPM device (y-axis in Fig. 1). The FG-OPM automatically mapped the magnetic field distribution from the target samples with the scanning system controlled by our LabView program. The scanning protocol generally consisted of five steps: (1) one edge of a sample (⁠$x=y=0$⁠) was aligned with the FG tips at the stand-off distance of $∼50 μ$m (set by the precision actuator in the z-axis); (2) at the start of the LabView program, the sample was modulated in the z direction by the z-axis actuator with a modulation frequency of 0.55 Hz (the maximum frequency achieved by the actuator) and a modulation amplitude of 450 μm; (3) first, the sample moved in the y direction at x = 0 with a given step $Δy$ to scan and record the magnetic fields; (4) when the sample reached the maximum y position, it moved by a given step $Δx$ in the x direction, came back to y = 0, and it was scanned again through the y direction; (5) when the sample reached both the maximum x and y positions, the modulation was halted and the program terminated. In order to find the start position (⁠$x=y=0$⁠), we placed a 100 μm-diameter thin wire loop, which generated an AC field at 10 Hz in the y direction, right next to the sample's starting position.

Figure 2(b) shows the magnetic image of a target sample containing a 22 μm-diameter magnetic particle as indicated in Fig. 2(a). $Δy$ and $Δx$ were set to 50 μm and 100 μm, respectively. The FG-OPM device detected the modulation signal at 0.55 Hz; amplitude was obtained from the corresponding peak in the Fast Fourier transform (FFT) spectrum. Because the 1/f corner frequency of the FG-OPM was measured to be ∼10 Hz mainly due to the thermal magnetic noise originating from the FGs,³ the FG-OPM sensitivity at the modulation frequency decreased by a factor of five. That resulted in the increase of the measurement time to suppress the background noise: the data were collected for 20 s at each scan position, which led to the total measurement time of about 1 h. In the near future, the actuator will be replaced with a piezo stage to increase the modulation frequency over the 1/f corner, thereby reducing the measurement time at each scan position to 1 s. As shown in Figure 2(b), the FG-OPM clearly detected the presence of the magnetic particle. We investigated the spatial resolution of the manufactured FGs by fitting a Gaussian model function, $f(y)=a+bωπ/2e−2(y−c)2ω2$ where the fitting parameters ω, a, b, and c are, respectively, the width, the offset, the area, and the position of the center of a Gaussian, to the data obtained at $x=400 μ$m, in which the width $ω=(300±11) μ$m is equivalent to the spatial resolution. The fit results in the 300 μm spatial resolution of FG-OPM, which is comparable to the previously measured value with coils of 250 μm.³ 

We also obtained a microscopic magnetic image of a target sample containing a 10 μm-diameter particle as shown in Fig. 3(b). For this image, $Δy$ and $Δx$ were set to 80 μm and 100 μm. The magnetic image of the FG-OPM clearly pinpointed the position of the magnetic particle. It is known that the magnetic field B from dipolar sources of different diameters d has the relation of $B1/B2∝d13/d23$ where 1 and 2 denote two different sources. Compared to Figure 2(b), the measured magnetic field of the 10 μm-diameter particle is about 10 times smaller, which is in good quantitative agreement with the above relation, $(22 μ$m)$3/(10 μ$m)³= 10.65. This estimate of course is based on the assumption that the magnetization of two particles is the same and that the shapes are similar, close to spherical. Note also that the optical image is far less sensitive to the magnetic particle than the magnetic image, so our FG-OPM device would be indeed of great value in biological imaging where magnetic particles can be masked by other inclusions and by non-uniformity of patterns.

In addition, Fig. 4(b) shows the magnetic image of a target sample, which contains two 10 μm-diameter magnetic particles at different locations as indicated in Fig. 4(a). $Δy$ and $Δx$ were set at 80 μm and 120 μm. The FG-OPM device could detect distinct two peaks from the two particles and clearly find their locations.

To examine the propagation of magnetic flux from a micron-size magnetic particle to the OPM vapor cell, we performed 3D numerical simulations using finite element analysis software (COMSOL Multiphysics 4.3). A stand-off distance from the FG tips, the tips’ gap, and the shape of FGs were chosen to closely resemble experimental ones (see the inset in Fig. 5(a)). A magnetized spherical particle in the sensitive direction of the FG-OPM was defined by filling its volume with a uniform magnetization M of $7.5×105$ A/m, which is the typical value for NdFeB magnets. Because of the demagnetization factor N, the internal magnetic field is somewhat reduced, $Bint=(1−N)μ0$ M. The numerical calculation estimated that $Bint$ is 0.6 T, which is in good agreement with $Bint$ analytically calculated with the known value of N = 1/3 for the spherical shape. The magnitude of the surface field at the nearest position to the FG tips was estimated to be 0.3 T; this surface field can be used to obtain the fields at large distances by using a cubic fall off of a magnetic dipole source.

Figures 5(a) and 5(b) show numerically calculated magnetic fields at the position of the center of the OPM vapor cell as a function of the stand-off distance, from 22 μm- and 10 μm-diameter spherical particles, and magnetic field patterns when the particles relocate along the sensitive direction of FG-OPM with respect to the center of FGs at the 50 μm stand-off distance, respectively. The data were fit to the following model of $f(z)=a1/(z+a2)3+a3$⁠, where z is the stand-off distance and a₁, a₂, and a₃ are free fitting parameters. At the stand-off distance of 50 μm, the field transfer coefficients of the FGs, the ratios of the fields measured by the FG-OPM to the surface fields of the particles, were estimated to be $3.4×10−8$ and $2.4×10−9$ for 22 μm- and 10 μm-diameter particles. That revealed that the sensitivities of the FG-OPM to the surface fields of 22 μm- and 10 μm-diameter particles at the 50 μm stand-off distance were $2.9×10−7$ T and $4.1×10−6$ T assuming an improved OPM operating at $10$ fT intrinsic sensitivity³ (note that in experiments we have significant 1/f noise but it can be removed by increasing the modulation frequency by using a piezo stage). According to the estimated field transfer coefficient, the surface fields on the magnetic particles in Figs. 2–4 were estimated to be $∼1$ mT, 200 times smaller than the initial surface field of 0.2 T in the magnet from which the particles were made. The demagnetization could be due to oxidation of neodymium or mechanical shock during the preparation of the particles as discussed above. On the other hand, if we could maintain the same magnetization in small particles as in the bulk (perhaps by preventing the oxidization of the sample and assuring that the particle remains in the saturated state), then by using cubic scaling with the size, one can conclude that potentially the FG-OPM should be able to detect as small particles as 100 nm.

We also performed the above numerical calculations with the optimized FGs (shown in Fig. 5(b) in Ref. 3), which improve both the spatial resolution and the sensitivity of FG-OPM. We found that the field transfer coefficients of the optimized FGs at the stand-off distance of 50 μm were $4.3×10−8$ and $3.1×10−9$ for 22 μm- and 10 μm-diameter particles, which results in calculated sensitivity of the FG-OPM to the particles of $2.4×10−7$ T and $3.2×10−6$ T. In addition, we numerically investigated the dependence of the field transfer coefficient on the FG tips’ gap. We found that the coefficient of both manufactured (used in the experiment) and optimized (proposed for future improvement) FGs at the tips’ gap lower than 100 μm is held constant in the optimal value while it drastically drops 10 times at the zero tips’ gap (i.e., the FG tips touch).

Since the home-made magnetic particles are not perfectly spherical in shape, we also numerically investigated a disk-shaped particle with M of $7.5×105$ A/m. The internal and surface fields of the disk-shaped particle depend on the particle's diameter-to-height ratio (DHR): the internal field at the center exponentially increases with DHR while the surface field exponentially decreases. For example, at DHR of 2 and 10, the internal fields were estimated to be 0.75 T and 0.90 T, which correspond to N of 0.204 and 0.045 while the surface fields were 0.18 T and 0.05 T. Thus, some decrease in the surface field of the home-made magnetic particles to 1 mT level, stated above, could be also attributed to the particle's flat shape. These results are valid for any diameters. In the case of a disk-shaped particle with a DHR of 2 and a diameter of 22 μm, the field transfer coefficient at the 50 μm stand-off distance was estimated to be $4.75×10−8$⁠.

This scanning FG-OPM magnetic imaging system can be also employed to detect magnetic impurities on a material of interest. Since most high-precision experiments to test fundamental symmetries such as the search for the permanent electric dipole moment (EDM) of elementary particles^10,11 and exotic spin-dependent interactions¹² are aiming to detect minute magnetic fields as the physical observable, magnetic impurities on their experimental systems can be a dominant source of systematic effects. For example, in the case of the recently proposed neutron EDM experiment,^10,13 to be conducted at the spallation neutron source at Oak Ridge National Laboratory, the known systematic effects are caused by magnetic field non-uniformities in the measurement cells.¹⁰ Hence, magnetic impurities (mainly iron particles) buried in the material of measurement cells will create magnetic gradients inside the measurement cells, which mimics an EDM. The high-sensitivity magnetic microscopic imaging of the material will be critically important to the success of the EDM experiment by detecting magnetic impurities, thereby removing magnetic gradients.

The authors are grateful for helpful discussion with Dr. Steven Clayton. The authors gratefully acknowledge that this work was supported by the Los Alamos National Laboratory LDRD office through grant 20150300ER.