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Magnetic compensation coils are often used to improve the effectiveness of a magnetically shielded room (MSR), but a distortion of the field is caused by the shielding layer consisting of high-permeability material, which leads to a reduction in compensation capacity. To solve this problem, a new method is presented in this article based on a target-field method, an image method, and particle swarm optimization. By this way, a magnetic compensation system composed of biplanar coils is designed and fabricated to compensate the background field for a wearable magnetoencephalography device inside the MSR, and the coupling effect between the magnetic shielding material and the compensation field is effectively avoided. Experimental data show that these compensation coils produce uniform fields and field gradients with the inhomogeneity of less than 3.8%, consistent with the simulation results. In addition, this system realizes a real-time compensation to the residual field and field gradient in the MSR. [ABSTRACT FROM AUTHOR]

In this article, an iterative optimization algorithm is proposed to design biplanar coils, which is used for dynamic magnetoencephalography to compensate for residual fields in the magnetic shielding room. The effects of magnetic shielding layers and plane’s side length on the uniformity are both considered for designing coils. The iterative calculation is used to minimize the side length of the coil plane. The biplanar coils with 1.3-m side length are designed, which consist of three homogeneous-field coils ($B_{x}, B_{y},\; { \rm and }\; B_{z}\; { \rm coils }$) and five gradient-field coils ($dB_{x}/dy, dB_{x}/dz, dB_{y}/dy, dB_{y}/dz,\; { \rm and }\; dB_{z}/dz\; { \rm coils }$). The coil system can produce homogeneous and gradient fields within 1% error over the volume of 40 cm × 40 cm × 40 cm. Through active magnetic shielding, the central field inside the magnetic room is reduced from 7.56 to 0.17 nT, and standard deviation from the mean value in the target area falls from 1.366 to 0.177 nT. The dynamic auditory stimulation experiment proves that the biplanar coil system will improve the quality of the evoked signals. [ABSTRACT FROM AUTHOR]

The magnetic noise generated by the ferrite magnetic shield affects the performance of ultra-sensitive atomic sensors. Differential measurement can effectively suppress the influence of common-mode (CM) magnetic noise, but the limit of suppression capability is not clear at present. In this paper, a finite element analysis model using power loss to calculate differential-mode (DM) magnetic noise under a ferrite magnetic shield is proposed. The experimental results confirm the feasibility of the model. An ultrahigh-sensitive magnetometer was built, the single channel magnetic noise measured and the differential-mode (DM) magnetic noise are 0.70 fT/Hz1/2 and 0.10 fT/Hz1/2 @30 Hz. The DM magnetic noise calculated by the proposed model is less than 5% different from the actual measured value. To effectively reduce DM magnetic noise, we analyze and optimize the structure parameters of the shield on the DM magnetic noise. When the outer diameter is fixed, the model is used to analyze the influence of the ratio of ferrite magnetic shielding thickness to outer diameter, the ratio of length to outer diameter, and the air gap between magnetic annuli on DM magnetic noise. The results show that the axial DM magnetic noise and radial DM magnetic noise reach the optimal values when the thickness to outer diameter ratio is 0.08 and 0.1. The ratio of length to outer diameter is negatively correlated with DM magnetic noise, and the air gap (0.1–1 mm) is independent of DM magnetic noise. The axial DM magnetic noise is less than that of radial DM magnetic noise. These results are useful for suppressing magnetic noise and breaking through the sensitivity of the magnetometer. [ABSTRACT FROM AUTHOR]

This article presents a design method of cylindrical uniform field coil based on quasi-elliptic function fitting (EFF) method with multiple optimizations. The EFF method is a type of discrete wire techniques aiming at simplifying the coil structure. Combing with particle swarm optimization (PSO) algorithm, the optimized parameters of EFF coil are obtained for highly uniform magnetic field. To further improve the uniformity of magnetic field in the central space, a new regional points selection optimization method is proposed. The calculation results show that after PSO optimization, the absolute maximum relative error in the target region is optimized to 0.098% by EFF coil comparing with modified single saddle coil (3.08%), nest coil (2.4%), and target field method (TFM) coil (0.11%). After regional points selection optimization, the volume proportion of absolute magnetic field relative error less than $1\times 10^{-4}$ increases from 35.24% to 54.38% by EFF coil comparing with TFM coil. In addition, the simple EFF coil structure is verified to be easy to process and keep high performance through experiments. As the EFF coil’s high uniformity and simple structure, the new method has important significance for the miniaturization of atomic sensors. [ABSTRACT FROM AUTHOR]

Atomic magnetometers are widely acknowledged as one of the most sensitive devices for magnetic field measurement. Our study presents a novel method that enables bandwidth expansion of single-beam magnetometers in the spin-exchange relaxation-free regime. This method bases on increasing the modulation amplitude of magnetic field combining with negative feedback with proportional gain. Through our method, the magnetometer’s total relaxation rate is moderately increased by elevating modulation amplitude and frequency, and correspondingly, the detection bandwidth experiences dramatic improvement from 230 Hz to 1380 Hz. The application of negative feedback with proportional gain further increases this bandwidth to higher than 4 kHz, which is over 17 times of its original value. The sensitivity of the magnetometer under this condition is measured as 25 fT/ $\text {Hz}^{\text {1/2}}$ for open-loop scheme and 35 fT/ $\text {Hz}^{\text {1/2}}$ for closed-loop scheme. Comparatively, the sensitivity measured on conventional conditions in our experiment is 12 fT/ $\text {Hz}^{\text {1/2}}$. This approach offers a profitable trade-off that extraordinary expansion of detection bandwidth can be acquired with the price of a little sensitivity loss. Our method is advantageous for miniaturization of atomic magnetometers as no extra hardware is added, which is of special interest for applications including biomagnetic measurement where large detection bandwidth is sometimes in need. [ABSTRACT FROM AUTHOR]

Magnetic field shields are important for electronic equipment, ultrahigh-sensitivity sensors, and electrical instruments. For ultrahigh-sensitivity atomic sensors, in particular, ferrite shields with low intrinsic magnetic noise are widely used. In this article, the calculation methods of longitudinal and transverse magnetic noise, which are calculated by loss, are analyzed. The experimental results confirm the feasibility of the model. Using the loss separation method, it is proved that the loss of ferrite magnetic shielding is mainly hysteresis loss, which is below 100 Hz. To effectively reduce the magnetic noise, we analyze the effect of structure parameters on the longitudinal and transverse magnetic noise, and the optimized parameters are obtained. The results show that the longitudinal magnetic noise decreases with the increasing aspect ratio and stabilize eventually. When the aspect ratio exceeds 1, the transverse magnetic noise remains practically unchanged. When the external diameter is fixed, by optimizing the thickness of the magnetic shield, the optimal solution for the longitudinal and transverse magnetic noise is obtained. [ABSTRACT FROM AUTHOR]

We propose non-magnetic heating film based on indium tin oxide (ITO) and apply it in a miniaturized spin exchange relaxation free (SERF) gradient magnetometer. To achieve ultrahigh sensitivity, alkali metal atoms inside the vapor cell of the magnetometer require an elevated temperature field that is stable and uniform. ITO is a transparent and electrically conductive material which is suitable for such application and can be used as resistance wire to form the heating film. A film structure composed of an insulation layer sandwiched between two ITO layers with the same optimized pattern is used to configure the heating current to double back on itself to reduce the magnetic noise caused by it. Experiments show the proposed film can be heated to over 200 °C, which is sufficient for vaporizing alkali metal atoms such as potassium, rubidium, and cesium. The magnetic current coefficients of the heating films are below 0.2 nT/mA and with the high frequency heating current, low-frequency magnetic noise can be further reduced. We compare ITO-based heating films and conventional flexible printed circuit (FPC) heating films side by side in the same gradient magnetometer and with ITO films a more uniform temperature field and better intrinsic magnetic field sensitivity of 22 fT/cm/Hz $^{1/2}$ is achieved. The proposed ITO-based non-magnetic heating film can be used not only in atomic magnetometers but also in other atomic devices such as chip scale gyroscopes and atomic clocks. [ABSTRACT FROM AUTHOR]

An improved approach for designing highly linear gradient coils based on the target-field method is presented for application in a magnetoencephalography system. With this method, two novel current density functions are expanded in a trigonometric series with single-Fourier coefficients that need to be determined. Their determination is resolved by selecting field points and desired field values in the target area of interest. The coil winding patterns are then given by the level contours of the stream function. Compared with the discrete-wire design method, the advantage of this method is that the coil size is predetermined prior to the calculation and better linearity in the field is obtained that overcomes size constraints. A numerical simulation shows that in a cube with a side length of $0.5~{R}$ , the field linearity of the proposed transverse gradient coil is improved by 2.5 times that of the Golay coil, and the designed longitudinal gradient coil by 1.2 times that of the Maxwell coil. Moreover, with the optimized transverse gradient coil being manufactured by flexible printed circuit technology, the magnetic field generated by it matches that produced in theoretical simulations. Measurement results show that the linearity of this transverse gradient coil is $6\times 10{^{- {\,\,\textbf {3}}}}$ along the ${z}$ -axis in the range of $\pm 0.25~{R}$. [ABSTRACT FROM AUTHOR]

Atomic magnetometers operated in spin-exchange relaxation-free (SERF) have the potential to replace superconducting quantum interference devices (SQUIDs) in the field of biomagnetism. Here, we demonstrate the dual-axis closed-loop control of a single-beam SERF magnetometer that allows sensing of two orthogonal magnetic fields simultaneously and independently with suppressed crosstalk effect, achieved by applying a rotating modulation field and using the negative feedback. Operating in the dual-axis closed-loop mode with a miniature 4 $\times $ 4 $\times $ 4 mm 87Rb cell, we achieve the magnetic field sensitivity of 20 fT/Hz1/2 and a bandwidth of 1.8 kHz. In addition to the experimental study of the sensitivity and bandwidth, we perform a theoretical analysis of the dual-axis response and develop an effective decoupling method. The implementation of closed-loop control enables the magnetometer to be robust against the disturbance of the ambient field, which could enlarge the dynamic range, enhance the systematic stability, and suppress the crosstalk effect. Such a simple, yet high-performance SERF magnetometer could be suitable as a promising candidate in the field of biomagnetism, allowing for a denser sensor array and opening up new possibilities for noninvasive biomagnetic imaging. [ABSTRACT FROM AUTHOR]

Cylindrical ferrite shields consisting of multiple annuli can provide low-magnetic-noise environments. However, the gaps between different parts of the shield adversely affect the shielding performance. In this study, we numerically study the influence of the gaps on both the axial and radial magnetic noise of the multi-annular ferrite shield with different gap widths, permeabilities, and aspect ratios using the generalized Nyquist relation and the finite element method. Our study indicates that as the gap width increases, the axial magnetic noise decreases, while the radial magnetic noise increases. For the shield with a gap width of 0.10 mm and an aspect ratio of one in our study, the axial magnetic noise decreases by 5.2%, and the radial magnetic noise increases by 8.3%–33.5%. The difference in the increase is related to the permeability, and gaps have smaller effect on the radial magnetic noise of the shield with lower permeabilities. Therefore, compared with the no-gap shield, the multi-annular ferrite shield can provide an even better low-magnetic-noise environment along the axial direction. Although the gaps can induce an increase of the radial magnetic noise, this detrimental effect can be suppressed significantly by using a ferrite material with lower permeability and reducing the gap width. Our findings can aid in the application and optimization of low-noise ferrite shields. [ABSTRACT FROM AUTHOR]

Mu-metal shields are widely used in atomic devices, but their magnetic noise related to loss is the key performance limit. The magnetic noise can be calculated by using complex permeability and the magnetic field intensity in the shield. In this study, Bertotti loss separation is used for the first time to accurately calculate the changes of complex permeability due to the hysteresis loss in different frequencies and magnetic field intensities, and we further consider the change in magnetic field intensity due to the induced eddy current, which also increases the accuracy of the magnetic noise calculation. For extremely low frequencies below 20 Hz, the improved noise simulation model differs from the measured results by less than 11%. If the loss separation is not considered, the difference between the measured value and the simulated value would be as high as 54%. The high agreement between the calculation and the experimental results proves the accuracy of the proposed method. Our method can be used in the design and optimization of low-noise magnetic shields to improve the sensitivity of atomic devices [ABSTRACT FROM AUTHOR]

A set of five-layer cylindrical magnetic shields is designed and constructed to attenuate external geomagnetic field to less than 10 nT (ideally zero). We aim to achieve a shield design having high shielding factor, low magnetic noise, and small volume. However, magnetic noise is incompatible with shielding factor and volume. Thus, there is a compromise. This paper presents an optimization method to acquire a sufficiently effective, low-noise, and lightweight multi-layer shield. The optimization objective and constraints are provided in the form of analytic expressions. The mathematical model is constructed in MATLAB. The optimization is executed in iSIGHT software integrated MATLAB. By optimizing the nonlinear programming quadratic line (NLPQL) algorithm, theoretically the axial shielding factor ${\sf\textit {S}}_{\text {tot}}^{\sf\textit {A}}$ can be increased by a factor of about 390.3, on the premise that the magnetic noise and volume have increased negligibly. Apart from better shielding performance, a combination of optimum parameters is obtained. This optimization method has good universality. As long as certain shielding requirements are determined, the corresponding optimum parameters can be acquired accurately. This method is of great significance for future improvements to shield design. [ABSTRACT FROM AUTHOR]

A stable magnetic field environment is one of the key factors to realize the ultrasensitive magnetic field detection. Ferrite materials, which possess both high electrical resistivity and high permeability, are ideal magnetic shielding materials. Gaps and holes usually exist in the large size magnetic shield which effects shielding effectiveness. In this paper, the variation of the DC magnetic shielding ratio, for different gaps and access hole dimensions, is quantificationally investigated using the finite element method. The shielding ratio in the simulation is close to the theoretical calculation for the closed shield when the thickness of gaps is very small. Our study indicates that gaps and holes separately reduced the shielding effectiveness, and the coexistence of gaps and holes aggravated the reduction of shielding effectiveness. Compared with the shielding ratio of the ferrite enclosure without gaps and holes for the known size shield, the transverse and longitudinal direction of the shielding ratio increase by 9% and 274% with gaps (thickness = 0.1 mm) and holes (diameter = 25 mm), respectively. The simulation results are partially verified with experimentally using a cylindrical ferrite shield made of Zn0.17Mn0.74Fe2.06O4 and Zn0.33Mn0.58Fe2.06O4. The difference between the experimental and simulation results is less than 10%. [ABSTRACT FROM AUTHOR]

Many sensitive atomic devices require magnetic shield to reduce external magnetic field interference. Mn–Zn ferrites are optimistic candidates for shielding because they provide a high shielding factor and a low magnetic noise. This study evaluated the magnetic noise of Mn–Zn ferrite magnetic shield based on its grain size. The morphologies of Mn–Zn ferrite samples were characterized to establish a correlation between their grain sizes and magnetic permeability, which can be used to calculate magnetic noises. The correlation was then used to evaluate the shielding performance of another Mn–Zn ferrite, where the magnetic noise of the magnetic shield made from the ferrite was calculated to be 2.53 f −1/2fT. The magnetic noise of the magnetic shield was also measured experimentally using a spin-exchange relaxation-free atomic magnetometer. The measured magnetic noise of ferrite shield was 2.61 f −1/2fT, while the white noise of the atomic magnetometer was 0.71 fT/Hz1/2 below 100 Hz. The consistency between the experimental results and predicted values suggests the viability of the proposed approach, providing a convenient, efficient, and precise method for developing ferrite ceramics materials for low-noise magnetic shields. [ABSTRACT FROM AUTHOR]

[Display omitted] • A novel in-situ method to measure complex magnetic permeability (CMP) based on the magnetic shielding mechanism is presented. • By measuring the magnetic field at the center of shielding, the effective CMP of a large dimensional ferrite shielding can be determined. • The addition of Co significantly improved the thermal stability of CMP by 6.62 times and reduce the magnetic noise. • This method ensures a real-time observation of CMP and magnetic noise under different temperatures. Magnetic shielding made of low noise ferrite materials is used in many ultra-sensitive measurements. The complex magnetic permeability (CMP) of ferrites directly affects the magnetic shielding performance, so the measurement of CMP is particularly important. Conventional measurements omit the effects of temperature on ferrites' magnetic properties and can only measure samples with specific shapes. Here a novel measurement method of CMP based on the magnetic shielding mechanism is presented. By in-situ measuring the magnetic field, the effective CMP of large dimensional ferrite shielding can be determined. Also, the intrinsic magnetic noise of a MnZn ferrite shielding was observed using the proposed method. Using the finite elements method (FEM), we identified the influencing factors of air gap in the CMP measurements. We also analyzed the influence of element doping on the thermal stability of CMP. This study ensures a real-time observation of CMP and magnetic noise under different temperatures. [ABSTRACT FROM AUTHOR]

A stable magnetic environment that is devoid of interference from ambient magnetic fields is crucial to precise measuring magnetic fields. In this study, a novel magnetic shield with a winding shape, similar to a spiral, is proposed to simultaneously increase the shielding coefficient and reduce the magnetic noise produced by the magnetic shield. In the winding-shaped magnetic shielding structure, an entire mu-metal strip is rolled into multiple layers to form a cylindrical barrel shape. Each layer is separated by insulating adhesives. The effects of the number of turns of the strip and the insulating adhesive on the shielding coefficient and the magnetic noise were analyzed. The simulation results demonstrated that the DC shielding coefficient of this novel structure increased by 123 % and the magnetic noise was reduced by 47 % compared to that of the conventional structures. In addition, the shielding coefficient and the magnetic noise of the two structures were experimentally measured, confirming the superiority of the proposed structure. [Display omitted] • A novel magnetic shielding structure with winding shape. • Improvement of magnetic shielding coefficient and reduction of magnetic noise. • Detailed analysis of shielding coefficient and magnetic noise of new winding-shaped magnetic shield. • Further promote the application of ultra-high sensitivity quantum sensing technology. [ABSTRACT FROM AUTHOR]