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With the widespread use of magneto-sensitive elements, magnetic shields are an important part of electronic equipment, ultra-sensitive atomic sensors, and in basic physics experiments. Particularly in Spin-exchange relaxation-free (SERF) co-magnetometers, the magnetic shield is an important component for maintaining the SERF state. However, the inherent noise of magnetic shield materials is an important factor limiting the measurement sensitivity and accuracy of SERF co-magnetometers. In this paper, both amorphous and nanocrystalline materials were designed and applied as the innermost magnetic shield of an SERF co-magnetometer. Magnetic noise characteristics of different amorphous and nanocrystalline materials used as the internal magnetic shielding layer of the magnetic shielding system were analyzed. In addition, the effects on magnetic noise due to adding aluminum to amorphous and nanocrystalline materials were studied. The experimental results show that compared with an amorphous material, a nanocrystalline material as the inner magnetic shield layer can effectively reduce the magnetic noise and improve the sensitivity and precision of the rotation measurement. Nanocrystalline material is very promising for inner shield composition in SERF co-magnetometers. Furthermore, its ultra-thin structure and low cost have significant application value in the miniaturization of SERF co-magnetometers. [ABSTRACT FROM AUTHOR]

The ferrite magnetic shield is widely used in ultra-high-sensitivity atomic sensors because of its low noise characteristics. However, its noise level varies with temperature and affects the performance of the spin-exchange relaxation-free (SERF) co-magnetometer. Therefore, it is necessary to analyze and suppress the thermal magnetic noise. In this paper, the thermal magnetic noise model of a ferrite magnetic shield is established, and the thermal magnetic noise of ferrite is calculated more accurately by testing the low-frequency complex permeability at different temperatures. A temperature suppression method based on the improved heat dissipation efficiency of the ferrite magnetic shield is also proposed. The magnetic noise of the ferrite is reduced by 46.7%. The experiment is basically consistent with the theory. The sensitivity of the co-magnetometer is decreased significantly, from 1.21 × 10 − 5 ° /s/Hz 1 / 2 to 7.02 × 10 − 6 ° /s/Hz 1 / 2 at 1 Hz. The experimental results demonstrate the effectiveness of the proposed method. In addition, the study is also helpful for evaluating the thermal magnetic noise of other materials. [ABSTRACT FROM AUTHOR]

This study proposes a high-performance magnetic shielding structure composed of MnZn ferrite and mu-metal film. The use of the mu-metal film with a high magnetic permeability restrains the decrease in the magnetic shielding coefficient caused by the magnetic leakage between the gap of magnetic annuli. The 0.1–0.5 mm thickness of mu-metal film prevents the increase of magnetic noise of composite structure. The finite element simulation results show that the magnetic shielding coefficient and magnetic noise are almost unchanged with the increase in the gap width. Compared with conventional ferrite magnetic shields with multiple annuli structures under the gap width of 0.5 mm, the radial shielding coefficient increases by 13.2%, and the magnetic noise decreases by 21%. The axial shielding coefficient increases by 22.3 times. Experiments verify the simulation results of the shielding coefficient of the combined magnetic shield. The shielding coefficient of the combined magnetic shield is 16.5%. It is 91.3% higher than the conventional ferrite magnetic shield. The main difference is observed between the actual and simulated relative permeability of mu-metal films. The combined magnetic shielding proposed in this study is of great significance to further promote the performance of atomic sensors sensitive to magnetic field. [ABSTRACT FROM AUTHOR]

This paper presents a temperature compensation method based on the genetic algorithm (GA) and backpropagation (BP) neural network to reduce the temperature induced error of the spin-exchange relaxation-free (SERF) co-magnetometer. The fluctuation of the cell temperature results in the variation of the optical rotation angle and the probe light absorption. The temperature fluctuation of the magnetic field shielding layer induces the variation of the magnetic field. In addition, one of the causes of light power variation is temperature fluctuation of the optical element. In summary, temperature fluctuations cause a variety of SERF co-magnetometer errors, and the relationship between these errors and temperature fluctuations has the characteristics of time-variance and non-linearity. There are two kinds of methods to suppress these errors. One way is to reduce temperature fluctuations of the SERF co-magnetometer. However, this method requires additional hardware and high cost, which are not suitable for miniaturization and low cost applications. Another effective method to suppress nonlinear and time-varying errors is to utilize intelligent algorithms for temperature compensation. In this paper, the BP neural network is applied for temperature compensation, and the GA is utilized to overcome the disadvantages of the BP neural network. The training data were obtained by changing the ambient temperature of the SERF co-magnetometer. The experimental results show that the method proposed in this work can significantly improve the accuracy of the co-magnetometer at complex ambient temperatures, and the stability of the SERF co-magnetometer at room temperature can be improved by at least 45%. [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]

An on-site and fast synchronous measurement of coil constant and nonorthogonal angle, using an all-optical atomic magnetometer, was reported in this article. Based on the spectrum analysis of electron paramagnetic resonance of spin-polarized potassium under different magnetic fields, the measurement models of coil constant and nonorthogonal angle were established, according to which we experimentally obtained the weighted average results with related estimated uncertainties: the coil constants in the $x$ -, $y$ -, and $z$ -axes were (145.9 ± 0.3) nT/mA, (149.5 ± 0.3) nT/mA, and (129.6 ± 0.1) nT/mA, respectively; the nonorthogonal angles existing in the $x z$ and $y z$ axes were (0.11 ± 0.02)° and (0.23 ± 0.02)°, respectively. The determination results of the residual magnetic field in the $z$ -axis, with two comparative experiments, demonstrated the validity of this on-site synchronous measurement method. The present method can be easily used in calibrating coil constant and nonorthogonal angle for all-optical atomic magnetometers, especially for miniaturized ones. [ABSTRACT FROM AUTHOR]

Spin-exchange relaxation-free (SERF) co-magnetometer is considered to be a promising nuclear spin gyroscope due to its ultrahigh rotation measurement sensitivity and magnetic field disturbance cancellation ability. Recent experiments indicate that the relaxation of the noble-gas spins would result in reduction of the magnetic field disturbance cancellation ability, which means that magnetic noise from the passive magnetic shield in a SERF co-magnetometer can cause rotation rate measurement error. In this paper, the magnetic field frequency response of a SERF atomic magnetometer is derived based on state space method and the magnetic noise of different shield materials are measured. The magnetic noise error model in a SERF co-magnetometer is then derived and the magnetic noise induced rotation rate measurement error is quantitatively evaluated. The superiority of ferrite shield is shown by the performance of a K-Rb-21Ne co-magnetometer. Experimental results show that ferrite shield with lower magnetic noise and better temperature stability is a more favorable choice for the inner shield of the co-magnetometer. [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]

The performance of a multilayer magnetic shield directly affects and limits the sensitivity improvement of an atomic magnetometer. To better meet the requirements of spin-exchange relaxation free atomic magnetometer for the environmental magnetic field, the magnetic shield should be optimized. At present, the optimizations have focused only on a single objective, such as the axial shielding factor. However, the importance of other goals should not be neglected. In this paper, multiobjective optimization of the shield is carried out to obtain a better comprehensive performance. First, according to the structural characteristics of the multilayer shield, a multiobjective optimization model is established. Then, a multiobjective genetic algorithm is utilized to optimize the shield. After optimization, a Pareto optimal solution set is obtained. Furthermore, depending on the desired design requirements, two sets of optimal combinations of target values and variable parameters are selected, based on the fuzzy comprehensive evaluation method and the lowest magnetic noise. This method can obtain a balance between different optimization objectives and effectively improve the comprehensive performance of the shield. [ABSTRACT FROM AUTHOR]

Spin-exchange relaxation-free gyroscope (SERFG) is a promising rotation sensor, and the bias error is one of its most important characteristics. It is identified that rotation measurement noise induced by thermal magnetization fluctuations inherent in the ferrite shield in a SERFG limits its bias stability. The root cause of this error lies in the low-frequency magnetic field sensitivity dominated by the nuclear spin relaxation rate. In this paper, the steady state response model of the SERFG is modified considering the non-negligible nuclear relaxation rate and the pressure-dependent magnetic field sensitivity is experimentally studied. Our results show that reducing nuclear spin relaxation is an effective method to suppress the bias error induced by thermal magnetization fluctuations. Finally, in case of $Pneon=1$ atm, it is estimated that a bias stability limit of $5 \times {10^{ - 4}}$ deg/h is set by the lowest thermal magnetization noise of $4.4f^{-1/2}\,\,{\text {fT}} $ ever reported in a ferrite shield. [ABSTRACT FROM AUTHOR]

The light shift is an important error source for atomic magnetometers. It would vanish if the frequency of the circularly polarized light is tuned to the optical resonance center. For high-density alkali-metal atomic magnetometers, the vapor cell has a large optical depth near the resonance, resulting in the difficulty in obtaining the exact resonance center by measuring the optical absorption line. In order to solve this problem, we propose a method to tune the pump light to a frequency where the shift is minimum based on the magnetic field zeroing technique. In addition, we also compare our results with the fitting center of the optical absorption line based on the measurement data far detuned from the resonance. The experimental results show that our method achieves a better suppression result of the light shift. [ABSTRACT FROM AUTHOR]

This paper aims to review the technology, developments, and applications of spin exchange relaxation free (SERF) atomic magnetometers. The generalized comparisons between the SERF magnetometer and the other types of weak magnetic sensors are elaborated. Further, the fundamental composition and operational principle of the SERF atomic magnetometer are elucidated. The development history and recent technological developments with respect to several aspects, including the alkali metal vapor source, atom heating method, pump and probe lasers, and magnetic shielding system, are presented. The classification and respective advantages and disadvantages of these technologies are described in detail. Finally, the existing and potential applications, as well as the prospective future development trends are presented. [ABSTRACT FROM AUTHOR]

The ultrahigh sensitivity atomic spin magnetometer as the magnetic measurement sensor has received much concern. The performance of the magnetic shielding cylinder is one of the key factors constraining the atomic spin magnetometer’s sensitivity. In order to effectively improve the performances of the magnetic shielding, the parameter optimization models of the magnetic shielding cylinder were established in this paper. Under the condition of changing only one parameter while the others keeping constant, the effects of various parameters influencing the axial shielding coefficient were comprehensively analyzed, and the results showed that the smaller the innermost length, the innermost radius, and the radial spacing were, and the greater the axial spacing was, the better the shielding performance could be obtained. According to these results and the actual needs, the magnetic shielding cylinder was optimally designed, and then the shielding effects were simulated via the software Ansoft. The simulation results showed that the optimized magnetic shielding cylinder had the advantages of small size, high shielding performance, and lager uniformity than that of the nonoptimized one. The actual measurement results showed that the residual magnetism in the optimized magnetic shielding cylinder was below 0.1 nT, which was 2~4 times lower than the nonoptimized one. [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]

Magnetic field interference poses a major challenge to the proper functioning of electronic equipment, electronic instruments and ultra-sensitive sensors, so magnetic field shield is a vital component. Particularly for ultra-sensitive atomic sensors, there is a pressing need for magnetic shields with superior performance and reduced magnetic noise. This paper introduces the application of nanocrystalline alloy magnetic shields in ultra-sensitive atomic sensors. We have analyzed the calculation of the longitudinal and transverse magnetic noise of nanocrystalline magnetic shields using a loss separation based approach and establish a magnetic noise model for nanocrystalline alloy magnetic shields. Meanwhile, we investigate the impact of structural parameters on longitudinal and transverse magnetic noise to effectively minimize magnetic noise in the shield. Additionally, we present an error model for magnetic noise, providing valuable theoretical support for mitigating magnetic noise errors in K-Rb- 21 Ne SERF co-magnetometers. This study contributes to the advancement of magnetic shield technology for ultra-sensitive atomic sensors, improving their overall performance and accuracy. • Innovative application of nanocrystals in high-precision atomic sensors as low noise magnetic shielding. • A noise model of nanocrystalline magnetic shielding was established and analyzed, and it was determined that hysteresis loss dominates at 100 Hz, especially at around 1 Hz, which is much greater than other losses. • The longitudinal and transverse magnetic noise effects of cylindrical nanocrystalline shield parameters with different thickness, aspect ratio and aperture diameter were also analyzed using FEM. • We present an error model for magnetic noise, providing valuable theoretical support for mitigating magnetic noise errors in K-Rb-21Ne SERF co-magnetometers. • This study provides a new research direction for reducing system magnetic noise and miniaturization in the future. Under the same noise level, the volume of nanocrystals is much smaller than that of ferrite. [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 novel strategy for designing uniform magnetic field and gradient magnetic field coils considering the boundary effect of magnetic shielding is proposed in this study. This strategy uses intelligent optimization algorithm to skillfully transform the complex coil design problem into the spatial optimization problem of individual population. The mirror method is combined with Green's function to accurately calculate the magnetic field, and the target field method (TFM) is combined with the whale optimization algorithm to optimize the stream functions using adaptive ridge regression. The minimum fitness function is defined as the real-time magnetic field relative error, and the optimal ridge coefficient is continuously obtained by determining the current density coefficient. The proposed method significantly reduces the magnetic field deviation in the target area compared to the conventional TFM, with reductions ranging from 12.2 % to 0.11 % (B x coil), 0.3 % to 0.02 % (B z coil), 20 % to 10 % (d B x / d z coil) and 2.9 % to 2.4 % (d B z / d z coil). The strategy has been effectively validated by analytical simulations and experimental results, and is expected to be applied to the design of uniform field coils and gradient coils for ultra-high precision atomic sensors. [Display omitted] • The coupling problem between the magnetic shielding system and the designed magnetic field coil is greatly reduced. • This method determines the fitness evaluation function according to the real-time actual current density. • The magnetic field coil designed by the hybrid optimization method proposed in this paper reduces the magnetic field deviation by nearly one to two orders of magnitude compared to the conventional TFM. • The proposed method significantly reduces the magnetic field deviation in the target area compared to the conventional TFM. [ABSTRACT FROM AUTHOR]

The magnetic field performance of the uniform coils will be affected by magnetic shields and produce errors in the atomic magnetometer. It is necessary to analyze the influencing factors and guide the coil design. Aiming at the above shortcomings, this paper analyzes the coupling effect of magnetic shield and coil and proposed a Lee-Whiting coil design method based on the linearly decreasing inertia weight particle swarm optimization (LDW-PSO) algorithm. Firstly, the magnetic field model under the ferromagnetic boundary is established, and the effects of the size, thickness and permeability of the magnetic shield on the magnitude and uniformity of the Lee-Whiting coil magnetic field are analyzed. The results show that the coupling coefficient of the coil changes monotonically with the change of the size of the magnetic shield, while the uniformity error has a minimum value with the change of the size of the shield. In addition, an improved Lee-Whiting coil is designed by combining the LDW-PSO algorithm, which improves the uniformity of the coil. Compared with the original coil, the measured uniformity error of the improved coil is reduced from 8. 39 × 1 0 − 4 to 2. 81 × 1 0 − 4 . The accuracy of the theoretical analysis is verified by experiments. This paper is of great significance to study the coupling and optimization design of the coil based on the magnetic shields in atomic magnetometers. [Display omitted] • The influence of magnetic shield parameters on coil uniformity is analyzed. • The optimal coil size for the uniformity in magnetic shield is given by analysis and testing. • The improved Lee-Whiting coil is designed by intelligent optimization algorithm. • Improved Lee-Whiting coil overcomes the coupling effect between coil and magnetic shield. • The correctness of the analysis and the effectiveness of the design are proved by experiments. [ABSTRACT FROM AUTHOR]

Spin-exchange relaxation-free (SERF) co-magnetometer presents promising applications in both inertial navigation and basic physical experiments because of its ultrahigh rotation measurement sensitivity and magnetic field disturbance cancellation capacity. Magnetic shielding system is an essential part of the co-magnetometer, and the intrinsic magnetic noise of shielding material is one of the main factors limiting the sensitivity of co-magnetometer. This paper presents a low-noise nanocrystalline magnetic shield for SERF co-magnetometer. The transfer function model of SERF co-magnetometer to transverse magnetic noise was established based on Bloch equation. The amplitude and frequency band of the co-magnetometer signal noise caused by transverse magnetic noise were quantitatively obtained, and the magnetic noise characteristics of nanocrystalline and other shielding materials were analyzed by theoretical calculation and experimental measurement in the obtained frequency band. The superiority of nanocrystalline in low magnetic noise was verified. Experimental results show that the signal noise and bias instability of the SERF co-magnetometer can be considerably decreased by using the nanocrystalline shield as the inner shield. [Display omitted] • A low-noise nanocrystalline shield for atomic co-magnetometer is proposed. • The transfer function model of the co-magnetometer to biaxial magnetic noise is established based on Bloch equation. • The advantages of nanocrystalline shield in magnetic noise characteristics are confirmed. • The signal noise and bias instability of the co-magnetometer are significantly reduced. [ABSTRACT FROM AUTHOR]