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.

Square coils with a high magnetic field uniformity have a wide range of applications. This article innovatively proposes a hybrid design optimization method for uniform magnetic field coils. The Taylor series expansions of the three components (3-TE) are applied to the design of multiple pairs of square coils for the first time, and on this basis, field relative errors of the target field points are further combined to improve the uniformity of the target area. Through this hybrid optimization method, the design of the coils is transformed into a constrained nonlinear optimization problem, and the structural parameters are obtained through the particle swarm optimization algorithm. Simulation and experimental results establish that in comparison with the conventional square Helmholtz coil, the uniformity of the coils designed by the 3-TE method has been optimized by 52.83%, and the introduction of target field points further improved the uniformity by 86.61% in the target area. Simultaneously, the proportion of areas with a field relative error of less than 10 ⁻⁴ increased from 5.71 to 21.43% as a consequence of this method.

In optically pumped alkali vapor cell with high density of atoms, the attenuation of the pump light generates a spatially non-uniform distribution of the electronic spin polarization of alkali atoms, which is detrimental to biomagnetism applications of magnetometers as well as the hyperpolarization of noble gas atoms. Therefore, in this study, we propose a new scheme to generate a nearly uniform, unsaturated spin polarization region based on counter-propagating pump beams and atomic diffusion. A finite element method (FEM)-based simulation is used to demonstrate the three-dimensional distribution of the spin polarization in a spherical cell. The effects of cell temperature and pump light power on the homogeneity of the spin polarization are studied. The distribution of spin polarization near the center of the cell is experimentally measured and a 1-cm uniform spin polarization region is achieved in the center of the cell. The uniformity of spin polarization in the center region of the cell increased by 50% compared with single beam pumping. The advantage of our proposed scheme is that it can generate an unsaturated uniform region of spin polarization in the center of a cell using a single species of alkali atoms.

MnZn ferrite, characterized by the low power loss, the high electrical resistivity, and the high magnetic permeability, is a promising candidate for the low-noise magnetic shielding applications. However, as the dissipative material, MnZn ferrites inherently generate a magnetic noise, which fundamentally limits the sensitivity of the magnetometers operating in the spin-exchange relaxation-free (SERF) regime. Herein, we report a synergistic co-doping strategy using Co₂O₃ and Bi₂O₃ to effectively suppress the intrinsic magnetic noise of MnZn ferrites. By systematically tuning the concentrations of Co₂O₃ and Bi₂O₃, the power loss, complex magnetic permeability, and microstructural evolution of undoped, singly doped, and co-doped MnZn ferrites are comprehensively investigated. Notably, co-doping with 1600 ppm Co₂O₃ and 400 ppm Bi₂O₃ reduces the low-frequency magnetic noise by more than 50%, which is attributed to refined grain boundary structures and suppressed hysteresis losses. The optimized MnZn ferrite is further employed to fabricate a magnetic shield for a SERF magnetometer, achieving a single-channel sensitivity of 0.25 fT·Hz^-1/2. This study paves an effective materials-engineering route to minimize magnetic noise in ferrite-based shielding systems, providing a solid foundation for the development of next-generation ultra low-noise platforms for the quantum precision measurements.

Triaxial uniform coils housed in magnetic shields are extensively used in atomic sensors. The coil constant can be affected by the magnetic shield that imposes a ferromagnetic boundary. This study numerically and experimentally analyzes the coil constant dependence on the Mn–Zn ferrite magnetic shield thickness, aspect ratio, air gaps between the magnetic annuli, and the distance from the coils. Results show that the radial coil constant (saddle-shaped coil) only depends upon the distance between the coil and the magnetic shield. The axial coil constant (Lee–Whiting coil) depends on the aspect ratio, distance between the coil and the magnetic shield, and air gap width between the magnetic annuli. The axial coil constant is linearly related to the air gap. When the thickness of the magnetic shield is greater than 2 mm, the radial and axial coil constants are independent of the shield thickness. The difference between the simulated and measured values is only 3.9%. The numerical calculation accuracy was verified by experimental measurements. This study can aid in the design and research of coils in the ferrite magnetic shield in atomic sensors.