Spatial distribution of magnetic noise in P-CA composite magnetic shielding devices under the superposition effect of leakage magnetic flux

Permalloy-cobalt-based amorphous composite magnetic shielding devices (P-CA MSDs) offer high shielding effectiveness and low intrinsic noise, making them essential for creating ultra-weak magnetic field environments in biomagnetic signal detection. However, magnetic noise (MN) within such devices often exhibits significant spatial non-uniformity, primarily caused by leakage flux induced by structural imperfections. Existing models offer limited spatial resolution and frequency-domain accuracy in resolving magnetic noise variations induced by structural leakage, which constrains precision assessment in shielding-based measurement systems. To enable quantitative prediction, we formulate an anisotropy-aware MN model incorporating residual background interference as measurable input parameters. In addition, an integral-equation-based method is proposed to calculate leakage flux. Combined with finite element simulations and experimental measurements using Quspin atomic magnetometers, the spatial distributions of magnetic fields and noise in both perforated and non-perforated P-CA structures are analyzed and validated. Results show that the relative error between theoretical and measured MN at the center of the X, Y, and Z axes is within 12.4 %, with the lowest error of 6.3 % observed on the X-axis after perforation. This study elucidates how leakage flux modulates localized spectral characteristics of low-frequency MN, revealing measurable spatial asymmetries through combined modeling and instrumentation.