Magnetic noise calculation of mu-metal shields at extremely low frequencies for atomic devices

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.