Studies of weak magnetic fields are generally influenced by magnetic noise emanating from thermal agitation of electric charge (Johnson noise) in electrically conducting materials surrounding the magnetic-field sensor. In this article, the thermal magnetic noise fields generated by slabs with high electric conductivity (copper, aluminum) or high magnetic permeability (mu metal) are studied. The analysis is based both on a previously published phenomenological model and on measurements with an ultrasensitive superconducting magnetometer. Both the spectral densities and spatial correlations of the magnetic field fluctuations are evaluated. The computed correlation coefficients are utilized to develop a practical method for estimating the thermal noise due to thin conducting foils, such as thermal radiation shields in a cryogenic measurement Dewar. Also experiments to reduce the Dewar noise are reported. Finally, estimations are presented for the thermal noise fields arising in the walls of a magnetically shielded room. In practice, thermal magnetic noise, particularly due to the superinsulation in cryogenic Dewars, can be the limiting factor of sensitivity in measurements of weak biomagnetic signals arising in the human heart and brain. The results are useful in the estimation and minimization of the contribution of thermal noise.

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