Sensitivity of Fields Generated within Magnetically Shielded Volumes to Changes in Magnetic Permeability

Future experiments seeking to measure the neutron electric dipole moment (nEDM) require stable and homogeneous magnetic fields. Normally these experiments use a coil internal to a passively magnetically shielded volume to generate the magnetic field. The stability of the magnetic field generated by the coil within the magnetically shielded volume may be influenced by a number of factors. The factor studied here is the dependence of the internally generated field on the magnetic permeability $\mu$ of the shield material. We provide measurements of the temperature-dependence of the permeability of the material used in a set of prototype magnetic shields, using experimental parameters nearer to those of nEDM experiments than previously reported in the literature. Our measurements imply a range of $\frac{1}{\mu}\frac{d\mu}{dT}$ from 0-2.7\%/K. Assuming typical nEDM experiment coil and shield parameters gives $\frac{\mu}{B_0}\frac{dB_0}{d\mu}=0.01$, resulting in a temperature dependence of the magnetic field in a typical nEDM experiment of $\frac{dB_0}{dT}=0-270$~pT/K for $B_0=1~\mu$T. The results are useful for estimating the necessary level of temperature control in nEDM experiments.