How magnetic fields are shielded by ferromagnetic materials
If a magnetic field H is applied to a volume shielded by a ferromagnetic material with magnetization (net magnetic dipole moment per unit volume) M the magnetic flux density B is given by:
B = μ0H + M
where B is in Teslas (T), H and M are in Amperes/meter (A/m) and μ0 = 4π × 10-7 henry per meter.
Magnetization changes are the result of domain wall motion and domain rotation, including rotation of particles too small to have formed more than a single domain. In domain wall motion, magnetic domains oriented in the direction of the external field grow at the expense of domains with other orientations. In domain rotation, a domain rotates from its energetically favored easy axis towards alignment with the external field.
Magnetization of the shield material is key to shielding the interior volume, and ease of domain wall motion and domain rotation is associated with high permeability. Put simply, inside a volume enclosed by a ferromagnetic magnetic shield, a change in applied magnetic field causes a change in shield magnetization that acts to (partially) offset the change in field in the shielded region.
Hysteresis and coercivity
Domain wall motion for small displacements and domain rotation through small angles are generally reversible in that removing the external magnetic field causes a return to original conditions. If the domain wall moves past an obstruction, or the domain direction reverses, the original condition may not be restored when the field is removed and the change is considered “irreversible”.
If the external field is then removed, the sample remains magnetized due to its irreversible magnetization component. The size of the reverse magnetic field needed to return the sample to its initial demagnetized state is the coercive field.
What material are magnetic shields made from?
Amumetal™, Co-Netic™, HyMu“80”™, Magnifier 7904™, MuMETAL™ (see also Mu-metal), Permalloy 80™, Permalloy, and many others are trade names for a Ni, Fe, Mo alloy conforming to U.S. Military Specification MIL-N-14411C Composition 1, containing 79% to 80.6% Ni, 3.8% to 5.0% Mo, with a maximum of 0.95% Mn, 0.43% Si, and very low levels of C (<0.03%), P (<0.02%) and S (<0.006%), the balance being Fe.
Permalloy was the name given by Arnold and Elmen to the binary Ni, Fe alloy with 78.5% Ni and 21.5% Fe (close to Ni3Fe). To achieve highest permeability, binary Permalloy needs heat treatment with uniform rapid cooling through the ordering temperature below 600 °C. Uniform rapid cooling is not feasible for bulk materials but the addition of Mo allows for much slower cooling.
Heat treatment after fabrication consists of heating to relieve mechanical stress and to about 1120 °C in a hydrogen atmosphere to remove traces of C and S, followed by controlled cooling.
Magnetic shielding test results
Placed in a steady magnetic field, the flux density inside a permalloy-shielded volume decreases over hours and days
See: B. Feinberg and H Gould AIP Advances 8, 035303 (2018)
Following the application of an external magnetic field to a HyMu“80”™ thin-wall cylinder, demagnetized in zero field, the magnetic flux density at the center of the shielded volume rises in less than one second as the eddy current effects fade. But then over minutes, hours, and days the magnetic flux density in the center decreases, reaching a roughly 20% change over hours to days as seen in the figure.
We measured this effect for applied magnetic fields from 0.48 A/m to 16 A/m, the latter being comparable to the Earth’s magnetic field at its weakest point. Delayed changes in magnetization are also measured following alternating current demagnetization.
Magnetic Shielding Test Facility
Magnetic fields (magnetic flux densities) were measured using fluxgate magnetometers. including a custom-built Magson digital fluxgate magnetometer which was used down to about 2 × 10-11 T
To extend our measurements, we plan to build or acquire a Spin-Exchange-Relaxation-Free Cs atom magnetometer.
The shield measurements were performed on a test stand (Fig. 3) that positioned the shield’s cylindrical axis vertically. The test stand is made of wound paper cylinders and wood, held together with small amounts of stainless steel hardware.
Transverse fields are produced by rectangular coils wound on long wood frames while vertical (axial) fields are produced by a by the solenoid coil seen in Fig. 3.
For additional details see B. Feinberg and H Gould AIP Advances 8, 035303 (2018)