Every engineer who works with magnetics eventually asks the same two questions. First: why does a magnet grab a piece of iron but ignore a copper pipe sitting right next to it? Second: if I need to shield a magnetic field, what material do I reach for, and why?
The answer to both sits in the same place — the electron structure of the atom. This article walks through it from the ground up, avoiding hand-waving. No "magnetic lines of force" metaphors. Just the physics, as an engineer would need it.
1. Magnetism Starts With a Single Electron
An atom's magnetic behavior comes from its electrons. Two contributions matter: orbital angular momentum (the electron circling the nucleus) and spin angular momentum (the electron spinning on its own axis). In practice, for the transition metals we care about — iron, nickel, cobalt, copper — the orbital contribution is largely quenched by the crystal field. The spin moment dominates.
Every electron carries a magnetic moment of approximately one Bohr magneton (μB = 9.274 × 10−24 J/T). The direction is either "up" or "down." When two electrons occupy the same orbital, the Pauli exclusion principle forces them into opposite spin states. Their magnetic moments cancel exactly. The atom carries zero net moment.
This is copper's situation. Copper has atomic number 29, electron configuration [Ar] 3d10 4s1. The 3d subshell is completely filled — five orbitals, each holding two electrons with opposite spins. Total spin magnetic moment: zero. The single 4s electron doesn't help because in the metallic solid state, those conduction electrons are delocalized across the lattice and don't contribute a localized moment.
Copper is diamagnetic. When you place it in an external field, the orbiting electrons adjust their motion slightly to oppose the applied field (Lenz's law at the atomic scale). The effect is tiny: copper's magnetic susceptibility χ is approximately −1.0 × 10−5. For engineering purposes, copper is non-magnetic.
2. Iron: Four Unpaired Electrons Change Everything
Iron is element 26: [Ar] 3d6 4s2. In the metallic state, the 3d electrons distribute across five d-orbitals. Hund's rules dictate that electrons fill orbitals to maximize total spin. The result: four unpaired electrons in the 3d shell, all with parallel spins.
That's four Bohr magnetons per atom, all pointing the same direction. The magnetic moment per iron atom is 2.2 μB in the bulk metal — slightly less than 4 because of band-structure effects in the solid, but still substantial.
Having unpaired electrons is necessary but not sufficient. You also need those moments to align across many atoms. This is where the exchange interaction enters.
3. The Exchange Interaction: Why Neighbors Align
The exchange interaction is a purely quantum-mechanical effect with no classical analog. It arises from the combination of the Pauli exclusion principle and the Coulomb repulsion between electrons on neighboring atoms. In iron, cobalt, and nickel, the interatomic spacing and the shape of the 3d electron wavefunctions create a situation where parallel spin alignment lowers the total energy of the system.
Think of it this way: if two neighboring iron atoms align their spins parallel, the Pauli principle forces their electrons to occupy different spatial regions. This reduces the electrostatic repulsion between them. The system settles into a lower-energy state. Parallel alignment is the default, not an excited state.
This is the Bethe-Slater curve in action: plot the exchange integral against the ratio of interatomic distance to 3d orbital radius, and you find that iron, cobalt, and nickel sit in the narrow positive region where ferromagnetic coupling is favored. Most other elements fall outside this region — either the coupling is too weak (paramagnetism), or it favors antiparallel alignment (antiferromagnetism, as in chromium and manganese).
4. Magnetic Domains: From Atoms to Bulk Material
Even though every iron atom wants to align with its neighbors, a macroscopic piece of iron is not automatically a magnet. The reason is domains.
In an unmagnetized iron bar, the atomic moments are aligned locally but not globally. The material divides itself into regions called magnetic domains, typically 1–100 μm across. Within each domain, all moments point the same way. But neighboring domains point in different directions, and the net magnetization of the whole piece cancels out.
Why domains? Because a single-domain piece of iron would generate a large external magnetic field. That field stores energy (specifically, magnetostatic energy, proportional to ∫ B·H dV). By breaking into multiple domains with closed flux paths, the material minimizes this energy. Domain walls — the boundaries where spins gradually rotate between orientations — cost some exchange and anisotropy energy, but the tradeoff is energetically favorable.
When you bring a permanent magnet near the iron, its external field applies a pressure on the domain walls. Domains aligned with the field grow at the expense of misaligned ones. This is magnetization. When you remove the external field, some domains remain aligned (remanence), which is why the iron bar now acts as a weak permanent magnet.
5. Magnetic Permeability: The Engineering Parameter
Permeability (μ) is the ratio of magnetic flux density B to applied field strength H: B = μH. In vacuum, μ0 = 4π × 10−7 H/m. Relative permeability μr = μ/μ0 tells you how much more flux a material can carry than empty space.
| Material | μr (approx.) | Type |
|---|---|---|
| Vacuum / Air | 1 | — |
| Copper | 0.99999 | Diamagnetic |
| Aluminum | 1.00002 | Paramagnetic |
| Austenitic SS (304) | 1.01–1.02 | Paramagnetic (mostly non-magnetic) |
| Ferritic SS (430) | 1,000–1,800 | Ferromagnetic |
| Low-carbon steel (1010) | 2,000–5,000 | Ferromagnetic |
| Pure iron (99.95%) | 5,000–10,000 | Ferromagnetic |
| Silicon steel (3% Si) | 7,000–10,000 | Ferromagnetic |
| Permalloy (80% Ni, 20% Fe) | 50,000–100,000 | Ferromagnetic (soft) |
| Mu-metal (77% Ni, 16% Fe, 5% Cu, 2% Cr) | 80,000–100,000 | Ferromagnetic (soft) |
| Annealed mu-metal (hydrogen) | up to 600,000 | Ferromagnetic (soft) |
The practical significance: if μr = 1, the material is magnetically transparent. If μr > 1,000, the material will concentrate magnetic flux into itself. This is the foundation of magnetic shielding.
6. Magnetic Shielding: Why It's Redirection, Not Blocking
You cannot block a magnetic field the way you block light with an opaque solid. There is no magnetic insulator. Magnetic field lines must form closed loops. They don't terminate.
What you can do is provide a lower-reluctance path. Reluctance R = l/(μ0μrA), where l is path length and A is cross-sectional area. A high-μ material has low reluctance. Magnetic flux, like electric current, prefers the path of least resistance.
Place a mu-metal shield around a sensitive component, and the external magnetic flux diverts through the shield material rather than passing through the interior air space. The field inside the enclosed volume is attenuated. This is shunt shielding.
6.1 Which Materials Shield DC/Low-Frequency Fields
For static or slowly varying magnetic fields (DC to a few hundred Hz), the effective shielding materials are all ferromagnetic:
Mu-metal and Permalloy. Relative permeability 50,000–600,000 after hydrogen annealing. The gold standard for precision shielding in magnetometers, MRI rooms, electron microscopes, and sensitive electronics. Saturation flux density is relatively low (0.7–0.8 T), so they saturate in strong fields. Often used as the inner layer of a two-layer shield.
Low-carbon steel. Permeability 2,000–5,000. Saturation flux density up to 2.0 T. Much cheaper than mu-metal. Used as the outer layer in multi-layer shields — the steel handles the strong external field, reducing it to a level that the mu-metal inner layer can handle without saturating.
Silicon steel (electrical steel). The workhorse of power engineering. 3–4% silicon added to iron increases electrical resistivity, reducing eddy current losses in AC applications. Used in transformer cores and motor laminations. Not typically used for precision shielding.
Ferrite. Ceramic iron-oxide compounds with very high electrical resistivity. Effective at RF frequencies (above ~100 kHz) where metallic shields suffer from eddy current heating. At DC, ferrites have much lower permeability than mu-metal but are cheap and don't require annealing.
6.2 Which Materials Are Useless for DC Shielding
Copper, aluminum, brass, gold, silver, titanium, and austenitic stainless steels (304, 316) have μr ≈ 1. They are magnetically transparent at DC. Placing a copper sheet between a magnet and a sensor does essentially nothing to the static field.
These materials are effective against high-frequency AC magnetic fields (above ~10 kHz) through eddy current shielding: the changing field induces currents in the conductor, which generate an opposing field. But at DC, there are no eddy currents. A copper shield at DC is invisible.
6.3 The Saturation Problem
Every ferromagnetic material has a saturation flux density Bsat. Above this point, the material cannot carry additional flux. The permeability drops toward 1, and the shield stops shielding.
For NdFeB magnets producing surface fields of 0.3–0.5 T, a single layer of mu-metal will saturate. The solution is a two-layer shield: an outer layer of mild steel (high Bsat, moderate μ) reduces the field to perhaps 0.05–0.1 T, then an inner layer of mu-metal (high μ, low Bsat) handles the remainder.
7. How Gleagle Uses These Principles
In our levitation products, we design with these fundamentals daily. The levitation gap between the base electromagnet and the floating magnet is essentially an air gap in a magnetic circuit. The reluctance of this gap dominates the system. The base must generate enough magnetomotive force (NI, ampere-turns) to overcome the gap reluctance and produce the required holding force.
Shielding matters too. The alternating electromagnetic field from the levitation coil couples into nearby conductive parts. Our aluminum base housings provide eddy-current shielding for the AC component, but the DC bias field is managed by the geometry of the magnetic circuit itself — the flux returns through the ferromagnetic core, not through free space.
When we evaluate a new material for a magnetic component — whether a core lamination, a shield can, or a flux concentrator — we're looking at the same parameters discussed above: saturation flux density, permeability, coercivity, and electrical resistivity. The physics hasn't changed since Faraday. What's changed is our ability to model it, measure it, and machine it to micron tolerances.