Magnetization & Magnetic Materials

Every atom is a tiny magnet, or can become one. How those tiny magnets respond to a field sorts all matter into three magnetic families.

Atomic magnets#

Electrons orbiting a nucleus are little current loops, so each has an orbital magnetic moment. On top of that, every electron has a permanent spin angular momentum (explained only by quantum mechanics) and a matching spin magnetic moment of fixed size, μ_s = 9.285 × 10⁻²⁴ J/T. Nuclei have moments thousands of times smaller. An atom’s moment is the vector sum of all these.

Electron moments tend to cancel in pairs (the two electrons of helium cancel exactly), so many atoms have zero net moment, while some keep a permanent one.

Magnetization#

In a piece of material whose atoms have permanent moments, the moments point at random, so any volume holding thousands of atoms has no net moment. A field exerts torques that try to line them up, while thermal motion keeps scrambling them: the alignment is partial, growing with stronger fields and lower temperatures. When it is nearly complete, the material is saturated.

Three kinds of response#

A current loop’s field at its centre points along its moment (the opposite of an electric dipole, whose field at its centre points against p⃗). So atomic moments lined up with an applied field add extra field in the same direction: the field inside the material is stronger than the applied field.

• Paramagnetism: permanent atomic moments, partly aligned by the field; the field inside is slightly increased.
• Ferromagnetism: neighbouring atomic moments line up with each other even without a field, through a quantum effect called exchange coupling. Permanent magnets are made of these materials.
• Diamagnetism: atoms with no net moment get moments induced by the field, and by Lenz’s law these oppose it; the field inside is slightly reduced. Every material has this response, but wherever permanent moments exist, para- or ferromagnetism swamps it.

Domains#

An unmagnetized ferromagnet is divided into domains, regions up to a millimetre across (a cubic millimetre holds about 10²⁰ atoms) in which all moments point one way. Different domains point different ways, so the whole is unmagnetized. In a field, domains along it grow as their walls move, and others rotate toward it. That is why even a small field produces a large magnetization.