Magnetic susceptibility

Magnetic susceptibility χ is the simplest possible model of a magnetic material: the magnetization is proportional to the applied H-field, M = χ H, and χ is a single dimensionless number that characterises the material. The relative permeability is related by μ_r = 1 + χ, and the B-field inside is B = μ₀(1 + χ)H = μ₀μ_r H.

Three regimes appear in the periodic table. Diamagnetic materials have χ slightly negative, typically of order −10⁻⁵, because every electron orbit in any atom Lenz-responds to an applied field by developing a tiny counter-current that opposes it — a universal response, usually swamped by stronger effects when present. Paramagnetic materials have χ positive and small, of order 10⁻³ to 10⁻⁵, because thermal motion competes with the field's tendency to align their permanent atomic magnetic moments; Curie's law gives χ ≈ C/T, with the susceptibility dropping as temperature rises. Ferromagnetic materials, below their Curie temperature, have enormous effective susceptibilities — χ of order 10³ to 10⁶ — because neighbouring atomic moments spontaneously align via exchange interaction, so even a tiny applied field propagates through the whole domain structure.

Susceptibility is only useful for linear materials — those where the M-vs-H curve is a straight line through the origin. Ferromagnets obey this approximately at very low fields, but above that they saturate, hysterese, and remember previous magnetisations; for ferromagnets you need the full B-vs-H loop, not a single susceptibility number. For dia- and paramagnets, though, χ is an accurate description over the entire range of experimentally accessible fields.