Solution (source code)

= Solution

Write <magnetization> as <magnetic dipole moment> per volume. In weak-field linear response, $\mathbf M=\chi\mathbf H$ and $\mathbf B=\mu_0(\mathbf H+\mathbf M)$.

\b[<Paramagnetism>] has positive susceptibility: permanent spin or orbital moments tend to align with a field against thermal disorder. Independent localized moments in the classical weak-field regime give $\chi\propto1/T$, the <Curie law>. Conduction-electron <Pauli paramagnetism> has a different origin and need not follow that <temperature> law.

\b[<Diamagnetism>] is the induced magnetic response opposing the applied field, giving negative susceptibility. Changes in orbital motion underlie this response; it exists even without permanent moments. It is often relatively weak and only weakly <temperature> dependent, although particular quantum systems have stronger or more complicated behaviour.

\b[<Ferromagnetism>] arises from interactions favouring parallel magnetic order. Below the <Curie temperature> a domain can have spontaneous <magnetization> even at zero applied field. A sample can nevertheless have nearly zero net moment if differently oriented domains cancel. Domain rearrangement and rotation produce a nonlinear <magnetization> curve, saturation, <remanence> and <coercivity>; <hysteresis> dissipates <energy> in a field cycle. Above the ordering <temperature> the spontaneous order disappears, and a Curie-Weiss susceptibility is a useful mean-field approximation. \b[The signs of weak-field susceptibility distinguish para- and <diamagnetism>; spontaneous order and domain dynamics distinguish <ferromagnetism> from independent-moment alignment.]