Ferromagnetism

Ferromagnetism is a form of magnetic order in which interacting microscopic magnetic moments align predominantly parallel, producing spontaneous magnetization below a characteristic temperature. Iron, cobalt, and nickel are familiar examples. A ferromagnet can therefore be magnetized without a continuously applied magnetic field, although an unmagnetized specimen may have little overall magnetization because differently oriented regions cancel one another. Ferromagnetism supplies the physical basis for many permanent magnets and magnetic components. (ocw.mit.edu)

Microscopic origin

The magnetic moments of matter arise principally from electrons, through their spin angular momentum and orbital motion. Within an atom, paired electron spins can cancel, whereas unpaired electrons can contribute a net moment. Possessing atomic moments alone is insufficient for ferromagnetism: interactions must also stabilize collective alignment against thermal disorder. (ocw.mit.edu)

The central mechanism is the exchange interaction, whose origin lies in quantum mechanics. The Pauli exclusion principle constrains the combined spatial and spin states of electrons, and their electrostatic interaction makes different spin arrangements differ in energy. Exchange is not simply the classical attraction between tiny bar magnets; ordinary magnetic dipole interactions alone generally cannot explain the ordering temperatures of common ferromagnets. (ocw.mit.edu)

A simplified description uses the Heisenberg model, with exchange contribution

Here each pair is counted once, $\mathbf{S}_i$ represents a spin, and $J_{ij}$ describes its coupling to another spin. Under this sign convention, positive coupling favors parallel alignment. In metals, electrons extend through the solid, so electronic band structure supplements localized-spin descriptions. (physics.iisc.ac.in)

Domains and magnetic anisotropy

Bulk ferromagnets commonly divide into magnetic domains, regions with approximately uniform magnetization but different orientations. This arrangement reduces the energy associated with the specimen’s external stray field. Consequently, local magnetic order may remain strong even when the specimen’s total magnetic moment is nearly zero. (cambridge.org)

Adjacent domains are separated by domain walls, across which the magnetization changes direction gradually. Their structure reflects competition between exchange, which favors neighboring moments remaining aligned, and magnetic anisotropy, which favors particular directions. Crystal structure, specimen shape, and mechanical stress can all influence the preferred orientation. (cambridge.org)

An applied field can increase magnetization by expanding favorably oriented domains and rotating their moments toward the field. At sufficiently high fields, the material approaches magnetic saturation. The magnetization process therefore involves rearranging an already ordered structure, rather than creating atomic magnetic moments from nothing. (ocw.mit.edu)

Hysteresis and magnetic response

Ferromagnetic response depends on magnetic history. Cycling the applied field typically produces a hysteresis loop rather than a single reversible curve. Remanence is the magnetization remaining after a magnetizing field is removed. Coercivity measures the reverse field required to bring magnetization, or magnetic induction under the corresponding measurement convention, to zero. These definitions distinguish resistance to demagnetization from the strength of the remaining magnetization. (ocw.mit.edu)

Hysteresis reflects irreversible magnetization changes and barriers associated with anisotropy and microstructure. Its loop area represents energy dissipated during a magnetic cycle when expressed using the appropriate field and magnetization variables. Narrow loops are desirable in components undergoing repeated magnetization, whereas substantial coercivity helps permanent magnets resist reversal. (ocw.mit.edu)

In the International System of Units, magnetization $M$ is magnetic moment per unit volume, measured in amperes per metre. Magnetic induction obeys $\mathbf{B}=\mu_0(\mathbf{H}+\mathbf{M})$. Because ferromagnetic magnetization is nonlinear and history-dependent, a single constant magnetic susceptibility does not describe its full response. (ocw.mit.edu)

Temperature and collective ordering

Increasing temperature introduces fluctuations that weaken magnetic order. At the Curie temperature, spontaneous ferromagnetic magnetization disappears; above it, the material normally exhibits paramagnetism. Iron’s Curie temperature is approximately 770 °C. Losing spontaneous order does not mean losing every magnetic response: a field can still induce magnetization in the paramagnetic state. (ocw.mit.edu)

This phase transition is an important example of collective behavior. Spontaneous magnetization serves as an order parameter, and selecting a magnetization direction illustrates spontaneous symmetry breaking. Weiss mean-field theory approximates neighboring spins by an average effective field and predicts a Curie–Weiss susceptibility above the transition. It neglects fluctuations, however, limiting its accuracy near the critical temperature. (physics.iisc.ac.in)

Related orders and applications

Ferromagnetism differs from antiferromagnetism, where opposing magnetic sublattices compensate in the ideal case. In ferrimagnetism, oppositely oriented sublattices have unequal contributions and can produce a net magnetization. Ferrimagnetic materials may exhibit domains, remanence, and hysteresis resembling those of ferromagnets, but their microscopic ordering is different. (ocw.mit.edu)

Soft magnetic materials, including suitable iron-based alloys, are readily magnetized and demagnetized. They guide magnetic flux in transformers, inductors, and parts of electric motors. Hard magnetic materials retain magnetization and resist reversal; examples include alnico, samarium–cobalt, and neodymium–iron–boron magnets. Magnetic recording exploits distinguishable magnetization states, while device performance depends on composition, anisotropy, grain structure, temperature, and geometry—not merely on whether a material is ferromagnetic. (ocw.mit.edu)