Magnetization

Magnetization, usually denoted by M, is the magnetic dipole moment per unit volume of a material. It is a vector quantity that describes both the strength and direction of the material’s magnetic state. In macroscopic electromagnetism, magnetization connects microscopic magnetic moments with the magnetic field produced by matter. It is distinct from magnetic flux density B and magnetic field strength H, although these quantities are closely related. (farside.ph.utexas.edu)

Definition and units

For a small representative volume $\Delta V$ containing magnetic moments $\mathbf m_i$, the local magnetization is expressed as

The volume must contain enough microscopic constituents for a meaningful average while remaining small compared with the scale of macroscopic variations. Angular brackets indicate an appropriate statistical average. For uniform magnetization, the total magnetic moment is $\mathbf m=\mathbf M V$; more generally, it is the volume integral of M. (farside.ph.utexas.edu)

In the International System of Units, magnetic moment has units of ampere square metre, so magnetization is measured in amperes per metre, A/m. Moment per unit mass, sometimes called specific magnetization, instead has units of A·m²/kg. These normalizations must not be confused. In the commonly used cgs electromagnetic convention, $1\ \mathrm{emu/cm^3}$ corresponds to $10^3\ \mathrm{A/m}$. Magnetic polarization, defined as $\mathbf J=\mu_0\mathbf M$, is a related quantity measured in teslas rather than A/m. (nist.gov)

Microscopic origins

Magnetization arises from the magnetic moments associated with microscopic constituents. In ordinary magnetic materials, important contributions come from electrons, including their orbital motion and intrinsic spin. A circulating electric current provides a classical model of a magnetic dipole, but spin is an intrinsic property described by quantum mechanics, not literal rotation of a charged sphere. The macroscopic magnetization depends on how these moments combine and respond to their environment. (farside.ph.utexas.edu)

A collection of moments can have zero average magnetization even when its individual moments are nonzero. An applied field can favor particular orientations, whereas thermal agitation tends to oppose alignment. In paramagnetism, this competition produces a field-induced net moment. Interactions between neighboring moments can also support collective ordering, as in ferromagnetism. Thus, magnetization need not be solely an immediate response to an external field. (farside.ph.utexas.edu)

Relation to magnetic fields

The macroscopic SI relation is

where $\mu_0$ is the vacuum magnetic permeability. B describes magnetic flux density and enters the magnetic part of the Lorentz force. H is an auxiliary field useful for separating free-current contributions from those represented by magnetization. Sharing the same units does not make H and M interchangeable. (farside.ph.utexas.edu)

In a linear, isotropic material,

Here $\chi_m$ is the dimensionless volume magnetic susceptibility. This constitutive relation is an approximation, not the definition of magnetization. Positive susceptibility characterizes ordinary paramagnetic response; negative susceptibility characterizes diamagnetism, in which induced magnetization opposes the field. Ferromagnetic response generally cannot be represented by one constant susceptibility over an entire magnetization cycle. (farside.ph.utexas.edu)

Spatial variation of magnetization contributes an equivalent volume current density,

This representation allows microscopic magnetic contributions to be incorporated into Maxwell’s equations without resolving individual atomic currents. It describes their macroscopic electromagnetic effect rather than ordinary charge transport through the specimen. (farside.ph.utexas.edu)

Domains, saturation, and hysteresis

Below their ordering temperature, ferromagnets can possess spontaneous magnetization without an applied field. Nevertheless, a bulk specimen may have little net magnetic moment because it contains magnetic domains pointing in different directions. Within each domain, moments are ordered; cancellation between domains can leave the specimen macroscopically demagnetized. Domain formation reflects a balance between exchange, magnetostatic, crystalline, and strain-related energies. (farside.ph.utexas.edu)

An applied field changes the domain configuration and favors alignment. At sufficiently strong fields, the magnetization approaches saturation, where further field increases produce comparatively little additional alignment. Saturation also occurs in paramagnets when the field-alignment energy greatly exceeds the thermal energy. It therefore does not uniquely identify ferromagnetism. (farside.ph.utexas.edu)

In magnetic hysteresis, magnetization depends on the field’s previous history as well as its present value. A specimen may retain remanent magnetization after the magnetizing field is removed. Reversal requires an opposing field; the field at which M reaches zero defines a magnetization-based coercive field. This should be distinguished from the field at which B reaches zero on a flux-density hysteresis loop. (farside.ph.utexas.edu)

Temperature dependence and measurement

Temperature strongly affects magnetization. For an ideal collection of weakly interacting localized moments in the weak-field regime, susceptibility follows Curie’s law, $\chi_m=C/T$. In a ferromagnet, spontaneous magnetization disappears at the Curie temperature. Above that temperature, Curie–Weiss behavior, $\chi_m=C/(T-\theta)$, often approximates the response; the fitted Weiss temperature $\theta$ need not equal the actual transition temperature. (farside.ph.utexas.edu)

Magnetometers measure a specimen’s magnetic moment, from which volume- or mass-normalized magnetization can be calculated. Common instruments include vibrating-sample magnetometers and devices based on a superconducting quantum interference device (SQUID). Reference specimens with certified magnetic properties support instrument calibration and metrological traceability. Reports must identify the normalization used, because magnetic moment, volume magnetization, and specific magnetization are different quantities. (nist.gov)