Magnetic materials and dipoles

Magnetic dipoles

The basic magnetic object is a dipole. A current loop has magnetic dipole moment

ec{mu}=IAhat{n}

where $I$ is current, $A$ is loop area, and $hat{n}$ is the direction given by the right-hand rule. In an external magnetic field, a dipole experiences torque

ec{ au}=ec{mu} imesec{B}

The potential energy of a magnetic dipole is

U=-ec{mu}cdotec{B}

The lowest energy occurs when the dipole aligns with the magnetic field.

Atomic origins of magnetism

Magnetism in materials arises from microscopic magnetic moments associated with electron orbital motion and electron spin. Electron spin is a quantum property with intrinsic magnetic moment.

Different materials respond differently depending on how these microscopic moments interact and whether they cancel or align.

Magnetization

Magnetization ec{M} is magnetic dipole moment per unit volume. It describes the collective magnetic response of a material. In many materials, magnetization is related to applied magnetic field intensity ec{H} by

ec{M}=chi_mec{H}

where $chi_m$ is magnetic susceptibility.

The magnetic field inside materials is often described using

ec{B}=muec{H}

where $mu$ is magnetic permeability.

Diamagnetism

Diamagnetic materials develop weak magnetization opposite the applied field. They are weakly repelled by magnetic fields. Diamagnetism occurs in all materials but is often hidden by stronger effects.

In diamagnetic materials, induced microscopic currents oppose changes in magnetic flux, consistent with Lenz's law at a microscopic level.

Diamagnetic susceptibility is negative:

$chi_m<0$

Paramagnetism

Paramagnetic materials have microscopic magnetic moments that tend to align weakly with an external field. Thermal motion randomizes them, so the effect is usually small.

Paramagnetic susceptibility is positive:

$chi_m>0$

A simple high-temperature trend is Curie's law:

chi_m=rac{C}{T}

where $C$ is a material-dependent constant. Higher temperature makes alignment harder because thermal agitation is stronger.

Ferromagnetism

Ferromagnetic materials, such as iron, cobalt, and nickel, can exhibit strong spontaneous magnetization. Neighboring atomic moments interact in a way that favors alignment. The material forms domains, regions where many moments align.

An unmagnetized ferromagnet may have domains pointing in different directions, so the total magnetization is small. Applying a field can grow domains aligned with the field, producing strong magnetization.

Hysteresis

Ferromagnets often show hysteresis: magnetization depends on history, not just the current applied field. A plot of magnetization or $B$ versus applied field forms a loop. After the external field is removed, some magnetization may remain. This is remanence.

The field needed to reduce magnetization to zero is related to coercivity. Hard magnetic materials have large coercivity and are good permanent magnets. Soft magnetic materials magnetize and demagnetize easily, useful in transformer cores.

The big idea

Magnetic materials respond through microscopic magnetic dipoles. Diamagnets weakly oppose fields, paramagnets weakly align with fields, and ferromagnets can strongly magnetize through domain alignment. Magnetic dipole energy, torque, susceptibility, permeability, and hysteresis connect microscopic moments to macroscopic magnetic behavior.