Classification of Magnetic Materials

Based on their behaviour in a magnetising field, magnetic materials are sorted into three families: diamagnetic, paramagnetic, and ferromagnetic. The differences trace back to what happens at the atomic level -- whether individual atoms have zero or non-zero net magnetic moment, and whether neighbouring atomic moments interact strongly enough to spontaneously align in small regions called domains -- and they show up macroscopically as the sign and size of $\chi_m$, th …

Every electron orbiting a nucleus is a tiny current loop with its own orbital magnetic moment; because different electrons' orbital planes are randomly oriented, the vector sum is normally zero for each atom. When a uniform external field is switched on, by Lenz's law some orbital motions speed up and others slow down, producing a small induced magnetic moment opposed to the applied field; this induced moment disappears the instant the field is removed. In a non-uniform field, the interaction between this induced moment and the field pushes the material from the stronger part of the field toward the weaker part -- i.e. diamagnetic materials are repelled. Their properties: (i) susceptibility is negative; (ii) relative permeability is slightly less than unity; (iii) field lines are repelled/expelled from the material; (iv) susceptibility is nearly temperature independent. Examples: bismuth, copper, wate …

In some materials, each atom or molecule already has a net magnetic dipole moment (the vector sum of its electrons' orbital and spin moments is non-zero), but random thermal orientation still averages the bulk moment to zero. An external field exerts a torque on each atomic dipole, partially aligning them along the field and producing a net induced moment in the direction of the field; this induced alignment persists only as long as the field is present. In a non-uniform field, paramagnetic materials move from the weaker part toward the stronger part of the field -- they are weakly attracted. Properties: (i) susceptibility is positive and small; (ii) relative permeability is slightly greater than unity; (iii) field lines are drawn into the material; (iv) susceptibility is inversely proportional to temperature. Raising the temperature increases thermal jostling, which upsets the alignment, giving Curie's law: …

A ferromagnetic atom, like a paramagnetic one, has a net magnetic dipole moment. What sets ferromagnets apart is that neighbouring atomic moments interact so strongly (an effect that arises from electron spin and depends on inter-atomic distance) that they spontaneously align within small regions called ferromagnetic domains -- each domain is fully magnetised in some direction, but different domains point in different, randomly-distributed directions, so the unmagnetised specimen shows zero net magnetisation overall. Applying an external field triggers two processes: (1) domains already aligned close to the field grow at the expense of their neighbours, and (2) misaligned domains rotate to line up with the field -- together producing a very strong net magnetisation in the field's direction. In a non-uniform field, ferromagnetic materials are pulled strongly from the weaker to the stronger region. Properties: (i) susceptibility is positive and large; (ii) relative permeability is very large; (iii) field lines are strongly drawn in; (iv) susceptibility is inversely proportional to temperature. As temperature rises, increased thermal agitation progressively destroys the domain alignment until, at the Curie temperature $T_C$, the material turns fully paramagnetic; above $T_C$ the susceptibilit …