6.6.2 Domain Movement in Ferromagnetic Materials

This spontaneous magnetization is not apparent in materials which are in virgin state or have not been exposed to the magnetic field (point O). This is again similar to the case of ferroelectrics, because these materials also contain the domains which are randomly oriented in a virgin material.

Upon application of magnetic field, these domains start aligning in the direction of applied field (Point B) and when completely aligned, give rise to saturation magnetization, M_S(Point B) (- M_S in the opposite direction).

The domain growth in ferromagnetic materials occurs by growth of favourably oriented domains at the expense of unfavourably oriented domains unlike in ferroelectric materials where favourably oriented domains nucleate and grow.

When the field is reduced to zero (point C), the domains do not come back to their configuration in the virgin state; rather adopt a configuration so that there is a net magnetization in the absence of field called as remnant magnetization, M_r ( -M_r in the opposite direction). To bring the magnetization of the material back to zero, one needs to apply an extra field in the opposite direction which is called coercive field of is - H_c. (+H_c in the opposite direction). A ferromagnetic material is a hard magnet when it has large coercivity or soft magnet when coercivity is small.

Often, magnetic hysteresis loops are also represented as B-H curves where B is magnetic induction (B = μ₀ (H+M) = μ₀ μ_r H) and H is the applied field. Hence equivalent points in a B-H curve would be B_s (saturation induction) and B_r (magnetic remanence).

Another feature which is used to explain hard and soft magnets is the area of B-H or M-H curve which represents the power dissipated as heat and is expressed as

So, since a hysteresis curve implies loss of a certain amount of energy, typically soft magnets show lower energy losses as compared to hard magnets. Soft magnets with reasonably large M_r  and smaller H_c are useful for transformer and motor cores where energy dissipation due to AC fields is low while hard magnets are useful as permanent magnets and magnetic memories.

Again, the formation of domains and their size in these materials is basically due to balance between various kinds of energies associated:

• Exchange energy (we will see its origin later) which makes the magnetic moments align in one direction without violating Pauli’s exclusion principle;

• Magnetostatic energy in response to the flux lines at the surface of the material in the mono-domain state which increases as alignment increases or in other words high surface magnetic charges;

• Magnetocrystalline or anisotropy energy which, due to coupling between the spins and crystal lattice or spin-orbit coupling, is dependent on the crystal structure governing the direction of magnetic moment orientation as there are some crystallographic directions along which the sample is easy to magnetize than others such as for most cubic materials [111] is the easy axis except for those containing cobalt which have [100] as easy axis. As a consequence, hard and easy directions have different coercivities; and

• Magnetoelastic energy due to changes in the lattice parameters of the material as a result of spin-orbit coupling. The phenomenon is called as magnetostriction and quite useful from the application point of view.