Magnetic Materials

Magnetisation

Put a rod of some material inside a long solenoid and pass a current. The atoms of the rod carry tiny magnetic moments, and the field of the solenoid lines some of them up, or makes new ones. The rod becomes magnetised. Its magnetisation is its net magnetic moment per unit volume. A moment in A m² divided by a volume in m³ gives the unit A/m.

The field inside the rod now has two sources. One is the current in the solenoid, which is called a free current because it flows in wires we control. The other is the lined-up atoms, which act like a current round the surface of the rod, as in Lesson 1. The first source alone sets the magnetic intensity \(\vec H\). In a long solenoid \(H = nI\), whatever the core, where \(n\) is the number of turns per metre.

So \(\vec B = \mu_0(\vec H + \vec M)\). In most materials the magnetisation grows in proportion to \(H\). The ratio is the susceptibility, \(\chi = M/H\), a pure number. Then \(B = \mu_0(1 + \chi)H\). The number \(\mu_r = 1 + \chi\) is the relative permeability, and \(\mu = \mu_0\mu_r\) is the permeability of the material.

That is why the solenoid of an electromagnet, in the chapter Sources of the Magnetic Field, is wound on iron. The current sets the same \(H\) either way. The lined-up atoms of the iron multiply the field hundreds of times.

Three kinds of material

Every material falls into one of three groups by its susceptibility. A diamagnetic material has a small negative \(\chi\), about \(-10^{-5}\). Copper, water, gold and bismuth are diamagnetic. A paramagnetic material has a small positive \(\chi\), from about \(10^{-5}\) to \(10^{-3}\). Aluminium, with \(\chi\) about \(2 \times 10^{-5}\), platinum and oxygen are paramagnetic. A ferromagnetic material has a large positive \(\chi\), from hundreds to many thousands. Iron, nickel and cobalt are ferromagnetic.

Fig 5.1 shows the difference. A paramagnet draws field lines into itself, so the field inside is stronger than outside. A diamagnet pushes some lines out, so the field inside is weaker. Where a field is stronger on one side, a paramagnet is pulled towards the stronger region. A diamagnet is pushed towards the weaker one. A paramagnetic rod turns to lie along the field; a diamagnetic rod turns across it.

The causes differ. In a diamagnet the atoms have no moment of their own. The applied field slightly changes the orbits of the electrons, and the change opposes the field. The chapter Faraday's Law, Lenz's Law and Motional EMF explains why. Every material has this effect, but it is weak. In a paramagnet each atom has a moment. The field turns them partly into line, while the thermal jiggling of the atoms keeps knocking them out of line.

A ferromagnet is different in kind. Neighbouring atomic moments in iron hold one another parallel by a strong quantum effect. So iron is made of domains, small regions up to about a millimetre across, each already fully magnetised. In unmagnetised iron the domains point every way and cancel. A field makes the domains that point along it grow at the expense of the others, and then turns them. Even a small \(H\) therefore gives a huge \(M\).

Heat against order

In a paramagnet the field lines up the atomic moments, and thermal jiggling knocks them out of line. The hotter the material, the harder the jiggling and the smaller the magnetisation for a given field. For a paramagnet the susceptibility is inversely proportional to the absolute temperature. This is Curie's law, found by Pierre Curie in 1895.

A paramagnetic salt with \(\chi = 2 \times 10^{-4}\) at \(300\,\text{K}\) has, at \(150\,\text{K}\), \(\chi\) \(= 2 \times 10^{-4} \times 300/150\) \(= 4 \times 10^{-4}\). Halving the absolute temperature doubles the susceptibility.

Heat also destroys ferromagnetism. Above a temperature called the Curie temperature, the jiggling breaks up the domains, and a ferromagnet becomes an ordinary paramagnet. For iron this is \(1043\,\text{K}\), or \(770\,°\text{C}\). For nickel it is about \(631\,\text{K}\) and for cobalt about \(1388\,\text{K}\). That is why the molten core of the Earth, thousands of kelvin hot, cannot be a permanent magnet.

A material that remembers

Take an unmagnetised iron rod in a solenoid and raise \(H\) slowly. \(B\) rises along a curve and levels off when nearly every domain lines up: the iron is saturated. Now lower \(H\) back to zero. The domains do not all return, so \(B\) stays well above zero. Reverse the current, and a reverse \(H\) is needed to bring \(B\) to zero. Carry on round, and \(B\) traces a closed loop. This lagging of \(B\) behind \(H\) is hysteresis.

The field left when \(H\) returns to zero is the retentivity, point R. The reverse intensity needed to bring \(B\) to zero is the coercivity, point C. In Fig 5.2 both materials keep about \(1.25\,\text{T}\) at R. Soft iron needs only \(0.5\,\text{kA/m}\) to clear it, while steel needs \(3\,\text{kA/m}\). The steel loop is fat and the soft-iron loop thin.

Going round the loop costs energy. Each cycle drags the domain walls to and fro, and the work done turns into heat in the material. The area enclosed by the loop on a \(B\)-\(H\) graph is the energy lost per cycle in each cubic metre. Its unit, tesla times A/m, is J/m³. In Fig 5.2 the steel loop has about five times the area of the soft-iron loop.

A material's loop decides its use. An electromagnet, a transformer core or the core of a galvanometer must magnetise easily and let go cleanly. So it needs soft iron: high permeability, low retentivity and low coercivity, a thin loop that wastes little energy. A permanent magnet must keep its magnetism against knocks and stray fields. So it needs a material like steel: high retentivity and high coercivity, a fat loop.