Curie Temperature and Hysteresis Loop: Concepts Explained

The Curie temperature is the temperature above which a ferromagnetic material like iron, nickel or cobalt loses its permanent magnetism and behaves like a weak paramagnetic material. Below this temperature, tiny regions called magnetic domains inside the material stay strongly aligned and the material can remain magnetised on its own. Above it, thermal vibration becomes so violent that the domains lose their alignment.

This idea matters because almost every magnetic device has a temperature limit. A magnet used in a motor, a transformer core, or a magnetic latch will silently stop working if it gets too hot. Engineers also use the related hysteresis loop, a graph of magnetic field B versus applied field H, to judge how much energy a magnetic material wastes as heat in every magnetisation cycle.

Key Concepts

• Ferromagnetism: strong magnetism shown by iron, nickel, cobalt and their alloys, caused by aligned magnetic domains.
• Curie temperature (Tc): the critical temperature at which ferromagnetism disappears. For iron Tc is about 1043 K, for nickel about 631 K and for cobalt about 1400 K.
• Magnetic domains: microscopic regions, each magnetised to saturation, whose alignment produces the overall magnetisation.
• Hysteresis: the lagging of magnetisation B behind the applied field H; B does not return to zero when H is removed.
• Retentivity (remanence): the residual magnetisation left in the material when the external field is reduced to zero.
• Coercivity: the reverse field needed to bring the residual magnetisation back to zero.
• Hysteresis loop: the closed B-H curve traced in one full cycle of magnetising and demagnetising the material.

Formulas

The energy lost as heat in one magnetisation cycle is given by the area enclosed by the hysteresis loop: W = area of B-H loop, where W is the energy loss per unit volume per cycle, measured in joules per cubic metre (J/m³). If the material is cycled at frequency f (in hertz) and has volume V (in m³), the power loss is P = W × V × f, measured in watts. This assumes the same loop is repeated every cycle, which holds for steady AC operation.

Above the Curie temperature, magnetic susceptibility follows the Curie-Weiss law: χ = C / (T − Tc), where χ is the dimensionless susceptibility, C is the Curie constant of the material, T is the absolute temperature in kelvin and Tc is the Curie temperature. This law is valid only for T greater than Tc, where the material is paramagnetic.

Worked Example

A transformer core has a volume of 0.01 m³. The area of its hysteresis loop is 500 J/m³ per cycle. The transformer runs on 50 Hz AC. Find the hysteresis power loss.

1. Energy lost per cycle in the whole core = W × V = 500 × 0.01 = 5 J.
2. Number of cycles per second = f = 50.
3. Power loss P = 5 × 50 = 250 J/s = 250 W.

So 250 watts of electrical energy is continuously wasted as heat in the core just because of hysteresis. This is why transformer cores use soft iron with a very narrow loop, which has a much smaller area and far less loss.

Common Misconceptions

• Heating a magnet above Tc destroys it forever. Wrong. The material only loses its magnetisation while hot. On cooling below Tc it becomes ferromagnetic again and can be re-magnetised, though the original magnetisation does not return by itself.
• All magnets have the same Curie temperature. Wrong. Tc is a property of the material: iron, nickel and cobalt all have different values, and alloys like alnico have their own.
• A wider hysteresis loop is always bad. Wrong. A wide loop means high retentivity and coercivity, which is exactly what a permanent magnet needs. A narrow loop is wanted only where the magnetisation must reverse easily, as in transformer cores.

Real-World Applications

Transformer and motor cores are made of soft iron or silicon steel because their narrow hysteresis loops minimise heat loss. Permanent magnets in loudspeakers, compass needles and magnetic door catches use hard materials like steel or alnico with wide loops so they stay magnetised. The sharp loss of magnetism at Tc is used in safety devices: some rice cookers and temperature controllers use a ferrite that loses its magnetism at a set temperature and releases a switch. Magnetic recording tapes and hard disks also rely on controlled hysteresis to store bits as tiny magnetised regions.

In short, the Curie temperature tells you the heat limit of a magnetic material, while the hysteresis loop tells you how it stores magnetisation and how much energy it wastes each cycle. Choosing the right loop shape, narrow for cores and wide for permanent magnets, is one of the most practical decisions in electrical engineering.