Curie temperature

The Curie temperature (\(T_C\)) is the temperature above which a ferromagnetic material changes into a paramagnetic material. The remanence of a magnetised ferromagnet also disappears above the Curie temperature. The phenomenon was discovered by the French physicist Pierre Curie in 1895.

To understand this effect, the physical basis of remanence should be briefly explained. When a ferromagnet is exposed to an external magnetic field, magnetisation occurs. The material itself becomes magnetic and remains magnetic even when the external magnetic field is switched off. This remaining magnetisation is called remanence. The physical reason for the existence of the Curie temperature lies in the nature of ferromagnetism. Ferromagnetism occurs because magnetic moments caused by electron spin are aligned and stabilised in a material when the material is exposed to an external magnetic field.

This alignment is very stable in ferromagnets due to the exchange interaction between the electron spins. The exchange interaction prevents the alignment of the spins from being lost again due to thermal motion at room temperature.

However, at higher temperatures, the movement of the electron spins increases. Initially, the spins remain aligned in parallel over large areas, the so-called Weiss domains. It may just be that the orientation of the spins shifts simultaneously over a larger area. This is known as a Barkhausen jump and results in the formation of a new Weiss domain. Above a characteristic temperature, i.e. the Curie temperature, the kinetic energy of the electron spins (also referred to as thermal energy) exceeds the energy of the exchange interaction.

This causes the electron spins to intermix, and the parallel alignment is completely lost. If the thermal energy of the electron spins is greater than the exchange interaction, the magnetisation of the material in an external magnetic field is much smaller than in a ferromagnet. This is referred to as paramagnetism. The thermal energy of the electron spins exceeds the exchange interaction, which is characteristic of every material, just above the Curie temperature. This is why the Curie temperature is also material-specific. It is 769 °C for iron, 1127 °C for cobalt and 358 °C for nickel.

Behaviour above the Curie temperature

In a paramagnet, the electron spins are statically orientated as long as no external magnetic field is present. The magnetised material will demagnetise again immediately after the external field is switched off.

For paramagnets, the magnetic susceptibility χ of the material, and thus also the magnetic permeability µ, continues to be highly temperature-dependent above the Curie temperature. The higher the temperature, the harder it is for the spins to be aligned by the external field, and the less the external magnetic field is amplified by the paramagnetic material.

The dependence of the magnetic susceptibility χ on the temperature T can be described above the Curie temperature T_C, i.e. for T > T_C, by the Curie-Weiss law.

The Curie-Weiss law reads:
\(\chi = \frac{C}{T-T_C}\),

whereby C is the so-called Curie constant. The Curie constant is also material-specific (i.e. based on the type of material). This law was first formulated by the physicist Pierre Curie in 1896 and then further developed by the French physicist Pierre-Ernest Weiss in 1907.

Curie temperatures of certain ferromagnetic materials

Table: Overview of the Curie temperature of various ferromagnetic and ferrimagnetic materials according to sources [1]-[4].

Material	Chemical Formula	Curie temp. (K)	Curie temp. (°C)	Magnetism
Cobalt	Co	1388	1115	Ferromagnetic
Iron	Fe	1043	770	Ferromagnetic
Iron(III) oxide	Fe2O3	948	675	Ferrimagnetic
Nickel iron oxide	NiOFe2O3	858	585	Ferrimagnetic
Copper iron oxide	CuOFe2O3	728	455	Ferrimagnetic
Magnesium iron oxide	MgOFe2O3	713	440	Ferrimagnetic
Manganese bismuth	MnBi	630	357	Ferromagnetic
Nickel	Ni	627	354	Ferromagnetic
Neodymium-iron-boron	Nd2Fe14B	593	320	Ferromagnetic
Manganese antimonide	MnSb	587	314	Ferromagnetic
Manganese iron oxide	MnOFe2O3	573	300	Ferrimagnetic
Yttrium iron garnet	Y3Fe5O12	560	287	Ferrimagnetic
Chromium(IV) oxide	CrO2	386	113	Ferrimagnetic
Manganese arsenide	MnAs	318	45	Ferromagnetic
Gadolinium	Gd	292	19	Ferromagnetic
Terbium	Tb	219	-54	Ferromagnetic
Dysprosium	Dy	88	-185	Ferromagnetic
Europium(II) oxide	EuO	69	-204	Ferromagnetic

Sources:
[1] A. F. Holleman, E. Wiberg, N. Wiberg: Lehrbuch der Anorganischen Chemie. 102. Auflage. [Textbook of Inorganic Chemistry. 102nd edition] Walter de Gruyter, Berlin 2007, ISBN 978-3-11-017770-1, p. 1682.
[2] C. Rau, S. Eichner: Evidence for ferromagnetic order at gadolinium surfaces above the bulk Curie temperature. In: Physical Review B. Volume 34, No. 9, November 1986, p. 6347–6350, doi:10.1103/PhysRevB.34.6347
[3] C. Kittel: Introduction to Solid State Physics (sixth ed.). John Wiley and Sons, 1986. ISBN 0-471-87474-4.
[4] M. Jackson: Wherefore Gadolinium? Magnetism of the Rare Earths (PDF). IRM Quarterly. Institute for Rock Magnetism. 10 (3), 2000

The table shows a selection of materials that have various interesting applications due to their interesting magnetic properties. Neodymium-iron-boron, for example, is frequently used for permanent magnets and has a Curie temperature of 320 °C. All the materials mentioned are only ferromagnetic or ferrimagnetic below the Curie temperature; above this temperature, the materials become paramagnetic, as the exchange interaction of the electron spins is cancelled out by the thermal motion.

For many materials, the exact magnetic properties depend precisely on the specific composition and manufacturing conditions. MnAs, for example, is known for its phase transitions and associated magnetic property changes, making it an interesting candidate for thermal storage applications and sensors. The exact magnetic properties of MnAs, including its Curie temperature, depend strongly on the crystal structure and microstructure of the material.