Curie temperature

In physics and materials science, the Curie temperature, or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can be replaced by induced magnetism. The Curie temperature is named after Pierre Curie, who showed that magnetism is lost at a critical temperature.
The force of magnetism is determined by the magnetic moment, a dipole moment within an atom that originates from the angular momentum and spin of electrons. Materials have different structures of intrinsic magnetic moments that depend on temperature; the Curie temperature is the critical point at which a material's intrinsic magnetic moments change direction.
Permanent magnetism is caused by the alignment of magnetic moments, and induced magnetism is created when disordered magnetic moments are forced to align in an applied magnetic field. For example, the ordered magnetic moments change and become disordered at the Curie temperature. Higher temperatures make magnets weaker, as spontaneous magnetism only occurs below the Curie temperature. Magnetic susceptibility above the Curie temperature can be calculated from the Curie–Weiss law, which is derived from Curie's law.
In analogy to ferromagnetic and paramagnetic materials, the Curie temperature can also be used to describe the phase transition between ferroelectricity and paraelectricity. In this context, the order parameter is the electric polarization that goes from a finite value to zero when the temperature is increased above the Curie temperature.

Curie temperatures of materials

History

That heating destroys magnetism was already described in De Magnete :

Iron filings, after being heated for a long time, are attracted by a loadstone, yet not so strongly or from so great a distance as when not heated. A loadstone loses some of its virtue by too great a heat; for its humour is set free, whence its peculiar nature is marred..

in 1895, Pierre Curie used strong magnets and precision balances to study the magnetic phase transition. He also proposed the Curie's law.
In 1911, Pierre Weiss derived his Curie–Weiss law to explain this transition.

Magnetic moments

At the atomic level, there are two contributors to the magnetic moment, the electron magnetic moment and the nuclear magnetic moment. Of these two terms, the electron magnetic moment dominates, and the nuclear magnetic moment is insignificant. At higher temperatures, electrons have higher thermal energy. This has a randomizing effect on aligned magnetic domains, leading to the disruption of order, and the phenomena of the Curie point.
Ferromagnetic, paramagnetic, ferrimagnetic, and antiferromagnetic materials have different intrinsic magnetic moment structures. At a material's specific Curie temperature, these properties change. The transition from antiferromagnetic to paramagnetic occurs at the Néel temperature, which is analogous to Curie temperature.

Materials with magnetic moments that change properties at the Curie temperature

Ferromagnetic, paramagnetic, ferrimagnetic, and antiferromagnetic structures are made up of intrinsic magnetic moments. If all the electrons within the structure are paired, these moments cancel out due to their opposite spins and angular momenta. Thus, even with an applied magnetic field, these materials have different properties and no Curie temperature.

Paramagnetic

A material is paramagnetic only above its Curie temperature. Paramagnetic materials are non-magnetic when a magnetic field is absent and magnetic when a magnetic field is applied. When a magnetic field is absent, the material has disordered magnetic moments; that is, the magnetic moments are asymmetrical and not aligned. When a magnetic field is present, the magnetic moments are temporarily realigned parallel to the applied field; the magnetic moments are symmetrical and aligned. The magnetic moments being aligned in the same direction are what causes an induced magnetic field.
For paramagnetism, this response to an applied magnetic field is positive and is known as magnetic susceptibility. The magnetic susceptibility only applies above the Curie temperature for disordered states.
Sources of paramagnetism include:

All atoms that have unpaired electrons;
Atoms that have inner shells that are incomplete in electrons;
Free radicals;
Metals.

Above the Curie temperature, the atoms are excited, and the spin orientations become randomized but can be realigned by an applied field, i.e., the material becomes paramagnetic. Below the Curie temperature, the intrinsic structure has undergone a phase transition, the atoms are ordered, and the material is ferromagnetic. The paramagnetic materials' induced magnetic fields are very weak compared with ferromagnetic materials' magnetic fields.

Ferromagnetic

Materials are only ferromagnetic below their corresponding Curie temperatures. Ferromagnetic materials are magnetic in the absence of an applied magnetic field.
When a magnetic field is absent the material has spontaneous magnetization which is a result of the ordered magnetic moments; that is, for ferromagnetism, the atoms are symmetrical and aligned in the same direction creating a permanent magnetic field.
The magnetic interactions are held together by exchange interactions; otherwise thermal disorder would overcome the weak interactions of magnetic moments. The exchange interaction has a zero probability of parallel electrons occupying the same point in time, implying a preferred parallel alignment in the material. The Boltzmann factor contributes heavily as it prefers interacting particles to be aligned in the same direction. This causes ferromagnets to have strong magnetic fields and high Curie temperatures of around.
Below the Curie temperature, the atoms are aligned and parallel, causing spontaneous magnetism; the material is ferromagnetic. Above the Curie temperature the material is paramagnetic, as the atoms lose their ordered magnetic moments when the material undergoes a phase transition.

Ferrimagnetic

Materials are only ferrimagnetic below their corresponding Curie temperature. Ferrimagnetic materials are magnetic in the absence of an applied magnetic field and are made up of two different ions.
When a magnetic field is absent the material has a spontaneous magnetism which is the result of ordered magnetic moments; that is, for ferrimagnetism one ion's magnetic moments are aligned facing in one direction with certain magnitude and the other ion's magnetic moments are aligned facing in the opposite direction with a different magnitude. As the magnetic moments are of different magnitudes in opposite directions there is still a spontaneous magnetism and a magnetic field is present.
Similar to ferromagnetic materials the magnetic interactions are held together by exchange interactions. The orientations of moments however are anti-parallel which results in a net momentum by subtracting their momentum from one another.
Below the Curie temperature the atoms of each ion are aligned anti-parallel with different momentums causing a spontaneous magnetism; the material is ferrimagnetic. Above the Curie temperature the material is paramagnetic as the atoms lose their ordered magnetic moments as the material undergoes a phase transition.

Antiferromagnetic and the Néel temperature

Materials are only antiferromagnetic below their corresponding Néel temperature or magnetic ordering temperature, T_N. This is similar to the Curie temperature, since above the Néel temperature the material undergoes a phase transition and becomes paramagnetic. That is, the thermal energy becomes large enough to destroy the microscopic magnetic ordering within the material. It is named after Louis Néel, who received the 1970 Nobel Prize in Physics for his work in the area.
The material has equal magnetic moments aligned in opposite directions resulting in a zero magnetic moment and a net magnetism of zero at all temperatures below the Néel temperature. Antiferromagnetic materials are weakly magnetic in the absence or presence of an applied magnetic field.
Similar to ferromagnetic materials the magnetic interactions are held together by exchange interactions preventing thermal disorder from overcoming the weak interactions of magnetic moments. When disorder occurs it is at the Néel temperature.
Listed below are the Néel temperatures of several materials:

Substance	Néel temperature
MnO	116
MnS	160
MnTe	307
MnF₂	67
FeF₂	79
FeCl₂	24
FeI₂	9
FeO	198
FeOCl	80
CrCl₂	25
CrI₂	12
CoO	291
NiCl₂	50
NiI₂	75
NiO	525
KFeO₂	983
Cr	308
Cr₂O₃	307
Nd₅Ge₃	50

Curie–Weiss law

The Curie–Weiss law is an adapted version of Curie's law.
The Curie–Weiss law is a simple model derived from a mean-field approximation, this means it works well for the materials temperature,, much greater than their corresponding Curie temperature,, i.e. ; it however fails to describe the magnetic susceptibility,, in the immediate vicinity of the Curie point because of correlations in the fluctuations of neighboring magnetic moments.
Neither Curie's law nor the Curie–Weiss law holds for.
Curie's law for a paramagnetic material:
The Curie constant is defined as
The Curie–Weiss law is then derived from Curie's law to be:
where:
is the Weiss molecular field constant.
For full derivation see Curie–Weiss law.