In physics and materials science, the Curie temperature (T<sub>C</sub>), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) 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 (ferromagnetic, Figure 1) change and become disordered (paramagnetic, Figure 2) 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

{| class="wikitable sortable" style="float:right; clear:right; margin-left:1em;

|+ The Curie points of various materials

! rowspan=2|Material

! colspan=3|Curie temperature in

|-

! K

! °C

! °F

|-

| Iron (Fe)

| 1043–1664

|

|

|-

| Cobalt (Co)

| 1400

|

|

|-

| Nickel (Ni)

| 627

|

|

|-

| Gadolinium (Gd)

| 293.2

|

|

|-

| Dysprosium (Dy)

| 88

|

|

|-

| Manganese bismuthide (MnBi)

| 630

|

|

|-

| Manganese antimonide (MnSb)

| 587

|

|

|-

| Chromium(IV) oxide (CrO<sub>2</sub>)

| 386

|

|

|-

| Manganese arsenide (MnAs)

| 318

|

|

|-

| Europium(II) oxide (EuO)

| 69

|

|

|-

| Iron(III) oxide (Fe<sub>2</sub>O<sub>3</sub>)

| 948

|

|

|-

| Iron(II,III) oxide (FeOFe<sub>2</sub>O<sub>3</sub>)

| 858

|

|

|-

| NiO–Fe<sub>2</sub>O<sub>3</sub>

| 858

|

|

|-

| CuO–Fe<sub>2</sub>O<sub>3</sub>

| 728

|

|

|-

| MgO–Fe<sub>2</sub>O<sub>3</sub>

| 713

|

|

|-

| MnO–Fe<sub>2</sub>O<sub>3</sub>

| 573

|

|

|-

| Yttrium iron garnet (Y<sub>3</sub>Fe<sub>5</sub>O<sub>12</sub>)

| 560

|

|

|-

| Neodymium magnets

|

|

|

|-

| Alnico

|

|

|

|-

| Samarium–cobalt magnets

|

|

|

|-

| Strontium ferrite

|

|

|

|}

History

That heating destroys magnetism was already described in De Magnete (1600):<blockquote>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. (Book 2, Chapter 23).</blockquote>in 1895, Pierre Curie used strong magnets and precision balances to study the magnetic phase transition (now called the Curie point or Curie temperature). He also proposed the Curie's law.

In 1911, Pierre Weiss derived his Curie–Weiss law to explain this transition.

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 (or vice versa) occurs at the Néel temperature (), which is analogous to Curie temperature.

{|

|-

! Below !! Above

|-

| Ferromagnetic ||↔ Paramagnetic

|-

| Ferrimagnetic ||↔ Paramagnetic

|-

! Below !! Above

|-

| Antiferromagnetic ||↔ Paramagnetic

|}

<gallery caption="Orientations of magnetic moments in materials" heights="120" mode="packed">

File:Diagram of Ferromagnetic Magnetic Moments.png|Ferromagnetism: The magnetic moments in a ferromagnetic material are ordered and of the same magnitude in the absence of an applied magnetic field.

File:Diagram of Paramagnetic Magnetic Moments.png|Paramagnetism: The magnetic moments in a paramagnetic material are disordered in the absence of an applied magnetic field and ordered in the presence of an applied magnetic field.

File:Diagram of Ferrimagnetic Magnetic Moments.png|Ferrimagnetism: The magnetic moments in a ferrimagnetic material have different magnitudes (due to the crystal containing two different types of magnetic ions) which are aligned oppositely in the absence of an applied magnetic field.

File:Diagram of Antiferromagnetic Magnetic Moments.png|Antiferromagnetism: The magnetic moments in an antiferromagnetic material have the same magnitudes but are aligned oppositely in the absence of an applied magnetic field.

</gallery>

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 (materials which have Curie temperatures) 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 the atoms are ordered, and the material is ferromagnetic. 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.

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. It is named after Louis Néel (1904–2000), 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.

Listed below are the Néel temperatures of several materials:

{| class="wikitable sortable"

|-

! Substance

! Néel temperature (K)

|-

| MnO

| 116

|-

| MnS

| 160

|-

| MnTe

| 307

|-

| MnF<sub>2</sub>

| 67

|-

| FeF<sub>2</sub>

| 79

|-

| FeCl<sub>2</sub>

| 24

|-

| FeI<sub>2</sub>

| 9

|-

| FeO

| 198

|-

| FeOCl

| 80

|-

| CrCl<sub>2</sub>

| 25

|-

| CrI<sub>2</sub>

| 12

|-

| CoO

| 291

|-

| NiCl<sub>2</sub>

| 50

|-

| NiI<sub>2</sub>

| 75

|-

| NiO

| 525

|-

| KFeO<sub>2</sub>

| 983

|-

| Cr

| 308

|-

| Cr<sub>2</sub>O<sub>3</sub>

| 307

|-

| Nd<sub>5</sub>Ge<sub>3</sub>

|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:

<math display="block">\chi = \frac{M}{H} =\frac{M \mu_0}{B} =\frac{C}{T} </math>

{|

|-

! Definition !!

|-

| ||the magnetic susceptibility; the influence of an applied magnetic field on a material

|-

| ||the magnetic moments per unit volume

|-

| || the macroscopic magnetic field

|-

| ||the magnetic field

|-

| ||the material-specific Curie constant

|}

The Curie constant is defined as

<math display="block">C = \frac{\mu_0 \mu_\mathrm{B}^2}{3 k_\mathrm{BN_\text{A} g^2 J(J+1)</math>

{|

|-

| <math>N_\text{A}</math>

| the Avogadro constant

|-

| || the permeability of free space. Note: in CGS units is taken to equal one.

|-

| || the Landé g-factor

|-

| || the eigenvalue for eigenstate J<sup>2</sup> for the stationary states within the incomplete atoms shells (electrons unpaired)

|-

| || the Bohr magneton

|-

| || the Boltzmann constant

|-

| total magnetism || is number of magnetic moments per unit volume

|}

The Curie–Weiss law is then derived from Curie's law to be:

<math display="block">\chi = \frac{C}{T-T_\mathrm{C</math>

where:

<math display="block">T_\mathrm{C} = \frac{C \lambda }{\mu_0}</math>

is the Weiss molecular field constant.

For full derivation see Curie–Weiss law.

Physics

Approaching Curie temperature from above

As the Curie–Weiss law is an approximation, a more accurate model is needed when the temperature, , approaches the material's Curie temperature, .

Magnetic susceptibility occurs above the Curie temperature.

An accurate model of critical behaviour for magnetic susceptibility with critical exponent :

<math display="block">\chi \sim \frac{1}.</math>

Applications

A heat-induced ferromagnetic-paramagnetic transition is used in magneto-optical storage media for erasing and writing of new data. Famous examples include the Sony Minidisc format as well as the now-obsolete CD-MO format. Curie point electro-magnets have been proposed and tested for actuation mechanisms in passive safety systems of fast breeder reactors, where control rods are dropped into the reactor core if the actuation mechanism heats up beyond the material's Curie point. Other uses include temperature control in soldering irons and stabilizing the magnetic field of tachometer generators against temperature variation.

See also

Notes

References

  • Ferromagnetic Curie Point. Video by Walter Lewin, M.I.T.