Curie temperature

 ( Critical Phenomena ) 

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 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.

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 Ferromagnetism 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.

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:

$$\backslash chi\; =\; \backslash frac\{M\}\{H\}\; =\backslash frac\{M\; \backslash mu\_0\}\{B\}\; =\backslash frac\{C\}\{T\}$$

The Curie constant is defined as $$C\; =\; \backslash frac\{\backslash mu\_0\; \backslash mu\_\backslash mathrm\{B\}^2\}\{3\; k\_\backslash mathrm\{B\}\}N\_\backslash text\{A\}\; g^2\; J(J+1)$$

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

$$\backslash chi\; =\; \backslash frac\{C\}\{T-T\_\backslash mathrm\{C\}\}$$

where:

$$T\_\backslash mathrm\{C\}\; =\; \backslash frac\{C\; \backslash lambda\; \}\{\backslash mu\_0\}$$

is the Weiss molecular field constant.
     

For full derivation see Curie–Weiss law.

Magnetic susceptibility occurs above the Curie temperature.

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

$$\backslash chi\; \backslash sim\; \backslash frac\{1\}.$$

• K. H. J. Buschow (2025). 9780080431529, Elsevier. ISBN 9780080431529
• Charles Kittel (1986). 9780471874744, John Wiley & Sons. ISBN 9780471874744
• (2025). 9780471332329, John Wiley & Sons. ISBN 9780471332329
• Nicola A. Spaldin (2025). 9780521886697, Cambridge University Press. ISBN 9780521886697
• (2025). 9783540938033, Springer. ISBN 9783540938033
• Robert A. Levy (1968). 9780124457508, Academic Press. . ISBN 9780124457508
• H. Y. Fan (1987). 9780471859871, Wiley-Interscience. ISBN 9780471859871
• Adrianus J. Dekker (2025). 9780333106235, Macmillan. ISBN 9780333106235
• (1994). 9780471928058, Wiley. . ISBN 9780471928058
• (1989). 9780198555544, Oxford Univ. Press. ISBN 9780198555544
• K. Mendelssohn (1977). 9780850661194, Taylor and Francis. ISBN 9780850661194
• H. P. Myers (1997). 9780748406609, Taylor & Francis. ISBN 9780748406609
• Charles Kittel (1996). 9780471111818, Wiley. ISBN 9780471111818
• John Palmer (2025). 9780817646202, Birkhäuser. ISBN 9780817646202
• (1999). 9780849383472, CRC Press published in cooperation with IEEE Press. ISBN 9780849383472
• R. W. Whatmore (1991). 9781461367031, Springer. ISBN 9781461367031
• Attay Kovetz (1990). 9780521399975, Cambridge University Press. ISBN 9780521399975
• Rolf E. Hummel (2025). 038795144X, Springer. 038795144X
• K. J. Pascoe (1973). 9780471669111, J. Wiley and Sons. ISBN 9780471669111

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