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Brillouin function
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A graph showing the magnetization of a paramagnetic substance approaching saturation along a Brillouin curve, with separate data series for temperatures 1.30 K, 2.00 K, 3.00 K, and 4.21 K. The y-axis shows Bohr magnetons per ion, and the x-axis shows B/T in teslas per degree. Three curves labeled I, II, and III demonstrate higher saturation at lower temperatures.
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Brillouin function

physics
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A graph showing the magnetization of a paramagnetic substance approaching saturation along a Brillouin curve, with separate data series for temperatures 1.30 K, 2.00 K, 3.00 K, and 4.21 K. The y-axis shows Bohr magnetons per ion, and the x-axis shows B/T in teslas per degree. Three curves labeled I, II, and III demonstrate higher saturation at lower temperatures.
magnetization of paramagnetic substances Figure 15: The approach to saturation in the magnetization of a paramagnetic substance following a Brillouin curve. Curves I, II, and III refer to ions of chromium, potassium alum, iron ammonium alum, and gadolinium sulfate octahydrate for which g = 2 and j = 3/2, 5/2, and 7/2, respectively.

The Brillouin function is a mathematical expression used in physics, specifically in the study of paramagnetism. It describes the relationship between the magnetic moment of a substance and the applied magnetic field, taking into account the thermal energy of the particles.1

The function's value depends on the ratio of magnetic energy to thermal energy, often expressed as B/T, where B represents the magnetic field and T is the temperature. At low magnetic fields, the magnetization is directly proportional to the field strength. As the magnetic energy significantly exceeds the thermal energy, the material approaches its maximum saturation magnetization.1

The concept is named after Louis M. Brillouin, a French physicist. While the term "Brillouin zone" relates to solid-state physics and electron behavior in crystals, the Brillouin function specifically applies to understanding magnetic properties.21

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3 Britannica Sources
  1. magnetism - Role of exchange interaction
  2. magnetism - Paramagnetism
  3. Brillouin zone

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