Curie–Weiss law

The Curie–Weiss law describes the magnetic susceptibility χ of a ferromagnet in the paramagnetic region above the Curie point: The Curie–Weiss law describes the magnetic susceptibility χ of a ferromagnet in the paramagnetic region above the Curie point: where C is a material-specific Curie constant, T is absolute temperature and Tc is the Curie temperature, both measured in kelvin. The law predicts a singularity in the susceptibility at T = Tc. Below this temperature the ferromagnet has a spontaneous magnetization. The magnetic moment of a magnet is a quantity that determines the torque it will experience in an external magnetic field. A loop of electric current, a bar magnet, an electron, a molecule, and a planet all have magnetic moments. The magnetization or magnetic polarization of a magnetic material is the vector field that expresses the density of permanent or induced magnetic moments. The magnetic moments can originate from microscopic electric currents caused by the motion of electrons in individual atoms, or the spin of the electrons or the nuclei. Net magnetization results from the response of a material to an external magnetic field, together with any unbalanced magnetic moment that may be present even in the absence of the external magnetic field; for example, in sufficiently cold iron. We call the latter spontaneous magnetization. Other materials that share this property with iron, like Nickel and magnetite, are called ferromagnets. The threshold temperature below which a material is ferromagnetic is called the Curie temperature and varies between materials. In many materials the Curie–Weiss law fails to describe the susceptibility in the immediate vicinity of the Curie point, since it is based on a mean-field approximation. Instead, there is a critical behavior of the form with the critical exponent γ. However, at temperatures T ≫ Tc the expression of the Curie–Weiss law still holds true, but with Tc replaced by a temperature Θ that is somewhat higher than the actual Curie temperature. Some authors call Θ the Weiss constant to distinguish it from the temperature of the actual Curie point. According to Bohr–van Leeuwen theorem when statistical mechanics and classical mechanics are applied consistently, the thermal average of the magnetization is always zero. Magnetism cannot be explained without quantum mechanics. However we list some classical approaches to it as they are easy to understand and relate to even though they are incorrect. The magnetic moment of a free atom is due to the orbital angular momentum and spin of its electrons and nucleus. When the atoms are such that their shells are completely filled they do not have any net magnetic dipole moment in the absence of external magnetic field. When present, such field distorts the trajectories (classical concept) of the electrons so that the applied field could be opposed as predicted by the Lenz's law. In other words the net magnetic dipole induced by the external field is in the opposite direction and such materials are repelled by it. These are called diamagnetic materials. Sometimes an atom has a net magnetic dipole moment even in the absence of an external magnetic field. The contributions of the individual electrons and nucleus to the total angular momentum do not cancel each other. This happens when the shells of the atoms are not fully filled up (Hund's Rule). A collection of such atoms however may not have any net magnetic moment as these dipoles are not aligned. An external magnetic field may serve to align them to some extent and develop a net magnetic moment per volume. Such alignment is temperature dependent as thermal agitation acts to disorient the dipoles. Such materials are called paramagnetic.