In magnetism, the Curie–Weiss law describes the magnetic susceptibility χ of a ferromagnet in the paramagnetic region above the Curie temperature: where C is a material-specific Curie constant, T is the absolute temperature, and TC is the Curie temperature, both measured in kelvin.
Materials with this property are known as ferromagnets, such as iron, nickel, and magnetite.
However, when these materials are heated up, at a certain temperature they lose their spontaneous magnetization, and become paramagnetic.
The Curie–Weiss law describes the changes in a material's magnetic susceptibility,
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.
Some authors call Θ the Weiss constant to distinguish it from the temperature of the actual Curie point.
That means that it can not be explained without taking into account that matter consists of atoms.
Next are listed some semi-classical approaches to it, using a simple atom model, as they are easy to understand and relate to even though they are not perfectly correct.
The magnetic moment of a free atom is due to the orbital angular momentum and spin of its electrons and nucleus.
In other words, the net magnetic dipole induced by the external field is in the opposite direction, and such materials are repelled by it.
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.
Such alignment is temperature dependent as thermal agitation acts to disorient the dipoles.
In some materials, the atoms (with net magnetic dipole moments) can interact with each other to align themselves even in the absence of any external magnetic field when the thermal agitation is low enough.
In the case of anti-parallel, the dipole moments may or may not cancel each other (antiferromagnetism, ferrimagnetism).
We take a very simple situation in which each atom can be approximated as a two state system.
The thermal energy is so low that the atom is in the ground state.
In this ground state, the atom is assumed to have no net orbital angular momentum but only one unpaired electron to give it a spin of the half.
In the presence of an external magnetic field, the ground state will split into two states having an energy difference proportional to the applied field.
The spin of the unpaired electron is parallel to the field in the higher energy state and anti-parallel in the lower one.
, one can write Von Neumann's equation tells us how the density matrix evolves with time.
are positive real numbers which are independent of which atom we are looking at but depend on the mass and the charge of the electron.
This is justified by the fact that even for highest presently attainable field strengths, the shifts in the energy level due to
Degeneracy of the original Hamiltonian is handled by choosing a basis which diagonalizes
We get In case of diamagnetic material, the first two terms are absent as they don't have any angular momentum in their ground state.
Even though this is a reasonable assumption in the case of diamagnetic and paramagnetic substances, this assumption fails in the case of ferromagnetism, where the spins of the atom try to align with each other to the extent permitted by the thermal agitation.
Ising model is one of the simplest approximations of such pairwise interaction.
In order to simplify the calculation, it is often assumed that interaction happens between neighboring atoms only and
where kB is the Boltzmann constant, N the number of magnetic atoms (or molecules) per unit volume, g the Landé g-factor, μB the Bohr magneton, J the angular momentum quantum number.