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The materials do show an ordering temperature above which the behavior reverts to ordinary paramagnetism (with interaction). Ferrofluids are a good example, but the phenomenon can also occur inside solids, e.g., when dilute paramagnetic centers are introduced in a strong itinerant medium of ferromagnetic coupling such as when Fe is substituted ...
The Hamiltonian for an electron in a static homogeneous magnetic field in an atom is usually composed of three terms = + (+) + where is the vacuum permeability, is the Bohr magneton, is the g-factor, is the elementary charge, is the electron mass, is the orbital angular momentum operator, the spin and is the component of the position operator orthogonal to the magnetic field.
In a paramagnetic system, that is, a system in which the magnetization vanishes without the influence of an external magnetic field, assuming some simplifying assumptions (such as the sample system being ellipsoidal), one can derive a few compact thermodynamic relations. [4]
Still, such materials typically do show a weak magnetic behaviour, e.g. due to diamagnetism or Pauli paramagnetism. The more interesting case is when the material's electron spontaneously break above-mentioned symmetry.
It only holds for high temperatures and weak magnetic fields. As the derivations below show, the magnetization saturates in the opposite limit of low temperatures and strong fields. If the Curie constant is null, other magnetic effects dominate, like Langevin diamagnetism or Van Vleck paramagnetism.
The magnitude of the paramagnetism is expressed as an effective magnetic moment, μ eff. For first-row transition metals the magnitude of μ eff is, to a first approximation, a simple function of the number of unpaired electrons, the spin-only formula. In general, spin–orbit coupling causes μ eff to deviate from the spin-only formula.
On top of the applied field, the magnetization of the material adds its own magnetic field, causing the field lines to concentrate in paramagnetism, or be excluded in diamagnetism. [1] Quantitative measures of the magnetic susceptibility also provide insights into the structure of materials, providing insight into bonding and energy levels .
When Langevin published the theory paramagnetism in 1905 [12] [13] it was before the adoption of quantum physics. Meaning that Langevin only used concepts of classical physics. [17] Niels Bohr showed in his thesis that classical statistical mechanics can not be used to explain paramagnetism, and that quantum theory has to be used. [17]