Wiess field model of Paramagnetism

Wiess field model of paramagnetism In the ferromagnetic materials the magnetic moments (spins) are magnetized spontaneously. (Mean field theory) In 1907, Weiss developed a theory of effective fields Magnetic moments (spins) in ferromagnetic material aligned in an internal (Weiss) field. (Molecular field theory) Weiss assumed that this field is proportional to the magnetization B E = M is the Weiss constant,which is temperature independent. Weiss called this field the molecular field and thought that this field results from all the molecules in the sample. In reality, the origin of this field is the exchange interaction

Exchange mechanism The exchange interaction is the consequence of the Pauli exclusion principle and the Coulomb interaction between electrons. For two electron system there are two possible arrangements for the spins of the electrons either parallel or antiparallel If parallel, the exclusion principle requires the electrons to remain far apart. If they are antiparallel, the electrons may come closer together and their wave functions overlap considerably. electrostatic energy of an electron system depends on the relative orientation of the spins.

The difference in energy defines the exchange energy The exchange interaction is short ranged. Therefore, only nearest neighbour atoms are responsible for producing the molecular field. The magnitude of the molecular (exchange) field is very large of the order of 10 ⁷ G or 10 ³ T. It is not possible to produce such field in laboratories. Coulomb repulsion energy high Coulomb repulsion energy lowered

The paramagnetic region Consider magnetization in the region well above the curie temperature For T>Tc the spontaneous magnetization become zero An external field is required to produce magnetization This field should weak enough to avoid the saturation state

The Curie-Weis law describes fairly well the observed susceptibility variation in the paramagnetic region above the Curie point. Only in the vicinity of the Curie temperature a notable deviations are observed. This due to the fact that strong fluctuations of the magnetic moments close to the phase transition temperature can not be described by the mean field theory which was used for deriving the Curie-Weiss law. Accurate calculations predict that at temperatures very close to T C.

Curie temperatures of some ferromagnetic materials iron (Fe) 1,043 K cobalt (Co) 1,394 K nickel (Ni) 631 K gadolinium (Gd) 293 K manganese arsenide (MnAs) 318 K

Weiss theory is a good phenomenological theory of magnetism, But does not explain source of large Weiss field. Heisenberg and Dirac showed that ferromagnetism is a quantum mechanical effect that fundamentally arises from Coulomb interaction.(Exchange model) The Weiss theory gives information about the magnitude of magnetization, but nothing can be said about the direction Ferromagnetic Paramagnetic Curie Temperature Antiferromagnetic Paramagnetic Neel Temperature At these temperatures, the available thermal energy simply overcomes the interaction energy between the spins. Paramagnetic effects are quite small: the magnetic Susceptibility is of the order of 10 −3 to 10 −5 for most paramagnets Some paramagnetic material aluminium,oxygen,titanium and iron oxide..

Obviously spontaneous ordering of magnetic moments minimizes the entropy and consequently it cannot happen just at any temperature. At certain temperature the thermal energy k B T becomes greater than the exchange energy E ex and the material becomes disordered (entropy wins) and behaves as paramagnetic. namesymbol energy between parallel neighbours (J) ironFe cobaltCo nickelNi

By Muhammad Dawood Khan Department of Physics University of Peshawar KPK Pakistan date :22/05/2019