• Wolfgang NoltingEmail author
  • Anupuru Ramakanth


Paramagnetism presumes the existence of permanent magnetic moments. These permanent moments can be, for example, due to the itinerant conduction electrons of a metallic solid (Pauli spin paramagnetism). First, we will investigate, for the Sommerfeld model (free Fermi gas), the response of these itinerant moments to an external magnetic field at T = 0. A discussion on the temperature and exchange corrections will be added to this. The temperature corrections turn out to be not significant. The exchange corrections are a result of the Coulomb interactions which were neglected in the Sommerfeld model. We apply the jellium model to approximately evaluate the exchange corrections.

In insulators, the permanent magnetic moments originate from the partially filled electron shells of the respective ions in the solid. These are localized moments, which, in the first approximation, are non-interacting. Three influences determine the susceptibility of such a paramagnet: the thermal energy k B T, the field energy μ B B 0 and the spin–orbit coupling energy ħ2Λ. For very high temperatures, in all cases, the inverse susceptibility has a linear temperature dependence (Curie law).

A special case is the practically temperature-independent van Vleck paramagnetism, which is observed in systems, where the localized permanent moment originates from a shell which is exactly one electron short from being half-filled.


Partition Function Localize Electron Orbit Coupling Exchange Correction Canonical Partition Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Humboldt-Universität zu Berlin, Institut für PhysikBerlinGermany
  2. 2.Department of PhysicsKakatiya UniversityWarangalIndia

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