Annales Henri Poincaré

, Volume 16, Issue 1, pp 45–97 | Cite as

On the Atomic Orbital Magnetism: A Rigorous Derivation of the Larmor and Van Vleck Contributions

  • Baptiste SavoieEmail author


The purpose of this paper is to rigorously investigate the orbital magnetism of core electrons in three-dimensional crystalline ordered solids and in the zero-temperature regime. To achieve that, we consider a non-interacting Fermi gas subjected to an external periodic potential modeling the crystalline field within the tight-binding approximation (i.e., when the distance between two consecutive ions is large). For a fixed number of particles in the Wigner–Seitz cell and in the zero-temperature limit, we derive an asymptotic expansion for the bulk zero-field orbital susceptibility. We prove that the leading term is the superposition of the Larmor diamagnetic contribution, generated by the quadratic part of the Zeeman Hamiltonian, together with the ‘complete’ orbital Van Vleck paramagnetic contribution, generated by the linear part of the Zeeman Hamiltonian, and related to field-induced electronic transitions.


Magnetic Susceptibility Asymptotic Expansion Resolvent Operator Canonical Condition Seitz Cell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© European Union 2014

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of AarhusÅrhus CDenmark

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