On the atomic orbital magnetism: A rigorous derivation of the Larmor and Van Vleck contributions

Baptiste Savoie (1)

1 Aarhus University [Aarhus]

The purpose of this paper is to rigorously investigate the orbital magnetism of core electrons in 3-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 within the framework of 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 two terms: the Larmor diamagnetic contribution, generated by the quadratic part of the Zeeman Hamiltonian, together with the 'complete' orbital Van Vleck contribution, generated by the linear part of the Zeeman Hamiltonian, and related to field-induced electronic transitions.

Mots clés: Gauge invariant magnetic perturbation theory; Orbital magnetism; Atomic magnetism; Zero-field susceptibility; Langevin formula; Larmor diamagnetism; Van Vleck paramagnetism; Tight-binding approximation; Geometric perturbation theory; Gauge invariant magnetic perturbation theory.

Domaines: Physique mathématique [math-ph]; Gaz Quantiques [cond-mat.quant-gas]; Mécanique statistique [cond-mat.stat-mech]

Baptiste Savoie. On the atomic orbital magnetism: A rigorous derivation of the Larmor and Van Vleck contributions. 2013. ⟨hal-00785100v2⟩