Ab initio based study of the diamagnetism of diamond, silicon and germanium

Diamond, silicon and germanium are widely used technological materials, whose electron structures are tabulated and understood very well. Yet the detailed picture of various diamagnetic contributions and their interplay with the paramagnetic effect, especially at the ab initio level, due to the complexity of this problem remains largely unknown. In our study, based on the ab initio electron band structure approach, all possible magnetic contributions, including the Langevin (Larmor) diamagnetism and the Van Vleck paramagnetism accounted in the second order of the perturbation treatment, are analyzed quantitatively. The Van Vleck contribution has been adapted to the band structure calculations by performing integration over k-points. Also, the partial diamagnetic contributions of core and valence electrons are obtained and discussed in detail. Of all terms there is only one - the Langevin diamagnetism of the valence electrons, which is not well defined quantitatively due to the contribution from the interstitial region. We discuss possible approaches to partitioning this contribution among neighboring crystal sites, based on the Bader charge separation and introducing the area of depleted electron density, excluded from the integration. Under various assumptions for the interstitial region, we have found that the magnetic susceptibilities for diamond, silicon and germanium lie in the range-13.4/-9.3,-4.7/-4.0 and-8.4/-8.8 (volume values, in units of 10-7), correspondingly. In general, this is consistent with the available experimental values, albeit the numerical uncertainty typically reaches tens of percent.