Relativistic effects on the magnetic shielding in solids: First-principles computation in a plane wave code

For computing the magnetic shielding in solids, density functional theory as implemented in a plane wave basis has proven to be a reasonably accurate and efficient framework, at least for lighter atoms through the third row of the periodic table. In materials with heavier atoms, terms not usually included in the electronic Hamiltonian can become significant, limiting accuracy. Here we derive and implement the zeroth-order regular approximation (ZORA) relativistic terms in the presence of both external magnetic fields and internal nuclear magnetic dipoles, to derive the ZORA-corrected magnetic shielding in the context of periodic boundary conditions and a plane wave basis. We describe our implementation in an open source code, Abinit, and show how it correctly predicts magnetic shieldings in various scenarios, for example the heavy atom next to light atom cases of the III-V semiconductors such as AlSb.