Ab initio description of de Haas–van Alphen oscillation using relativistic magnetic-Bloch-states

The ab initio description of the de Haas–van Alphen (dHvA) oscillation has been recognized as one of long-standing goals in material science. Here, we demonstrate that the dHvA oscillation can be described by the ab initio method for calculating relativistic magnetic-Bloch-states of materials immersed in a uniform magnetic field, the nonperturbative magnetic-field-containing relativistic tight-binding approximation (nonperturbative MFRTB) method. Furthermore, we provide two kinds of useful tables for calculating relativistic magnetic-Bloch-states. One is the relativistic version of the Slater–Koster table, and the other is a table of nonperturbative magnetic hopping integrals for all combinations related to d-orbitals. Since these tables can be commonly used not only for the nonperturbative MFRTB calculations but also for investigating magnetic properties caused by relativistic magnetic-Bloch-states, the publication of these two tables opens the way for material design that utilizes magnetic fields as parameters for controlling physical properties.