Calculation of magnetic oscillations via the magnetic-field-containing relativistic tight-binding approximation method: Revisiting the de Haas–van Alphen effect

Abstract

The magnetic-field-containing relativistic tight-binding approximation (MFRTB) method [Phys. Rev. B 91, 075122 (2015)] is the first-principles calculation method for electronic structures of materials immersed in the magnetic field. In this paper, the MFRTB method is applied to the simple cubic lattice immersed in the magnetic field. The total energy and magnetization oscillate with the inverse of the magnitude of the magnetic field, which means that the de Haas--van Alphen oscillation is revisited directly through the MFRTB method. It is shown that the conventional Lifshitz-Kosevich (LK) formula is a good approximation to the results of the MFRTB method in the experimentally available magnetic field. Furthermore, the additional oscillation peaks of the magnetization are found especially in the high magnetic field, which cannot be explained by the LK formula.