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Magnetic properties of metals are investigated through electronic structurecalculations based on the recently-proposed magnetic-field-containingrelativistic tight-binding approximation (MFRTB) method [Phys. Rev. B\textbf{91}, 075122 (2015)]. It is found that electronic energy bands for themetal immersed in the uniform magnetic field have a cluster structure in whichmultiple energy bands lie within a small energy width. Each cluster correspondsto the energy level that is derived on the basis of the semiclassicalapproximation. While the cluster is responsible for the de Haas-van Alphen(dHvA) oscillations, constituent energy bands of the cluster cause additionaloscillation peaks of the magnetization. Also, the energy width of the clusterleads to the reduction of the amplitude of the dHvA oscillations, which can beobserved as the pseudo Dingle temperature and/or the overestimation of thecurvature of the Fermi surface.

Calculations of Magnetic properties of metals through the magnetic-field-containing relativistic tight-binding approximation method