Impact of spin--orbit coupling on orbital diamagnetism in a narrow-gap semiconductor $\mathrm{Pb}_{1-x}\mathrm{Sn}_x\mathrm{Te}$

Abstract

We study the influence of spin--orbit coupling (SOC) on orbital magnetism in $\mathrm{Pb}_{1-x}\mathrm{Sn}_x\mathrm{Te}$, a narrow-gap semiconductor. Using the $\pi$-matrix method, we calculate material-specific Landau levels and evaluate the magnetization, fully including interband effects. The system exhibits diamagnetism for both $x = 0$ and $x = 0.35$, with the latter showing a stronger response due to its smaller gap. The magnitude of diamagnetism increases monotonically with SOC strength, particularly in strong magnetic fields. To clarify the underlying mechanism, we introduce the free--Zeeman--Dirac (fZD) model and fit its parameters to the calculated Landau levels. The analysis reveals that SOC enhances the Dirac-type interband contribution relative to the Zeeman term, leading to increased diamagnetism. These results demonstrate that SOC can play a key role in orbital magnetism through interband effects.