Impact of spin--orbit coupling on orbital diamagnetism in a narrow-gap semiconductor ${\mathrm{P}\mathrm{b}}_{1-x}{\mathrm{S}\mathrm{n}}_x\mathrm{T}\mathrm{e}$

We study the influence of spin–orbit coupling (SOC) on orbital magnetism in ${\mathrm{P}\mathrm{b}}_{1-x}{\mathrm{S}\mathrm{n}}_x\mathrm{T}\mathrm{e}$, 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.