Single-layer magnet phase in intrinsic magnetic topological insulators, $[\mathrm{MnTe}][\mathrm{Bi}_{2}\mathrm{Te}_{3}]_{\mathrm{n}}$, far beyond the thermodynamic limit

The intrinsic magnetic topological insulator (IMTI) family $[\mathrm{MnTe}][\mathrm{Bi}_{2}\mathrm{Te}_{3}]_{\mathrm{n}}$ has demonstrated magneto-topological properties dependent on $n$, making it a promising platform for advanced electronics and spintronics. However, due to technical barriers in sample synthesis, their properties in the large $n$ limit remain unknown. To overcome this, we utilized the atomic layer-by-layer molecular beam epitaxy (ALL-MBE) technique and achieved IMTIs with $n$ as large as 15, far beyond the previously reported in bulk crystals or thin films. Then, we discover that the "single-layer magnet (SLM)" phase, primarily determined by intralayer ferromagnetic coupling, emerges for $n >$ $\sim 4$ and remains little affected up to $n = 15$. Nonetheless, still, non-zero, interlayer ferromagnetic coupling is necessary to stabilize the SLM phase, suggesting that the SLM phase eventually disappears in the $n\to\infty$ limit. This study uncovers the secrets of IMTIs beyond the thermodynamic limit and opens a door to diverse magneto-topological applications.