Size-Dependent Critical Temperature and Anomalous Optical Dispersion in Ferromagnetic CrI₃ Nanotubes

Using first principles calculations, we explored the magnetic and optical properties of chromium(III) iodide (CrI₃) nanotubes (NTs) by changing their chirality and diameter. Here, we considered six types of NTs: (5,0), (5,5), (7,0), (10,0), (10,10), and (12,0) NTs. We found that both zigzag and armchair NTs had a ferromagnetic ground with a direct band gap, although the band gap was dependent on the chirality and diameter. Using the Monte Carlo simulation, we found that the Curie temperatures (T_c) exhibited chirality and diameter dependence. In zigzag NTs, the larger the tube diameter, the larger the T_c, while it decreased with increasing diameter in the armchair tube. We found that the T_c was almost doubled when the diameter increased two-fold. This finding may guide development of room temperature ferromagnetism in zigzag NTs. We also found that the CrI₃ NTs displayed anisotropic optical properties and anomalous optical dispersion in the visible range. Specifically, the (10,0) zigzag NT had a large refractive index of 2 near the infrared region, while it became about 1.4 near blue light wavelengths. We also obtained large reflectivity in the ultraviolet region, which can be utilized for UV protection. Overall, we propose that the CrI₃ NTs have multifunctional physical properties for spintronics and optical applications.