Coexistence of magnetic and phononic second-order topological phases in two-dimensional NiZrCl6

Second-order topological phases (SOTPs) in two-dimensional (2D) magnetic and phononic systems are rarely reported. In this Letter, using first-principles calculations, we propose that the NiZrCl6 monolayer with space group P312 (No. 149) is a 2D ferromagnetic material with rich SOTPs: (i) magnetic SOTPs can be found in the band structures of both spin channels in NiZrCl6. NiZrCl6 hosts topologically protected corner states that have a quantized fractional charge (e/3) and are spin-polarized and pinned at the corners of the sample in real space. The SOTP nature in the NiZrCl6 monolayer is resistant to the spin-orbit coupling effect. (ii) Phononic SOTPs can be found in the phonon curves of NiZrCl6. The corner vibrational modes appear inside the frequency gap around 7.98 THz of the NiZrCl6 monolayer, and the secondary topological index can verify the nontrivial phase. The proposed 2D NiZrCl6 material can be a starting point for exploring higher-order topological phases in 2D magnetic and phononic systems.