Researchers from Monash University, part of the FLEET Centre, and China's Weifang University, have reported a generic approach towards intrinsic magnetic second-order topological insulators - materials that can be beneficial for spintronics.

Two-dimensional ferromagnetic semiconductors, such as CrI_{3}, Cr_{2}Ge_{2}Te_{6}, and VI_{3}, have been extensively studied in recent years and are fundamental to spintronics. Topological insulators are materials with unique properties where the interior is insulating, but the boundary can conduct electrons. In three-dimensional topological insulators like Bi_{2}Se_{3}, the surface hosts two-dimensional Dirac fermions. Second-order topological insulators, a new concept extending the idea of topological insulators, exhibit (m-2)-dimensional boundary states in m-dimensional materials, such as one-dimensional hinge states in three-dimensional materials and zero-dimensional corner states in two-dimensional materials.

Intrinsic ferromagnetic semiconductors are typically strong correlated materials, characterized by strong electron-electron correlations. These interactions are so pronounced that there is rarely “electron communication” between adjacent atoms, resulting in a system that resembles an atomic insulator devoid of topological property. Consequently, bridging these two states is challenging.

This research, led by Dr. Zhao Liu and Professor Nikhil Medhekar under FLEET THEME 1, found a novel solution. They discovered that in some intrinsic ferromagnetic semiconductors, the p orbitals from the ligand anions and d orbitals from the metal cations can form an inverted orbital order. Traditional ferromagnetic semiconductors have normal ordered p-d orbitals, i.e. p orbitals have a much lower energy than d orbitals, so p orbitals share closed shell and work as a messenger in “delivering” super-exchange interactions between two metal cations with open d shell. However, when partial p orbitals have higher energy than all the d orbitals, an inverted p-d orbitals occur. Since p and d orbitals share opposite parity, it is expected that inverted and normal ordered p-d orbitals give nontrivial and trivial topological phases, respectively.

Applying advanced density-functional theory calculations and wave function symmetry analysis, the researchers identified 1T-VS_{2 }and CrAs monolayer as potential candidates of intrinsic magnetic second-order topological insulators. 1T-VS_{2} shares a hexagonal lattice, while CrAs monolayer has a square lattice. In both, the spin up channel shows inverted p-d orbitals, resulting in nontrivial topology, while the spin down channel possesses normal ordered p-d orbitals with trivial topology. With 1T-VS_{2} nanoflakes grown into hexagonal or triangular shape, CrAs into square shape, spin-polarized scanning tunnelling microscope can be used to detect these states, which localized at corners only.

“Our work can be generalized to Kondo insulators, where d and f orbitals play similar roles to the p and d orbitals studied here. It would be exciting to discover second-order topological Kondo insulators considering that topological Kondo insulators have been recognized in this field”, said Professor Medhekar.

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**Posted:**Sep 12,2024 by Roni Peleg