Topological electronic structures of non-collinear magnetic phases in a multi-orbital Hubbard model with spin-orbit interactions

TL;DR

This paper investigates the topological electronic structures of non-collinear magnetic phases in a multi-orbital Hubbard model with spin-orbit interactions, revealing how different magnetic orders and symmetries influence topological properties and surface states.

Contribution

It introduces a generalized t-J model considering Dresselhaus and Rashba spin-orbit interactions and characterizes the topological phases of various magnetic orders using Z2 and Z4 indices.

Findings

Dresselhaus interaction leads to collinear antiferromagnetic order.

Rashba interaction causes spins to tilt in the xy-plane.

Surface states become gapless when parallel to ferromagnetic components.

Abstract

We explore topological electronic structure of magnetic phases in a multi-orbital Hubbard model with spin-orbit interactions. To account for more general antiferromagnetic orders that go beyond the collinear N\'eel order, two different spin-orbit interactions, Dresselhaus and Rashba spin-orbit interactions, are considered. By performing the canonical transformation, we derive the corresponding generalized t-J model. At half filling, employing self-consistent magnetic order calculations, we find distinctive spin arrangements under Dresselhaus or Rashba spin-orbit interactions. For the Dresselhaus spin-orbit interaction, the spin configuration exhibits collinear antiferromagnetic order. On the other hand, Rashba interaction results in spins antiferromagnetically aligning in xy-plane and a small interaction controlled by hopping parameter induces spin tilting, causing antiferromagnetic alignment in xy-plane but ferromagnetic alignment in z-direction. We categorize topological properties of these phases for low doping in the generalized t-J model.: for 3D collinear antiferromagnetic order, the system possesses a modified time-reversal symmetry, characterized by the Z2 index. In contrast, for systems with tilted antiferromagnetic orders, it is protected by inversion symmetry and characterized by the Z4 index. We further examine the bulk-edge correspondence for non-collinear magnetic phases, revealing that the surface state becomes gapless when the surface is parallel to the ferromagnetic component of tilted antiferromagnetic order; otherwise, the surface state exhibits a gap. Our findings offer a comprehensive topological characterization for doped and canted antiferromagnetic insulators with spin-orbit interactions, providing valuable insights into the interplay between spin arrangements, symmetries, and topological properties in systems governed by the multi-orbital Hubbard model.