Spin-helix driven insulating phase in two dimensional lattice

TL;DR

This paper investigates a novel insulating phase driven by spin helix formation in 2D lattices with spin-orbit coupling, revealing conditions for magnetic ordering and potential applications in 2D magnetic materials.

Contribution

It identifies the conditions for a spin helix driven insulating phase with emergent SU(2) symmetry in 2D lattices with Rashba and Dresselhaus couplings, and explores magnetic ordering mechanisms.

Findings

Perfect Fermi surface nesting occurs under specific conditions.

Magnetic insulator with spiral magnetic order is stabilized.

Applicable to van-der Waals materials and heterostructures.

Abstract

Motivated by emergent $SU(2)$ symmetry in the spin orbit coupled system, we study the spin helix driven insulating phase in two dimensional lattice. When both Rashba and Dresselhaus spin orbit couplings are present, the perfect Fermi surface nesting occurs at a special condition depending on the lattice geometry. In this case, the energies of spin up at any wave vector $\vec{k}$ are equivalent to the ones of spin down at $\vec{k}\!+\!\vec{Q}$ with so-called the \textit{shifting wave vector} $\vec{Q}$. Thus, the system stabilizes magnetic insulator with spiral like magnetic ordering even in the presence of tiny electron-electron interaction where the magnetic ordering wave vector is proportional to $\vec{Q}$. We first show the condition for existence of the \textit{shifting wave vector} in general lattice model and emergent $SU(2)$ symmetry in the spin orbit coupled system. Then, we exemplify this in square lattice at half filling and discuss the insulating phase with (non-) coplanar spin density wave and charge order. Our study emphasizes possible new types of two dimensional magnetic materials and can be applicable to various van-der Waals materials and their heterostructures with the control of electric field, strain and pressure.