Dzyaloshinskii-Moriya Interaction and Spiral Order in Spin-orbit Coupled Optical Lattices

Ming Gong,V W Scarola,Chuanwei Zhang,Yinyin Qian,Mi Yan

doi:10.1038/srep10050

Abstract

We show that the recent experimental realization of spin-orbit coupling in ultracold atomic gases can be used to study different types of spin spiral order and resulting multiferroic effects. Spin-orbit coupling in optical lattices can give rise to the Dzyaloshinskii-Moriya (DM) spin interaction which is essential for spin spiral order. By taking into account spin-orbit coupling and an external Zeeman field, we derive an effective spin model in the Mott insulator regime at half filling and demonstrate that the DM interaction in optical lattices can be made extremely strong with realistic experimental parameters. The rich finite temperature phase diagrams of the effective spin models for fermions and bosons are obtained via classical Monte Carlo simulations.

Highlights

We show that the recent experimental realization of spin-orbit coupling in ultracold atomic gases can be used to study different types of spin spiral order and resulting multiferroic effects
We show that the power of optical lattice systems to emulate magnetism can be combined with recent experimental developments[21,22,23,24] realizing SO coupling to emulate multiferroic behavior
We show that SO coupling leads to an effective in-plane Dzyaloshinskii-Moriya (DM) term, an essential ingredient in models of spiral order and multiferroic effects in general

Summary

Introduction

We show that the recent experimental realization of spin-orbit coupling in ultracold atomic gases can be used to study different types of spin spiral order and resulting multiferroic effects. Nowadays construction and design of high-T c magnetic ferroelectrics is still an open and active area of research[11] These materials incorporate different types of interactions, including electron-electron interactions, electron-phonon interactions, spin-orbit (SO) couplings, lattice defects, and disorder, making the determination of multiferroic mechanisms a remarkable challenge for most materials[12,13]. The realization of a superfluid to Mott insulator transition of ultracold atoms in optical lattices 14 opens fascinating prospects[15] for the emulation of a large variety of novel magnetic states[16,17,18] and other strongly correlated phases found in solids because of the high controllability and the lack of disorder in optical lattices It has been shown[16,17] that the effective Hamiltonian of spin-1/2 atoms in optical lattices is the XXZ Heisenberg model in the deep Mott insulator regime. The DM term is of the same order as the Heisenberg coupling www.nature.com/scientificreports/

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