Real-space observation of incommensurate spin density wave and coexisting charge density wave on Cr (001) surface

Yining Hu,Chen Chen,Shuyue Ding,Dongming Zhao,Tong Zhang,Tianzhen Zhang,Donglai Feng,Wentao Yang,Haitao Wang,Chihao Li,Xu Wang

doi:10.1038/s41467-022-28104-2

Abstract

In itinerant magnetic systems, a spin density wave (SDW) state can be induced by Fermi surface nesting and electron-electron interaction. It may intertwine with other orders such as charge density wave (CDW), while their relation is still yet to be understood. Here via spin-polarized scanning tunneling microscopy, we directly observed long-range spin modulation on Cr(001) surface, which corresponds to the well-known incommensurate SDW of bulk Cr. It displays 6.0 nm in-plane period and anti-phase behavior between adjacent (001) planes. Meanwhile, we simultaneously observed the coexisting CDW with half the period of SDW. Such SDW/CDW have highly correlated domain structures and are in-phase. Surprisingly, the CDW displays a contrast inversion around a density-of-states dip at −22 meV, indicating an anomalous CDW gap opened below EF. These observations support that the CDW is a secondary order driven by SDW. Our work is not only a real-space characterization of incommensurate SDW, but also provides insights on how SDW and CDW coexist.

Highlights

In itinerant magnetic systems, a spin density wave (SDW) state can be induced by Fermi surface nesting and electron-electron interaction
Unlike the IC-SDW, the exact origin of such charge density wave (CDW) is yet to be understood. It was often considered as the second-order harmonics of ICSDW12, corresponding to a nesting vector QCDW = 2QSDW that connects the two folded bands at Γ (Fig. 1a); alternatively, it was suggested as a lattice strain wave induced by magneto-elastic coupling to the IC-SDW6
Some dislocation lines are observed where the atomic lattice on their two sides displays certain shift. These dislocations do not show influence to SDW/CDW discussed below, more details are presented in Supplementary Fig. S1

Summary

Introduction

A spin density wave (SDW) state can be induced by Fermi surface nesting and electron-electron interaction. It may intertwine with other orders such as charge density wave (CDW), while their relation is still yet to be understood. Unlike the IC-SDW, the exact origin of such CDW is yet to be understood It was often considered as the second-order harmonics of ICSDW12, corresponding to a nesting vector QCDW = 2QSDW that connects the two folded bands at Γ (Fig. 1a); alternatively, it was suggested as a lattice strain wave induced by magneto-elastic coupling to the IC-SDW6. A few SPSTM studies have been performed on various Cr surfaces[17,18,19,20,21,22,23,24,25,26], the real-space evidence of IC-SDW was rarely reported (some studies found CDW modulation on Cr (110) surface[23,27], and argued the satellite FFT spots as an indication of IC-SDW23)

Methods

Results

Conclusion