Revealing the unique domain boundary structure and topological defects of spin-density-wave state*

Understanding the atomic-scale structure of magnetic domain walls is of fundamental importance for both the basics and applications of magnetism. Although the domain wall structures of local-moment magnets are well studied, little is known about those of itinerant magnetism, such as the spin-density-wave (SDW) state. Here by using scanning tunneling microscopy, we studied the domain wall structure of the SDW in Cr and its coexisting CDW state. On the Cr (001) surface, two single-Q (stripe-like) SDW/CDW domains with their wave vector Q perpendicular to each other are identified. On their domain boundaries, we observed grid-like CDW modulations. Detailed analysis shows that such modulations are not from the direct adding of two CDW stripes, but are the result of the coherent superposition of two single-Q SDW. This means a unique double-Q SDW state is formed at the domain wall. Moreover, the observed domain wall has a finite wall width, indicating an energy cost of forming a double-Q SDW state. Our simulation shows that the single-Q state exponentially decays when entering the double-Q region, which is a characteristic of the itinerant nature of SDW. Further, we observed topological defects of SDW state. Our work not only discovered a new type of magnetic domain wall which differs completely from local-moment magnetism, but also brings insights into the microscopic mechanisms of SDW state.