Via spin-polarized scanning tunneling microscopy, we revealed a long-range ordered spin density wave (SDW) for the first time on a Cr (001) surface, corresponding to the well-known incommensurate SDW of bulk Cr. It displays a (~ 6.0 nm) long-period spin modulation in each (001) plane and an anti-phase behavior between adjacent planes, which are confirmed by changing the magnetization of the tip. Meanwhile, we simultaneously observed the coexisting charge density wave (CDW) with half the period of the SDW. Taking advantage of real-space measurement, we found the charge and spin modulations are in-phase, and their domain structures are highly correlated. Surprisingly, the phase of CDW in dI/dV map displays a {pi} shift around a density-of-states dip at about -22 meV, indicating an anomalous CDW gap opened below EF. These observations support that the CDW is a secondary order driven by SDW. Therefore, our work is not only the first real space characterization of incommensurate SDW, but also provide new insights on how SDW and CDW coexist.
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