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From neutron diffraction measurements on a quasi-1D Ising-like Co$^{\rm 2+}$spin compound BaCo$_{\rm 2}$V$_{\rm 2}$O$_{\rm 8}$, we observed an appearanceof a novel type of incommensurate ordering in magnetic fields. This ordering isessentially different from the N{\' e}el-type ordering, which is expected forthe classical system, and is caused by quantum fluctuation inherent in thequantum spin chain. A Tomonaga-Luttinger liquid (TLL) nature characteristic ofthe gapless quantum 1D system is responsible for the realization of theincommensurate ordering.

Longitudinal SDW order in a quasi-1D Ising-like quantum antiferromagnet