The field induced magnetic phase transitions of Cs$_2$CuBr$_4$ were investigated by means of magnetization process and neutron scattering experiments. This system undergoes magnetic phase transition at Ne{e}l temperature $T_mathrm{N}=1.4$ K at zero field, and exhibits the magnetization plateau at approximately one third of the saturation magnetization for the field directions $Hparallel b$ and $Hparallel c$. In the present study, additional symptom of the two-third magnetization plateau was found in the field derivative of the magnetization process. The magnetic structure was found to be incommensurate with the ordering vector $boldsymbol{Q}=(0, 0.575, 0)$ at zero field. With increasing magnetic field parallel to the c-axis, the ordering vector increases continuously and is locked at $boldsymbol{Q}=(0, 0.662, 0)$ in the plateau field range $13.1 mathrm{T} < H < 14.4 mathrm{T}$. This indicates that the collinear textit{up-up-down} spin structure is stabilized by quantum fluctuation at the magnetization plateau.
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