(x=0.12)*

The high-temperature superconducting cuprates display intriguing physical phenomena due to the presence of competing or intertwined phases. One of the remarkable observations in both Sr-doped La_2-xSr_xCuO₄ (LSCO) system and O-doped La₂CuO_4+y is the so-called Y-shift, which refers to a small shift of both spin density wave (SDW) and charge density wave (CDW) peak positions from the high-symmetry Cu-Cu bond direction. However, the ordering temperatures for the SDW and CDW are different. Above the superconducting transition temperature (T_c), there is only incipient spin fluctuation coexisting with the CDW order. In this talk, I will present our recent high-resolution inelastic neutron scattering experiment which characterized the Y-shift in the spin fluctuation regime in LSCO (x=0.12). The implication of the result will be discussed. Our study provides important information on the nature of the spin fluctuation in this system.