Nature of e_g Electron Order in La_1-xSr_1+xMnO₄

X-ray scattering measurements of the low-temperature structure of La_1-xSr_1+xMnO₄ ( 0.33≤x≤0.67) indicate the existence of three distinct regions: a disordered phase (x<0.4), a charge-ordered phase (x≥0.5), and a mixed phase (0.4≤x<0.5). For x>0.5, the modulation vector associated with the charge order is incommensurate with the lattice and depends linearly on the concentration of e_g electrons. The primary superlattice reflections are strongly suppressed along the modulation direction and the higher harmonics are weak, implying the existence of a largely transverse and nearly sinusoidal structural distortion, consistent with a charge-density wave of the e_g electrons.