Nature of eg Electron Order in La₁₋ₓSr₁₊ₓMnO₄

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Synchrotron x-ray scattering measurements of the low-temperature structure of the single-layer manganese oxide La₁₋ₓSr₁₊ₓMnO₄, over the doping range 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 eg 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 eg electrons.