Abstract

In this paper we present x-ray scattering results of charge and orbital ordering in the bilayer manganite ${\mathrm{La}}_{2\ensuremath{-}2x}{\mathrm{Sr}}_{1+2x}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ with doping levels $x=0.5$ and $x=0.475.$ Using high-energy x-ray scattering, the structural modulation due to the Jahn-Teller ordering and the charge ordering due to the ${\mathrm{Mn}}^{3+}/{\mathrm{Mn}}^{4+}$ pattern have been measured. Both the $x=0.5$ and $x=0.475$ samples are found to display charge and Jahn-Teller order. We have confirmed that the wave vectors of the Jahn-Teller order, charge order, and orbital order are $\stackrel{\ensuremath{\rightarrow}}{Q}=(0.25,0.25,0),$ $\stackrel{\ensuremath{\rightarrow}}{Q}=(0.5,0.5,0)$ and $\stackrel{\ensuremath{\rightarrow}}{Q}=(0.25,0.25,0).$ The origin of these has been confirmed by resonant x-ray scattering in the vicinity of the Mn K edge using polarization analysis. Contrary to previous studies, the Jahn-Teller order is found to be not reentrant, but is found to reduce in intensity at temperatures below 140 K for both samples. Charge ordering was also detected in the $x=0.5$ sample below this temperature.

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