Resonant soft x-ray powder diffraction study to determine the orbital ordering in A-site-ordered ${\mathrm{SmBaMn}}_2{\mathrm{O}}_6$

Soft x-ray resonant powder diffraction has been performed at the Mn $L_{2,3}$ edges of A-site-ordered ${\mathrm{SmBaMn}}_2{\mathrm{O}}_6$. The energy and polarization dependences of the (1/4 1/4 0) reflection provide direct evidence for a $(x^2-z^2)∕(y^2-z^2)$-type orbital ordering in contrast to single-layer manganite. The temperature dependence of the reflection indicates an orbital reorientation transition at $\approx 210\mathrm{K}$, below which the charge- and orbital-ordered ${\mathrm{MnO}}_2$ sheets show AAAA-type of stacking. The concurring reduction of the ferromagnetic superexchange correlations leads to further charge localization.

Figure 1

(Color online) (a) Image of a section of the resonant orbital powder diffraction ring (1/4 1/4 0) taken at the Mn $L_3$ edge $\left(643.25\mathrm{eV}\right)$ at $14\mathrm{K}$ with $\pi$ incident radiation located at $2\theta$ of approximately $120°$ of ${\mathrm{SmBaMn}}_2{\mathrm{O}}_6$. (b) Integrated intensity (vertical) of the image as a function of 2$\theta$.

Figure 2

(Color online) (a) Energy dependence of the fluorescence and integrated intensity of the (1/4 1/4 0) reflection of polycrystalline ${\mathrm{SmBaMn}}_2{\mathrm{O}}_6$ with $\pi$ incident radiation at $120\mathrm{K}$ compared with that of single-crystal ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{1.5}{\mathrm{MnO}}_4$ taken at $160\mathrm{K}$ (the intensity is scaled and shifted for easy comparison) (Ref. 15). (b) Energy dependence of the (1/4 1/4 0) reflection recorded with $\pi$ and $\sigma$ incident radiation at $235\mathrm{K}$. Inset: calculated energy dependence of the (1/4 1/4 0) reflection for $x^2-y^2$- and $3z^2-r^2$-type OO taken from Ref. 14.

Figure 3

(Color online) (a) Temperature dependence of the integrated x-ray intensity of the (1/4 1/4 0) reflection taken at the Mn $L_3$ edge $\left(643.25\mathrm{eV}\right)$ with $\pi$ incident radiation of polycrystalline ${\mathrm{SmBaMn}}_2{\mathrm{O}}_6$. The vertical lines indicate the various phase transitions as discussed in the text and the insets show the different orbital stackings. (b) Temperature dependence of the zero-field-cooled (ZFC) and field-cooled (FC) magnetization recorded in $H=400\mathrm{A}∕\mathrm{m}$ during cooling and heating (left axis) of polycrystalline ${\mathrm{SmBaMn}}_2{\mathrm{O}}_6$. In addition the temperature dependence of the resistivity is shown on a logarithmic scale (right axis).

Figure 4

(Color online) Energy dependence of the integrated intensity of the (1/4 1/4 0) reflection of polycrystalline ${\mathrm{SmBaMn}}_2{\mathrm{O}}_6$ recorded at various temperatures with $\pi$ incident radiation. The intensities are rescaled and an offset is added to allow a better comparison between the spectra. The labeling of the energy features are the same as in Ref. 16.