Thermally induced rotation of $3d$ orbital stripes in $\text{Pr}{\left({\text{Sr}}_{0.1}{\text{Ca}}_{0.9}\right)}_2{\text{Mn}}_2{\text{O}}_7$

We have investigated orbital ordering in the bilayer manganite, $\text{Pr}{\left({\text{Sr}}_{0.1}{\text{Ca}}_{0.9}\right)}_2{\text{Mn}}_2{\text{O}}_7$, using synchrotron x-ray diffraction techniques, in particular resonant soft x-ray diffraction. Diffraction signals are observed at $\left(0,\frac{1}{2},0\right)$ above 300 K and $\left(\frac{1}{2},0,0\right)$ below 300 K, corresponding to orbital stripes along the $a$ and $b$ axes, respectively. The previously observed transition at 300 K is evidence of a rotation of the orientation of the $3d$ orbital stripes. Large resonances of the orbital signals are observed at the $\text{Mn}L$ edges, with a complex dependence on incident photon energy indicative of a weakly Jahn-Teller distorted system. A structural transition observed at 92 K is found not to involve a further change in the orbital order.

Figure 1

(Color online) The crystal structure of $\text{Pr}{\left({\text{Sr}}_{0.1}{\text{Ca}}_{0.9}\right)}_2{\text{Mn}}_2{\text{O}}_7$. The Mn-O octahedra are shown by purple/gray polyhedra, with the black lines showing the extent of the crystallographic unit cell.

Figure 2

(Color online) Schematic of the orbital stripes running along the $a$ axis below $T_{\text{OO}1}$, and along the $b$ axis below $T_{\text{OO}2}$. Note that the structure is orthorhombic above $T_{\text{OO}1}$, facilitating preferential stripe directions.

Figure 3

(Color online) $\theta \text{−}2\theta$ scans showing the diffraction signals in the different orbital phases. All scans were measured at 652 eV. The inset shows the change in position of the reflection through the low-temperature transition $\left(T_S\right)$. The change in position of the reflection between 295 and 100 K is due to thermal contraction, and reflects a gradual change in lattice parameter rather than the abrupt change observed at 90 K.

Figure 4

(Color online) Anisotropy of the $\left(\frac{1}{2},0,0\right)$ and $\left(0,\frac{1}{2},0\right)$ orbital order reflections, measured by rotating the sample around the scattering vector. The solid line shows the calculated azimuthal dependence. Fitting errors of the peak intensity are within the symbol size.

Figure 5

(Color online) Temperature dependence of the orbital order reflections measured while cooling. The $\left(0,\frac{1}{2},0\right)$ reflection appears at $T_{\text{OO}1}$, with the $\left(\frac{1}{2},0,0\right)$ reflection forming at $T_{\text{OO}2}$. A further transition is observed at $T_S$. The inset shows the (800) and (080) reflections in the twinned sample measured at 9.26 keV at room temperature (solid line shows Gaussian fits).

Figure 6

(Color online) Energy scans at fixed wave vector from the orbital signal in different phases. The spectrum at 330 K is of the $\left(0,\frac{1}{2},0\right)$ reflection while the spectra at 270 and 60 K are of the $\left(\frac{1}{2},0,0\right)$ reflection. The energy spectra are all normalized at the main $L_2$ resonance, with the fluorescence (measured away from the reflection) on the same scale as the lowest intensity resonance at 330 K.

Figure 7

(Color online) The lattice parameters of $\text{Pr}{\left({\text{Sr}}_{0.1}{\text{Ca}}_{0.9}\right)}_2{\text{Mn}}_2{\text{O}}_7$ measured though the positions of Bragg reflections in each direction. Measurements were taken using 100 keV x rays at beamline BW5, HASYLAB. The solid lines are guides to the eye.

Figure 8

(Color online) Energy scans at fixed wave vector from the orbital signal on either side of $T_S$ through cooling the sample, showing no spectral change that would be indicative of an orbital occupancy change.