Orbital Order at Mn and O Sites and Absence of Zener Polaron Formation in Manganites

We report the doping dependence of the ground state of $A$-site ordered manganites below and above half doping. Energy and polarization dependence of the orbital reflection, taken by resonant soft-x-ray powder diffraction, at both Mn $L_{2,3}$ and O $K$ edges, provides direct evidence for orbital order at ${\mathrm{Mn}}^{3+}$ and oxygen sites and absence of Zener polaron formation. For $x\ge 0.2$ anomalous melting of the orbital order is observed, which is coupled neither to magnetic ordering nor to a structural transition, indicating a two-dimensional character of the interactions.

Figure 1

Energy dependence of the integrated intensity of the orbital reflection (${\delta }_x$, ${\delta }_x$, 0), measured at the Mn $L$ edges for systems above half doping ${\mathrm{Tb}}_{1-x}{\mathrm{Ca}}_x{\mathrm{BaMn}}_2{\mathrm{O}}_6$ and below half doping ${\mathrm{TbLa}}_y{\mathrm{Ba}}_{1-y}{\mathrm{Mn}}_2{\mathrm{O}}_6$. The experimental data have been normalized to the intensity at 643 eV for comparison.

Figure 2

(a) Energy dependence of the integrated intensity of the orbital reflection (${\delta }_x$, ${\delta }_x$, 0) of ${\mathrm{Tb}}_{1-x}{\mathrm{Ca}}_x{\mathrm{BaMn}}_2{\mathrm{O}}_6$ measured at the O $K$ edge for $x=0.2$, 0.33 and $x=0.4$ (see inset). For $x=0.4$ this energy dependence is shown for $\pi$ and $\sigma$ incident polarizations together with the fluorescence. The inset shows the momentum dependence of the ordering wave vector. (b) Energy dependence of the (0.225, 0.225, 0) orbital reflection of $x=0.1$ measured at the Mn $L_{2,3}$ edges for $\pi$ and $\sigma$ incident polarizations and the fluorescence. The inset shows rebinned powder reflection ($1/4$, $1/4$, 0) of ${\mathrm{TbBaMn}}_2{\mathrm{O}}_6$ collected with $\pi$ and $\sigma$ incident polarizations.

Figure 3

Comparison of the temperature dependence of the integrated (${\delta }_x$, ${\delta }_x$, 0) reflection in ${\mathrm{Tb}}_{0.8}{\mathrm{Ca}}_{0.2}{\mathrm{BaMn}}_2{\mathrm{O}}_6$, taken at the O $K$ edge (528.4 eV) and Mn $L_3$ edge (643 eV) measured with $\pi$ incident polarization.

Figure 4

Temperature dependence of the integrated intensity of the (${\delta }_x$, ${\delta }_x$, 0) reflection measured with $\pi$ incident radiation of polycrystalline ${\mathrm{Tb}}_{0.66}{\mathrm{Ca}}_{0.33}{\mathrm{BaMn}}_2{\mathrm{O}}_6$ at the O $K$ edge together with the relative change of the $\mathbf{q}$ vector. Also shown is the temperature dependence of the $\mathbf{q}$ vector of the (2, 2, 0) reflection, calculated from the unit cell parameters. ${\mathbf{q}}_0$ is taken as the value of $\mathbf{q}$ for the lowest measured temperature. The inset shows the variation of the unit cell volume as a function of temperature. LTP represents low temperature phase, and HTP high temperature phase.