Novel Orbital Ordering Induced by Anisotropic Stress in a Manganite Thin Film

A novel structure of orbital ordering is found in a ${\mathrm{Nd}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{MnO}}_3$ thin film, which exhibits a clear first-order transition, by synchrotron x-ray diffraction measurements. Lattice parameters vary drastically at the metal-insulator transition at 170 K ($=T_{\mathrm{MI}}$), and superlattice reflections appear below 140 K ($=T_{\mathrm{CO}}$). The electronic structure between $T_{\mathrm{MI}}$ and $T_{\mathrm{CO}}$ is identified as $A$-type antiferromagnetic with a $d_{x^2-y^2}$ ferro-orbital ordering. The new type of antiferro-orbital ordering characterized by the wave vector ($\frac{1}{4}\frac{1}{4}\frac{1}{2}$) in cubic notation emerges below $T_{\mathrm{CO}}$. The accommodation of the large lattice distortion at the first-order phase transition and the appearance of the novel orbital ordering are brought about by the anisotropy in the substrate, a new parameter for the phase control.

Figure 1

Temperature dependence of the electric resistivity of ${\mathrm{Nd}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{MnO}}_3$ thin films grown on ${\mathrm{SrTiO}}_3$ (001), (011), and (111) substrates [6] and of bulk ${\mathrm{Nd}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{MnO}}_3$ [20].

Figure 2

(a) Schematic view of the $a^{*}$ plane in reciprocal space at room temperature and 10 K. Twinning was observed at 10 K. (b) Temperature dependence of the lattice parameters $a$, $b$, and $c$ during a heating run. The lattice parameter of ${\mathrm{SrTiO}}_3$ is shown as $a$ because $a$ was locked into the lattice parameter of the substrate that can be measured precisely. The inset shows the peak profiles obtained at 180 and 160 K along the arrow through (002) shown in (a).

Figure 3

(a) Intensity distribution around ($\frac{3}{4}\frac{7}{4}\frac{3}{2}$), ($\frac{3}{4}\frac{7}{4}2$), ($12\frac{3}{2}$), and ($\frac{1}{2}\frac{3}{2}2$), which are characterized by the wave vectors ($\frac{1}{4}\frac{1}{4}\frac{1}{2}$), ($\frac{1}{4}\frac{1}{4}0$), ($00\frac{1}{2}$), and ($\frac{1}{2}\frac{1}{2}0$), respectively; the intensity is normalized so that the peak top of the (011) fundamental reflection is ${10}^6$. Assuming the structure of ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ having $CE$-OO [17], ($12\frac{3}{2}$) intensity of 6000 is expected. (b) Temperature dependence of ($\frac{3}{4}\frac{7}{4}\frac{3}{2}$) (circles) and ($\frac{1}{2}\frac{3}{2}2$) (squares) intensity measured with incident x rays of 6.552 keV, on-resonant energy. The intensity of the latter is multiplied by a factor of 2.5 for presentation. The open and closed symbols correspond to the cooling and heating run, respectively. The inset shows the energy spectrum of the ($\frac{1}{2}\frac{3}{2}2$) reflection at 10 K.

Figure 4

(a) Schematic view of the orbital arrangement of $CE$-OO (bulk structure). The ${\mathrm{Mn}}^{4+}$ ions are indicated by white spheres, while ${\mathrm{Mn}}^{3+}$ ions with the $3x^2-r^2$ ($3y^2-r^2$) orbital are indicated by yellow (red) symbols. (b) The same as (a) but for the $AP$-OO (film structure). (c) The orbital arrangement of the first monolayer with $CE$-OO on the (011) substrate observed from the $[011]$ direction. (d) That for $AP$-OO. (e) The same as (c) but for the first two monolayers. Bottom figure shows the view from the $[\overline{1}00]$ direction. The $[011]$ planes, which are parallel to the surface of the substrate, and the $[001]$ planes are represented by green and gray transparent plates, respectively. (f) That for $AP$-OO.