Crystal and magnetic structure of ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}\mathrm{Mn}{\mathrm{O}}_4$: Role of the orbital degree of freedom

The crystal and magnetic structure of ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}\mathrm{Mn}{\mathrm{O}}_4$ $(0⩽x⩽0.6)$ has been studied by diffraction techniques and high resolution capacitance dilatometry. There is no evidence for a structural phase transition related to octahedron tilting like those found in isostructural cuprates or nickelates, but there are significant structural changes induced by the variation of temperature and doping which we attribute to a rearrangement of the orbital occupation.

Figure 1

Typical diffraction patterns obtained for the layered manganates: (top) a neutron powder diffraction pattern measured on the 3T.2 diffractometer for ${\mathrm{La}}_{0.75}{\mathrm{Sr}}_{1.25}\mathrm{Mn}{\mathrm{O}}_4$; (bottom) an x-ray diffraction pattern determined on a D5000-diffractometer. Points designate the intensity data, dark lines the profile fits, and fine lines the intensity differences. Vertical bars indicate the Bragg positions.

Figure 2

(a) Crystal structure of ${\mathrm{La}}_{1.0}{\mathrm{Sr}}_{1.0}\mathrm{Mn}{\mathrm{O}}_4$ at room temperature; (b) antiferromagnetic structure of ${\mathrm{La}}_{1.0}{\mathrm{Sr}}_{1.0}\mathrm{Mn}{\mathrm{O}}_4$; the two domains are shown (the ferromagnetic planes are shaded for the two domains); (c) schematic drawing of the $e_g$ orbital state in the pseudospin space. The angles $\theta =-2\pi ∕3$, $\pi$, $2\pi ∕3$, and 0 correspond to the $3y^2-r^2$, $x^2-y^2$, $3x^2-r^2$, and $3z^2-r^2$ orbitals, respectively.

Figure 3

(Upper panel) Temperature dependence of the lattice constants in ${\mathrm{La}}_{1.0}{\mathrm{Sr}}_{1.0}\mathrm{Mn}{\mathrm{O}}_4$ as a function of temperature (the arrow indicates the Néel temperature). The inset shows the temperature dependence of the lattice constants in ${\mathrm{La}}_{0.875}{\mathrm{Sr}}_{1.125}\mathrm{Mn}{\mathrm{O}}_4$ where Néel order occurs at $\sim 62\mathrm{K}$. (Lower panel) Thermal expansion coefficient (parallel and perpendicular to the $\mathrm{Mn}{\mathrm{O}}_2$ layers) determined by capacitance dilatometry and the normalized intensity of the antiferromagnetic superstructure reflection (0.5 0.5 0) measured by neutron diffraction for ${\mathrm{La}}_{1.0}{\mathrm{Sr}}_{1.0}\mathrm{Mn}{\mathrm{O}}_4$ (left) and for ${\mathrm{La}}_{0.875}{\mathrm{Sr}}_{1.125}\mathrm{Mn}{\mathrm{O}}_4$ (right).

Figure 4

Doping dependence of the lattice parameters (a), the Mn-$\mathrm{O}$ bond lengths (b), the ratio of the two Mn-$\mathrm{O}$ bond lengths (c), and the three distinct bond lengths in the $(\mathrm{La},\mathrm{Sr}){\mathrm{O}}_9$ polyhedron (d) for the series ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}\mathrm{Mn}{\mathrm{O}}_4$. Calculated bond-valence sum for the central Mn-ion (e) [closed circles denote the values obtained with the split bond lengths, open circles those calculated with the average Mn-$\mathrm{O}$ bond length and stars values calculated for $\mathrm{La}\mathrm{Mn}{\mathrm{O}}_3$ (Ref. 25) and ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{0.5}\mathrm{Mn}{\mathrm{O}}_3$ (Ref. 34)], and bond valence sums for the La/Sr place (f). Drawn lines are guides to the eye. All data are taken at room temperature if not specified.

Figure 5

Temperature dependence of the lattice parameters in ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}\mathrm{Mn}{\mathrm{O}}_4$ for concentrations $x⩾0.25$.

Figure 6

Anisotropic displacement parameters of the two oxygen sites as function of temperature and doping. Note that ${\mathrm{U}}_{22}\left(\mathrm{O}1\right)$ and ${\mathrm{U}}_{33}\left(\mathrm{O}2\right)$ correspond to the displacement of the oxygen parallel to the bonds.