Shear Strain in ${\mathrm{Nd}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ at High Pressures

High-pressure x-ray powder diffraction has been measured on the half doped rare earth manganite ${\mathrm{Nd}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ up to a pressure of 15 GPa. We report the presence of a quantifiable amount of shear distortion of the ${\mathrm{MnO}}_6$ octahedra in ${\mathrm{Nd}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ at high pressures. The lattice strain of ${\mathrm{Nd}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ is minimal at a crossover pressure of $p^{*}\sim 7\mathrm{GPa}$, with the same lattice strain above and below this pressure achieved by shear and Jahn-Teller–type distortions, respectively. The increase in shear strain with increasing pressure provides a mechanism for the insulating behavior of manganites at high pressures that has not been considered before.

Figure 1

Pressure dependence of the crystal lattice of ${\mathrm{Nd}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$. (a) Lattice parameters. The solid lines have been obtained by a fit of a Birch-Murnaghan equation of state (EOS) to the individual lattice parameters; the linear compressibility $\beta$ along the three symmetry directions are indicated [17]. (b) Volume of the unit cell. The solid line is a fit to the Birch-Murnaghan EOS. (c) The evolution of WD (the solid line is a guide to the eye). (d) Volume of the ${\mathrm{MnO}}_6$ octahedra ($V_B$) normalized to their zero-pressure value ($V_{B_0}$). The dash-dotted line represents the volume of the unit cell normalized to the zero-pressure value [obtained from (b)].

Figure 2

Pressure dependence of the local strain of ${\mathrm{Nd}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$. (a) $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}$ distances in the $ac$ plane. The average of the two distances is also given. The dotted line is a guide to the eye. (b) $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}$ distance along the $b$ axis. The dotted line is a guide to the eye. The inset shows the pressure evolution of the $\mathrm{Mn}\mathrm{\text{−}}\mathrm{Mn}$ distance in the $ac$ plane (calculated from $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}$ distances and $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}\mathrm{\text{−}}\mathrm{Mn}$ angles). The solid line is the value calculated from the average $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}$ distance in the $ac$ plane. (c) Diagonal components of the local strain tensor. $e_{11}$ is the compression strain along the $b$ symmetry direction and $e_{22}$ and $e_{33}$ are the compression strains along the directions of $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}(2\mathrm{a})$ and $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}(2\mathrm{b})$, respectively. (d) Shear components of the local strain tensor. $e_{23}$ is the shear strain between $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}(2\mathrm{a})$ and $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}(2\mathrm{b})$. The shear strain elements $e_{12}$ and $e_{13}$ involve $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}$ along $b$ with $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}(2\mathrm{a})$ and $\mathrm{Mn}\mathrm{\text{−}}\mathrm{O}(2\mathrm{b})$, respectively. Error bars indicate one standard uncertainty. Data points at $p=4.36$ and 7.58 GPa were considered outliers and were removed from the plots.

Figure 3

Pressure dependence of strain in manganites. (a) ${\sigma }_B$ of ${\mathrm{Nd}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ (see text). (b) Ratio of the polyhedral volumes $V_A/V_B$ of ${\mathrm{Nd}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ (open circle and dashed line), ${\mathrm{LaMnO}}_3$ (open diamonds and dash-dotted line, from Ref. [9]), ${\mathrm{La}}_{0.75}{\mathrm{Ca}}_{0.25}{\mathrm{MnO}}_3$ (solid triangles and solid line, from Ref. 8). $V_A$ and $V_B$ are the polyhedral volumes of the $A$-site and $B$-site cations, respectively. $V_B$ for ${\mathrm{Nd}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ was calculated from the atomic coordinates of the oxygen atoms and the lattice parameters, while that for ${\mathrm{La}}_{0.75}{\mathrm{Ca}}_{0.25}{\mathrm{MnO}}_3$ and ${\mathrm{LaMnO}}_3$ was calculated from the average Mn-O distances and are likely to be slightly underestimated. The lines are obtained from the EOS fits of the unit cell volume and $V_B$ data, respectively.