Influence of the ionic size on the evolution of local Jahn-Teller distortions in cobaltites

The thermodynamic and atomic structure properties of ${\mathrm{La}}_{1-x}{A}_x\mathrm{Co}{\mathrm{O}}_3$ ($A={\mathrm{Ba}}^{2+}$ and ${\mathrm{Ca}}^{2+}$) with $0⩽x⩽0.5$, a class of compounds that exhibit magnetoresistance in the presence of an applied magnetic field, have been investigated via magnetic and transport measurements and neutron scattering. While in the parent compound, the ${\mathrm{Co}}^{3+}$ ion undergoes a spin-state transition from the low-spin ground state to a dynamic intermediate-spin configuration thermally, with hole doping, the intermediate-spin state becomes static as evidenced by the Jahn-Teller octahedral splitting of the Co-O bonds. The size of the split depends strongly on the tolerance factor, where small or no Jahn-Teller distortions are observed in samples with small tolerance factors (i.e., Ca), but as the tolerance factor approaches 1 (i.e., Ba), the bond split can be as much as $0.2\mathrm{\AA }$. At the same time, ferromagnetic ordering is also influenced by the tolerance factor. As it gets closer to 1, ferromagnetic coupling is enhanced due to the straightening of the Co-O-Co bonds, where the angle becomes almost 180° that, in turn, favors double-exchange interactions between Co ions. With the ferromagnetic transition, the system becomes metallic and shows a negative magnetoresistance with field. As the tolerance factor is reduced from 1, the ferromagnetic coupling is weak and the bond angle is about 160°.

Figure 1

(Color online) Magnetization and resistivity measurements for ${\mathrm{La}}_{0.8}{\mathrm{Ca}}_{0.2}\mathrm{Co}{\mathrm{O}}_3$. In (a), the magnetization is shown for different values of magnetic field as a function of temperature. It is evident that a ferromagnetic transition occurs at $T_c\sim 150\mathrm{K}$. The temperature at which the magnetization rises tends to increase with applied field. In (b), the resistivity is plotted for different values of magnetic field as a function of temperature. A broad hump is observed at $T_c$, and it is clear that the maximum of the hump shifts to higher temperature as the field is increased. As the temperature is decreased below $\sim 100\mathrm{K}$, the resistivity increases, indicating insulating behavior. The temperature at which the increase occurs is also dependent on the applied magnetic field.

Figure 2

(Color online) The transition temperature of LBCO as a function of $x$. The values of $T_c$ were determined from the magnetization measurements. Above $x=0.2$, changing the doping concentration has little effect on $T_c$. Representative magnetization data $(x=0.2)$ is shown in the inset under different applied fields.

Figure 3

(Color online) The scaled ${\left(001\right)}_c$ magnetic reflections as a function of doping for (a) LBCO and (b) LCCO. In LCCO, the Bragg peak first appears at $x=0.1$ and then saturates around $x=0.2$. On the other hand, in LBCO, the Bragg peak first appears at $x=0.2$ and continues to increase in intensity until $x=0.4$.

Figure 4

(Color online) Elastic scattering along $\left(00L\right)$ around (001) of $x=0.05$ of LCCO. At $5\mathrm{K}$, a broad ferromagnetic intensity appears, indicating the presence of static, short-range ferromagnetic correlations. In the inset, the ferromagnetic order parameter is shown by measuring the temperature dependence of the (001) Bragg peak.

Figure 5

(Color online) (a) The LCCO structural phase diagram. Circles indicate where data points were taken. The data points for $x=0.15$ are taken from Ref. 53. The fading between colors is intended to represent the uncertainty in the phase diagram. (b) The crystal model for the $R\overline{3}c$ phase. (c) The crystal model corresponding to the Pnma phase. Only the Co-O octahedra are shown.

Figure 6

(Color online) Results of the Rietveld refinement of LCCO as a function of temperature and concentration: (a) the unit cell volume and (b) the Co-O-Co bond angles. Values derived from the Pnma phase are shown in blue, while values from the $R\overline{3}c$ phase are shown in red. The unit cell volume for the Pnma phase has been divided by 2 due to the fact that it has twice as much volume as the $R\overline{3}c$ unit cell.

Figure 7

(Color online) Results of Rietveld refinement of LBCO as a function of temperature and concentration. The $R\overline{3}c$ lattice parameter, $\alpha$, is shown in (a). The deviation of $\alpha$ from the cubic value of 60° provides an indication of the degree of trigonal distortion. It is clear that either increasing the temperature or increasing the doping reduces the degree of trigonal distortion. In (b), the Co-O-Co bond angles are shown. These bonds significantly straighten with doping.

Figure 8

(Color online) (a) Experimental and model PDFs for ${\mathrm{La}}_{0.9}{\mathrm{Ba}}_{0.1}\mathrm{Co}{\mathrm{O}}_3$ at $12\mathrm{K}$. (b) The model partial PDFs indicate the pairs of atoms that contribute to the various peaks in the PDF. The sum of all the partial PDFs gives rise to the total model PDF and is compared to the experimental data of (a). Note that the first peak in the PDF has no other contribution than from the Co-O bonds.

Figure 9

(Color online) The first PDF peak corresponding to the Co-O octahedral bonds is shown at $T=12$, 300, and $500\mathrm{K}$ for the LBCO system at three different concentrations. The nearly symmetric peak at $12\mathrm{K}$ broadens asymmetrically at 300 and $500\mathrm{K}$ due to the formation of a shoulder on the right side. This is observed for all $x$.

Figure 10

(Color online) Gaussian fits of the Co-O experimental peak for LBCO at several different concentrations and as a function of temperature. The experimental data are shown in solid line and the Gaussian fits are shown in dotted lines.

Figure 11

(Color online) The Co-O bond length as a function of $x$ of the LBCO system. The bondlengths derived from fits of the PDFs are shown in solid circles, while the bond lengths from Rietveld refinement are shown in solid triangles.

Figure 12

(Color online) The percent of JT active sites in the LBCO system obtained from the integrated intensity of the area under the Co-O peaks at 12, 300, and $500\mathrm{K}$.

Figure 13

(Color online) The first PDF peak corresponding to the Co-O octahedral bonds is shown for LCCO at 10, 300, and $550\mathrm{K}$. The peaks are somewhat asymmetric, but are not as asymmetric and do not show a clear split as in the LBCO system.

Figure 14

(Color online) Gaussian fits of the Co-O experimental peak for LCCO at several different concentrations as a function of temperature. The octahedral Co-O bonds are reasonably well fitted with one Gaussian except for the $x=0.20$ at $550\mathrm{K}$, where a clear long Co-O bond length is observed.