Crystal structures, strain analysis, and physical properties of Sr${}_{0.7}$Ce${}_{0.3}$MnO${}_3$

We have studied the crystal structure of mixed-valence Sr${}_{0.7}$Ce${}_{0.3}$MnO${}_3$ from 4.2 to 973 K using high-resolution neutron powder diffraction. The crystal structure is tetragonal in space group $I$4/mcm at 4.2–923 K and cubic in $Pm\overline{3}m$ at T ≥ 948 K. Lattice parameters and Mn-O bond distances, obtained by Rietveld refinement, have been used to derive the spontaneous strains and MnO${}_6$ octahedral distortion, which are interpreted in terms of strain/order parameter coupling using a single Landau free-energy expansion for a $Pm\overline{3}m$ reference structure with two instabilities ($R_4^{+}$ and ${\Gamma }_3^{+}$). Two phase transitions were proposed: an octahedral tilting transition at $T_{c,\phi }$ $\sim$ 938 K ($Pm\overline{3}m$↔ $I$4/mcm, $R_4^{+}$), and an isosymmetric, electronically driven (Jahn-Teller–like) transition at $T_{c,JT}$ $\sim$ 770 K ($I$4/mcm, $R_4^{+}$ ↔ $I$4/mcm, $R_4^{+}$ and ${\Gamma }_3^{+}$). The nature of the tilting transition appears to be tricritical, while that of the Jahn-Teller–like transition is second order. In addition to the contributions from octahedral tilting and Jahn-Teller–like distortions, there is an excess octahedral distortion at temperatures below 250 K; this is speculated to be associated with an anomaly observed over the temperature range of 275–300 K in the heat-capacity measurements.

Figure 1

Neutron diffraction pattern recorded at 4.2 K from Sr${}_{0.7}$Ce${}_{0.3}$MnO${}_3$. The crosses represent the observed data, and the continuous line is the fit obtained by the Rietveld method using the tetragonal structure in $I$4/mcm. The vertical marks show the peak positions expected in this structure, and the line beneath the pattern records the difference between the observed and calculated patterns. $R$-point reflections are associated with out-of-phase tilting of the MnO${}_6$ octahedra. Arrows indicate where magnetic peaks are expected based on a C-type antiferromagnetic structure, as reported for Sr${}_{0.9}$Ce${}_{0.1}$MnO${}_3$.[8] The inset shows the perspective view along the $c$-axis of the structure, as prepared using the computer program ATOMS (Shape Software, 2003).

Figure 2

Temperature dependence of (a) the appropriately scaled lattice parameters $a_{\mathrm{pc}}$ ( $=$ $a$/$\sqrt{2}$) and $c_{\mathrm{pc}}$ ( $=$ $c$/2), and (b) the equivalent primitive cell volume for Sr${}_{0.7}$Ce${}_{0.3}$MnO${}_3$. The solid line in (b) is a fit to the data in the cubic phase using the equation $V_{\mathrm{o}}=V_1+V_2{\Theta }_{s1}\coth \frac{{\Theta }_{s1}}{T}$ with ${\Theta }_{\mathrm{s}1}$ fixed at 150 K (see text for details). The solid line in (a) is the reference parameter $a_{\mathrm{o}}$, obtained from $a_{\mathrm{o}}$ $=$ $V_{\mathrm{o}}$${}^{1/3}$. Note that experimental uncertainties are smaller than the size of the symbols used.

Figure 3

Temperature dependence of the fourth power of the octahedral tilt angle for Sr${}_{0.7}$Ce${}_{0.3}$MnO${}_3$. The solid line is a fit to the data using the Landau solution ${\phi }^4=A\frac{{\Theta }_{s2}}{T_{c,\phi }}[\coth \left(\frac{{\Theta }_{s2}}{T_{c,\phi }}\right)-\coth \left(\frac{{\Theta }_{s2}}{T}\right)]$,[15] with $A$ $=$ $1957.6^{\circ 4}$, ${\Theta }_{s2}$ $=$ 131.5 K, and $T_{c,\phi }$ $=$ 938.1 K.

Figure 4

Temperature dependence of the symmetry-adapted strains, $e_{\mathrm{t}}$ and $e_{\mathrm{a}}$. The irregularity of this unusual pattern of evolution shows clearly that there is more than one process contributing to the overall structural changes.

Figure 5

The tetragonal strain, $e_{\mathrm{t}}$, as a function of the square of the tilt angle (${\phi }^2$), showing an irregular dependence with a marked break in slope (corresponding to T $\sim$ 800 K). The straight line is a fit to data obtained at 803 ≤ T ≤ 923 K; it is within experimental uncertainty of passing through the origin.

Figure 6

Mn-O bond lengths as a function of temperature. The open circles, open triangles, and solid triangles represent the Mn-O distance for apical oxygens ($d_{\mathrm{Mn}-\mathrm{O}1}$), the Mn-O distance for equatorial oxygens ($d_{\mathrm{Mn}-\mathrm{O}2}$), and the bond distance in the cubic phase, respectively. The average Mn-O bond length in the tetragonal phase is also plotted (solid circles connected by straight lines). Vertical lines shown at 938, 800, and 293 K correspond, respectively, to the octahedral tilting transition temperature, the approximate position for the onset of additional octahedral distortions, and a peak in the heat capacity (see following section).

Figure 7

The octahedral distortion as a function of the square of the tilt angle (${\phi }^2$), showing a linear relationship between $T_{c,\phi }$ and $\sim$800 K. A straight-line fit in this temperature range gives the amount of distortion expected for a given tilt angle (−0.0001014${\phi }^2$). At $\mathrm{T}<250$ K, the octahedral distortion decreases further.

Figure 8

Excess octahedral distortion (including the “Jahn-Teller” component), calculated as the difference between the observed distortion and the contribution from octahedral tilting, as a function of temperature. Vertical lines are at the same temperatures as shown in Fig. 6.

Figure 9

The square of the excess octahedral distortion as a function of temperature. The solid curve is a fit to the data between 293 and 783 K using the equation ${\left(\mathrm{Octahedral}\mathrm{distortion}\right)}^2=A\frac{{\Theta }_{\mathrm{s}3}}{T_{\mathrm{c},\mathrm{JT}}}\left[\coth \left(\frac{{\Theta }_{\mathrm{s}3}}{T_{\mathrm{c},\mathrm{JT}}}\right)-\coth \left(\frac{{\Theta }_{\mathrm{s}3}}{T}\right)\right],$ giving $A$ $=$ 7.233 $\times$ 10${}^{-6}$, $T_{\mathrm{c},\mathrm{JT}}$ $=$ 770 K, and ${\Theta }_{\mathrm{s}3}$ $=$ 256 K.

Figure 10

Temperature dependence of the magnetic susceptibility (χ) and its reciprocal (χ${}^{-1}$) collected in the field-cooling (FC) and zero-field-cooling (ZFC) conditions. The solid line is a fit of the data using the Curie-Weiss (CW) law over the temperature range 390–300 K. The inset shows the hysteresis loop opening below $\sim$40 K in the $M$($B$) dependence.

Figure 11

The $C_{\mathrm{p}}$/$T$ ratio as a function of temperature. The solid line is a lattice contribution derived from the Debye approximation. Depicted in the inset are the magnetic contribution $\Delta C_{\mathrm{p}}$/$T$ and magnetic entropy $\Delta S_{\mathrm{m}}$ at temperatures below 120 K.