Impact of Jahn-Teller active Mn${}^{3+}$ on strain effects and phase transitions in Sr${}_{0.65}$Pr${}_{0.35}$MnO${}_3$

The mixed-valence manganite Sr${}_{0.65}$Pr${}_{0.35}$MnO${}_3$ has been prepared and its crystal and magnetic structure investigated between 7 and 1200 K using high-resolution powder neutron diffraction. The structural and lattice parameter data have been used to determine the octahedral tilting and spontaneous strains associated with the structural, electronic, and magnetic phase transitions. At room temperature, the structure is tetragonal and is characterized by cooperative out-of-phase tilts of the MnO${}_6$ octahedra about the $c$ axis and a large Jahn–Teller-type distortion due to the presence of Mn${}^{3+}$. The sample exhibits a reversible phase transition from the cubic $Pm\overline{3}m$ perovskite to a tetragonal $I$4/mcm structure at 750 K. The $Pm\overline{3}m$ ↔ I4/mcm phase transition is continuous, and the tetragonal strain, which is dominated by the Jahn–Teller-type distortion of the MnO${}_6$ octahedra, exhibits an unusual $e_{\mathrm{t}}$${}^{0.5}$ ∝ ($T_c$ $-$ $T$) temperature dependence. At low temperatures, a C-type antiferromagnetic structure develops with a Neel temperature $T_N$ of 250 K. The Mn magnetic moment at 7 K is 2.99(2) ${\mu }_B$/Mn. The magnetic ordering introduces additional tetragonal strain, and this strain shows the expected quadratic dependence on the magnetic moment at low temperatures. An increase in the octahedral tilt angle at $T_N$ demonstrates an effective coupling between the magnetic ordering process and octahedral tilting.

Figure 1

Observed, calculated, and difference neutron diffraction patterns for Sr${}_{0.65}$Pr${}_{0.35}$MnO${}_3$ at 7, 260, and 1000 K. The crosses represent the data, the red/dark gray line is the calculated profile, the green/medium gray line is the difference profile, and vertical markers are the allowed Bragg reflections. The inserts (a) and (b) are representations of the refined cubic ($Pm\overline{3}m$) and tetragonal ($I$4/mcm) structures, respectively, where Sr,Pr; Mn; O. The inset (c) highlights the quality of both the neutron diffraction data and the fit.

Figure 2

Temperature dependence of ordered magnetic moments in C-type AFM ground states of Sr${}_{0.65}$Pr${}_{0.35}$MnO${}_{3.}$ The solid line is a fit to a Brillouin function [Eq. (1)] with $T_N$ $=$ 255 K. The inset illustrates the Mn spin alignment in the C-type AFM ground state.

Figure 3

Temperature dependence of the reduced lattice parameters $a_{\mathrm{e}}$ ≈ $a_{\mathrm{p}}/\sqrt{2}$ and $c_{\mathrm{e}}$ ≈ $a_{\mathrm{p}}/2$ of Sr${}_{0.65}$Pr${}_{0.35}$MnO${}_3$. The hollow symbols are from data collected during recooling the sample. Where not apparent, the estimated standard deviations are smaller than the symbols. The solid lines are fits from an equation of the form V${}_{\mathrm{o}}$ $=$ V${}_1$ $+$ V${}_2$$\Theta$coth($\Theta$/$T$), where $\Theta$ $=$ 110 K; see text for details.

Figure 4

Temperature dependence of the Mn-O bond lengths in Sr${}_{0.65}$Pr${}_{0.35}$MnO${}_3$. The hollow symbols are from data obtained during recooling of the sample. Where not apparent, the esds are smaller than the symbols. The solid line is a fit of the bond distances in the cubic phase to an equation similar to Eq. (2), and the dashed line is the average Mn-O distance.

Figure 5

The temperature dependence of (a) the volume strain $e_{\mathrm{a}}$ and (b) the tetragonal shear strain $e_{\mathrm{t}}$.

Figure 6

Temperature dependence of $e_{\mathrm{t}}$${}^{0.5}$ illustrating linear dependence in the paramagnetic region${}_{.}$ The line is a fit to an equation similar to Eq. (2) using data points between 250 and 700 K; $\Theta$ was fixed at 110 K.

Figure 7

Temperature dependence of the square of tilt angle, $\Phi$${}^2$ in Sr${}_{0.65}$Pr${}_{0.35}$MnO${}_3$. The hollow symbols are from data obtained during recooling of the sample. The solid line is a linear fit to data between 430 and 680 K, which extrapolates to zero at 732 K.

Figure 8

(a) Temperature dependence of the distortion parameter $\Delta d=\frac{1}{\sqrt{3}}\left(\frac{2d_{\mathrm{Mn}-\mathrm{O}1}-2d_{\mathrm{Mn}-\mathrm{O}2}}{\left(1/3\right)\left(d_{\mathrm{Mn}-\mathrm{O}1}+2d_{\mathrm{Mn}-\mathrm{O}2}\right)}\right)$ in Sr${}_{0.65}$Pr${}_{0.35}$MnO${}_{3.}$ (b) The tetragonal distortion varies linearly with $\Phi$${}^4$ at high temperatures, but there are anomalies associated with changes in magnetic properties evident at lower temperatures. The solid line in (b) is a linear fit to the high temperature data.

Figure 9

(a) The square root of the tetragonal strain $e_{\mathrm{t}}$ shows a linear dependence on the square of the tilt angle at high temperatures. At low temperatures, this relationship breaks down due to the influence of magnetic interactions. The straight line is a fit to the data between 450 and 670 K. (b) The volume strain $e_{\mathrm{a}}$ shows a linear dependence on the square of the tilt angle, except at low temperatures, where magnetic effects become important.

Figure 10

Relationship between the excess tetragonal strains estimated from the data shown in Fig. 6 and the square of the magnetic moment per Mn obtained from the neutron diffraction data. The solid line is a linear fit constrained to pass through the origin.

Figure 11

Temperature dependence of magnetic susceptibility χ($T$) of Sr${}_{0.65}$Pr${}_{0.35}$MnO${}_3$ recorded with an applied magnetic field of 0.5 T. The solid line is the Curie–Weiss law fit (for details, see the text). The inset shows the field cooled (FC)–zero-field cooled (ZFC) curves at the vicinity of the $T_N$ $=$ 150 K.

Figure 12

Field dependencies of magnetization $M$ collected at various temperatures. The inset shows the full hysteresis curve obtained at 15 K.

Figure 13

Temperature dependence of heat capacity $C_{\mathrm{p}}$($T$) of Sr${}_{0.65}$Pr${}_{0.35}$MnO${}_3$. Inset shows the $C_{\mathrm{p}}$/$T$ ratio.