Orbital-order phase transition in ${\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ probed by photovoltaics

The phase diagram of ${\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ (PCMO) is modified for $x\le 0.3$, which suggests a reevaluation of the phase diagram of other manganites in that doping region. Rather than an orbital-ordered phase reaching up to high temperatures of ∼800–1100 K, we propose a loss of spontaneous orbital order near room temperature. Above this temperature, the phase is characterized by a finite orbital polarization and octahedral tilt pattern. The tilt pattern couples to the Jahn-Teller distortion and thus induces a remaining orbital order, which persists up to high temperatures, where the tilt order is lost as well. This explains the experimental observation of orbital order up to high temperatures. The reevaluation of the orbital-order transition is based on observed anomalies of various physical properties at temperatures of 220–260 K in epitaxial thin films of PCMO $x=0.1$, i.e., in the photovoltaic effect, electric transport, magnetization, optical, and ultrafast transient pump probe studies. Finite-temperature simulations based on a tight-binding model with carefully adjusted parameters from first-principles calculations exhibit an orbital-order phase transition at $T_{\mathrm{OO}}\approx 300\mathrm{K}$ for PCMO $x=0.1$. This is consistent with the experimental observation of temperature-dependent changes in lattice parameter for bulk samples of the same doping at 300 K for $x=0.1$ and 350 K for $x=0$, typical for second-order phase transitions. Since our reassignment of the orbital-order phase transition toward lower temperature challenges a well-established and long-accepted picture, we provide results of multiple complementary measurements as well as a detailed discussion.

Figure 1

Ordered states and onset of polaron photovoltaic effect in ${\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ (PCMO). (a) Phase diagram in zero magnetic field according to Refs. [8, 9, 10]. Our results on the onset of polaron photovoltaic effect are indicated by yellow circles. Inset: Schematic sketch of orbital-ordered structure of alternating orbitals for PMO. (b) Temperature dependence of the open circuit voltage $U_{\mathrm{oc}}\left(T\right)$ in ${\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3-\mathrm{Sr}{\mathrm{Ti}}_{1-y}{\mathrm{Nb}}_y{\mathrm{O}}_3$ heterojunctions for $x=0.1$, 0.34, and 0.95 for monochromatic photon excitation of lowest manganite transitions. The onset of linear increases coincides with the antiferromagnetic ($x=0.95$) and the charge-order/orbital-order phase transitions ($x=0.34$) [11]. As it is shown in this paper, the onset for PCMO $x=0.1$ reflects the onset of spontaneous orbital order which is at 220–260 K in thin films and at 300 K in the bulk.

Figure 2

Photovoltaic properties of the PCMO $x=0.1$/STNO junction at the orbital-order phase transition. (a) Cross-plane current voltage characteristics above ($T=240\mathrm{K}$) and below ($T=200\mathrm{K}$) the phase transition in the dark and under polychromatic illumination. (b) Temperature dependence of open-circuit voltage $U_{\mathrm{oc}}$ and short-circuit current density $J_{\mathrm{sc}}$ measured under different spectral illumination ranges: $E_{\max }=1.6\mathrm{eV}$, $E_{\max }=2.0\mathrm{eV}$, and polychromatic illumination.

Figure 3

Temperature dependence of in-plane resistivity and logarithmic derivative $E_A$ in zero magnetic field as well as magnetic field of ${\mu }_{0}H=9\mathrm{T}$ for a PCMO $x=0.1$ film on (100) STO, postannealed for 20 h at 900 °C. The magnetic field was applied perpendicular to the substrate, i.e., parallel to the dominating [001] direction.

Figure 4

Temperature dependence of magnetization and magnetic susceptibility of PCMO $x=0.1$ films on STO. The data are corrected with respect to substrate contributions, and the magnetic field is applied parallel to the substrate. (b) Temperature dependence of field-cooled magnetization in Bohr magnetons per unit cell for different applied fields. The inset shows the hysteric behavior of field-dependent magnetization at 10 K. Temperature dependence of the DC magnetic susceptibility at two different applied fields. The inset shows the residuum of the experimental data with respect to a linear fit of $1/{\chi }_{\mathrm{PCMO}}$ at temperatures T > 300 K.

Figure 5

Temperature dependence of optical absorption of a PCMO $x=0.1$ film on (100) STO under top-side illumination. (a) Spectral dependence of the absorption coefficient $\alpha$ ($E_{ph}$) at various temperatures. (b) Temperature dependence of the optical bandgap $E_g$ deduced from Tauc plots.

Figure 6

Pump-probe transmission experiment for PCMO $x=0.1$ film on MgO (100). (a) Transient transmission at different sample temperatures between 20 and 300 K for an incident fluence of $3.2\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$. (b) Change in the signal decay time τ back to the initial state with temperature showing a decrease with increasing temperature. A small anomaly is observed ∼200 K. (c) Transient transmission change at ∼90 ps delay for a combined cooling and heating temperature cycle with small temperature steps. The data are normalized to the value of the transient transmission change at 20 K. The strong anomaly observed for temperatures >170 K is due to a phase transition with hysteretic effects on temperature cycling.

Figure 7

Sketch of the orbital structures occurring in the low-temperature phase at $x\approx 0.1$. We mainly observe the ${\mathrm{PrMnO}}_3$-like alternating orbitals $d_{z^2-x^2}/d_{z^2-y^2}$, together with clusters combining alternating hole and $d_{x^2-y^2}$ orbitals. Orbitals drawn with a smaller scale indicate a reduced orbital polarization, which can occur on sites between the two types of orbital ordering.

Figure 8

(a) Order parameter $C_Q^{\mathrm{av}}\left(\frac{2\pi }{a},0\right)$ for the orbital-order transition in PCMO $x=0.1$ as a function of temperature obtained in our simulations, scaled to its ground state value. Six simulation runs are shown for each temperature. The system was first heated from the ground state to nonzero temperatures, shown with red crosses. The system was subsequently cooled from the 400 K heating calculations to lower target temperatures (cooling 1), and in a second step from the 200 K cooling calculations back to 20 K (cooling 2), shown with blue squares and magenta circles, respectively. More details on the heating and cooling cycles are provided in the Supplemental Material [38]. (b) In-plane Jahn-Teller correlation function $C_Q^{\mathrm{av}}\left(q_a,q_b\right)$ of a typical heating simulation close to the ground state (20 K), during the transition (280 K), and above the transition (400 K). The white dotted line marks the shape of the reciprocal unit cell. The peaks have been broadened by a Gaussian. Near the ground state, we clearly see the ${\mathrm{PrMnO}}_3$-like alternating orbital structure at $\left(q_a,q_b\right)=\left(\frac{2\pi }{a},0\right)$, respectively, $\left(q_a,q_b\right)=\left(0,\frac{2\pi }{b}\right)$. At 400 K, nearly all possible diffraction spots of our unit cell have the same weight.

Figure 9

Temperature-dependent x-ray diffraction (XRD) analysis of polycrystalline bulk ${\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ samples with $x=0$ and 0.1. (a) Intensity distributions of (004) PCMO $x=0$ reflections at different temperatures. The data are normalized to the position and the height of the intensity maximum. (b)–(d) Temperature dependence of lattice parameters of PCMO $x=0$ and PCMO $x=0.1$. The lattice parameters correspond to Pbnm notation and are converted into a pseudocubic setting to facilitate the quantitative comparison.

Figure 10

(a) Change of Jahn-Teller modes $\mathrm{\Delta }{Q}_3$ and $\mathrm{\Delta }{Q}_2$ relative to the room temperature values as well as octahedral tilt angle for PCMO $x=0$ (closed symbols) and PCMO $x=0.1$ (open symbols). (b) Pseudocubic lattice parameters corresponding to the $\mathrm{\Delta }{Q}_2$, $\mathrm{\Delta }{Q}_3$, and tilt angle $\theta$ shown in (a) (symbols) as well as the experimentally obtained values replotted from Fig. 8 (lines).

Figure 11

Order parameters for the free energy of Eq. (8) as a function of temperature. The full line describes the orbital-order parameter $x$, and the dashed line represents the tilt angle. Both are scaled to their low-temperature value without coupling. The dotted lines show the order parameters in the absence of coupling.

Figure 12

Proposed modified bulk phase diagram of PCMO: Data points included in the phase diagram are based on the following published results [7, 8, 9, 16, 17, 76, 79, 80, 81] and are listed in Appendix pp3. For undoped $x=0$ and low-doped $x=0.1$, our experimental results based on temperature anomaly of lattice parameters are shown (squares). In addition, the results from theoretical simulations (crossed out squares) redefine the low-doped region. The data points for the high-temperature phase transition are included: For undoped PCMO $x=0$ (1) is an observed change in the thermoelectric power [30], (2) an O/O′ transition [73], and (3) the disappearance of residual orbital order measured by resonant x-ray spectroscopy for PCMO $x=0.25$ [64]. Note that various magnetic subphases are not indicated; see Refs. [8, 9, 37] as well as possible changes in properties of the polaron liquid/glass phases as a function of doping found in other manganites [82]. Since induced orbital order is different from spontaneous orbital order, it is not indicated as a true phase, as discussed in the text.

Figure 13

Temperature dependence of different contributions to the magnetic moment at $B_0=200\mathrm{mT}$. $m_{\mathrm{STO}}$: blank STO substrate (black symbols). $m_{\mathrm{tot}}$: PCMO $x=0.1$ on STO (red symbols). Difference $m_{\mathrm{tot}}-m_{\mathrm{STO}}$ (blue symbols). $m_{\mathrm{film}}$: paramagnetic PCMO $x=0.1$ contribution (green line). $\mathrm{\Delta }{m}_s$: temperature-independent contribution due to STO surface ferromagnetism (black line).