Effect of ionic size on the orbital ordering transition in RMnO3+δ

We present high-temperature powder x-ray diffraction data of the orbital-order-induced structural distortion of RMnO3, with R a rare earth element. The associated phase transition takes place in a temperature interval of ≈200 K in which the orbitally ordered phase and the orbitally disordered phase coexist. We analyse the evolution of the RMnO3 perovskite structure with the size of the rare-earth ion and with temperature. We show that the rotation of the MnO6 octahedra stabilizes the cooperative Jahn–Teller distortion to higher temperature.


Introduction
The rare-earth perovskites RTO 3 , with R a rare-earth element and T a transition metal, have been intensively studied because of their wide variety in physical phenomena such as superconductivity, ferroelectricity and colossal magnetoresistance. In all these phenomena, the electronic properties are intimately related to the lattice. Many of the interesting phenomena involve a complex interplay between the spin, charge and orbital degrees of freedom, accompanied with subtle displacements in the crystal lattice. While it is commonly accepted that spin and charge determine the electronic properties in perovskites, it has become of recent interest to study the consequences of orbital degeneracy on physical properties.
In RMnO 3 perovskites, the degeneracy of the e g orbital is removed by a cooperative Jahn-Teller (JT) distortion below a transition temperature T JT . This distortion results in a long-range ordering of the occupied 3d 3x 2 −r 2 and 3d 3y 2 −r 2 orbitals. The most extensively studied compound throughout the RMnO 3 series, i.e. LaMnO 3 , exhibits a structural phase transition at T JT ≈ 800 K [1,2]. The orbital ordering induces changes in the crystal structure and has pronounced effects on the electronic properties. This transition is associated with drastic changes in the resistivity, thermo-electric power, and thermal conductivity [3]. This behaviour is associated with two consecutive transitions with decreasing temperature from an orbitally disordered, via a shortrange ordered regime, T * < T < T JT , to a long-range orbitally ordered state [3]. Furthermore, these authors suggest that the phase transition changes from first order for LaMnO 3 to second order for smaller rare earth ions, i.e. NdMnO 3 and PrMnO 3 [3]. In contrast with the interpretation of these transport experiments, structural studies indicate that all the phase transitions are first order, with a varying temperature range of hysteresis [2,4,5]. Thus the nature of the phase transition and the effect of ionic size of the rare earth ion remain subjects to debate.
Although the room temperature (RT) crystal structure was studied in great detail [6,7] for all the members of all the RMnO 3 compounds, the high-temperature structural behaviour has been much less analysed. It is clear from local probe techniques that local Jahn-Teller distortions persist above the ordering transition. In principle, the orbital order-disorder transition can be either first order, with no restriction on the symmetry relation between the two states, or second order, in which case the symmetry relation should be a group-subgroup relation. For the t 2gbased systems, a number of cases have been studied. Here, the orbital ordering takes place below room temperature. For various RVO 3 perovskites, the orbital order-disorder transition is second order, and at a distinctly different transition temperature than the magnetic ordering. The symmetry of the orbitally ordered state is still subject to intense study. For the RTiO 3 systems, the situation regarding the symmetry is less clear. For some systems, orbital ordering has been reported, but further studies seem necessary. For the e g -based manganites both firstand second-order transitions have been reported. The situation is experimentally more easy, because the JT distortions are typically five times larger than for t 2g -based systems. It is widely accepted that for the manganites the orbital and magnetic ordering take place at different transition temperatures.
For a better understanding of the nature of the orbital ordering and the relationship with the electronic properties in RMnO 3 , detailed high-temperature structural studies are of significant importance. Here, we present the results of the high-temperature structural study in NdMnO 3 using powder x-ray diffraction (PXD) experiments. Combining our work with earlier studies, we find that a smaller rare-earth ionic radius stabilizes the cooperative JT distortion to higher temperature in RMnO 3 perovskites.

Experimental procedures
Polycrystalline samples of NdMnO 3 were prepared by conventional solid-state reaction by mixing stoichiometric amounts of Nd 2 O 3 and MnO 2 . The Nd 2 O 3 is very sensitive to carbon dioxide and moisture, and was dried before use at 1000 • C overnight. The obtained powders were heated in air at 1200 • C overnight. In order to avoid the formation of unwanted Mn 4+ (i.e. NdMnO 3+δ ), the heating process was done in a nitrogen atmosphere. The temperature-dependent PXD experiments were performed on a Bruker-D8 diffractometer, using Cu-K α 1 radiation for 20 • < 2θ < 65 • and a step size of 2θ = 0.04 • with 30 s per step. The temperature was controlled using an Anton-Paar TDK-1600 with kapton windows either in air or in a vacuum of 10 −2 mbar.

Experimental results
The crystal structure of RMnO 3 perovskites distorts from the cubic parent structure due to the small radius of the R-ion. The RO 3 sublattice originates from a fcc packing of anions, common to many ionic solids (such as MgO), by replacing the face centred anions by R 3+ . This results in an oxygen sublattice of corner-sharing octahedra. Because the ionic size of R 3+ is smaller than that of O 2− , the cubic scaffold distorts. The resulting cooperative buckling and tilting of the cornersharing octahedra yield for RMnO 3 at room temperature the orthorhombic Pbnm symmetry (figure 1). These distortions are known as the GdFeO 3 distortions [8,9]. Besides the rotations, the oxygen octahedra can distort due to the degeneracy of the high-spin d 4 configuration of the Mn 3+ ions, without reducing the Pbnm symmetry further. Thus, one distinguishes two substructures with orthorhombic space group Pbnm, denoted as the O-and O -structures. For the O-structure, the distortion consists of GdFeO 3 rotations of the octahedra, and thus c/ √ 2 > a and a < b. The O -orthorhombic structure is obtained if a cooperative JT distortion superimposes on the rotation of the MnO 6 octahedra. Here, the relation between the unit cell parameters is c/ √ 2 < a < b [10,11]. Thus, one can distinguish between these two structures by comparing the a and c/ √ 2 orthorhombic unit cell parameters.
In this paper we will show that these two types of cooperative distortions are related. We can vary the rotation by the ionic size of the R 3+ -ion. We will show that the ordering temperature of the orbital degree of freedom increases significantly with decreasing R 3+ ionic size, even though the magnitude of the JT distortion is not influenced by the R 3+ ionic size.
We study the high-temperature structure of NdMnO 3 by performing PXD experiments in air and in vacuum in the temperature interval 300-1473 K. The transition from the O to O structure is expected to be reflected in the temperature dependence of the lattice parameters.
The structural refinement at RT was performed in space group Pbnm. We used the structural parameters taken from [6] as a starting point. The oxygen displacements and the Debye-Waller factors have a large influence on the intensities of the weak peaks of the powder patterns. The measured intensity to background ratio of these peaks is low, leading to difficulties in separating the contribution of the oxygen displacements from the contribution of the Debye-Waller factors. Therefore we cannot accurately refine the oxygen positions for a quantitative determination of the bond lengths and angles and thus of the JT distortion parameter and rotation parameter.
All peaks could be indexed with Pbnm symmetry at all temperatures over the entire range 20 • < 2θ < 65 • . Regardless of the precise refinement of the oxygen fractional coordinates, the positions of the peaks enable a refinement of the lattice parameters with high accuracy. Thus we performed our refinements by fixing the oxygen positions at the RT values taken from [6] and by refining the following parameters: scale factor, background coefficients, zero-point error, unit cell parameters and Gaussian parameters. The peak profiles were very well reproduced by a Gaussian peak shape. For all the measured patterns, the refinements proceeded smoothly, and we noted no indication for considering a different symmetry.
From the evolution of the lattice parameters, the structural change from the orbitally ordered in the temperature dependence of the lattice parameters and of the molecular volume at the transition between the two phases indicates a first-order phase transition. The structural phase transition is attributed to the orbital order-disorder transition, occurring in the temperature interval ≈1023 < T < 1223 K. The coexistence of the O and O phases in a temperature interval is in agreement with an earlier structural study [4]. Furthermore, recent transport measurements [3] observed a large drop of the thermoelectric power over a temperature interval denoted by the authors as T * < T < T JT . The two temperatures, i.e. T * and T JT , are interpreted by them as the transition temperatures for the melting of the cooperative orbital ordering and for setting in of the short range orbital ordering of the occupied e g orbitals of the MnO 6 octahedra, respectively. The differences in the transition temperature intervals reported in these studies, i.e. 873 < T < 1023 K [4] and 800 < T < 1123 K [3], compared with our results obtained from the measurements performed in air, i.e. ≈1023 < T < 1223 K, can be the result of different amounts of Mn 4+ impurities, due to differences in stoichiometry. Exposure to air at high temperatures will introduce non-JT active Mn 4+ ions, which will reduce the orbital order-disorder transition temperatures. The coexistence of the O -and O-orthorhombic phases over a temperature interval was also observed for LaMnO 3 [2], PrMnO 3 [5] and SmMnO 3 [4]. By comparing the results of the high-temperature structural study in LaMnO 3 with the results obtained in the detailed study of La 1−x Ca x MnO 3 , it can be inferred that the width of the temperature interval in which the two phases coexist, depends on x, decreasing from ≈200 K for x = 0.19 [12] to 10 K for x = 0 [2].
We analysed the effect of the Mn 4+ ions on the JT transition by comparing the measurements performed in air with measurements performed in vacuum (10 −2 mbar). We used the lattice parameters of the Pt-heater stripe sample holder and a Pt-Rh 10% thermocouple as temperature gauges. We observe that the temperature dependence of the lattice parameters of the platinum in both air and vacuum is the same within the standard deviation. This shows that no systematic 1273 K temperature errors occur between measurements in air and in vacuum. We notice that in vacuum, the orbital order-disorder transition in NdMnO 3 occurs in the temperature interval 1200-1400 K which is 200 K higher than the interval measured in air. This result is evidence that the measurements in air probe oxidized NdMnO 3+δ with δ ≈ 0.2. This introduces non-JT active Mn 4+ ions. Although our results indicate that the measurements performed in vacuum are less sensitive to the formation of Mn 4+ , in the following we will refer to the transition interval resulting from the measurements performed in air. This allows us to compare our results to the reports in the literature [1,2,4,5].  Figure 4. Rotation of the MnO 6 [6,7] and FeO 6 [14] octahedra of RMnO 3 and RFeO 3 , respectively, versus the R ionic radius at RT. The lines are guides for the eye.
As our data do not allow the refinement of the fractional coordinates of the oxygen positions, we cannot determine the temperature dependence of the rotation and JT distortion. However, from the evolution of the unit cell parameters we can conclude that the JT parameter decreases to zero at the temperature at which the orbital ordering is completely suppressed, i.e. 1273 K. This is analogous to LaMnO 3 . The large difference between the a, b and c/ √ 2 at 1273 K indicates a large rotation parameter above the transition. This is in contrast with the result obtained above T JT in LaMnO 3 with a ≈ b ≈ c/ √ 2 [1,13]. This difference can be ascribed to the smaller ionic radius of Nd 3+ than of La 3+ .

Discussion
In order to understand the high temperature behaviour of the different RMnO 3 perovskites, we first discuss the evolution of the rotation and JT distortion of the oxygen octahedra with the size of the R ion. The RT structure of RMnO 3 (R = La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Y, Er) was studied in great detail by Alonso et al [6] and by Mori et al [7]. The contribution of each of the two parameters is obtained by comparing the RMnO 3 series with the non-JT series RFeO 3 [14].
The rotations of the octahedra are reflected in the deviation from 180 • of the Mn-O-Mn tilting angle. The distortions associated with the JT effect are of two types and are denoted by Q2 and Q3. The Q3 is a tetragonal distortion which results in an elongation or a contraction of the MnO 6 octahedron corresponding to the filled 3z 2 − r 2 orbital or x 2 − y 2 orbital, respectively. The Q2 is an orthorhombic distortion obtained by a certain superposition of the 3z 2 − r 2 and x 2 − y 2 orbitals. The distortion modes characterizing the JT effect are defined as: Q2 = 2(l − s)/ √ 2 and Q3 = 2(2m − l − s)/ √ 6 with l and s the long and short Mn-O distances in the ab plane and m the medium out of plane Mn-O bond length [15,16].
In figure 4 we plot the rotation parameter for RMnO 3 [6,7] and RFeO 3 [14,17] as a function of the size of the R-ion. The rotation parameter, defined as the deviation of the T-O-T tilting and −Q3 components of the JT distortion versus the R ionic radius. We used the data from [6,7].
angle from 180 • , shows for both systems a linear increase with decreasing R-ionic radius. In figure 5(a) we plot the long (l), medium (m), short (s) and average Mn-O bond lengths versus the R-ionic radius. The medium bond length m deviates from the average bond length, such that m < (l + s)/2. This indicates that the JT distortion is not a purely Q2-type, but also partially Q3-type. Thus the distortion of the octahedra is defined by the deviation of the Mn-O distances from the average d value: = (1/6) n=1,6 [(d n − d )/ d ] 2 [16]. Figure 5(b) shows that is similar for all R ions except for La 3+ . The authors of [6] suggest that the deviation from the common value for YMnO 3 and ErMnO 3 results from the presence of significant amounts of Mn 4+ ions due to the syntheses conditions (a O 2 flow was used to minimize the formation of the RMnO 3 hexagonal phase). The ionic size dependence of the Q2 and Q3 components of the JT distortion are shown in the inset of figure 5( [6,7] and RFeO 3 [14,17]  ab plane and a medium out-of-plane Mn-O 1 (m) bond length) and does not change significantly with the size of the R ion. From the above relations we can evaluate the effect of the R-ionic radius on the lattice parameters in RFeO 3 [6,7] and RMnO 3 [14,17] shown in figures 6(a) and (b). In the RFeO 3 perovskites, the rotation distorts the parent cubic structure to the O structure with b > c/ √ 2 > a. Moreover, with decreasing R-ionic radius, the c/( √ 2a) ratio increases, driven by the increased tilting of the octahedra. For the RMnO 3 perovskites, the cooperative JT distortion gives the O structure with c/ √ 2 < a < b. From figure 4, we observe that the rotation is similar for RFeO 3 and RMnO 3 for a given R. Thus the change in c/( √ 2a) and b, is mainly affected by the JT distortion. The JT distortion for RMnO 3 perovskites is almost independent of the R-ionic size (see figure 5(b)). hatched area represents an extrapolation to small R-ionic radii of this coexistence region. We used the data from [2] for LaMnO 3 , from [5] for PrMnO 3 and from [4] for NdMnO 3 to DyMnO 3 .
of different RMnO 3 [3]- [5]. This shows that the orbital order-disorder transition occurs over a temperature interval T * < T < T JT in which the two Pbnm structures, i.e. O and O, coexist (the data were taken from [2,4,5]). We observe in figure 7 that the transition temperature T JT increases with decreasing R-ionic size. However, the JT parameter ( figure 5(b)) shows a very small change with the R-ionic radius. The difference between the lattice parameters, i.e. a, b and c/ √ 2 above T JT , and thus the rotation above T JT , increases with decreasing R-ionic radius. This shows that the rotation of the octahedra stabilizes the orbitally ordered state to higher temperatures. However, the magnitude of the JT distortion is not significantly affected by this rotation.

Conclusions
High-temperature x-ray powder diffraction of NdMnO 3 indicates that the orbital order-disorder transition takes place within a temperature interval of 1000 < T < 1200 K. In this interval, the orbitally ordered O phase coexists with the orbitally disordered O phase. The discontinuity in the temperature dependence of the lattice parameters and of the molecular volume at the transition between the two phases proves a first-order phase transition. Moreover, we found that for the measurements performed in air, the orbital order-disorder transition occurs 200 K lower than for the measurements performed in vacuum. Thus the measurements in air probe an oxidized phase NdMnO 3+δ , which introduces non-JT-active Mn 4+ ions.
With decrease in R-ionic size, the orbital order-disorder transition temperatures T * and T JT increase significantly. In contrast, the magnitude of the JT distortion shows a very small variation with the R-ionic radius. We conclude that the rotation of the MnO 6 octahedra is responsible for the stabilization of the cooperative JT distortion to higher temperatures.