Structure and phase transitions in A -site ordered RBaMn2 O6 (R=Pr, Nd) perovskites with a polar ground state

PHYSICAL REVIEW B 103, 064105 (2021) Structure and phase transitions in A-site ordered RBaMn2O6(R=Pr, Nd) perovskites with a polar ground state J. Blasco ,1,*G. Subías ,1M. L. Sanjuán ,1J. L. García-Muñoz ,2F. Fauth ,3and J. García1 1Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain and Departamento de Física de la Materia Condensada, Universidad de Zaragoza, C/ Pedro Cerbuna 12, 50009 Zaragoza, Spain 2Institut de Ciència de Materials de Barcelona, ICMAB-CSIC, Campus UAB, 08193, Bellaterra, Spain 3CELLS-ALBA Synchrotron Light Source, 08290 Cerdanyola del Vallès, Barcelona, Spain (Received 26 November 2020; revised 18 January 2021; accepted 2 February 2021; published 18 February 2021) We report here a structural study of RBaMn2O6(R=La, Pr, and Nd) compounds by means of synchrotron radiation x-ray powder diffraction and Raman spectroscopy. The three compounds are A-site ordered perovskites adopting the prototypical tetragonal structure at high temperature. A ferromagnetic transition is observed in the LaBaMn2O6sample and the lattice parameters undergo anisotropic changes at TCrelated to the orientation of the magnetic moments. Both PrBaMn2O6and NdBaMn2O6have a structural transition coupled to an electronic localization and an antiferromagnetic transition. In both cases, the x-ray diffraction patterns reveal that the lowtemperature phase is orthorhombic with lattice parameters a+b,b−a,andcwith respect to the tetragonal phase. Two possible solutions belonging to the space groups Pmam and P21am can yield accurate refinements of the x-ray patterns. However, the active modes in the low-temperature phase disclosed by the Raman spectroscopy clearly point to the noncentrosymmetric space group, P21am. The symmetry analysis of this transition unveils that the primary modes belong to the irreducible representations M5−and GM5−and the main distortions correspond to rotations of the MnO6octahedra and an asymmetric combination of stretching and scissoring modes of the basal oxygens in these octahedra. We conclude that the low-temperature phase is polar and the main contribution comes from the displacement of oxygen atoms from their centrosymmetric positions. However, negligible contribution from the asymmetric stretching associated with a Jahn-Teller distortion is found in this structural transition, suggesting the lack of ferroic orbital ordering of eg(3dx2−y2) orbitals in the orthorhombic ab plane. There is only one inequivalent site for the Mn atom in the low-temperature polar phase so charge ordering cannot account for the electronic localization having a structural origin. DOI: 10.1103/PhysRevB.103.064105 I. INTRODUCTION The physical properties of perovskite manganites have been widely studied in the last decades. These properties include colossal magnetoresistance, metal-insulator transitions, charge ordering (CO) transitions, orbital ordering (OO) transitions, and giant magnetocaloric effect among others. This variety of fascinating properties is due to the interplay between electronic, charge, magnetic, and orbital degrees of freedom [1–3]. These competitive forces manifest themselves especially in half-doped manganites [4]. At first, it was thought that large cations located in the Asite of the perovskite structure (rare earth and divalent atoms) were limited to stabilizing both the crystal structure and the hole doping of the Mn sublattice. However, recent studies have revealed that the laminar ordering of Aatoms strongly affects the physical properties of half-doped manganites [5]. It seems clear that these differences in the physical properties of compounds with *Mailing address: Javier Blasco Instituto de Nanociencia y Materiales de Aragón, Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza. C/ Pedro Cerbuna 12, 50009 Zaragoza, Spain; [email protected] the same chemical composition but with different ordering degree of the Asublattice are strongly related to differences in the crystallographic structure that are not yet well understood. A prototype example of half-doped manganite with a simple perovskite structure where there is a solid solution between the rare earth atoms and the divalent dopant in the perovskite Asite is Nd0.5Sr0.5MnO3. This sample undergoes two successive magnetic transitions [6,7]. It develops a ferromagnetic (FM) order at TC≈280K and then a spin reorientation to yield an antiferromagnetic (AFM) order at TN≈160 K. The latter transition is accompanied by a metal-insulator transition and a sudden change of the lattice parameters which consists of a strong shrinkage of the caxis while aand b axes expand [6]. The AFM structure is CE-type consisting of FM zigzag chains in the ab planes that are AFM coupled to each other and along the caxis [6]. This magnetic order is coupled to other arrangements: a charge ordering (CO) between Mn3+and Mn4+ions and an orbital ordering (OO) between two configurations of eg(3dz2) orbitals of Mn3+ cations. This arrangement is common to other half-doped manganites that present the same kind of CO transition such as La0.5Ca0.5MnO3,Pr 0.5Ca0.5MnO3,orPr 0.5Sr0.5MnO3[8–10]. The crystal structure of the ordered phase was refined in a monoclinic cell with the P21/mspace group (SG) and two 2469-9950/2021/103(6)/064105(15) 064105-1 ©2021 American Physical Society J. BLASCO et al. PHYSICAL REVIEW B 103, 064105 (2021) nonequivalent Mn sites [11]. However, both crystallographic refinements and spectroscopic measurements have determined that the CO between the two nonequivalent Mn atoms is only about 20%–25% of the maximum theoretical separation of one charge unit [11–13]. Amazingly, small changes in the hole doping lead to a different magnetic order in Nd1–xSrxMnO3(0.51 <x⩽0.60) compounds [6]. These samples exhibit similar metal-insulator transition coupled to similar changes in the lattice parameters but they undergo a single magnetic transition to A-type AFM structure formed by FM layers that are AFM coupled each other along the caxis. This magnetic ground state was explained on the basis of a homogeneous ferroic OO of eg (3dx2−y2) orbitals in the ab planes. In this way, A-type structure arises from the AFM superexchange between the localized t2g spins along the caxis and the FM double exchange between eg(3dx2−y2) spins in the ab plane. This model also implies a strong anisotropy in the transport properties with an insulating gap along the caxis and metallic behavior in the ab plane [14,15]. Different properties are observed in compounds where Aatoms are not randomly distributed. This happens in RBaMn2O6(R=rare earth atom or Y) where Rand Ba are ordered in alternating [0 0 1] perovskite layers. This makes the MnO2sublattice sandwiched between the RO and BaO sublattices of very different sizes [5,16]. Accordingly, asymmetric distortions are forced in the MnO6octahedron. Regarding the physical properties, significant differences are observed depending on the Rsize. For compounds with smaller Ratoms (R=Sm-Ho) or Y, the CO transition temperature is raised well above room temperature and different transitions and OO are reported depending on the Ratom [17–20]. However, for light Ratoms (La, Pr, Nd), the FM correlations are enhanced with respect to the parent simple perovskites [5,16,21]. On cooling, the FM transition is followed by a spin reorientation in Prand Nd-based compounds transforming to an A-type AFM structure. Preliminary studies on these compounds reported that the crystal structure remains tetragonal with no CO or OO transitions at any temperature [16]. However, neutron powder diffraction experiments [22] outlined a more complicated scenario and a fractional transition from the FM to AFM (CE-type, instead of A-type) phase was observed in LaBaMn2O6. Likewise, the coexistence of a minority fraction of CE-type and majority A-type phases is noticed in the ground state of PrBaMn2O6whereas a pure A-type phase is present for NdBaMn2O6. It was thought that RBaMn2O6(R=Pr, Nd) has no tilts of MnO6octahedra but a recent study of single-crystal x-ray diffraction detected two successive transitions in NdBaMn2O6 which imply the rotations of these octahedra [23]. The authors concluded that the ground state of this sample is a noncentrosymmetric SG, P21am, and a spontaneous electric polarization along the aaxis is predicted. The authors also concluded that the metal-insulator transition is coupled to an OO transition at 290 K without the concomitant CO observed in related simple perovskites. However, the magnetic transition temperature is lowered down to 235 K on the basis of the temperature dependence of the anisotropic magnetic susceptibility curves. In this way, spectroscopic ellipsometry and Raman scattering spectroscopy also detected anomalies associated with the electric and magnetic transitions at 290 and 235 K, respectively [24]. Significant charge transfer between O2pand Mn 3dstates was also found. Such a low value of TNis at odds with previous neutron powder diffraction studies where the long-range AFM order was observed in the range 275–290 K [22,25]. In a later study the same authors, using a larger crystal, identified a series of superstructure peaks that were not compatible with the structure previously proposed and concluded that the NdBaMn2O6is isostructural with SmBaMn2O6and not compatible with an A-type magnetic ordering [26]. Therefore, the crystallographic and magnetic structures of NdBaMn2O6are now an open question. The same can be said for PrBaMn2O6which has similar properties [22,27] and whose crystal structure at low temperature has not been deeply studied. A cause might be that the study of the structural properties of these compounds using single-crystal diffraction is a challenging task due to the occurrence of strong twinning, multiple scattering, and self-absorption problems. These difficulties are less relevant in powder diffraction and these obstacles can be overcome using synchrotron xray powder diffraction (SXRPD) measurements with higher angular resolution and flux than conventional diffractometers. In this work we report a structural study of NdBaMn2O6 and PrBaMn2O6using SXRPD between 100 and 400 K. Our study has revealed that both compounds are isostructural in the two limit temperatures but a different sequence of phase transitions is found at intermediate temperatures. The study is completed with a symmetry analysis and Raman spectroscopy in order to identify the condensed modes that account for the phase transitions and elucidate the presence or absence of a symmetry center at low temperature. II. EXPERIMENTAL SECTION Single crystals of PrBaMn2O6and NdBaMn2O6were grown using the floating zone method from polycrystalline precursors. Stoichiometric amounts of dried Pr6O11 (or Nd2O3), BaCO3, and Mn2O3were mixed, ground, and heated at 1000 °C overnight. The resulting powder is reground, pressed into pellets, and sintered at 1250 °C in a gas flow of H2/Ar mixture (2% H2) saturated in water vapor to achieve a reductive atmosphere (PO2 ≈10−11 bars). This is required to prevent the formation of BaMnO3impurity [21]. Then, the pellets are reground, pressed into rods, and sintered at 1375°C for 24 h in the same atmosphere. This procedure was also used to obtain polycrystalline LaBaMn2O6from dried La2O3.The rods were mounted in a homemade floating zone (FZ) furnace with two semielliptical mirrors [28]. The growth was carried out in the same reductive atmosphere with an overpressure of 2 bars. The seed and feed bars with diameters of 3.5 mm rotated in opposite directions at 20 rpm with a growth speed of 6 mm/h and the total lengths of the growth were 50 and 52 mm for Prand Nd-based samples, respectively. Some parts of the boules spontaneously split, leaving bright faces corresponding to the (0,0,1)tplane. After this step, the obtained products are oxygen deficient RBaMn2O5+δ(R=La, Pr, Nd), with δ≈0.1. The next step consists of topotactic oxidation by heating the boules (or sintered rod for polycrystalline samples) at 400 ◦C–450 ◦Cin an oxygen current flow for 24 h yielding the stoichiomet064105-2 STRUCTURE AND PHASE TRANSITIONS IN A-SITE … PHYSICAL REVIEW B 103, 064105 (2021) ric RBaMn2O6compounds. Some parts of the boules were ground and analyzed by powder x-ray-diffraction. Rietveld analysis of the x-ray patterns using the FULLPROF package program [29] indicated that the crystals were single phase without detectable impurities. The chemical composition of the powders was also tested using the wavelength dispersive x-ray fluorescence spectrometry (Advant’XP+model from Thermo-ARL) and the R:Ba:Mn stoichiometry agreed with the expected values within the experimental error (1%). SXRPD patterns were measured at the MSPD beamline [30] of the ALBA synchrotron (Cerdanyola del Vallès, Spain) using high-throughput position sensitive detector MYTHEN. Both the high photon flux of the beamline and the good signal to noise sensitivity of the detector allows detecting minor superstructure peaks. The samples were loaded in a borosilicate glass capillary (diameter of 0.5 mm) and kept spinning during data acquisition. A short wavelength, λ=0.4128Å, was selected to reduce absorption. The value of λwas calibrated using a NIST standard silicon. We have performed two types of measurements; standard patterns to refine unit cells were collected in heating and cooling ramps between 100 and 440 K. The rate was 0.5Kmin−1and the total acquisition time was 6 min. With this procedure, we collected a pattern every 3 K on average. Secondly, SXRPD patterns with very good statistics were measured at selected temperatures for each sample with a total acquisition time of 30 min/pattern to perform a full structural characterization. Magnetic measurements were carried out with a commercial Quantum Design (SQUID) magnetometer. The dc magnetization was measured between 5 and 400 K with an external field ranging between 0.5 and 1 kOe. Electrical dc resistivity measurements were made between 10 and 350 K on rectangular bars cut from polycrystalline pellets with a typical size of 2 ×2×9mm3. A Quantum Design physical property measurement system (PPMS) was utilized for this purpose. The conventional four-probe configuration was employed, and electrodes were made using silver paint. Differential scanning calorimetry (DSC) was measured by using a DSC 2910 from TA instruments with samples sealed in aluminum pans. Raman spectra of single-crystalline samples were recorded in a DILOR XY spectrometer equipped with a liquid-nitrogen cooled CCD detector. The 496.5 and 514.5 nm lines of an Ar+-ion laser and the 647.1 nm line of a Kr+laser were used as excitation sources. An ULWD 50×microscope objective lens of an Olympus BH-2 microscope was used both for excitation and dispersed light collection. Variable-temperature measurements were performed from 77 to 295 K using an Air-Liquide cryostat and liquid-nitrogen refrigeration. III. RESULTS AND DISCUSSION A. LaBaMn2O6 LaBaMn2O6is a prototype of A-site ordered perovskite. It adopts the tetragonal structure without MnO6tilts and SG P4/mmm [21]. It undergoes a magnetic transition as can be seen in the M(T) curves in Fig. 1. The transition is typical of a FM ordering whose onset occurs at 356 K with a TC=329 K taken at the inflection point. SXRPD patterns were collected between 150 and 440 K for this sample and the tetragonal 0 2 4 6 8 10 7.800 7.805 7.810 7.815 7.820 7.825 7.830 7.835 7.840 160 200 240 280 320 360 400 440 Lattice parameters ( Å ) M/H (emu/mol Oe) T (K) C 2 a TC FIG. 1. Temperature dependence of the magnetization and the lattice parameters for LaBaMn2O6.Theaaxis has been multiplied by 2 for the sake of comparison. symmetry is preserved in the whole temperature range. The only notable anomaly is the sudden change observed in the lattice parameters at TC(see Fig. 1). The aaxis shows a small downturn at TCwhile the anomaly is more abrupt in the caxis with a local minimum at TCand then an expansion of this axis just below TC. These changes are clearly related to the magnetic arrangement of LaBaMn2O6where the Mn moments are oriented along the caxis [22] producing a small expansion of this axis. The refined structural parameters at three selected temperatures (150, 295, and 440 K) are given in Table Iand the observed and calculated patterns of the SXRPD Rietveld profiles are shown in Fig. S1 in the Supplemental Material [31]. B. PrBaMn2O6 Figure 2shows the temperature dependence of the magnetization and electrical resistivity for PrBaMn2O6.Two magnetic transitions can be observed in the temperature range between 5 and 400 K with a remarkable hysteresis. Focusing on the cooling curve, the sample is clearly paramagnetic (PM) above 330 K. Below this temperature, there is a pronounced increase of the magnetization signal characteristic of a FM order with a TC=309 K. Further cooling the sample, an abrupt drop in the magnetization is noticeable below 245 K and the second transition takes place at TN=235K indicating a long AFM order. Both transition temperatures have been taken at their respective inflection points of the M(T) curve. In the warming curve, TNgoes up to 260 K whereas TCremains unchanged. The AFM transition is coupled to a jump of the electrical resistivity and both features are characterized by a significant temperature hysteresis between the measurements made on heating and on cooling. The hysteresis agrees with a first-order transition. All these properties match those previously reported for similar compounds [16,22]. Regarding the structural properties of PrBaMn2O6,the SXRPD pattern measured at the highest temperatures 064105-3 J. BLASCO et al. PHYSICAL REVIEW B 103, 064105 (2021) TABLE I. Structural parameters of LaBaMn2O6obtained from the Rietveld analysis at the indicated temperatures. The space group for all temperatures is P4/mmm. Atom xy z B iso(Å2) T=440 K a=3.91946(1) Å La 0 0 0 0.83(4) c=7.81037 (2) Å Ba 0 0 1 20.55(4) V=119.369(1) Å3Mn 1 2 1 20.24933(44) 0.47(1) Rp(%) =4.95 O1 1 2 1 20 2.42(44) Rwp(%) =7.13 O2 1 20 0.23372(62) 1.27(7) RBragg(%) =2.5O3 1 2 1 2 1 20.79 (22) χ2=2.95 T=295 K a=3.91189(1) Å La 0 0 0 0.65(4) c=7.80047(2) Å Ba 0 0 1 20.40(4) V=120.005(1) Å3Mn 1 2 1 20.24872(49) 0.35(1) Rp(%) =4.75 O1 1 2 1 20 1.13(51) Rwp(%) =6.65 O2 1 20 0.23625(67) 0.99(7) RBragg(%) =2.2O3 1 2 1 2 1 20.46(40) χ2=4.2 T=150 K a=3.90560(1) Å La 0 0 0 0.49(2) c=7.79766(3) Å Ba 0 0 1 20.15(2) V=118.943(1) Å3Mn 1 2 1 20.25063(36) 0.25(8) Rp=4.93 O1 1 2 1 20 0.35(24) Rwp =7.20 O2 1 20 0.23138(51) 0.84(9) RBragg =2.4O3 1 2 1 2 1 20.33(25) χ2=6.2 (440 K) exhibits a tetragonal cell with no MnO6octahedra tilts isostructural to LaBaMn2O6. The comparison between the patterns collected at 400 and 100 K shows clear differences [see Supplemental Material [31]]. These can be classified into two types: the splitting of a good number of main peaks and 10 100 1000 10000 100000 0 5 10 15 20 25 30 35 40 100 150 200 250 300 350 400 T (K) M (emu/g) ρρ (Ohms.cm) FIG. 2. Resistivity and magnetization of PrBaMn2O6as a function of temperature in cooling and heating runs indicated by arrows. The applied magnetic field in the magnetic measurement was 1 kOe. the appearance of superstructure peaks indexed as (h 2,k 2,l)t in the 100 K pattern, where the subscript trefers to the hightemperature tetragonal cell (Fig. S3) [31]. On heating, these superstructure peaks vanish at TN, suggesting a structural phase transition coupled to the magnetic one and a nontetragonal unit cell below TN. In order to determine the structure of this compound at low temperature, we have applied the symmetry adapted mode description of distorted structures using the tool ISODISTORT [32]. The high-temperature tetragonal phase is considered as the parent structure and we have identified the irreducible representation (Irrep) M5−,k=(1 2,1 2,0), with respect to P4/mmm as associated with the rotation of MnO6octahedra. In order to further limit the search, we have taken advantage of the results obtained by neutron diffraction that have shown that the magnetic ground state of this compound is an A-type AFM ordering. We have identified this ordering with the magnetic Irrep mGM5−,k=(0,0,0). In this way, the possible distorted structures that present MnO6rotations compatible with the reported magnetic structure are Pmma (orthorhombic and centrosymmetric), Pmc21 (orthorhombic and noncentrosymmetric), and P21/m(monoclinic and centrosymmetric). The latter can be discarded as no evidence of monoclinic distortion has been found in our SXRPD patterns. The refinements with the two orthorhombic models give results with similar goodness factors. In fact, the occurrence of both cells was deduced from a previous symmetry analysis and the main difference concerns the type of MnO6octahedra tilting [33]. According to the symmetry 064105-4 STRUCTURE AND PHASE TRANSITIONS IN A-SITE … PHYSICAL REVIEW B 103, 064105 (2021) FIG. 3. (a) Crystal structure of PrBaMn2O6with the oxygen shifts produced by the modes belonging to the Irrep M5−. (b) Detail of the base of the MnO6octahedron with bond lengths and the displacements due to the modes belonging to Irrep GM5−and the expected polarization direction. analysis, the transition from P4/mmm into Pmma is expected to be continuous while the transition into Pmc21should be of first order in agreement with the hysteresis in its physical properties (see Fig. 2). However, the definitive answer is given by the Raman spectroscopy as can be seen later. The spectra disclose that the number of observed modes at low temperature is only compatible with the noncentrosymmetric structure. Therefore, we have refined the low SXRPD pattern using the SG P21am (a setting of Pmc21by exchanging aand caxes). The relationship for the lattice parameters between the parent and the distorted phases is ao≈√2at,bo≈√2at, and co≈ct. It is worth emphasizing that this structure is similar to that published for NdBaMn2O6in a study by Yamada et al. [23]. We have performed the mode decomposition to relate parent and distorted phases. There are 17 active modes belonging to 5 Irreps: GM1+,GM5−,M2+,M3+, and M5−. The primary modes belong to Irreps GM5−and M5−with global amplitude values of 0.42(4) and 0.36(2) Å, respectively. The contributions of modes belonging to M2+ and M3+are negligible and those from GM1+are much smaller. It should be noted here that the distortion associated with the Irrep M3+corresponds to a Jahn-Teller distortion of the basal oxygens and the refinement yields a null contribution of it. Figure 3shows the main modes involved in the structural transition. The oxygen shifts associated with the Irrep M5− correspond to a corner-linked tilting of the MnO6octahedra in agreement with the two-tilt system a−a−c0following Glazer’s terminology [34]. It is composed of three individual modes. The basal oxygens have opposite shifts along the c axis as indicated in Fig 3(a). These movements are coupled and they have point symmetry A1. On the other hand, the apical oxygens also have opposite shifts along the baxis (point symmetry Bu) but they are not coupled and, in fact, the displacement of O1 is significantly smaller than that of O3, probably due to the steric effect produced by the large size of the Ba2+cation. This makes the MnO6octahedron no longer regular when rotating. It is noteworthy that the distortion belonging to the Irrep M2+implies the tilt a0a0c+and although its amplitude is practically zero in this case, the rotational distortion of MnO6octahedra in this SG belongs to the three-tilt system a−a−c+as indicated in Ref. [33]. Regarding the displacements ascribed to Irrep GM5−, the most significant are shown in Fig. 3(b) and concern the basal oxygens. They are composed by an asymmetric stretching mode (point symmetry B1) and an asymmetric scissoring mode (B2). The result is two short and two long Mn-O2 distances resulting in a trapezoid shape for the base of the MnO6octahedra. Another two modes of the Irrep GM5−with significant amplitude (Bu) are acting on the two apical oxygens with shift along the b axis. However, the amplitude of the GM5−modes acting on the cations is negligible. The bond lengths between Mn atoms and apical oxygens are Mn-O1 =1.931(3) Å and Mn-O3 = 1.901(4) Å. Accordingly, the octahedral coordination of Mn is composed of four short distances (around 1.92 Å) and two long ones (about 2.02 Å) but the geometric arrangement has nothing to do with a Jahn-Teller distortion so that the ferroic OO of 3dx2−y2egorbitals in this compound at low temperature is very unlikely. On the other hand, the approximation of two basal oxygens to the Mn atom suggests an increase in the covalence of these bonds in agreement with previous spectroscopic studies on a related compound [24]. The refined structural parameters are summarized in Table II and the fits are shown in Fig. S2 [31]. Focusing on the structural transition, this is associated with strong splitting of many diffraction peaks as can be seen in the example of Fig. 4(a). Moreover, there is a wide temperature range where the highand low-temperature phases coexist. We have performed Rietveld analysis quantifying the phase ratio in this temperature range in the heating and cooling runs and the results are collected in Fig. 4(b). We have observed a temperature hysteresis similar to the one observed in the macroscopic properties [compare Figs. 2and 4(b)]. Another interesting feature is the phase transformation. It is complete in the heating run indicating that the orthorhombic phase is fully transformed into the tetragonal one at 275 K. However, the diffraction peaks from the high-temperature phase get smaller and wider on cooling but at low temperature, they transform into diffuse scattering hard to quantify. This diffuse contribution is still noticeable at 100 K [see Fig. S4 in the Supplemental Material [31]] and suggests the occurrence of nanoscopic regions of the high-temperature phase at this temperature. This fact could account for the metamagnetic transitions reported [35] for this compound as an external magnetic field would favor the stability of the ferromagnetic high-temperature phase. Figure 5shows the evolution of the structural parameters as a function of the temperature obtained under heating conditions. The strong changes can be seen by comparing the equivalent axes in the two phases. Thus, the tetragonal aaxis undergoes a strong expansion at around TN. The orthorhombic distortion is clear just below the transition temperature but it decreases on cooling to give a pseudotetragonal phase at 100 K. The opposite trend is observed in the caxis with a strong shrinkage at the phase transition. These features are typical of CO transition in manganites without layered ordering but this scenario can be discarded for the present compound as there is a unique site for Mn atoms in the low-temperature phase. If we look at the evolution of the unit cell volume on cooling, a sharp expansion is noticeable at the transition indicating that the volume of the orthorhombic phase is greater than the tetragonal one. This is in accordance with the virial theorem for metal-insulator transitions where an electron localization is accompanied by an expansion of the unit cell volume because changes in the kinetic and potential 064105-5 J. BLASCO et al. PHYSICAL REVIEW B 103, 064105 (2021) TABLE II. Structural parameters of PrBaMn2O6obtained from the Rietveld analysis at the indicated temperatures. Atom xy zBiso(Å2) T=440 K (P4/mmm) Pr 0 0 0 1.07(4) a=3.90856(1) Å Ba 0 0 1 20.68(4) c=7.76706(2) Å Mn 1 2 1 20.24880(31) 0.58(1) V=118.656(1) Å3O1 1 2 1 20 2.42(35) Rp(%) =4.7O2 1 20 0.22947(45) 1.48(6) Rwp(%) =6.8O3 1 2 1 2 1 20.71(21) RBragg(%) =2.1 χ2=5.4 T=330 K(P4/mmm) Pr 0 0 0 0.90(3) a=3.90442(1) Å Ba 0 0 1 20.58(2) c=7.75327(3) Å Mn 1 2 1 20.24882(29) 0.51(1) V=118.194(1) Å3O1 1 2 1 20 2.09(30) Rp(%) =4.6O2 1 20 0.23015(42) 1.13(5) Rwp(%) =6.8O3 1 2 1 2 1 20.52(13) RBragg(%) =2.25 χ2=5.4 T=100 K (P21am) a=5.55775(3) Å Pr 0.000 0.7435(3) 0 0.34(2) b=5.55462(3) Å Ba 0.000 0.7487(4) 1 20.41(3) c=7.62299(1) Å Mn 0.000 0.2500 0.2471(2) 0.31(1) V=235.331(2) Å3O1 −0.035(6) 0.281(4) 0 0.21(19) Rp(%) =4.3O2 10.732(2) 0.003(2) 0.7827(10) 0.28(13) Rwp(%) =5.8O2 20.232(2) 0.503(2) 0.7594(10) 0.31(13) RBragg(%) =1.61 O3 −0.018(8) 0.233(7) 1 20.52(13) χ2=4.3 energies across a first-order transition are opposite in sign [36]. When comparing the refined data for the highand lowtemperature phases, the changes are minimal in the average Mn-O (Mn-O) distance being 1.954 Å for the data refined at 440 and 100 K. However, the temperature dependence of MnOalso shows an anomaly at the phase transition temperature as can be seen in Fig. 5(d). This average distance decreases in the high-temperature phase mirroring the evolution of the unit cell volume and exhibits an abrupt jump at TNthat compensates the previous decrease. Below TN,Mn-Oremains almost constant. Another significant difference concerns the distribution of the Mn-O bond lengths in the ab plane. There 0 50000 100000 150000 200000 8.45 8.50 8.55 8.60 8.65 8.70 8.75 220 K 240 K 244 K 248 K 252 K 256 K 260 K 264 K 268K 280 K Intensity (counts) 2-Theta (deg.) (110)t(102)t (112)o (200)o + (020)o (a) 0 20 40 60 80 100 160 180 200 220 240 260 280 300 T (K) Orthorhombic Tetragonal Phase composition (%) heating cooling (b) FIG. 4. (a) Comparison of a region of SXRPD pattern collected at selected temperatures after heating from 100 K for PrBaMn2O6. Subscripts in the index refer to orthorhombic (o) and tetragonal (t) cells. (b) Quantification of the orthorhombic (open symbols) and tetragonal (closed symbols) phases obtained from the Rietveld analysis of the SXRPD patterns when heating from 100 K (red squares) and cooling from 440 K (blue circles). 064105-6 STRUCTURE AND PHASE TRANSITIONS IN A-SITE … PHYSICAL REVIEW B 103, 064105 (2021) FIG. 5. Temperature dependence of the lattice parameters for PrBaMn2O6in the heating ramp: (a) aand baxes, (b) caxis, and (c) unit cell volume. The parameters of the ab plane have been multiplied by 2 (tetragonal case) and 2 (orthorhombic case) for the sake of comparison. (d) Temperature dependence of the average Mn-O-Mn bond angle (circles) and Mn-O lattice distance (squares) in the cooling ramp. is a single Mn-O2 distance in the tetragonal phase which becomes a mixture of two long and two short distances in the low-temperature phase as indicated in Fig. 3(b).Amore important change is observed in the evolution of the average Mn-O-Mnbond angle. It reaches a value of 174.1° at 440 K and only 169.8 ° at 100 K. Figure 5(d) shows that the change is abrupt at the temperature where electronic localization occurs [compare Figs. 2and 5(d)]. The decrease of Mn-O-Mnproduces a narrowing of the electronic bandwidth and opens a gap at the Fermi energy. However, the low-temperature phase only has a single nonequivalent site for Mn atoms so electronic localization cannot lead to a CO. Instead, our results suggest that this system is metalliclike for small distortions but a periodic distortion alternating long and short Mn-O bonds in the ab plane opens a gap at the Fermi energy in the low-temperature phase. In this way, it could be considered as a type of effective charge density wave centered on the Mn-O bonds without charge transfer between neighboring MnO6octahedra. A similar mechanism was proposed for metal-insulator transitions in related nickelates associated with a breathing distortion [37]. In the present case, the electronic localization is coupled to the asymmetric stretching of the MnO6octahedra. Damped by the large structural modifications observed at TN, it is difficult to appreciate the small changes observed at TC. As in the FM transition of LaBaMn2O6, a small contraction of the aaxis coupled to a small expansion of the caxis can be seen at TCin Figs. 5(a) and 5(b). This indicates that both compounds, LaBaMn2O6and PrBaMn2O6, have a similar FM transition with the magnetic moments oriented along the same direction (caxis). C. NdBaMn2O6 Figure 6compares the temperature dependence of the magnetization and electrical resistivity in NdBaMn2O6. We find many similarities with the properties reported in PrBaMn2O6. In this way, we observe a similar jump of the electrical resistivity with a significant temperature hysteresis between the heating and cooling runs. Regarding the magnetic properties, we find some difference since in this case two magnetic 064105-7 J. BLASCO et al. PHYSICAL REVIEW B 103, 064105 (2021) 1 10 100 0 1 2 3 4 5 100 150 200 250 300 350 400 ρρ (Ohms.cm) T (K) M (emu/g) FIG. 6. Resistivity and magnetization of NdBaMn2O6as a function of temperature in cooling and heating runs indicated by arrows. The applied magnetic field in the magnetic measurement was 500 Oe. transitions are not so clearly evidenced. The magnetization curves in Fig. 6exhibit a sharp peak in accordance with previous reports [22,23,25]. The magnetization curves obtained from cooling or heating measurements present a wide range of irreversibility between 297 and 200 K which coincides with the hysteresis observed in the electrical properties of the same sample. The peak is achieved at 292 K when the sample is heated from 5 K while it is at 287 K on cooling from 350 K. The shape of the magnetization curve can be explained by referring to a previous neutron diffraction study indicating that NdBaMn2O6develops an A-type AFM ordering [22]. This accounts for the sharp decrease of the magnetization below the peak temperature. From the inflection point of the M(T) curve, one can infer the value of TN=287 K in the heating run (281 K in the cooling run). Above this magnetic transition, FM correlations are present in this compound producing an increase in the magnetization. However, neutron diffraction revealed that long-range FM ordering is not completely established in this compound but occurrence of short-range correlations is clearly evidenced [25]. This is the fundamental difference with respect to the PrBaMn2O6case where a longrange FM order was established in a short temperature range. Concerning the structural properties of NdBaMn2O6,we have measurements with very good statistics at four selected temperatures: 100, 295, 320, and 440 K. At 440 K, NdBaMn2O6is isostructural to the two previous samples with the same tetragonal structure. At 100 K, the pattern shows features similar to the ones observed in PrBaMn2O6, that is, the splitting of some fundamental diffraction peaks and the occurrence of similar (h 2,k 2,l)tsuperstructure peaks (see Fig. S7 in the Supplemental Material [31]). This suggests that PrBaMn2O6and NdBaMn2O6are isostructural at low temperature. According to Ref. [26], NdBaMn2O6could be isostructural to SmBaMn2O6. Our study does not support this statement. We did not find (h 4,k 4,l)tsuperstructure peaks in the SRXPD patterns at 100 K with a resolution limit for the intensity of five orders of magnitude related to the fundamental reflections. This limit is sufficient to detect the superstructure peaks of SmBaMn2O6[38]. Reference [26] suggests that (h 4,k 4,l)tpeaks are six orders of magnitude lower than the fundamental reflections. This would be below our resolution limit so we have explored this possibility. First of all, the refinement in the large cell isostructural to SmBaMn2O6did not improve our previous refinements despite a greater number of free parameters. The (h 4,k 4,l)tpeaks arise from distortion modes ascribed to the Irrep SM2 associated with the point (1 4,1 4,0) in the first Brillouin zone. Some of these modes give rise to two different environments for the Mn atoms. Our simulations have shown that mode amplitudes producing a charge segregation of only 0.06 e−between the two Mn atoms would be already visible in the SRXPD patterns. This result makes a CO transition in NdBaMn2O6highly unlikely. Finally, the CO/OO structure of SmBaMn2O6is not compatible with the A-type AFM ordering of the Mn atoms previously determined for PrBaMn2O6and NdBaMn2O6[22,25]. Therefore, we have utilized the same model used in the study of the PrBaMn2O6sample to refine the SXRPD data at 100 K of the NdBaMn2O6compound. In this case, equally good fits were obtained using both SGs: Pmam or P21am. As with PrBaMn2O6, Raman spectroscopy agrees with the second option. The refined parameters are summarized in Table III and the observed and calculated patterns of the SXRPD Rietveld profiles are displayed in Fig. S5 [31]. The set of condensed modes with respect to the parent structure are similar to those observed in the PrBaMn2O6compound. Again the primary modes belong to Irreps GM5−and M5−with global amplitude values of 0.40(4) and 0.43(2) Å, respectively (see Table IV). We observe an increase in the amplitude of M5− modes indicating an increase in the rotation of MnO6octahedra. Modes of the Irrep GM1+are secondary while modes of Irreps M2+and M3+are negligible. In this case, we have set the amplitude of the GM5−mode corresponding to the Ba atom to zero in order to fix the origin of the noncentrosymmetric structure and we notice small polar shifts of both Mn and Nd atoms which are added to the oxygen shifts already observed in the PrBaMn2O6sample. Anyway, the main polar shifts correspond to oxygen atoms and are similar to the ones observed in PrBaMn2O6(see Fig. 3). In this case the bond lengths between Mn atoms and apical oxygens are Mn-O1 = 1.919(2) Å and Mn-O3 =1.911(4) Å. The basal Mn-O distances are 2.034(13), 2.040(13), 1.902(14), and 1.905(14) with a distribution similar to the one displayed in Fig. 3(b). The solution found here is similar to the one reported by Yamada et al. in Ref. [23]. However, these authors analyzed their structural data based on a Jahn-Teller type distortion mode analysis deducing a ferroic OO of 3dx2−y2orbitals. In order to compare the results of both refinements, we have performed a mode decomposition of the structural parameters reported by Yamada et al. [23]. For this purpose we have used the AMPLIMODES program from the Bilbao Crystallographic server [39]. The comparison is summarized in Table IV.As can be seen, both refinements lead to similar mode decomposition. In this way, we observe similar amplitude for the main M5−modes and small amplitudes for modes of the Irreps GM1+,M2+, and M3+. In the case of the last two 064105-8 STRUCTURE AND PHASE TRANSITIONS IN A-SITE … PHYSICAL REVIEW B 103, 064105 (2021) TABLE III. Structural parameters of NdBaMn2O6obtained from the Rietveld analysis at the indicated temperatures. Atom xyzBiso(Å2) T=440 K (P4/mmm) Nd 0 0 0 0.96(2) a=3.90535(1) Å Ba 0 0 1 20.61(2) c=7.75177(2) Å Mn 1 2 1 20.2477(3) 0.49(1) V=118.228(1) Å3O1 1 2 1 20 2.11(19) Rp(%) =2.6O2 1 20 0.2311(2) 1.36(3) Rwp(%) =3.8O3 1 2 1 2 1 20.49(11) RBragg(%) =1.2 χ2=3.8 T=320 K(Cmmm) Nd 0.2502(3) 0 0 0.71(2) a=7.80583(6) Å Ba 0.2502(3) 0 1 20.48(2) b=7.80280(7) Å Mn 0 0.2496(3) 0.2470(2) 0.38(1) c=7.73213(1) Å O1 0 0.2759(13) 0 0.13(17) V=470.943(6) Å3O210 0 0.2316(21) 0.76(35) Rp(%) =2.6O2 201 20.2522(17) 1.81(36) Rwp(%) =3.7O2 31 4 1 40.2227(9) 0.56(16) RBragg(%) =1.2 O3 0 0.2559(21) 1 20.84(18) χ2=3.7 T=295 K(Cmmm) Nd 0.2506(3) 0 0 0.66(2) a=7.80949(3) Å Ba 0.2499(3) 0 1 20.47(2) b=7.79996(3) Å Mn 0 0.2495(3) 0.2470(2) 0.36(1) c=7.72405(1) Å O1 0 0.2759(16) 0 0.39(18) V=470.501(2) Å3O210 0 0.2260(16) 0.52(24) Rp(%) =2.5O2 201 20.2548(13) 1.42(25) Rwp(%) =3.5O2 31 4 1 40.2238(9) 0.79(11) RBragg(%) =1.1 O3 0 0.2607(23) 1 20.71(17) χ2=3.4 T=100 K (P21am) a=5.54805(3) Å Nd −0.0050(6) 0.7423(3) 0 0.47(2) b=5.54447(4) Å Ba 0.0000 0.7478(4) 1 20.12(2) c=7.62068(2) Å Mn −0.0041(19) 0.2475(5) 0.2483(3) 0.22(1) V=234.420(2) Å3O1 −0.033(4) 0.286(3) 0 0.18(15) Rp(%) =3.9O2 10.744(2) 0.019(2) 0.7833(9) 0.23(13) Rwp(%) =5.7O2 20.244(2) 0.519(2) 0.7526(9) 0.40(13) RBragg(%) =1.2O3−0.012(5) 0.248(4) 1 20.30(16) χ2=3.9 Irreps, the uncertainty overcomes the value of the individual amplitudes so we set them to zero in our last refinement. The main difference between both models concerns the amplitude of the modes belonging to the Irrep GM5−, a bit higher in our refinement. This could be related to the differences between both experimental techniques as Yamada et al. [23] performed a single-crystal study refining anisotropic temperature factors for all atoms. In any case, the condensed modes are alike in both models and none of them are compatible with a Jahn-Teller deformation as seen previously in the study of PrBaMn2O6. Therefore, we discard the occurrence of a ferroic OO in any of the two samples. TABLE IV. Summary of the mode decomposition with respect to its P4/mmm parent structure of the P21am structure of NdBaMn2O6 reported in this work and in Ref. [23]. Amplitude (Å) Kvector Irrep Direction Dim. This work Yamada et al. [23] (0, 0, 0) GM1+(a) 2 0.07(1) 0.02(1) (0, 0, 0) GM5−(a,a) 7 0.41(3) 0.21(1) (1 2,1 2,0) M2+(a) 1 0.00(7) 0.03(8) (1 2,1 2,0) M3+(a) 1 0.00(9) 0.03(5) (1 2,1 2,0) M5−(a,0) 6 0.44(2) 0.43(1) 064105-9