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Atomic distribution, local structure and cation size effect in o-R1−x Cax MnO3 (R = Dy, Y, and Ho)
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2013 J. Phys.: Condens. Matter 25 475901 (http://iopscience.iop.org/0953-8984/25/47/475901) View the table of contents for this issue, or go to the journal homepage for more
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IOP PUBLISHING
JOURNAL OF PHYSICS: CONDENSED MATTER
J. Phys.: Condens. Matter 25 (2013) 475901 (8pp)
doi:10.1088/0953-8984/25/47/475901
Atomic distribution, local structure and cation size effect in o-R1−xCaxMnO3 (R = Dy, Y, and Ho) Ning Jiang, X Zhang and Yi Yu Key Laboratory of Advanced Materials, School of Materials Science and Engineering, People’s Republic of China Beijing National Center for Electron Microscopy, Tsinghua University, Beijing 100084, People’s Republic of China E-mail: [email protected]
Received 20 July 2013, in final form 7 September 2013 Published 31 October 2013 Online at stacks.iop.org/JPhysCM/25/475901 Abstract We propose new interatomic potentials for the small rare-earth-based orthorhombic RMnO3 (R = Dy, Y, Ho), which accurately model the structural properties of these extreme cases of lanthanide manganate series. They are further employed to investigate the intrinsic defects in o-RMnO3 and the cation distribution and local structure in o-R1−x Cax MnO3 (R = Dy, Y, Ho). Schottky disorders are found to be the dominant structural defects, and the possibility of a small degree of anti-site disorder of R and Mn ions over A and B sites is found. The introduced Ca dopants tend to form chemically and structurally like CaMnO3 clusters in the lightly doped system, which can be regarded as representations of microscopic phase separation. The local structural disorder is reduced with increasing doping density. For o-R0.5 Ca0.5 MnO3 (R = Dy, Y, Ho), the charge ordering state is intrinsically favored, and the layer stripe model is shown to be energetically more favorable and structurally more reasonable. Moreover, the tendency to form charge ordered stripes increases with the decrease of R size. The local structure in the layer stripe pattern deviates largely from the average structure: RMnO3 -like and CaMnO3 -like layers are formed. The size of R ion has a significant influence on the doping effect on Jahn–Teller (JT) distortion and a manganate with a larger R will experience a larger reduction on the anisotropy of Mn–O bonds in Mn3+ O6 octahedra. However, the change of octahedral tilting upon doping does not vary much with R radii. (Some figures may appear in colour only in the online journal)
1. Introduction
attention due to their rich display of interesting basic physics problems and possible applications [1–3]. So far, the large R-based compounds (La, Pr, and Nd) have been intensely investigated, whereas few studies have concentrated on their small R (Dy, Y, and Ho) counterparts. Although physical properties might be expected to be similar for these two groups, there are in fact numerous qualitative differences [4–6]. Many questions regarding the phase topology of R1−x Ax MnO3 , including clusters and charge ordering stripes at different doping level, which is one of the most attractive areas of research, remain to be solved to understand the behaviors. In particular, the inhomogeneous distribution in the lightly doped manganates where the size scale of the formed clusters
Rare-earth manganates RMnO3 prepared under ordinary synthetic conditions crystallize in the orthorhombic perovskite structure Pnma (o-RMnO3 ) for R = La–Dy with large ionic radii and in the hexagonal structure P63 cm (h-RMnO3 ) for R = Y, Ho–Lu with smaller ionic radii. However, by means of special soft-chemistry synthesis, applying pressure, or epitaxial thin-film growth, the hexagonal structure can be converted into the more dense, albeit metastable orthorhombic phase. Perovskite manganates with mixed manganese valence, R1−x Ax MnO3 , where R is a trivalent rare-earth ion and A represents a divalent alkaline-earth ion, have attracted great 0953-8984/13/475901+08$33.00
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c 2013 IOP Publishing Ltd Printed in the UK & the USA
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varies extraordinarily from nanometer [7] to micrometer [8, 9] requires further understanding. For manganates with an extremely small average A-site cation size hrA i (hi denotes average value), whether the charge ordering phenomenon will be present still needs further confirmation [10, 11] and the real lattice image is still not clear [12]. The factors that should be responsible for the extraordinary sensitivity of charge ordering to hrA i are still uncertain [12, 13]. Besides, a probing of the local structure of the inhomogeneities in the doped manganates, which helps understanding the physical properties of these compounds, is of great value, but is still lacking. The aim of this study is to address the above issues using well-established atomistic modeling techniques. We develop new accurate and robust interatomic potentials for o-RMnO3 (R = Dy, Y, Ho), which are the last, much distorted terms of the RMnO3 series. Then a comprehensive calculation is performed to provide detailed investigations on the intrinsic defect chemistry of them, as well as possible cation distribution pattern and local structure in Ca2+ doped compounds with the doping range varying from 0 to 0.5. The cation size effects are also discussed.
where di is the relative displacement of core and shell of ion i. The ion polarization can be calculated as Y2 , (4) k where fitting parameters Y and k are the shell charge and harmonic force constant, respectively. Defects simulated at the infinitely dilute limit were achieved by the Mott–Littleton approach [23], where the lattice relaxation about charged defects and dopants is treated by partitioning the crystal lattice into two regions. Ions in a spherical inner region surrounding the individual defect are relaxed explicitly, while the remainder of the crystal, where the defect forces are relatively weak, is treated by more approximate quasi-continuum methods. In this way, long-range lattice relaxation is modeled effectively and the crystal is not considered simply as a rigid lattice. In this work, the initial structure we start with for studying o-RMnO3 (R = Dy, Y, and Ho) is the crystallographic unit cell, which has four R3+ ions, four Mn3+ ions, four O1 ions, and eight O2 ions. However, in order to meet the fractional occupancies in R1−x Cax MnO3 and make the calculations more efficient, the unit cell of RMnO3 is extended to a 3 × 2 × 3 supercell (Pnma space group). Previous first-principles calculations have contributed a lot to the theoretical investigations of these compounds, concerning their basic electronic properties [24] and nonconventional magnetic ordering [25, 26], the key ingredient for the rising of ferroelectric polarization [27], and the interplay between the lattice, magnetism, and ferroelectricity [26–28]. However, there is little information about the hole-doping induced processes and structures in the atomic scale. Compared with the first-principles approach, the classical atomistic simulation employed here has the merit of accessibility to a relatively large number of atoms with respect to the real lattice image and detailed structural distortion, which lie beyond the limits of purely quantum mechanical approaches. Although the study of rare-earth manganates RMnO3 (R = Dy, Y, and Ho) by classical atomistic simulation has been reported previously, the potentials therein fail to reproduce individual material accurately in particular [29] or is not universal for dopant calculation [30]. The lack of either a fully accurate potentials-based or ab initio-based study of small R-based o-RMnO3 and their promising compounds o-R1−x Cax MnO3 supports the necessity of the calculations reported here. α=
2. Simulation methods The atomistic simulation method used in this work has already been successfully demonstrated to describe the characteristic and properties of a range of oxide-based materials [14–19]. This technique, embodied in the GULP [20] code, is reviewed in detail elsewhere [21], hence only a brief description will be given here. Our simulation is based on the widely used successful Born model of ionic solids, where the effect of the electrons are subsumed into effective atoms, and the energy is decomposed into the sum of self-energies and the pairwise interaction of the total number of atoms. Within this model, the lattice energy E can be expressed as 1 X qi qj E= + V(rij ) , (1) 2 i,j rij where the first item is Coulombic energy introduced by long-range interactions of effective charges, and the second item is the short-range interaction which represents the interaction between atoms when they are bonded, and rij is the distance between two atoms. Short-range interaction is represented by a Buckingham potential in this work: V(rij ) = A exp(−rij /ρ) − Crij−6
(2)
3. Results and discussions
where A, ρ, and C are constants and fitting parameters derived empirically. Meanwhile, the core–shell [22] model is incorporated to describe the polarizability of the individual ion and its dependence on local atomic environment. In this model, each ion is treated as two coupled parts: a massive core with X charge and a massless shell with Y charge (X + Y is the formal charge of ion). The interaction between core and corresponding shell is regarded as harmonic with a spring constant k and represented as EV (di ) = 21 kdi2 ,
3.1. Potential development The main challenge in using interatomic potentials lies in identifying the valid potential which can accurately describe the material. In our calculations, k, Y, A, ρ, and C for selected interactions are all fitted empirically by a relaxed fitting procedure so that the structural parameters of the compounds are reproduced. Assuming that the short-range repulsion between the rare-earth ions and oxide ions depends only
(3) 2
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Table 1. Interatomic potentials and shell model parameters for o-RMnO3 . Short-range Buckingham potentials 6
Interaction
A (eV)
˚ ρ (A)
˚ ) C (eV A
Mn3+ –O2− O2− –O2− Dy3+ –O2− Y3+ –O2− Ho3+ –O2−
384.881 22 764.300 3468.034 3422.035 3318.034
0.4255 0.1490 0.2964 0.2964 0.2964
0.0 43.0 0.0 0.0 0.0
Shell model Species
Y (e)
˚ −2 ) k (eV A
Mn3+ O2− Dy3+ Y3+ Ho3+
2.8 −2.389 4.327 4.269 4.263
55.88 42.00 18.91 18.91 18.91
Figure 1. Comparison of calculated and experimental [32–35] lattice parameters of R1−x Cax MnO3 (R = Dy, Y, Ho).
The robustness of the proposed potential sets are further checked through investigation of the Ca doping concentration dependence of the lattice parameters of o-R1−x Cax MnO3 , and the comparison with experimental observations [32–35] is shown in figure 1. The potential and shell model parameters of CaMnO3 used in this work are taken from our earlier study [36]. Although Ca2+ is larger than all these rare-earth ions under consideration, the lattice shrinks upon the incorporation of dopants, indicating a change in the structural distortion. Our calculated results on the x-dependent lattice variation of o-R1−x Cax MnO3 accord well with experimental data [32–35], thus further proving the validity of our potentials.
Table 2. Lattice parameters and selected bond lengths of o-RMnO3 . Lattice parameter
Experiment [27] This work ˚ ˚ (A) (A)
DyMnO3
a b c Mn–O1 Mn–O2 Mn–O2
5.834 7.377 5.279 1.898 1.943 2.227
5.769 7.329 5.348 1.873 1.933 2.258
YMnO3
a b c Mn–O1 Mn–O2 Mn–O2
5.802 7.364 5.242 1.903 1.938 2.201
5.729 7.338 5.341 1.883 1.935 2.228
a b c Mn–O1 Mn–O2 Mn–O2
5.835 7.360 5.257 1.904 1.943 2.223
5.749 7.296 5.335 1.876 1.930 2.253
Crystal
HoMnO3
3.2. Intrinsic defect Intrinsic defects in an ionic solid, including Frenkel and Schottky-type disorder, can give rise to intrinsic diffusion of ions. The atomistic simulation technique enables such point defects to be examined in the atomic scale, which are difficult to study experimentally, thus providing a useful probe. The energies of isolated point defects (vacancies and interstitials) were first calculated. For all possible positions tested to confirm the optimal position of interstitial site, lower energies were found for those placed at the midpoint of four MnO6 octahedra, and thus only these were employed in the calculations detailed below. Formation energies for Frenkel disorder, full Schottky disorder and partial Schottky disorder in o-RMnO3 (R = Dy, Y, Ho) were then derived by combining the energies of these point defects. Additionally, we also examined the anti-site pair defect involving R3+ and Mn3+ interchange between their nonequivalent sites. This type of defect is worth considering because ‘intersite cation exchange’ effects have been observed in several perovskite materials [37–39], including analogous manganates LaMnO3 [37, 38] where it is expected to change the mode of Jahn–Teller (JT) distortion, and fundamentally affect the ferromagnetism. These defect reactions are described by the following equations. Note that Kr¨oger–Vink notation is used here.
on the differences of the ionic radii of lanthanide ions, the same value of ρ is used throughout for RMnO3 (R = Dy, Y, Ho). The potential parameters for Mn3+ and O2− are refined to the same values as well. The parameters of the newly derived potentials and the comparison between the reproduced structure parameters and experimental data [31] are listed in tables 1 and 2, respectively. It can be seen that the differences between experimental and calculated lattice parameters and bond lengths are all within 1.5%, and in most cases less than 1%, indicating that our potential well reproduced the complex crystal structure of o-RMnO3 (R = Dy, Y, Ho). The size effect in simulation is also considered. For different sizes of the supercell of RMnO3 containing 4–18 unit cells, the variation in lattice energy and lattice parameters is ˚ respectively. Therefore, the less than 0.001 eV and 0.0001 A, size effect can be neglected in our simulation. 3
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Table 3. Calculated energies for Frenkel disorder, partial Schottky disorder and full Schottky disorder in o-RMnO3 crystals. Energy/eV per defect Reaction
Equation
DyMnO3
YMnO3
HoMnO3
R Frenkel Mn Frenkel O1 Frenkel O2 Frenkel RMnO3 full Schottky R2 O3 partial Schottky Mn2 O3 partial Schottky Anti-site
(5) (6) (6) (7) (8) (9) (10) (11)
5.15 4.33 1.91 1.30 0.79 0.59 0.65 0.61
5.63 5.38 3.09 2.75 0.83 0.62 0.87 0.62
5.40 5.23 1.83 0.92 0.64 0.67 0.41 0.49
Rare-earth elements Frenkel disorder (R = Dy, Y, Ho): ••• 000 R× R → VR + Ri .
(5)
Manganese Frenkel disorder: 000 ••• Mn× Mn → VMn + Mni .
(6)
Oxygen Frenkel disorder: •• 000 O× O → VO + Oi .
(7)
RMnO3 full Schottky disorder: × × 000 000 •• R× R + MnMn + 3OO → VR + VMn + 3VO + RMnO3 . (8)
R2 O3 partial Schottky disorder: × 000 •• 2R× R + 3OO → 2VR + 3VO + R2 O3 .
(9)
Mn2 O3 partial Schottky disorder: × 000 •• 2Mn× Mn + 3OO → 2VMn + 3VO + Mn2 O3 .
Figure 2. Variation of average lattice energy difference between random configurations and cluster configurations of R1−x Cax MnO3 (R = Dy, Y, Ho) with Ca concentration x.
(10)
Anti-site disorder: × × × R× R + MnMn → RMn + MnR .
(11)
details of how the A-site cations distribute themselves in the small R-based system and the detail of the distinct local structure are not clear. In this paper, we investigate the possible Ca2+ cation distribution and local structure in R1−x Cax MnO3 (R = Dy, Y, Ho; x = 1/8, 1/6, 1/4, 1/3). We consider two possible kinds of configurations: one is the configuration with a randomly dispersed distribution of Ca ions and the other is that with a clustered Ca distribution. In all the configurations, Ca2+ ions are surrounded by Mn4+ ions. At every doping level, about 150 randomly dispersed configurations and 16–120 clustered configurations are simulated. For most of the randomly dispersed configurations, the lattice energy cannot converge and the corresponding lattice parameters deviate greatly from the experimental value, while for almost all the clustered configurations, the lattice energy converges and the calculated lattice parameters accord well with experimental data. The difference in the average lattice energy between all the converged clustered configurations and ten selected converged randomly dispersed configurations which deviate the least from experimental results is shown in figure 2. As can be seen, the average lattice energy of clustered configurations is lower than that of randomly dispersed configurations throughout the investigated doping range, indicating that the cluster configurations are more energetically favorable
The corresponding energies for all these types of intrinsic defects are listed in table 3. In order to enable comparisons between different types of disorder reactions, the energies are given as effective defect formation energies. For all the investigated disorders of o-RMnO3 , the Frenkel disorder energies are the highest, especially the cation Frenkel disorders. It can be concluded therefore that vacancies, not interstitials, will be the dominant structural defects. This is to be expected from the close-packed nature of the perovskite lattice. However, the low energies associated with the formation of Schottky defects possibly imply the structural metastable character of the orthorhombic structure for these last terms of the lanthanide manganates. Moreover, it is interesting to find that the anti-site pair seems to be likely within the structure. Our analysis of the local relaxation around RMn and MnR defects indicates very small changes of ˚ in the local R/Mn–O bond lengths. This result less than 0.08 A suggests the possibility of a small degree of anti-site disorder of R and Mn ions over A and B sites. 3.3. Clusters in lightly Ca2+ doped R1−x Cax MnO3 (R = Dy, Y, Ho; x = 1/8, 1/6, 1/4, 1/3) Although some studies have revealed possible evidence of inhomogeneities in mixed valence manganates [40–42], the 4
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than the random configurations. This confirms that these doped manganates are intrinsically inhomogeneous [43]. With the doping concentration increasing from 1/8 to 1/3, the difference in lattice energy between the two configuration types is enlarged from about 0.075 eV per unit cell to 0.27–0.34 eV per unit cell, indicating increasing stability of the clusters. This result seems to confirm the assumption that the phase separation behavior and the relative stabilities of the correlated structures in this kind of system depend crucially on the Mn4+ /Mn3+ ratio [12]. Moreover, the difference in lattice energy as well as the variation of it seems to be slightly larger for smaller R-based R1−x Cax MnO3 (rHo < rY < rDy ). This trend shows the possibly close relationship between the ionic radii of R and the tendency of cluster formation that inhomogeneities are favored by manganates with smaller hrA i [43]. The influence of R size becomes more obvious at higher doping level. The detailed local structure around the A-site cation R/Ca is further investigated. The average of R/Ca–Mn bond lengths at every doping level are shown in figure 3(a). It is found that the introduction of Ca2+ reduces the lattice distortion generally. More specifically, the average R–Mn bond length is slightly smaller than that of its parent compounds RMnO3 , and further decreases with increasing doping level, while the average Ca–Mn bond length is slightly larger than the Ca–Mn bond length in CaMnO3 and remains almost the same throughout the doping range. In order to quantify the relative local distortion around the A-site cation, we define the δR/Ca–Mn parameter, concerning the deviation of R/Ca–Mn distances with respect to the average hR/Ca–Mni value, as δR/Ca–Mn = (1/8)6n=1,8 [(dn − hdi)/hdi]2 . Figure 3(b) includes the variation of δR/Ca–Mn with the Ca concentration in R1−x Cax MnO3 . δCa–Mn are found to be significantly smaller than δR–Mn at all doping level, indicating a more distorted local environment around R3+ ions than Ca2+ . Besides, the anisotropy of R–Mn bonds seems to increase from Dy to Ho, possibly due to the reduction of ionic radii, while the δCa–Mn value does not significantly evolve with rR . A progressive decrease of the δR/Ca–Mn can also be observed for both R3+ and Ca2+ as Ca2+ concentration is increased. However, the magnitude of reduction seems not to be sensitive to R radii. It can be concluded from the discussion above that Ca2+ doping may lead to the formation of structurally and chemically distinct inhomogeneities, namely CaMnO3 -like clusters, embedded in a background of RMnO3 structure. According to our calculation, at the same doping level, the formation of a large cluster is even more favorable than that of several smaller ones. The trend is strengthened by smaller R ions. We believe that such behavior will be crucial to the complete theoretical study of these compounds, particularly in the context of phase separation.
Figure 3. Variation of (a) average eight R/Ca–Mn bond lengths and (b) δR/Ca–Mn of R1−x Cax MnO3 (R = Dy, Y, Ho) with Ca concentration x. hi denotes average value.
focused on the real-space images of charge ordering have proposed some stripe models [44–49] to illustrate the charge ordering patterns for La0.5 A0.5 MnO3 (A = Ca, Sr or Ba). But whether the stripe models suggested for large rare-earth manganates are appropriate for the cases of small rare-earth (R = Dy, Y, Ho)-based manganates or not is still unknown. We take Y0.5 Ca0.5 MnO3 as an example to investigate the arrangement of atoms in R0.5 Ca0.5 MnO3 (R = Dy, Y, Ho). Three types of configurations are considered: randomly dispersed configuration, paired stripe configuration [45–47] and layer stripe configuration [49]. The stripe configuration models are schematically shown in figures 4(a) and (b), respectively. Although the ordered distribution of Mn ions has been studied extensively, the distribution of A-site cations has not yet found consensus [50–53]. According to our simulation, the configurations in which Ca2+ and Mn4+ ions are separated far away are always structurally unreasonable. Thus for all the configurations investigated below, the Ca2+ ions are located close to Mn4+ . More specifically, for random configurations, Mn3+ and Mn4+ ions are randomly distributed and closely surrounded by Y or Ca ions, respectively; while for stripe configurations, Y/Ca ions are also ordered along with Mn3+ and Mn4+ stripes. The average lattice energy and lattice parameters of the simulated configurations and a comparison with experimental lattice parameters [33] of Y0.5 Ca0.5 MnO3 are demonstrated in figure 5. The charge ordered configuration therein is the average result of all the stripe configurations.
3.4. Charge ordering in R0.5 Ca0.5 MnO3 (R = Dy, Y, Ho) Charge ordering is one of the most fascinating aspects of alkaline-earth doped manganates, and has significant effects on their transport and magnetic properties. Earlier studies 5
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Figure 4. Charge ordering models of (a) paired stripe and (b) layer stripe of R0.5 Ca0.5 MnO3 ; and calculated [010] HRTEM image of (c) o-YMnO3 , (d) paired stripe of Y0.5 Ca0.5 MnO3 and (e) layer stripe of Y0.5 Ca0.5 MnO3 .
Figure 5. The average lattice energy and lattice parameters of the simulated configurations and comparison with experimental [33] lattice parameters of Y0.5 Ca0.5 MnO3 .
Figure 6. Mn–O bond length of the layer stripe model. hi denotes average value.
As demonstrated, the randomly dispersed configurations have the highest lattice energy, whose average value is 1.21 eV higher than that of configurations with charge ordered stripes, and the lattice parameters also deviate from the experimental value significantly. This seems to illustrate that the formation of charge ordered stripes are more energetically favorable and structurally reasonable. Besides, by comparing the two different stripe models, one may identify that the layer stripe model has an even lower lattice energy, and the corresponding lattice parameters accord better with experimental data as well. This indicates that the layered stripe should be a more reasonable atomic distribution configuration. However, the lattice energy difference between pair stripe and layer stripe is as slight as 0.34 eV. Therefore, it is likely that both the stripe patterns can be observed in Y0.5 Ca0.5 MnO3 compound. The
coexistence of different of charge ordered phase has indeed been observed experimentally [54, 55]. We further investigated the internal structure of layer stripes in Y0.5 Ca0.5 MnO3 . As illustrated in figure 4(b), there are three Mn3+ stripes and three Mn4+ stripes along the a direction in the Mn–O2 plane. The six Mn–O bond lengths around each Mn ion are calculated and shown in figure 6. The average Mn3+ –O bond length is larger and close to the average Mn3+ –O bond of YMnO3 while the average Mn4+ –O bond length is smaller and close to Mn4+ –O bond length in CaMnO3 . This seems to indicate that the local structure in Y0.5 Ca0.5 MnO3 is not homogeneous, but distinct for different stripes. To be more specific, the supercell under investigation can be divided into two chemically and structurally different parts: a YMnO3 -like layer and a CaMnO3 -like layer. 6
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The same configurations are performed on both Dy0.5 Ca0.5 MnO3 and Ho0.5 Ca0.5 MnO3 to investigate the possible influence of the size of R ion on the charge ordering behavior. The tendency to form layered stripes is found in both the compounds. Additionally, the difference of lattice energy between random configuration and layer stripe configuration increases from 0.79 eV for Dy0.5 Ca0.5 MnO3 to 1.83 eV for Ho0.5 Ca0.5 MnO3 , indicating that RMnO3 with smaller R ionic radii is more likely to become charge ordered, although simultaneously the size mismatch of A-site cation increases from Dy to Ho, which suppresses charge ordering [6]. Our results accentuate the role of A-site cation size in these compounds [56]. The variation of the two most important distortions in manganate perovskites [57]—JT distortion and tilt angle of MnO6 octahedra of every stripe along the a-direction—are included in figures 7(a) and (b), respectively. The JT distortion is evaluated by the 1d parameter [31], concerning the deviation of Mn–O distance with respect to the average hMn–Oi value, as 1d = (1/6)6n=1,6 [(dn − hdi)/hdi]2 . The octahedra tilt angle is obtained from the hMn–O–Mni bond angle hθ i as hωi = 180◦ − hθ i [31]. In both of the figures in figure 7, an obvious structural distinction between two layers can be observed for all the three compounds. The JT distortion is concentrated on the Mn3+ O6 octahedra, but is smaller than that in RMnO3 , whereas almost no distortion occurs on the Mn4+ O6 octahedra. This confirms the conclusion above that Ca2+ doped o-RMnO3 will be divided by ordered stripes and form RMnO3 -like and CaMnO3 -like layers. Furthermore, it can be observed that the reduction of 1d of Mn3+ O6 octahedra experiences a progressive decrease from Dy to Ho. It seems that the doping influence on JT distortion is related to the size of R ion to some degree, and that manganate with a smaller R is less affected. As to the tilting angle, a decrease upon doping can be observed over all the investigated supercell, which implies an increase of the tolerance factor, and thus a stabilizing of the structure. However, compared with the large reduction of Jahn–Teller distortion, the decrease of tilt angle is rather small. Besides, the octahedral tilt angle seems not to be sensitive to the ionic radii of R, as the difference between the maximum tilt angle reduction of Mn3+ O6 octahedra of Dy0.5 Ca0.5 MnO3 , Y0.5 Ca0.5 MnO3 and Ho0.5 Ca0.5 MnO3 is within 0.7◦ , and even smaller for Mn4+ O6 octahedra. Moreover, while the anisotropy of the Mn–O bonds shows a significant difference between the RMnO3 -like and CaMnO3 -like layers, the difference of tilt angle between the two layers is rather small. This seems to indicate that while steric effects associated with the octahedral tilts act cooperatively with the JT effect in the charge ordering state [58], it is the JT effect that dominates [59]. Above all, charge ordered stripes are predicted to present in R0.5 Ca0.5 MnO3 , in the form of RMnO3 -like layer and CaMnO3 -like layer, and the tendency grows as the R ionic radius decreases, where the JT effect is less affected. Based on further extending our simulation supercell along both aand c-axis directions, we calculated some HRTEM images to better illustrate the real lattice image of the charge ordering state. Figure 4(c) shows the calculated image of original
Figure 7. Local structure of the layer stripe model of R1−x Cax MnO3 (R = Dy, Y, Ho). (a) The Jahn–Teller distortion and (b) tilt angle of MnO6 octahedra along c-direction stripes.
o-YMnO3 single crystal, and figures 4(d) and (e) are the HRTEM images of the paired stripe model and layer stripe model of Y0.5 Ca0.5 MnO3 , respectively. The stripes of charge ordering are running along the c direction with a modulation ˚ and ∼3a ≈ 16.4 A, ˚ respectively. It period of ∼a ≈ 5.4 A can be clearly observed that charge ordering can introduce contrast in HRTEM images by different local chemistry composition and local structure [51].
4. Conclusions New interatomic potentials are proposed for small R-based orthorhombic RMnO3 (R = Dy, Y, Ho), which accurately model the structural properties of the compounds. They are further employed to investigate the intrinsic defects of these manganates as well as the formation of microscopic phases in mixed valence o-R1−x Cax MnO3 (R = Dy, Y, Ho). Schottky disorders are found to be the dominant structural defects in o-RMnO3 , and the possibility of a small degree of anti-site disorder of R and Mn ions over A and B sites is found. As the doping level increases, the doped Ca ions tend to aggregate in the system, and form chemically and structurally distinct CaMnO3 -like clusters embedded in the RMnO3 background. Charge ordered stripe structure is predicted for o-R0.5 Ca0.5 MnO3 , which consists of RMnO3 -like layer and CaMnO3 -like layer. Such inhomogeneous configurations are showed to be energetically preferable and structurally more 7
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reasonable. They may be a representation of microscopic phase separation. Moreover, the tendency to form charge ordered stripes increased with the decrease of R size. The size of R ion also significantly affects the doping effect on Jahn–Teller distortion that larger R indicates a larger reduction of the anisotropy of Mn–O bonds in Mn3+ O6 octahedra. However, the change of octahedral tilting upon doping does not vary much with the R radii.
[24] Filippetti A and Hill N A 2001 J. Magn. Magn. Mater. 236 176 [25] Picozzi S, Yamauchi K, Bihlmayer G and Bl¨ugel S 2006 Phys. Rev. B 74 094402 [26] Mizokawa T and Fujimori A 1996 Phys. Rev. B 54 8 [27] Yamauchi K, Freimuth F, Bl¨ugel S and Picozzi S 2008 Phys. Rev. B 78 014403 [28] Ren C-Y 2009 Phys. Rev. B 79 125113 [29] Woodley S M, Battle P D, Gale J D, Richard C and Catlow A 2003 Chem. Mater. 15 1669 [30] Rao M N, Kaur N, Chaplot S L, Gaur N K and Singh R K 2009 J. Phys.: Condens. Matter 21 355402 [31] Alonso J A, Mart´ınez-Lope M J, Casais M T and Fern´andez-D´ıaz M T 2000 Inorg. Chem. 39 917 [32] Moure C, Gutierrez D, Pe˜na O and Dur´an P 2002 Bol. Soc. Esp. Cer´am. Vidrio 41 519 [33] Causaa M T, Aliaga H, Vega D, Tovar M, Alascio B, Salva H R and Winkler E 2004 J. Magn. Magn. Mater. 81 272 [34] Takeda Y, Hoshino Y, Sakaki Y, Kawahara T, Imanishi N and Yamamoto O 1992 J. Mater. Sci. Lett. 11 1113 [35] Rout P P and Roul B K 2013 J. Mater. Sci. Mater. Electron. 24 2493–9 [36] Zhang X and Wang L 2003 J. Phys. Chem. Solids 64 1207 [37] Chukalkin Yu G and Teplykh A E 2006 Phys. Solid State 48 2310 [38] Gu M, Wang Z, Biegalski M D, Christen H M, Takamura Y and Browning N D 2013 Appl. Phys. Lett. 102 151911 [39] Singh D 2007 Phys. Rev. B 76 214115 [40] Mathieu R, Nordblad P, Nam D N H, Phuc N X and Khiem N V 2001 Phys. Rev. B 63 174405 [41] Serrao C R, Sahu J R and Ghosh A 2010 Bull. Mater. Sci. 33 169 [42] Wang X L, Horvat J, Liu H K and Dou S X 1998 J. Magn. Magn. Mater. 182 L1 [43] Shenoy V B, Sarma D D and Rao C N R 2006 Chem Phys Chem 7 2053 [44] Wollan E O and Koehler W C 1955 Phys. Rev. 100 545 [45] Hotta T, Feiguin A and Dagotto E 2001 Phys. Rev. Lett. 86 4922 [46] Brey L 2004 Phys. Rev. Lett. 92 127202 [47] Chen C H, Cheong S-W and Hwang H Y 1997 J. Appl. Phys. 81 4326 [48] Ahn K H and Millis A J 1998 Phys. Rev. B 58 3697 [49] Tang F L and Zhang X 2006 Phys. Rev. B 73 144401 [50] de Graaf C, Sousa C and Broer R 2004 Phys. Rev. B 70 235104 [51] Wang R, Gui J, Zhu Y and Moodenbaugh A R 2000 Phys. Rev. B 61 11946 [52] Mathieu R, Akahoshi D, Asamitsu A, Tomioka Y and Tokura Y 2004 Phys. Rev. Lett. 93 227202 [53] Shibata T, Bunker B, Mitchell J F and Schiffer P 2002 Phys. Rev. Lett. 88 207205 [54] Tao J, Niebieskikwiat D, Salamon M B and Zuo J M 2005 Phys. Rev. Lett. 94 147206 [55] Loudon J C and Midgley P A 2005 Phys. Rev. B 71 220408 [56] Blasco J, Garc´ıa J, de Teresa J M, Ibarra M R, P´erez J, Algarabel P A, Marquina C and Ritter C 1997 J. Phys.: Condens. Matter 9 10321 [57] Glazer A M 1975 Acta Crystallogr. A 31 756 [58] Dlouh´a M, Vratislav S, Jir´ak Z, Hejtm´anek J, Kn´ızek K and Sedmidubsk´y D 2004 Appl. Phys. A 74 (Suppl.) S673 [59] Rao C N R and Cheetham A K 1997 Adv. Mater. 9 13
Acknowledgments We would like to acknowledge financial support by the National Science Foundation of China (11074141, 11174169, 11234007) and the Ministry of Science and Technology of China (2009CB929202). This work made use of the resources of the Beijing National Center for Electron Microscopy.
References [1] Ziese M 2002 Rep. Prog. Phys. 65 143 [2] Jin S, Tiefel T H, McCormack M, Fastnacht R A, Ramesh R and Chen L H 1994 Science 264 413 [3] Radaelli P G, Marezio M, Hwang H Y, Cheong S-W and Batlogg B 1995 Phys. Rev. Lett. 75 4488 [4] Arulraj A, Gundakaram R, Biswas A, Gayathri N, Raychaudhuri A K and Rao C N R 1998 J. Phys.: Condens. Matter 10 4447 [5] Kumar N and Rao C N R 1997 J. Solid State Chem. 129 363 [6] Sundaresan A, Maignan A and Raveau B 1997 Phys. Rev. B 56 9 [7] Moreo A, Yunoki S and Dagotto E 1999 Science 283 2034 [8] Uehara M, Mori S, Chen C H and Cheong S-W 1999 Nature 399 560 [9] F¨ath M, Freisem S, Menovsky A A, Tomioka Y, Aarts J and Mydosh J A 1999 Science 285 1540 [10] Biˇskup N, de Andr´es A, Ochando I M and Casais M T 2006 Phys. Rev. B 73 184404 [11] Terai T, Sasaki T, Kakeshita T, Fukuda T and Saburi T 2001 Phys. Rev. B 61 5 [12] Rao C N R 2000 J. Phys. Chem. B 104 5877 [13] Arulraj A, Santhosh P N, Gopalan R S, Guha A, Raychaudhuri A K, Kumar N and Rao C N R 1998 J. Phys.: Condens. Matter 10 8497 [14] Zhang X and Catlow C R A 1993 Phys. Rev. B 47 5315 [15] Zhang X, Ong C K and Stoneham A M 1994 J. Phys.: Condens. Matter 6 5647 [16] Jiang N and Zhang X 2012 J. Phys.: Condens. Matter 24 235402 [17] Jiang N and Zhang X 2013 J. Appl. Phys. 113 164104 [18] Zacate M O, Minervini L, Bradfield D J, Grimes R W and Sickafus K E 2000 Solid State Ion. 128 243 [19] Stokes S J and Islam M S 2010 J. Mater. Chem. 20 6258 [20] Gale J D and Rohl A L 2003 Mol. Simul. 29 291 [21] Catlow C R A 1987 Solid State Chemistry: Techniques (Oxford: Clarendon) [22] Dick B G and Overhauser A W 1958 Phys. Rev. 112 90 [23] Mott N F and Littleton M T 1938 Trans. Faraday Soc. 34 0485
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Atomic distribution, local structure and cation size effect in o-R1−x Cax MnO3 (R = Dy, Y, and Ho)
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2013 J. Phys.: Condens. Matter 25 475901 (http://iopscience.iop.org/0953-8984/25/47/475901) View the table of contents for this issue, or go to the journal homepage for more
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IOP PUBLISHING
JOURNAL OF PHYSICS: CONDENSED MATTER
J. Phys.: Condens. Matter 25 (2013) 475901 (8pp)
doi:10.1088/0953-8984/25/47/475901
Atomic distribution, local structure and cation size effect in o-R1−xCaxMnO3 (R = Dy, Y, and Ho) Ning Jiang, X Zhang and Yi Yu Key Laboratory of Advanced Materials, School of Materials Science and Engineering, People’s Republic of China Beijing National Center for Electron Microscopy, Tsinghua University, Beijing 100084, People’s Republic of China E-mail: [email protected]
Received 20 July 2013, in final form 7 September 2013 Published 31 October 2013 Online at stacks.iop.org/JPhysCM/25/475901 Abstract We propose new interatomic potentials for the small rare-earth-based orthorhombic RMnO3 (R = Dy, Y, Ho), which accurately model the structural properties of these extreme cases of lanthanide manganate series. They are further employed to investigate the intrinsic defects in o-RMnO3 and the cation distribution and local structure in o-R1−x Cax MnO3 (R = Dy, Y, Ho). Schottky disorders are found to be the dominant structural defects, and the possibility of a small degree of anti-site disorder of R and Mn ions over A and B sites is found. The introduced Ca dopants tend to form chemically and structurally like CaMnO3 clusters in the lightly doped system, which can be regarded as representations of microscopic phase separation. The local structural disorder is reduced with increasing doping density. For o-R0.5 Ca0.5 MnO3 (R = Dy, Y, Ho), the charge ordering state is intrinsically favored, and the layer stripe model is shown to be energetically more favorable and structurally more reasonable. Moreover, the tendency to form charge ordered stripes increases with the decrease of R size. The local structure in the layer stripe pattern deviates largely from the average structure: RMnO3 -like and CaMnO3 -like layers are formed. The size of R ion has a significant influence on the doping effect on Jahn–Teller (JT) distortion and a manganate with a larger R will experience a larger reduction on the anisotropy of Mn–O bonds in Mn3+ O6 octahedra. However, the change of octahedral tilting upon doping does not vary much with R radii. (Some figures may appear in colour only in the online journal)
1. Introduction
attention due to their rich display of interesting basic physics problems and possible applications [1–3]. So far, the large R-based compounds (La, Pr, and Nd) have been intensely investigated, whereas few studies have concentrated on their small R (Dy, Y, and Ho) counterparts. Although physical properties might be expected to be similar for these two groups, there are in fact numerous qualitative differences [4–6]. Many questions regarding the phase topology of R1−x Ax MnO3 , including clusters and charge ordering stripes at different doping level, which is one of the most attractive areas of research, remain to be solved to understand the behaviors. In particular, the inhomogeneous distribution in the lightly doped manganates where the size scale of the formed clusters
Rare-earth manganates RMnO3 prepared under ordinary synthetic conditions crystallize in the orthorhombic perovskite structure Pnma (o-RMnO3 ) for R = La–Dy with large ionic radii and in the hexagonal structure P63 cm (h-RMnO3 ) for R = Y, Ho–Lu with smaller ionic radii. However, by means of special soft-chemistry synthesis, applying pressure, or epitaxial thin-film growth, the hexagonal structure can be converted into the more dense, albeit metastable orthorhombic phase. Perovskite manganates with mixed manganese valence, R1−x Ax MnO3 , where R is a trivalent rare-earth ion and A represents a divalent alkaline-earth ion, have attracted great 0953-8984/13/475901+08$33.00
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c 2013 IOP Publishing Ltd Printed in the UK & the USA
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varies extraordinarily from nanometer [7] to micrometer [8, 9] requires further understanding. For manganates with an extremely small average A-site cation size hrA i (hi denotes average value), whether the charge ordering phenomenon will be present still needs further confirmation [10, 11] and the real lattice image is still not clear [12]. The factors that should be responsible for the extraordinary sensitivity of charge ordering to hrA i are still uncertain [12, 13]. Besides, a probing of the local structure of the inhomogeneities in the doped manganates, which helps understanding the physical properties of these compounds, is of great value, but is still lacking. The aim of this study is to address the above issues using well-established atomistic modeling techniques. We develop new accurate and robust interatomic potentials for o-RMnO3 (R = Dy, Y, Ho), which are the last, much distorted terms of the RMnO3 series. Then a comprehensive calculation is performed to provide detailed investigations on the intrinsic defect chemistry of them, as well as possible cation distribution pattern and local structure in Ca2+ doped compounds with the doping range varying from 0 to 0.5. The cation size effects are also discussed.
where di is the relative displacement of core and shell of ion i. The ion polarization can be calculated as Y2 , (4) k where fitting parameters Y and k are the shell charge and harmonic force constant, respectively. Defects simulated at the infinitely dilute limit were achieved by the Mott–Littleton approach [23], where the lattice relaxation about charged defects and dopants is treated by partitioning the crystal lattice into two regions. Ions in a spherical inner region surrounding the individual defect are relaxed explicitly, while the remainder of the crystal, where the defect forces are relatively weak, is treated by more approximate quasi-continuum methods. In this way, long-range lattice relaxation is modeled effectively and the crystal is not considered simply as a rigid lattice. In this work, the initial structure we start with for studying o-RMnO3 (R = Dy, Y, and Ho) is the crystallographic unit cell, which has four R3+ ions, four Mn3+ ions, four O1 ions, and eight O2 ions. However, in order to meet the fractional occupancies in R1−x Cax MnO3 and make the calculations more efficient, the unit cell of RMnO3 is extended to a 3 × 2 × 3 supercell (Pnma space group). Previous first-principles calculations have contributed a lot to the theoretical investigations of these compounds, concerning their basic electronic properties [24] and nonconventional magnetic ordering [25, 26], the key ingredient for the rising of ferroelectric polarization [27], and the interplay between the lattice, magnetism, and ferroelectricity [26–28]. However, there is little information about the hole-doping induced processes and structures in the atomic scale. Compared with the first-principles approach, the classical atomistic simulation employed here has the merit of accessibility to a relatively large number of atoms with respect to the real lattice image and detailed structural distortion, which lie beyond the limits of purely quantum mechanical approaches. Although the study of rare-earth manganates RMnO3 (R = Dy, Y, and Ho) by classical atomistic simulation has been reported previously, the potentials therein fail to reproduce individual material accurately in particular [29] or is not universal for dopant calculation [30]. The lack of either a fully accurate potentials-based or ab initio-based study of small R-based o-RMnO3 and their promising compounds o-R1−x Cax MnO3 supports the necessity of the calculations reported here. α=
2. Simulation methods The atomistic simulation method used in this work has already been successfully demonstrated to describe the characteristic and properties of a range of oxide-based materials [14–19]. This technique, embodied in the GULP [20] code, is reviewed in detail elsewhere [21], hence only a brief description will be given here. Our simulation is based on the widely used successful Born model of ionic solids, where the effect of the electrons are subsumed into effective atoms, and the energy is decomposed into the sum of self-energies and the pairwise interaction of the total number of atoms. Within this model, the lattice energy E can be expressed as 1 X qi qj E= + V(rij ) , (1) 2 i,j rij where the first item is Coulombic energy introduced by long-range interactions of effective charges, and the second item is the short-range interaction which represents the interaction between atoms when they are bonded, and rij is the distance between two atoms. Short-range interaction is represented by a Buckingham potential in this work: V(rij ) = A exp(−rij /ρ) − Crij−6
(2)
3. Results and discussions
where A, ρ, and C are constants and fitting parameters derived empirically. Meanwhile, the core–shell [22] model is incorporated to describe the polarizability of the individual ion and its dependence on local atomic environment. In this model, each ion is treated as two coupled parts: a massive core with X charge and a massless shell with Y charge (X + Y is the formal charge of ion). The interaction between core and corresponding shell is regarded as harmonic with a spring constant k and represented as EV (di ) = 21 kdi2 ,
3.1. Potential development The main challenge in using interatomic potentials lies in identifying the valid potential which can accurately describe the material. In our calculations, k, Y, A, ρ, and C for selected interactions are all fitted empirically by a relaxed fitting procedure so that the structural parameters of the compounds are reproduced. Assuming that the short-range repulsion between the rare-earth ions and oxide ions depends only
(3) 2
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Table 1. Interatomic potentials and shell model parameters for o-RMnO3 . Short-range Buckingham potentials 6
Interaction
A (eV)
˚ ρ (A)
˚ ) C (eV A
Mn3+ –O2− O2− –O2− Dy3+ –O2− Y3+ –O2− Ho3+ –O2−
384.881 22 764.300 3468.034 3422.035 3318.034
0.4255 0.1490 0.2964 0.2964 0.2964
0.0 43.0 0.0 0.0 0.0
Shell model Species
Y (e)
˚ −2 ) k (eV A
Mn3+ O2− Dy3+ Y3+ Ho3+
2.8 −2.389 4.327 4.269 4.263
55.88 42.00 18.91 18.91 18.91
Figure 1. Comparison of calculated and experimental [32–35] lattice parameters of R1−x Cax MnO3 (R = Dy, Y, Ho).
The robustness of the proposed potential sets are further checked through investigation of the Ca doping concentration dependence of the lattice parameters of o-R1−x Cax MnO3 , and the comparison with experimental observations [32–35] is shown in figure 1. The potential and shell model parameters of CaMnO3 used in this work are taken from our earlier study [36]. Although Ca2+ is larger than all these rare-earth ions under consideration, the lattice shrinks upon the incorporation of dopants, indicating a change in the structural distortion. Our calculated results on the x-dependent lattice variation of o-R1−x Cax MnO3 accord well with experimental data [32–35], thus further proving the validity of our potentials.
Table 2. Lattice parameters and selected bond lengths of o-RMnO3 . Lattice parameter
Experiment [27] This work ˚ ˚ (A) (A)
DyMnO3
a b c Mn–O1 Mn–O2 Mn–O2
5.834 7.377 5.279 1.898 1.943 2.227
5.769 7.329 5.348 1.873 1.933 2.258
YMnO3
a b c Mn–O1 Mn–O2 Mn–O2
5.802 7.364 5.242 1.903 1.938 2.201
5.729 7.338 5.341 1.883 1.935 2.228
a b c Mn–O1 Mn–O2 Mn–O2
5.835 7.360 5.257 1.904 1.943 2.223
5.749 7.296 5.335 1.876 1.930 2.253
Crystal
HoMnO3
3.2. Intrinsic defect Intrinsic defects in an ionic solid, including Frenkel and Schottky-type disorder, can give rise to intrinsic diffusion of ions. The atomistic simulation technique enables such point defects to be examined in the atomic scale, which are difficult to study experimentally, thus providing a useful probe. The energies of isolated point defects (vacancies and interstitials) were first calculated. For all possible positions tested to confirm the optimal position of interstitial site, lower energies were found for those placed at the midpoint of four MnO6 octahedra, and thus only these were employed in the calculations detailed below. Formation energies for Frenkel disorder, full Schottky disorder and partial Schottky disorder in o-RMnO3 (R = Dy, Y, Ho) were then derived by combining the energies of these point defects. Additionally, we also examined the anti-site pair defect involving R3+ and Mn3+ interchange between their nonequivalent sites. This type of defect is worth considering because ‘intersite cation exchange’ effects have been observed in several perovskite materials [37–39], including analogous manganates LaMnO3 [37, 38] where it is expected to change the mode of Jahn–Teller (JT) distortion, and fundamentally affect the ferromagnetism. These defect reactions are described by the following equations. Note that Kr¨oger–Vink notation is used here.
on the differences of the ionic radii of lanthanide ions, the same value of ρ is used throughout for RMnO3 (R = Dy, Y, Ho). The potential parameters for Mn3+ and O2− are refined to the same values as well. The parameters of the newly derived potentials and the comparison between the reproduced structure parameters and experimental data [31] are listed in tables 1 and 2, respectively. It can be seen that the differences between experimental and calculated lattice parameters and bond lengths are all within 1.5%, and in most cases less than 1%, indicating that our potential well reproduced the complex crystal structure of o-RMnO3 (R = Dy, Y, Ho). The size effect in simulation is also considered. For different sizes of the supercell of RMnO3 containing 4–18 unit cells, the variation in lattice energy and lattice parameters is ˚ respectively. Therefore, the less than 0.001 eV and 0.0001 A, size effect can be neglected in our simulation. 3
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Table 3. Calculated energies for Frenkel disorder, partial Schottky disorder and full Schottky disorder in o-RMnO3 crystals. Energy/eV per defect Reaction
Equation
DyMnO3
YMnO3
HoMnO3
R Frenkel Mn Frenkel O1 Frenkel O2 Frenkel RMnO3 full Schottky R2 O3 partial Schottky Mn2 O3 partial Schottky Anti-site
(5) (6) (6) (7) (8) (9) (10) (11)
5.15 4.33 1.91 1.30 0.79 0.59 0.65 0.61
5.63 5.38 3.09 2.75 0.83 0.62 0.87 0.62
5.40 5.23 1.83 0.92 0.64 0.67 0.41 0.49
Rare-earth elements Frenkel disorder (R = Dy, Y, Ho): ••• 000 R× R → VR + Ri .
(5)
Manganese Frenkel disorder: 000 ••• Mn× Mn → VMn + Mni .
(6)
Oxygen Frenkel disorder: •• 000 O× O → VO + Oi .
(7)
RMnO3 full Schottky disorder: × × 000 000 •• R× R + MnMn + 3OO → VR + VMn + 3VO + RMnO3 . (8)
R2 O3 partial Schottky disorder: × 000 •• 2R× R + 3OO → 2VR + 3VO + R2 O3 .
(9)
Mn2 O3 partial Schottky disorder: × 000 •• 2Mn× Mn + 3OO → 2VMn + 3VO + Mn2 O3 .
Figure 2. Variation of average lattice energy difference between random configurations and cluster configurations of R1−x Cax MnO3 (R = Dy, Y, Ho) with Ca concentration x.
(10)
Anti-site disorder: × × × R× R + MnMn → RMn + MnR .
(11)
details of how the A-site cations distribute themselves in the small R-based system and the detail of the distinct local structure are not clear. In this paper, we investigate the possible Ca2+ cation distribution and local structure in R1−x Cax MnO3 (R = Dy, Y, Ho; x = 1/8, 1/6, 1/4, 1/3). We consider two possible kinds of configurations: one is the configuration with a randomly dispersed distribution of Ca ions and the other is that with a clustered Ca distribution. In all the configurations, Ca2+ ions are surrounded by Mn4+ ions. At every doping level, about 150 randomly dispersed configurations and 16–120 clustered configurations are simulated. For most of the randomly dispersed configurations, the lattice energy cannot converge and the corresponding lattice parameters deviate greatly from the experimental value, while for almost all the clustered configurations, the lattice energy converges and the calculated lattice parameters accord well with experimental data. The difference in the average lattice energy between all the converged clustered configurations and ten selected converged randomly dispersed configurations which deviate the least from experimental results is shown in figure 2. As can be seen, the average lattice energy of clustered configurations is lower than that of randomly dispersed configurations throughout the investigated doping range, indicating that the cluster configurations are more energetically favorable
The corresponding energies for all these types of intrinsic defects are listed in table 3. In order to enable comparisons between different types of disorder reactions, the energies are given as effective defect formation energies. For all the investigated disorders of o-RMnO3 , the Frenkel disorder energies are the highest, especially the cation Frenkel disorders. It can be concluded therefore that vacancies, not interstitials, will be the dominant structural defects. This is to be expected from the close-packed nature of the perovskite lattice. However, the low energies associated with the formation of Schottky defects possibly imply the structural metastable character of the orthorhombic structure for these last terms of the lanthanide manganates. Moreover, it is interesting to find that the anti-site pair seems to be likely within the structure. Our analysis of the local relaxation around RMn and MnR defects indicates very small changes of ˚ in the local R/Mn–O bond lengths. This result less than 0.08 A suggests the possibility of a small degree of anti-site disorder of R and Mn ions over A and B sites. 3.3. Clusters in lightly Ca2+ doped R1−x Cax MnO3 (R = Dy, Y, Ho; x = 1/8, 1/6, 1/4, 1/3) Although some studies have revealed possible evidence of inhomogeneities in mixed valence manganates [40–42], the 4
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N Jiang et al
than the random configurations. This confirms that these doped manganates are intrinsically inhomogeneous [43]. With the doping concentration increasing from 1/8 to 1/3, the difference in lattice energy between the two configuration types is enlarged from about 0.075 eV per unit cell to 0.27–0.34 eV per unit cell, indicating increasing stability of the clusters. This result seems to confirm the assumption that the phase separation behavior and the relative stabilities of the correlated structures in this kind of system depend crucially on the Mn4+ /Mn3+ ratio [12]. Moreover, the difference in lattice energy as well as the variation of it seems to be slightly larger for smaller R-based R1−x Cax MnO3 (rHo < rY < rDy ). This trend shows the possibly close relationship between the ionic radii of R and the tendency of cluster formation that inhomogeneities are favored by manganates with smaller hrA i [43]. The influence of R size becomes more obvious at higher doping level. The detailed local structure around the A-site cation R/Ca is further investigated. The average of R/Ca–Mn bond lengths at every doping level are shown in figure 3(a). It is found that the introduction of Ca2+ reduces the lattice distortion generally. More specifically, the average R–Mn bond length is slightly smaller than that of its parent compounds RMnO3 , and further decreases with increasing doping level, while the average Ca–Mn bond length is slightly larger than the Ca–Mn bond length in CaMnO3 and remains almost the same throughout the doping range. In order to quantify the relative local distortion around the A-site cation, we define the δR/Ca–Mn parameter, concerning the deviation of R/Ca–Mn distances with respect to the average hR/Ca–Mni value, as δR/Ca–Mn = (1/8)6n=1,8 [(dn − hdi)/hdi]2 . Figure 3(b) includes the variation of δR/Ca–Mn with the Ca concentration in R1−x Cax MnO3 . δCa–Mn are found to be significantly smaller than δR–Mn at all doping level, indicating a more distorted local environment around R3+ ions than Ca2+ . Besides, the anisotropy of R–Mn bonds seems to increase from Dy to Ho, possibly due to the reduction of ionic radii, while the δCa–Mn value does not significantly evolve with rR . A progressive decrease of the δR/Ca–Mn can also be observed for both R3+ and Ca2+ as Ca2+ concentration is increased. However, the magnitude of reduction seems not to be sensitive to R radii. It can be concluded from the discussion above that Ca2+ doping may lead to the formation of structurally and chemically distinct inhomogeneities, namely CaMnO3 -like clusters, embedded in a background of RMnO3 structure. According to our calculation, at the same doping level, the formation of a large cluster is even more favorable than that of several smaller ones. The trend is strengthened by smaller R ions. We believe that such behavior will be crucial to the complete theoretical study of these compounds, particularly in the context of phase separation.
Figure 3. Variation of (a) average eight R/Ca–Mn bond lengths and (b) δR/Ca–Mn of R1−x Cax MnO3 (R = Dy, Y, Ho) with Ca concentration x. hi denotes average value.
focused on the real-space images of charge ordering have proposed some stripe models [44–49] to illustrate the charge ordering patterns for La0.5 A0.5 MnO3 (A = Ca, Sr or Ba). But whether the stripe models suggested for large rare-earth manganates are appropriate for the cases of small rare-earth (R = Dy, Y, Ho)-based manganates or not is still unknown. We take Y0.5 Ca0.5 MnO3 as an example to investigate the arrangement of atoms in R0.5 Ca0.5 MnO3 (R = Dy, Y, Ho). Three types of configurations are considered: randomly dispersed configuration, paired stripe configuration [45–47] and layer stripe configuration [49]. The stripe configuration models are schematically shown in figures 4(a) and (b), respectively. Although the ordered distribution of Mn ions has been studied extensively, the distribution of A-site cations has not yet found consensus [50–53]. According to our simulation, the configurations in which Ca2+ and Mn4+ ions are separated far away are always structurally unreasonable. Thus for all the configurations investigated below, the Ca2+ ions are located close to Mn4+ . More specifically, for random configurations, Mn3+ and Mn4+ ions are randomly distributed and closely surrounded by Y or Ca ions, respectively; while for stripe configurations, Y/Ca ions are also ordered along with Mn3+ and Mn4+ stripes. The average lattice energy and lattice parameters of the simulated configurations and a comparison with experimental lattice parameters [33] of Y0.5 Ca0.5 MnO3 are demonstrated in figure 5. The charge ordered configuration therein is the average result of all the stripe configurations.
3.4. Charge ordering in R0.5 Ca0.5 MnO3 (R = Dy, Y, Ho) Charge ordering is one of the most fascinating aspects of alkaline-earth doped manganates, and has significant effects on their transport and magnetic properties. Earlier studies 5
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N Jiang et al
Figure 4. Charge ordering models of (a) paired stripe and (b) layer stripe of R0.5 Ca0.5 MnO3 ; and calculated [010] HRTEM image of (c) o-YMnO3 , (d) paired stripe of Y0.5 Ca0.5 MnO3 and (e) layer stripe of Y0.5 Ca0.5 MnO3 .
Figure 5. The average lattice energy and lattice parameters of the simulated configurations and comparison with experimental [33] lattice parameters of Y0.5 Ca0.5 MnO3 .
Figure 6. Mn–O bond length of the layer stripe model. hi denotes average value.
As demonstrated, the randomly dispersed configurations have the highest lattice energy, whose average value is 1.21 eV higher than that of configurations with charge ordered stripes, and the lattice parameters also deviate from the experimental value significantly. This seems to illustrate that the formation of charge ordered stripes are more energetically favorable and structurally reasonable. Besides, by comparing the two different stripe models, one may identify that the layer stripe model has an even lower lattice energy, and the corresponding lattice parameters accord better with experimental data as well. This indicates that the layered stripe should be a more reasonable atomic distribution configuration. However, the lattice energy difference between pair stripe and layer stripe is as slight as 0.34 eV. Therefore, it is likely that both the stripe patterns can be observed in Y0.5 Ca0.5 MnO3 compound. The
coexistence of different of charge ordered phase has indeed been observed experimentally [54, 55]. We further investigated the internal structure of layer stripes in Y0.5 Ca0.5 MnO3 . As illustrated in figure 4(b), there are three Mn3+ stripes and three Mn4+ stripes along the a direction in the Mn–O2 plane. The six Mn–O bond lengths around each Mn ion are calculated and shown in figure 6. The average Mn3+ –O bond length is larger and close to the average Mn3+ –O bond of YMnO3 while the average Mn4+ –O bond length is smaller and close to Mn4+ –O bond length in CaMnO3 . This seems to indicate that the local structure in Y0.5 Ca0.5 MnO3 is not homogeneous, but distinct for different stripes. To be more specific, the supercell under investigation can be divided into two chemically and structurally different parts: a YMnO3 -like layer and a CaMnO3 -like layer. 6
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The same configurations are performed on both Dy0.5 Ca0.5 MnO3 and Ho0.5 Ca0.5 MnO3 to investigate the possible influence of the size of R ion on the charge ordering behavior. The tendency to form layered stripes is found in both the compounds. Additionally, the difference of lattice energy between random configuration and layer stripe configuration increases from 0.79 eV for Dy0.5 Ca0.5 MnO3 to 1.83 eV for Ho0.5 Ca0.5 MnO3 , indicating that RMnO3 with smaller R ionic radii is more likely to become charge ordered, although simultaneously the size mismatch of A-site cation increases from Dy to Ho, which suppresses charge ordering [6]. Our results accentuate the role of A-site cation size in these compounds [56]. The variation of the two most important distortions in manganate perovskites [57]—JT distortion and tilt angle of MnO6 octahedra of every stripe along the a-direction—are included in figures 7(a) and (b), respectively. The JT distortion is evaluated by the 1d parameter [31], concerning the deviation of Mn–O distance with respect to the average hMn–Oi value, as 1d = (1/6)6n=1,6 [(dn − hdi)/hdi]2 . The octahedra tilt angle is obtained from the hMn–O–Mni bond angle hθ i as hωi = 180◦ − hθ i [31]. In both of the figures in figure 7, an obvious structural distinction between two layers can be observed for all the three compounds. The JT distortion is concentrated on the Mn3+ O6 octahedra, but is smaller than that in RMnO3 , whereas almost no distortion occurs on the Mn4+ O6 octahedra. This confirms the conclusion above that Ca2+ doped o-RMnO3 will be divided by ordered stripes and form RMnO3 -like and CaMnO3 -like layers. Furthermore, it can be observed that the reduction of 1d of Mn3+ O6 octahedra experiences a progressive decrease from Dy to Ho. It seems that the doping influence on JT distortion is related to the size of R ion to some degree, and that manganate with a smaller R is less affected. As to the tilting angle, a decrease upon doping can be observed over all the investigated supercell, which implies an increase of the tolerance factor, and thus a stabilizing of the structure. However, compared with the large reduction of Jahn–Teller distortion, the decrease of tilt angle is rather small. Besides, the octahedral tilt angle seems not to be sensitive to the ionic radii of R, as the difference between the maximum tilt angle reduction of Mn3+ O6 octahedra of Dy0.5 Ca0.5 MnO3 , Y0.5 Ca0.5 MnO3 and Ho0.5 Ca0.5 MnO3 is within 0.7◦ , and even smaller for Mn4+ O6 octahedra. Moreover, while the anisotropy of the Mn–O bonds shows a significant difference between the RMnO3 -like and CaMnO3 -like layers, the difference of tilt angle between the two layers is rather small. This seems to indicate that while steric effects associated with the octahedral tilts act cooperatively with the JT effect in the charge ordering state [58], it is the JT effect that dominates [59]. Above all, charge ordered stripes are predicted to present in R0.5 Ca0.5 MnO3 , in the form of RMnO3 -like layer and CaMnO3 -like layer, and the tendency grows as the R ionic radius decreases, where the JT effect is less affected. Based on further extending our simulation supercell along both aand c-axis directions, we calculated some HRTEM images to better illustrate the real lattice image of the charge ordering state. Figure 4(c) shows the calculated image of original
Figure 7. Local structure of the layer stripe model of R1−x Cax MnO3 (R = Dy, Y, Ho). (a) The Jahn–Teller distortion and (b) tilt angle of MnO6 octahedra along c-direction stripes.
o-YMnO3 single crystal, and figures 4(d) and (e) are the HRTEM images of the paired stripe model and layer stripe model of Y0.5 Ca0.5 MnO3 , respectively. The stripes of charge ordering are running along the c direction with a modulation ˚ and ∼3a ≈ 16.4 A, ˚ respectively. It period of ∼a ≈ 5.4 A can be clearly observed that charge ordering can introduce contrast in HRTEM images by different local chemistry composition and local structure [51].
4. Conclusions New interatomic potentials are proposed for small R-based orthorhombic RMnO3 (R = Dy, Y, Ho), which accurately model the structural properties of the compounds. They are further employed to investigate the intrinsic defects of these manganates as well as the formation of microscopic phases in mixed valence o-R1−x Cax MnO3 (R = Dy, Y, Ho). Schottky disorders are found to be the dominant structural defects in o-RMnO3 , and the possibility of a small degree of anti-site disorder of R and Mn ions over A and B sites is found. As the doping level increases, the doped Ca ions tend to aggregate in the system, and form chemically and structurally distinct CaMnO3 -like clusters embedded in the RMnO3 background. Charge ordered stripe structure is predicted for o-R0.5 Ca0.5 MnO3 , which consists of RMnO3 -like layer and CaMnO3 -like layer. Such inhomogeneous configurations are showed to be energetically preferable and structurally more 7
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reasonable. They may be a representation of microscopic phase separation. Moreover, the tendency to form charge ordered stripes increased with the decrease of R size. The size of R ion also significantly affects the doping effect on Jahn–Teller distortion that larger R indicates a larger reduction of the anisotropy of Mn–O bonds in Mn3+ O6 octahedra. However, the change of octahedral tilting upon doping does not vary much with the R radii.
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Acknowledgments We would like to acknowledge financial support by the National Science Foundation of China (11074141, 11174169, 11234007) and the Ministry of Science and Technology of China (2009CB929202). This work made use of the resources of the Beijing National Center for Electron Microscopy.
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