IR-active optical phonons in Pnma-1, Pnma-2 and R3c phases of
  LaMnO_{3+\delta}
IR-active optical phonons in Pnma-1, Pnma-2 and R3̄c phases of
LaMnO3+δ
I. S. Smirnova,∗ A. V. Bazhenov, T. N. Fursova,
A. V. Dubovitskii, L. S. Uspenskaya, and M. Yu. Maksimuk
Institute of Solid State Physics, Russian Academy of Sciences,
142432, Chernogolovka, Moscow distr.
Abstract
Infrared-active phonons in LaMnO3+δ were studied by means of the reflection and transmission
spectroscopy from 50 to 800 cm−1 at room temperature. Powder and ceramic samples of the
phases of Pnma-2 (δ = 0.02), Pnma-1 (δ = 0.08), and R3̄c (δ = 0.15) were investigated. Besides,
energies of the dipole-active phonons in Pnma-2, Pnma-1 phases were obtained by lattice-dynamics
calculations. The transformations of IR-active phonons with the increase of δ in the sequence of
Pnma-2, Pnma-1, R3̄c are discussed.
PACS numbers: 61.50.Ah, 78.30.-j
http://arxiv.org/abs/0704.1402v2
I. INTRODUCTION
Electrical and magnetic properties of perovskitelike compounds RxAyMO3+δ (R = rare
earth; A = Ca, Sr, Ba, Pb; M = Cu, Mn, Ti, V) can drastically change with varying
x, y. In last decades such materials have been intensively investigated. In 1986 super-
conductivity with Tc=30 K was found in La2−xBaxCuO4+δ.[1] Using of some other transi-
tion metals M can result in the compounds (La1−xAxMnO3+δ, for example) with “colossal”
magnetoresistance.2,3,4 Cuprates and manganites possess many common features: the crys-
tal structure (close to the perovskite) and strong electron–electron, electron–phonon, and
exchange interaction. With x = 0, δ = 0 they are antiferromagnetic dielectrics at low tem-
peratures. An increase of x results in a dielectric-metal transition.5
Some excess oxygen in La2CuO4+δ brings about the same transformation of the electronic
spectrum that results from the partial substitution of La by an alkali earth, the transforma-
tion going up to the superconducting phase.6 Similarities between cuprates and manganites
stimulated studies of the influence of excess oxygen on the electron and phonon spectra of
LaMnO3+δ.
It’s well known that the crystal structure of both LaMnO3+δ and La1−xAxMnO3 is or-
thorhombic at δ < 0.1, x < 0.2 and T < 500 K. An increase of δ and x results in a
rhombohedral phase R3̄c.7,8,9 In any case the crystal is insulating and paramagnetic above
200–300 K. With decreasing temperature the R3̄c phase transforms into an orthorhombic
phase, insulating and ferromagnetic at 0.11 < δ < 0.14, metallic and ferromagnetic at
δ > 0.14.7 Two orthorhombic phases of LaMnO3+δ have been found.
7,10,11,12 They were de-
noted as either Pnma-1, Pnma-2 (Ref. 12) or O, O′ (Ref. 7). The first one, Pnma-2 (O′),
is an insulating antiferromagnet at low temperatures and exists at small δ; the second one,
Pnma-2 (O), is an insulating ferromagnet at low temperatures and exists at larger δ.
Orthorhombic phases can belong to different space groups (the orthorhombic phase of the
La2CuO4, for example, belongs to the Cmca space group). To emphasize that both O
′ and
O phases of LaMnO3+δ belong to the same space group Pnma we, following Ref. 12, use the
notation Pnma-2, Pnma-1. Unfortunately, this notation does not show the local symmetries
of the atoms or the Wyckoff positions, which are subgroups of the point group D2h. It’s the
local symmetry that determines the number of modes in every irreducible representation.
The purpose of the present study was to examine the spectra of dipole-active optical
phonons in Pnma-2, Pnma-1 and R3̄c phases. Especially, we paid attention to transforma-
tions that phonon states undergo upon transitions from the phase Pnma-2 to Pnma-1 and
then to R3̄c, which are induced by a high-temperature treatment. Optical phonons in the
Pnma-2 and R3̄c phases were measured in Refs. 13,14 (Pnma-2, Raman); 15,16 (Pnma-2,
IR); 14,17,18 (R3̄c, Raman); and 17,19 (R3̄c, IR). In the present study, we focus on the IR
spectrum of the Pnma-1 phase of LaMnO3+δ. To our knowledge, there are no data on either
IR or Raman spectra of this phase at the moment.
The Pnma-2, Pnma-1 phases are isostructural, so the number of phonon modes should be
the same in both cases. However, the number of IR-active modes observed experimentally
in the spectra of the Pnma-1 phase is smaller than that for the Pnma-2 phase. In the R3̄c
phase an experiment shows more modes than group theory predicts for the R3̄c symmetry.
II. CRYSTAL STRUCTURE OF LaMnO3+δ PHASES
Since phonon modes are closely related to the crystal lattice symmetry, let us summarize
some well known data about crystal structure of four LaMnO3+δ phases. The structure of
the parent cubic phase Pm3̄m is shown in the centre of Fig. 1. At ambient pressure, this
phase exists at temperatures above 870 K. At room temperature there exist three phases:
orthorhombic Pnma-2, Pnma-1 and trigonal (rhombohedral) R3̄c.10,11,12,20
X-ray analisys shows the following:
• In the Pnma-2 phase the positions of O2 oxygens (see Fig. 1) deviate considerably from
those in the cubic phase. The oxygen octahedra are strongly distorted, particularly in
Mn–O2 plane, the Mn–O2 distances differ from each other (1.90 and 2.17 Å).
• In the Pnma-1 phase the positions of O2 oxygens slightly deviate from that in the
cubic phase, the oxygen octahedra are slightly distorted, the Mn–O2 distances being
close to each other.
• In comparison with the cubic phase, in both orthorhombic phases the oxygen octahedra
are rotated around [010] (cubic) axis by nearly the same angle (the difference is 1–3◦).
To distinguish between the Pnma-1 and Pnma-2 phases experimentally, it is sufficient to
determine the dimensions of the unit cell: a, b, c. In the Pnma-2 phase a > c and a− c ≈ 0.2
Å, in the Pnma-1 phase a < c and c− a is 0.04–0.08 Å.
[010]
[100][001]
[111]
[111]
[110]
[100]
[001]o
[110]
[001]cub
_[010]
[100]
[010]
[001]
Pnma-1
Pnma-2
Pnma-1, Pnma-2
FIG. 1: Crystal structure of the R3̄c (left), Pm3̄m (centre) and Pnma (right) phases of LaMnO3+δ.
In all considered phases, Mn atoms occupy symmetry-equivalent positions and their time-
average charges must be the same. Mn+4 should be defects chaotically distributed in the
sample volume. Symmetry forbids any long-range charge ordering in these phases. Such
ordering may occur only if the symmetry is lowered.
In contrast to the cubic phase and the trigonal phase, the orthorhombic phases contain
two types of inequivalent oxygen atoms. Therefore, these oxygen atoms can have different
charges and different amplitudes of displacements in the normal vibration modes. All the
six oxygen atoms in the unit cell of the R3̄c phase are symmetry-equivalent, therefore their
scalar parameters, in particular their charges, should be equal.
Arrows in the centre of Fig. 1 show that the point group D3d of the R3̄c phase and the
point group D2h of the Pnma phases are subgroups of the Oh point group of the Pm3̄m
phase and corresponding phase transitions of the second kind are allowed. The crossed
arrow in Fig. 1 shows that D2h is not a subgroup of D3d. As a result, phase transitions of
the second kind from the R3̄c phase to the Pnma-1, Pnma-2 phases are forbidden. Such
phase transitions can be possible only through an increase of symmetry, i. e., through the
intermediate cubic phase, which exists at high temperatures.
III. EXPERIMENTAL
LaMnO3+δ was prepared from La2MnO3, La(CO3)3·6H2O and Mn2O3. The stoichiometric
mixture of source materials was powdered in a ball planetary mill, after that it was calcined
at 900◦C, and then it was powdered once again. The main synthesis was conducted at
1100◦C during 10–20 hours. δ was measured by iodometric titration of the Mn+3, Mn+4
ions.
It is known that the Pnma-2 phase can be transformed to the Pnma-1 phase by annealing
in air. Upon further annealing in oxygen, the Pnma-1 phase transforms into the R3̄c phase.7
In Ref. 13 the Pnma-2 phase was obtained by heating of the R3̄c phase in N2 atmosphere
at 900◦C. We realized the reversible sequence of transformations: R3̄c ⇔ Pnma-1 ⇔ Pnma-
2. First, we kept LaMnO3+δ powder at 600
◦C during 10 hours, then different speeds of
cooling resulted in different phases. For the measurements of the IR reflection spectra,
ceramic pellets of the Pnma-1, R3̄c phases were prepared from the powder by pressing it
and subsequent annealing at 1000◦C during 10 hours. We could not obtain ceramic pellets
of the Pnma-2 phase.
Magnetic permeability of the Pnma-2, Pnma-1, R3̄c phases was measured in the 77–
300 K temperature range in the AC 2500 Hz magnetic field of 1 Oe at slow heating. The
measurements were performed on powder manually pressed into a quartz tube of 2 mm
in diameter. This technique results in some uncertainty in the amount of material under
investigation. Therefore, the absolute value of the permeability was obtained with some
uncertainty, yet we determined the main features of its temperature dependence.
IR reflection spectra of ceramic pellets and the IR transmission spectra of powder samples
were obtained using a Fourier-transform spectrometer in the spectral range 50–800 cm−1 at
room temperature. The reflection spectra were measured in the arrangement where the light
falls on a pellet surface near perpendicularly, and an aluminum mirror was used to obtain
a reference spectrum. In order to measure transmission spectra, either a polyethylene or
a KBr plate (depending on the spectral range) was covered by powder sample, and the
transmission spectrum of the plate was used as a reference. Transmission T then was
converted to absorbance D = − ln(T ).
IV. RESULTS AND DISCUSSION
According to X-ray analysis, the unit cell parameters of the Pnma-2, Pnma-1, R3̄c phases
we synthesized were the following:
phase a, Å b, Å c, Å
Pnma-1 5.505 7.776 5.513
Pnma-2 5.732 7.693 5.536
For R3̄c a∗ = 5.515 Å, c∗ = 13.291 Å in the hexagonal coordinates.
These parameters are concordant, for instance, with the results of Huang et al.12
Titration has shown the following percentage of Mn+4 ions in investigated samples: Pnma-
2, 5%; Pnma-1, 15%; R3̄c 30%. It corresponds to δ equal to 0.025, 0.075 and 0.15 for the
Pnma-2, Pnma-1 and R3̄c phases, respectively.
The magnetic permeabilities of Pnma-2, Pnma-1 and R3̄c are shown in Fig. 2. All
80 130 180 230 280
H, Oe
70350-35-70
Pnma-1
x3Pnma-2
117 K
110 K, a.u. 51.5
FIG. 2: Temperature dependence of the magnetic permeability χ(T ) of the Pnma-2 phase (black,
multiplied by 3), the Pnma-1 phase (red) and the R3̄c phase (blue). For the Pnma-1 phase,
permeability versus magnetic field χ(H) is plotted in the inset at 110 and 117 K.
phases are paramagnetic near the room temperature. At low temperature Pnma-1 and R3̄c
are ferromagnetic, and Pnma-2 is antiferromagnetic. Ferromagnetic behaviour is illustrated
by hysteretic dependence of the permeability upon the magnetic field, which appears below
the transition temperature and becomes more and more pronounced with decreasing tem-
perature, see the inset in Fig. 2. The temperature of the antiferromagnetic transition in
Pnma-2 is 140 K, in agreement with Refs. 7,12. To obtain the temperatures of the ferromag-
netic transitions in Pnma-1 and R3̄c, we plotted inverse permeability versus temperature,
and linearly extrapolated to zero value the high-temperature parts of these dependences. In
agreement with Ref. 7, the transition temperatures turned out to be 180 and 240 K in the
Pnma-1 and R3̄c phases, respectively. These results confirm that we really deal with the
Pnma-2, Pnma-1 and R3̄c phases.
In Fig. 3 the reflection spectra of the phases R3̄c (δ ∼ 0.15), Pnma-1 (δ ∼ 0.05),
0.4 -
0.4 Pnma-1
200 400 600
0.8 Pnma-2
Wavenumber, cm-1
FIG. 3: Solid lines: Reflection spectra of the R3̄c, Pnma-1 and Pnma-2 phases. (For the Pnma-2
phase the data are taken from Ref. 15). Crosses: the results of fitting.
and Pnma-2 (δ = 0) are shown. In the present wavenumber range reflection spectra are
determined by dipole-active phonons. We approximated our reflectivity spectra R(ω) using
a fitting procedure based on a set of Lorentz oscillators:
ǫ(ω) =
ω20,j − ω
2 − iγjω
; R(ω) =
ǫ(ω)− 1
ǫ(ω) + 1
ǫ(ω) is the complex dielectric function; Sj , ω0,j and γj are oscillator strength, frequency and
damping factor of mode j. The number of oscillators we used in every case was chosen as
the minimum number allowing a good fit. The crosses on Fig. 3 show the result of the
fitting.
Fig. 4 shows the conductivity contributions σj(ω) of the calculated Lorentz oscillators:
σj(ω) =
ω2γjSj
(ω20,j − ω
2)2 + γ2jω
200 400 600
100 x10
Wavenumber, cm-1
Pnma-1
Pnma-2
FIG. 4: Separate conductivity contributions of each Lorentz oscillator, which were obtained by
fitting of the reflection spectra shown in Fig. 3
Paolone et al.15 compared experimental and theoretically calculated21 phonon frequen-
cies of Pnma-2 phase. Taking into account the lowest and the highest phonon frequencies
obtained by Paolone et al.15, we corrected previously calculated21 phonon frequencies of the
Pnma-2 phase. Also, we calculated the phonon frequencies of the Pnma-1 phase using the
rigid-ion model with effective charges. Table I shows the results of these calculations along
with the phonon frequencies extracted from experimental data. We measured spectra of
ceramic samples. So the polarization symmetry of the IR-active phonons could not be ob-
tained from our experiments and the arrangement of the modes is tentatively done according
to their frequencies and intensities.
In Table I, “TO” and “LO” indices correspond to the “transverse” and “longitudinal”
frequencies. A TO frequency means a resonant frequency ω0,j (see Equation (1)) and coin-
cides with a maximum of σ(ω) (see Equation (2)). LO frequencies in Table I correspond to
maxima of the function −Im(1/ǫ) and represent oscillator strengths S = ω2LO − ω
A. IR spectra of the Pnma phases
According to group theory, the isostructural Pnma-1 and Pnma-2 phases should have 25
dipole-active optical phonon modes, 9B1u+7B2u+9B3u (see, for example, Ref. 21). Indeed,
Paolone et al.15 experimentally found 25 IR-active modes in Pnma-2 crystals at 10 K (and
18 modes at room temperature). However, in our Pnma-1 ceramic only 11 modes can be
distinguished at room temperature.
The lines in the Pnma-1 ceramic are substantially wider than in the Pnma-2 single crys-
tals (see damping factors γ in Table I). Let’s consider possible reasons for this broadening.
Decreasing of the phonon life time τ accompanied by increasing of γ = 1/τ could come
as a result of the phonon scattering on grain boundaries of ceramic. To check that, we
measured transmission spectra of the Pnma-1, Pnma-2 and R3̄c powders. The grain sizes
of our powders were measured22 using electron microscopy: in all samples the typical grain
size is found to be about 1 µm. In the transmission spectra, the widths of the phonon lines
increase monotonically with the increase of the excess oxygen content, i. e., in the sequence
Pnma-2, Pnma-1, R3̄c. That means that phonon scattering on grain boundaries is not the
main reason of line broadening in the spectra of the Pnma-1, R3̄c powders. The same is
even truer for the spectra of the Pnma-1, R3̄c ceramics, because in a ceramic the typical
TABLE I: Calculated and experimental TO(LO) frequencies (cm−1) of IR-active phonon modes;
w means a weak mode; γ is damping factor (cm−1)
Pnma-2 Pnma-1 R3̄c
calc. exp. calc. exp. exp.
ωTO(ωLO) ωTO(ωLO) γ ωTO(ωLO) ωTO(ωLO) γ ωTO(ωLO) γ
115(119) B1u 116(120) 4 111(115) B1u
116(118) B3u 120(130) B3u 125(135) 20 120(140) 62
138(140) B2u 143(148) B2u 147(180) 29
171(197) B2u 172(244) 6 166(196) B1u 163(209) 24 167(197) 38
175(195) B1u 182(195) 3 181(199) B2u 187(195) 27
231(232) B3u 201(203) 9 229(230) B3uw
233(249) B1u 244(255) 7 247(248) B1uw
249(250) B2u 300(302) B2uw
254(281) B3u 271(291) 5 253(253) B3uw
284(296) B1u 277(297) 9 270(291) B3u 258(267) 74 252(266) 88
297(305) B3u 285(293) 9 280(281) B1uw
309(309) B1u 332(354) B1u 327(381) 95 324(376) 97
330(341) B2u 335(363) 15 355(371) B1u
346(352) B1u 350(411) 16 368(370) B2uw
354(373) B3u 362(391) 10 377(440) B3u 372(401) 60 376(400) 68
420(426) B2u 400(401) 16 382(448) B1u
434(450) B1u 429(437) 18 416(417) B1uw 420(429) 59 431(442) 78
455(457) B1u 451(452) 12 437(444) B3u
473(479) B3u 474(480) 28 487(503) B2u 487(490) 40 498(592) 33
528(531) B3u 515(518) 18 564(568) B2u
573(598) B2u 561(606) 17 580(589) B3u 567(579) 49 576(592) 85
634(640) B2u 644(646) 39 584(641) B2u 599(618) 57 611(627) 65
644(650) B3u 615(616) B3uw
645(651) B1u 634(639) B1u 637(642) 51 649(653) 57
Pnma-1
200 400 600
Wavenumber, cm-1 
Pnma-2
1.0 Reflection
FIG. 5: Experimental absorption of the R3̄c (top), Pnma-1 (middle) and Pnma-2 (bottom, solid
line) powders. The dashed line in the bottom part represents the reflectivity of a Pnma-2 single
crystal taken from Ref. 15.
grains can be larger than that in a source powder. Moreover, we believe that even in our
Pnma-2 powder phonon scattering on grain boundaries is not the main reason of the line
broadening. In the bottom part of Fig. 5, the dashed line shows the reflection spectrum
of a Pnma-2 single crystal15, solid line represents our absorption spectrum of the Pnma-2
powder. Our calculations showed that, on average, the lines in the conductivity spectrum
of powder are three times wider than those in the spectrum of a crystal. Nevertheless, one
can reveal the same number of lines in both spectra. For example, 172 cm−1 and 182 cm−1
lines can be undoubtedly distinguished in our powder spectrum. It was shown15 that in a
doped LaMnO3 single crystal, containing 8% of Mn
+4, these lines could not be resolved at
room temperature. Our powder contained 5% of Mn+4 so it seems reasonable to attribute
the observed broadening of lines in our Pnma-2 powder as a result of oxygen doping.
The main factor of line broadening in the spectra of these samples should be the phonon
scattering on structural defects, which multiply with excess oxygen doping. These defects
could be oxygen atoms in interstitial sites, like those in La2CuO4+δ [23]. However as for
LaMnO3+δ and La1−xAxMnO3+δ (A=Ca, Sr, Ba), at the moment it is rather believed that
the nonstoichiometric oxygen Oδ is compensated by both La and Mn vacancies in equal
amounts.7,24 In such a case, vacancy contents of La or Mn in our samples δ/(3 + δ) would
be 0.7%, 2.6% and 5% for the Pnma-2, Pnma-1 and R3̄c phases respectively.
Line broadening can make difficult or impossible experimental detection of some lines
with small oscillator strength. In the Pnma-2 phase, that could be the phonons with the
frequencies 400 cm−1, 451 cm−1 (see Table I). We calculated the oscillator strength for all
IR-active modes of the Pnma-2 and Pnma-1 phases. It turns out that the number of modes
experimentally detected in the Pnma-1 phase is reduced in comparison with the Pnma-2
phase mainly because the oscillator strength of some phonons of the Pnma-1 phase becomes
very small. These Pnma-1 modes are marked by w in Table I. In the Pnma-1 phase, the
lengths of Mn–O bonds differ from each other very little (the difference comes in fourth
significant digit). The closeness of Mn–O bond lengths means that oxygen atoms are almost
symmetrically equivalent, i. e., the Pnma-1 crystal structure deviates from the cubic one
less than the Pnma-2 crystal structure where the difference in Mn–O bond lengths is 15%.
In the cubic structure, the number of IR-active phonons is less than in an orthorhombic
structure. Therefore, if a structure is close to cubic then some IR-active phonons are “on
the verge of disappearance”.
B. IR spectra of R3̄c
Our spectra of R3̄c are in satisfactory agreement with the spectra obtained in Ref. 17,19.
According to our experimental results, phonon damping factors of the R3̄c phase exceed
those of the Pnma-1 phase by a factor of 1.3 on average. The first reason is that the Mn+4
content in R3̄c is two times as large as it is in the Pnma-1 phase, so there are more structural
defects there. The second reason is disorder caused by the noncoherent dynamic Jahn-Teller
effect.
According to the group-theory analysis (see Ref. 21, for example), there are 8 IR-active
phonon modes in the R3̄c phase: 3A2u+5Eu. At room temperature, in reflection spectra of
the R3̄c ceramic we definitely distinguish 10 lines. The approximation by a set of Lorentz
oscillators revealed an additional very broad line near 120 cm−1. Therefore, we found in the
R3̄c phase the same amount of lines (11) as in the Pnma-1 phase.
Let us consider possible reasons for appearing of additional lines in spectra of the R3̄c
phase.
Local break of the inversion symmetry around a point defect could make some Raman-
active (IR-forbidden) modes to appear in IR spectra. However, comparison of the IR spectra
of the R3̄c phase with Raman spectra of Abrashev et al.17 shows that there is only one
Raman line near 649 cm−1 close to an IR line (640 cm−1), the other Raman lines have no
counterparts in our IR spectra.
In IR spectra there could appear maxima of the phonon density of states caused by
breaking of the long-range order. Iliev et al.14 analyzed the Raman spectra of doped rare-
earth manganites and interpreted them in the frame of the model used for description of
amorphous materials.25 The Raman spectra in this case are dominated by disorder-induced
bands, reflecting the phonon density of states smeared due to finite phonon lifetime. In other
words, the law of conservation of the quasimomentum k breaks and phonons with nonzero
k begin to interact with light. In general, the same mechanism could definitely work for IR
spectra too. Big linewidths prevent us from supporting or rejecting an influence of phonons
with k 6= 0 on IR spectra of the R3̄c phase. Though it worth to take into account that
according to Iliev et al.14 a Raman mode generally gives several maxima of density of states.
Probably the same is true for IR-active modes. However, our spectra of the R3̄c phase can
be fitted very well by a few Lorentz functions. So we think that the phonons with k 6= 0 can
have only a small influence on our spectra, they do not determine essential spectral features.
We explain additional lines in our IR spectra of the R3̄c phase as a result of the dynamic
Jahn-Teller effect. In the R3̄c phase of LaMnO3, the R3̄c symmetry exists only “on average”,
revealing itself in certain kinds of experiments such as X-ray diffraction. At any particular
moment of time, one of the octahedron O–Mn–O axes differs from two others due to dynamic
Jahn-Teller distortions; therefore, oxygen atoms are inequivalent and their charges are not
equal. It is the “instant”, not “average”, pattern that is probed in optical experiments.14
Obviously, normal phonon modes, measured by means of IR and Raman spectroscopy, are
normal modes of the “instant”, not average” pattern. In the “instant” view every octahedron
in the R3̄c phase looks deformed, mostly in the same way as the octahedra in the Pnma
phases. That’s why the phonon spectrum of the R3̄c phase resembles that of the Pnma
phases. Similarly, Abrashev et al.17 interpreted two strongest lines (649 cm−1 is one of
them) in their Raman spectra of the R3̄c phase as “forbidden” modes, analogous to the
respective modes in Pnma phases.
We can expect some correlations between the Jahn-Teller deformations of the octahedra
in the R3̄c phase. Qiu et al.26 found that in high-temperature (T > 1010 K) stoichiometric
rhombohedral LaMnO3 there are fully distorted MnO6 octahedra, ordered in clusters of
diameter ∼ 16 Å. According Ref. 7, the phase diagram of LaMnO3+δ containes an area
(0.11 < δ < 0.14) where a phase transition R3̄c ⇔ Pnma-1 exists at T = 300 K. As we
mentioned in Section II, such transition of a second kind is forbidden by symmetry. In Ref.
27 there was suggested a model of a phase transition through a virtual cubic phase. Taking
into account the known IR and Raman spectra of the R3̄c phase, as well as the results of Qiu
et al.26, we suggest that the R3̄c samples could contain nanoclusters of some Pnma phase.
Such inclusions may be growing centres at the transition R3̄c ⇔ Pnma-1 of a first kind.
V. THE INFLUENCE OF SELECTION RULES OF D2h POINT GROUP ON THE
IR SPECTRA
According to the selection rules, the irreducible representations B1u, B2u, B3u of D2h point
group correspond to IR-active modes, their total electric dipole moment M taking the form
M(B1u) = (0, 0,Mz),M(B2u) = (0,My, 0),M(B3u) = (Mx, 0, 0). Similarly, for every full
set of symmetrically equivalent atoms in the unit cell (O2, for example) the sum of their
atomic displacements
ui has only one non-zero component. (For a single atom inside
such a set, all three components can differ from zero.)
Let’s consider four lowest-frequency IR-active modes of the Pnma-2 phase. (Fig. 6)
The line with the lowest frequency (115 cm−1) can be distinctly seen in the spectra of the
Pnma-2 and Pnma-1 phases. In the spectrum of the R3̄c phase it substantially broadens
(Fig. 4). A similar line have been observed in reflection spectra of both the undoped (
x = 0 ) and doped by either Ca or Sr La1−xAxMnO3+δ, LaTiO3
28, YVO3
29. Theoretical
calculations21 and experimental results29 show that in the spectra of the Pnma-2 phase this
line consists of two modes with close frequencies and different polarizations (see the upper
part of Fig. 6).
In B1u, B3u modes, La and O1 atoms can vibrate only in the reflection plane m therefore
|Mx|>0
116(118)
z |Mz|>0
115(119) 
|My|>0
178(215)
|Mx|>0
185(197)
FIG. 6: Theoretically calculated patterns of some IR-active phonon modes of the Pnma-2 phase.
Thick arrows show atomic displacements in the direction of the total electric dipole moment M .
Thin arrows show atomic displacements in the other two main crystallographic directions. In the
left upper corners there shown corresponding irreducible representations. In the bottom there
shown corresponding theoretical TO(LO) frequencies.
having two degrees of freedom.
115 cm−1 mode (B1u) has the maximal displacements of La atoms along x axis. Nev-
ertheless, these components don’t contribute to the total electrical dipole moment because
their sum equals zero. Only small components of the La displacements uz along z axis (thick
arrows) contribute to M . The intensity of this mode in the optical conductivity spectrum is
determined by the displacements of O2, Mn, La atoms, their contributions adding together.
Relatively small contributions of O1 atomic displacements have the opposite sign.
The structure of atomic displacements of 116 cm−1 mode (B3u) is similar to the previous
one. The biggest displacements of La atoms are along z axis, M being parallel to x axis. The
intensity of this mode is determined by the adding contributions of O2, La displacements
and the subtracting contribution of Mn displacement.
In 178 cm−1 mode (B2u) O1 and La atoms can vibrate only along y axis, in 185 cm
mode (B3u) they can vibrate only in (0,1,0) plane. An essential difference between these
modes and 115 cm−1, 116 cm−1 modes is that in 178 cm−1, 185 cm−1 modes the maximal
displacements of every atom contribute to M (O1, O2, La are adding, Mn is subtracting).
That is why the oscillator strengths of 178 cm−1, 185 cm−1 modes are much higher than
that of 115 cm−1, 116 cm−1 modes.
Being isostructural, the Pnma-2 and Pnma-1 phases have close patterns of atomic dis-
placements in phonon modes. Still, there are some important differences between them. In
the upper part of Fig. 7 there are shown 233 cm−1 mode of the Pnma-2 phase and 247
cm−1 mode of the Pnma-1 phase. Big displacements of Mn and O1 along x axis, which
have comparable magnitudes for the Pnma-2 and Pnma-1 phases, don’t contribute to M .
In the both cases, the oscillator strengths are entirely determined by small displacements
along z axis, which are much less for the Pnma-1 phase (247 cm−1) than for the Pnma-2
phase (233 cm−1). As a result, the oscillator strength 247 cm−1 mode of the Pnma-1 phase
is very small.
In the bottom part of Fig. 7 there are shown another pair of similar modes. The oscillator
strength of 284 cm−1 mode (Pnma-2) is much higher than that of 280 cm−1 mode (Pnma-1),
because in the second case the displacements of Mn, O2 atoms along z axis are substantially
less. In addition, the displacements of O1 atoms, which decrease the resulting M , are of
much higher amplitude in 280 cm−1 mode (Pnma-1) than in 284 cm−1 mode (Pnma-2).
Our theoretical calculations showed that there are six modes in total, which strongly
z |Mz|>0
233(249)
z |Mz|>0
247(248)
z |Mz|>0
284(296)
z |Mz|>0
280(281)
Pnma-1
Pnma-1
Pnma-2
Pnma-2
FIG. 7: Theoretically calculated patterns of some IR-active phonon modes of the Pnma-2 and
Pnma-1 phases. Thick arrows show atomic displacements in the direction of the total electric
dipole moment M . Thin arrows show atomic displacements in the other two main crystallographic
directions. In the left upper corners there are shown corresponding irreducible representations. In
the bottom there shown corresponding theoretical TO(LO) frequencies.
decrease their oscillator strength for the Pnma-1 phase in comparison with that for the
Pnma-2 phase. (In Table I they are marked by w.) That’s why for the Pnma-1 phase the
number of modes seen in experiment is less than for the Pnma-2 phase.
The atomic displacements of all IR-active modes for the Pnma-2 phase are drawn in Fig.
5 of Ref. 21. Mostly, the displacements of O1, O2 atoms are much bigger than that of Mn,
La atoms. As a result, the small components were ignored there. For a strong mode, that
was reasonable. However for a weak mode, that could cause some misunderstanding. For
|My|>0
634(640) 
  Pnma 2
|My|>0
249(250)
  Pnma 2
FIG. 8: Theoretically calculated patterns of some IR-active phonon modes for the Pnma-2 phase.
Thick arrows show atomic displacements in the direction of the total electric dipole moment M .
Thin arrows show atomic displacements in the other two main crystallographic directions. In the
left upper corners there are shown corresponding irreducible representations. In the bottom there
shown corresponding theoretical TO(LO) frequencies.
example, all the displacements shown in Ref. 21 for 207 cm−1 and 562 cm−1 modes produce
the resulting M = 0. More correct patterns for these modes are shown in Fig. 8.
VI. CONCLUSIONS
The reversible sequence of transformations R3̄c ⇔ Pnma-1 ⇔ Pnma-2 was realized by
annealing of LaMnO3+δ powder at 600
◦C during 5–10 hours.
For the first time, IR transmission and reflection spectra of the Pnma-1 phase of
LaMnO3+δ were measured. In addition, IR spectra of the Pnma-2 and R3̄c phases were
measured and found to be in satisfactory agreement with previously published results.
Taking into account new experimental data for the Pnma-2 phase, we corrected our pa-
rameters of the rigid-ion model with effective charges and recalculated its phonon spectrum.
The frequencies and oscillator strengths of the IR-active phonons in Pnma-1 phase were
calculated as well.
The number of experimentally observed IR-active phonon modes in the Pnma-1 phase is
smaller than that in the Pnma-2 phase, although these phases have the same Pnma sym-
metry. According to theoretical calculations, it happens due to a decrease in the oscillator
strengths of several phonon modes of the Pnma-1 phase. The underlying reason is that in
the Pnma-1 phase MnO6 octahedra are much less distorted than in the Pnma-2 phase.
In the spectra of the R3̄c phase, the number of modes observed exceeds that predicted by
group theory. We attribute the additional modes to local distortions of oxygen octahedra
similar to those in Pnma phases.
Acknowledgments
We thank S. S. Nazin for useful discussion.
∗ Electronic address: smirnova@issp.ac.ru
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	Introduction
	Crystal structure of LaMnO3+ phases
	Experimental
	Results and discussion
	IR spectra of the Pnma phases
	IR spectra of Rc
	The influence of selection rules of D2h point group on the IR spectra
	Conclusions
	Acknowledgments
	References
