Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi₂V₂O₈
Vibrational Raman spectra of a single crystal of the coupled Haldane chain compound SrNi₂V₂O₈ with uniaxial anisotropy were investigated in the 10–1000 cm⁻¹ frequency range at temperatures 7–300 K. No structural phase transition was observed. The number of phonon lines observed in the experiment and...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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Kurnosov, V. Gnezdilov, V. Lemmens, P. Pashkevich, Y. Bera, A.K. Islam, A.T.M.N. Lake, B. 2021-01-31T20:37:52Z 2021-01-31T20:37:52Z 2017 Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi₂V₂O₈ / V. Kurnosov, V. Gnezdilov, P. Lemmens, Y. Pashkevich, A.K. Bera, A.T.M.N. Islam, B. Lake // Физика низких температур. — 2017. — Т. 43, № 12. — С. 1761-1772. — Бібліогр.: 36 назв. — англ. 0132-6414 PACS: 78.30.–j, 63.20.–e https://nasplib.isofts.kiev.ua/handle/123456789/175361 Vibrational Raman spectra of a single crystal of the coupled Haldane chain compound SrNi₂V₂O₈ with uniaxial anisotropy were investigated in the 10–1000 cm⁻¹ frequency range at temperatures 7–300 K. No structural phase transition was observed. The number of phonon lines observed in the experiment and their intensity were analyzed on the basis of the local symmetry considerations of different structural complexes. This approach was successful in explaining the discrepancy between the numbers of expected and experimentally observed phonon lines. Closeness of a real arrangement of some structural units to higher symmetry than the Wyckoff position results in strong interferential quenching of a number of Raman lines in the spectra. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Низкотемпературная оптическая спектроскопия Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi₂V₂O₈ Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi₂V₂O₈ |
| spellingShingle |
Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi₂V₂O₈ Kurnosov, V. Gnezdilov, V. Lemmens, P. Pashkevich, Y. Bera, A.K. Islam, A.T.M.N. Lake, B. Низкотемпературная оптическая спектроскопия |
| title_short |
Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi₂V₂O₈ |
| title_full |
Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi₂V₂O₈ |
| title_fullStr |
Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi₂V₂O₈ |
| title_full_unstemmed |
Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi₂V₂O₈ |
| title_sort |
phonon excitations in the quasi-one-dimensional haldane phase of srni₂v₂o₈ |
| author |
Kurnosov, V. Gnezdilov, V. Lemmens, P. Pashkevich, Y. Bera, A.K. Islam, A.T.M.N. Lake, B. |
| author_facet |
Kurnosov, V. Gnezdilov, V. Lemmens, P. Pashkevich, Y. Bera, A.K. Islam, A.T.M.N. Lake, B. |
| topic |
Низкотемпературная оптическая спектроскопия |
| topic_facet |
Низкотемпературная оптическая спектроскопия |
| publishDate |
2017 |
| language |
English |
| container_title |
Физика низких температур |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| format |
Article |
| description |
Vibrational Raman spectra of a single crystal of the coupled Haldane chain compound SrNi₂V₂O₈ with uniaxial anisotropy were investigated in the 10–1000 cm⁻¹ frequency range at temperatures 7–300 K. No structural phase transition was observed. The number of phonon lines observed in the experiment and their intensity were analyzed on the basis of the local symmetry considerations of different structural complexes. This approach was successful in explaining the discrepancy between the numbers of expected and experimentally observed phonon lines. Closeness of a real arrangement of some structural units to higher symmetry than the Wyckoff position results in strong interferential quenching of a number of Raman lines in the spectra.
|
| issn |
0132-6414 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/175361 |
| citation_txt |
Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi₂V₂O₈ / V. Kurnosov, V. Gnezdilov, P. Lemmens, Y. Pashkevich, A.K. Bera, A.T.M.N. Islam, B. Lake // Физика низких температур. — 2017. — Т. 43, № 12. — С. 1761-1772. — Бібліогр.: 36 назв. — англ. |
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Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 12, pp. 1761–1772
Phonon excitations in the quasi-one-dimensional
Haldane phase of SrNi2V2O8
V. Kurnosov1, V. Gnezdilov1, 2, P. Lemmens2, Yu. Pashkevich3, A.K. Bera4,
A.T.M.N. Islam4, and B. Lake4
1B. Verkin Institute for Low Temperature Physics and Engineering, NASU, Kharkov 61103, Ukraine
2Institute for Condensed Matter Physics, TU Braunschweig, D-38106 Braunschweig, Germany
3A.A. Galkin Donetsk Institute for Physics and Engineering, NASU, Kyiv 03680, Ukraine
4Helmholtz-Zentrum Berlin, Hahn-Meitner-Platz 1, Berlin 14109, Germany
E-mail: kurnosov@ilt.kharkov.ua
Received April 4, 2017, published online October 25, 2017
Vibrational Raman spectra of a single crystal of the coupled Haldane chain compound SrNi2V2O8 with uniax-
ial anisotropy were investigated in the 10–1000 cm−1 frequency range at temperatures 7–300 K. No structural
phase transition was observed. The number of phonon lines observed in the experiment and their intensity were
analyzed on the basis of the local symmetry considerations of different structural complexes. This approach was
successful in explaining the discrepancy between the numbers of expected and experimentally observed phonon
lines. Closeness of a real arrangement of some structural units to higher symmetry than the Wyckoff position re-
sults in strong interferential quenching of a number of Raman lines in the spectra.
PACS: 78.30.–j Infrared and Raman spectra;
63.20.–e Phonons in crystal lattices.
Keywords: Raman intensity, local symmetry consideration, interferential quenching.
1. Introduction
A remarkable feature of one-dimensional (1D) magnetic
systems is the suppression of long-range magnetic order
even at zero temperature by strong quantum spin fluctua-
tions. Spin-1 Heisenberg antiferromagnetic (AFM) chains
(Haldane chains) are of current interest due to their exotic
magnetic properties [1,2]. The Haldane phase of integer spin
chains has a unique many-body singlet ground state and
gapped magnetic excitations [3,4] in contrast to the gapless
continuum of multispinon excitations of its half-integer coun-
terpart, the spin-1/2 Heisenberg uniform AFM chain. The
magnetic excitation spectra of an isolated Haldane chain were
investigated in great detail using theoretical methods [5–7], as
well as experimental techniques [8,9].
Raman scattering was proven to be a versatile tool to in-
vestigate compounds that represent low-dimensional quantum
spin systems [10]. In addition to spin excitations, also excita-
tions of the lattice system or even coupled modes can be in-
vestigated. This may help to better understand the effect of the
lattice degrees of freedom on the spin system. Despite the
great interest in Haldane chains materials, there are very few
studies of these systems using Raman spectroscopy. To our
present knowledge, detailed investigations only exist for the
one S = 1 spin chain compound Y2BaNiO5 [11].
In real systems the presence of interchain interactions
and anisotropy leads to complex behaviors and a rich phase
diagram as theoretically described in Ref. 12. In this regard
compounds ANi2V2O8, where A = Sr or Pb, are of interest
since they have substantial interchain interactions and sin-
gle-ion uniaxial anisotropy [13,14]. According to earlier
experiments on powder samples [13,15] the ground state of
SrNi2V2O8 was suggested to be 3D ordered below ~7 K.
Later, in numerous experiments [16–22] it has been con-
vincingly shown that SrNi2V2O8 has a nonmagnetic spin-
singlet ground state.
Our present research activities aim to analyze phonon
excitations of the quasi-1D Haldane compound SrNi2V2O8
in detail. These are based on the study of the crystal sym-
metry and phonon excitations that in many cases help to
uncover fundamental properties.
2. Experimental
Details of the SrNi2V2O8 single crystals growth and char-
acterization can be found in Refs. 19, 20. Our Raman scatter-
© V. Kurnosov, V. Gnezdilov, P. Lemmens, Yu. Pashkevich, A.K. Bera, A.T.M.N. Islam, and B. Lake, 2017
V. Kurnosov, V. Gnezdilov, P. Lemmens, Yu. Pashkevich, A.K. Bera, A.T.M.N. Islam, and B. Lake
ing experiments were performed in a quasi-backscattering
geometry on ab and ac surfaces of SrNi2V2O8 single crystals.
A solid-state laser with the excitation wavelengths
λ = 532.1 nm and a power level P = 5 mW was used for the
spectra excitation. Spectra of the scattered radiation were col-
lected by a Dilor-XY triple spectrometer and recorded by a
liquid-nitrogen-cooled CCD detector (Horiba Jobin Yvon,
Spectrum One CCD-3000V) with a spectral resolution of
<0.5 cm−1. In our experiments we used parallel (aa, cc) and
crossed (ab, ac) light polarizations. Temperature dependences
of the Raman spectra were measured in a variable temperature
closed cycle cryostat (Oxford/Cryomech Optistat, RT-2.8 K).
3. Phonon spectra
3.1. Group theoretical analysis and polarization rules
The structure of SrNi2V2O8 is described by the space
group I41cd (#110, 12
4vC ) with z = 8 formula units per unit
cell [20,23]. According our knowledge, there is no evidence
of structural instabilities for temperatures below room tem-
perature. Due to the existence of the “rigid” ionic complexes
(VO4)3− the vibrational modes may be expressed formally in
terms of internal and external degrees of freedom of these
extended complexes and with respect to degrees of freedom
of the point ions Sr2+ and Ni2+ (see Table 1).
Table 1. Representation of SrNi2V2O8 vibrational modes in
terms of internal and external degrees of freedom of ionic com-
plexes (VO4)3− and translations of point ions Sr2+ and Ni2+ using
the space group I41cd and 8 formula units per unit cell
Ions, modes Irreps
Sr2+, translational 1A1+1A2+1B1+1B2+4E
Ni2+, translational 3A1+3A2+3B1+3B2+6E
(VO4)3−, translational 3A1+3A2+3B1+3B2+6E
(VO4)3−, rotational 3A1+3A2+3B1+3B2+6E
Lattice optical 9A1+10A2+10B1+10B2+21E
Lattice acoustic A1+E
(VO4)3−,
internal
ν1 (A1) 1A1+1A2+1B1+1B2+2E
ν2 (E) 2A1+2A2+2B1+2B2+4E
ν3 (F2) 3A1+3A2+3B1+3B2+6E
ν4 (F2) 3A1+3A2+3B1+3B2+6E
(VO4)3−, internal (total) 9A1+9A2+9B1+9B2+18E
There are 4 Raman-active irreps A1, B1, B2, and E
whose polarizability tensors in coordinates corresponding
to crystallographic directions of 4mm (C4v) have the form
1,
a
A z a
b
→
, 1
c
B c
→ −
, 2
d
B d
→
,
,
e
E x
e
→
, ,E y e
e
→
. (1)
If orientations of x and y axes are not precisely determined,
the above matrices, excluding fully symmetrical irrep A1, may
be generally rewritten as
1
cos 2 sin 2
( ) sin 2 cos 2
c c
B c c
θ θ
θ → θ − θ
,
2
sin 2 cos 2
( ) cos 2 sin 2
d d
B d d
− θ θ
θ → θ θ
, (2)
cos
, ( ) sin
cos sin
e
E x e
e e
θ
θ → θ
θ θ
,
sin
, ( ) cos
sin cos
e
E y e
e e
− θ
θ → θ
− θ θ
,
where θ is an angle between real crystallographic direction
and arbitrary direction in the basal plane of the crystal. Ac-
cording to (2) the uncertainty in the orientation leads to a mix-
ing of the polarization selection rules for Raman lines which
belong to phonons with B1 and B2 symmetry. On the one
hand, such mixing makes B1 and B2 modes unresolved, but,
on the other hand, it helps to resolve A1 and B1 (and/or B2)
ones. Polarization zz is “pure” for A1 modes, all other are for-
bidden. It seems that this property is useful for the identifica-
tion of A1 type modes and their selection in other polariza-
tions. But here we face some peculiarity: the polar character
of the A1 modes leads to a splitting of their longitudinal (LO)
and transversal (TO) components.
In opaque crystals the observation of LO and TO compo-
nents of polar phonons in Raman spectra depends on specifics
of experimental back scattering geometry. This information is
collected in Table 2.
Experimental Raman data were obtained using two
sample orientations so that plane of incident light reflec-
tion contained c4 axis of the crystal, or was perpendicular
to it. Table 2 shows, for instance, that in zz polarization
only A1 modes are present (and only TO components),
while in x′x′ polarization, besides B1 and B2 phonons, A1
modes are present (LO components). So, for A1 modes
possessing large LO−TO splitting zz and x′x′ polarized
spectra are different in the positions of the lines.
3.2. Structure of the Raman spectrum and molecular
vibrations of (VO4)3−
The free ion (VO4)3− is a tetrahedral complex and de-
scribed within the Td point group. It possesses 9 internal
degrees of freedom, which are grouped into 4 modes trans-
formed as A1(ν1)+E(ν2)+2F2(ν3+ν4) irreps of Td. Two of
them belong to so-called symmetric A1(ν1) and asymmetric
F2(ν3) stretchings of V−O valence bonds. They have a
priori the highest vibrational frequency. Two remaining
1762 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 12
Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi2V2O8
vibrational modes of the (VO4) tetrahedron are the symmet-
ric E(ν2) and asymmetric F2(ν4) bendings of the valence
angles. Their frequencies are very close in the free complex
and are more than twice less than the frequency of stretching
mode ν1. In crystals the characteristic frequency ranges of
these modes are: A1(ν1) — 800–900, E(ν2) — 300–450,
F2(ν3) — 700–900, F2(ν4) — 300–450 см–1 [24–30]. In
aqueous solutions of (VO4)3− containing salts the frequen-
cies are: A1(ν1) — 826±1, F2(ν3) — (804±4) см–1, E(ν2)
and F2(ν4) — (336±2) см–1 [31].
The O2– ion has a large enough ionic radius of ~1.38 Å
[32], so oxides structures often may be described like
a lattice of these close packed ions, voids between which
are occupied by “small” metallic ions. SrNi2V2O8 has
quite such structure, where the octahedral surrounding of
every Ni2+ ion consists of the same O2– ions that belong to
six different (VO4)3– complexes. Octahedral oxygen com-
plexes of transitional metals are very popular units repre-
senting metal-oxide crystal structures too. The internal
vibrations of (NiO6) octahedrons reach frequencies of
about 550 cm−1 [33–35], so the individuality of all internal
modes of (VO4)3− tetrahedra becomes doubtful. Looking
on the Raman spectra of SrNi2V2O8 one can divide them
into two ranges: 50–500 and 700–950 cm–1 (Fig. 1). It is
clear that the high-frequency region is occupied by vibra-
tions that originate from A1(ν1) and F2(ν3) internal modes
of 8 (VO4)3− tetrahedra contained in the primitive cell.
Only these modes keep their individuality and are well
isolated from the low-frequency “lattice” vibration region.
In contrast the bending modes of (VO4)3− tetrahedra merge
with other modes of the crystal, producing the so-called
“lattice” region. According to the Table 1, high-frequency
region of the SrNi2V2O8 Raman spectrum must contain
lines corresponding to 4A1+4B1+4B2+8E irreps (4A2 irreps
are silent). The lattice range corresponds to
14A1+15B1+15B2+31E Raman-active vibrational modes,
accordingly.
Let us consider the spectral features of the high-
frequency region: Spectra in all experimental polarizations
at low temperature are presented in Fig. 2. The decomposi-
tion into the series of Lorentz-shape-like spectral lines is
presented ibid. At low temperatures the most intensive A1
lines show an appreciable asymmetry on the high-
frequency slope. The high-temperature spectra don’t reveal
such features due to a temperature induced broadening of
the lines. The nature of such asymmetry is not in the center
of the present paper. As a suitable hypothesis we propose,
that it may be a result of the combination of intensive opti-
cal modes with acoustical modes. Asymmetry in this case
reflects a difference between the probabilities to excite and
annihilate acoustic phonons, which is larger at low temper-
atures. High temperature equalizes the probabilities and
makes the wings of the line symmetrical.
Table 2. Raman selection rules for phonons of a different symmetry in the quasi-back scattering geometry utilized in the experi-
ments. Symbols: q is direction of phonon wave-vector, ei and es are polarizations of an incident and scattered light, respectively,
α = cos θ, β = sin θ. Intensities of a scattering are evaluated using the tensor components from (1)
q ei es A1 E B1 B2
(0,0,1) (α,β,0) (α,β,0) a2 (LO) (α2−β2)2c2 4(αβ)2d2
(0,0,1) (α,β,0) (β,−α,0) 4(αβ)2c2 (α2−β2)2d2
(α,β,0) (0,0,1) (0,0,1) b2 (TO)
(α,β,0) (β,−α,0) (0,0,1) e2 (TO)
Fig. 1. (Color online) Raman spectra of SrNi2V2O8 single crystal
at T = 7 K in four polarizations. Irreps of Raman-active phonon
excitations for every polarization are indicated.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 12 1763
V. Kurnosov, V. Gnezdilov, P. Lemmens, Yu. Pashkevich, A.K. Bera, A.T.M.N. Islam, and B. Lake
All identified lines are collected in Table 3. The spectrum
in zz polarization with A1(TO) consists of 5 lines, four of
which are the Davydov components of ν1(A1) and ν3(F2)
stretching modes of the (VO4)3− tetrahedron (Fig. 2(a), (b)).
Note, that triple degeneracy of ν3(F2) mode is lifted due to
crystal field effect. The most intense line at 857.5 cm−1
must be attributed to the ν1 mode according to frequency
position. So, the highest-frequency line at 914 cm−1 most
likely refers to some kind of two-particle excitation. The
identical line is situated in x′x′ spectrum and has zero
LO−TO splitting (Fig. 2(c), (d)). This spectrum contains a
set of lines belonging to A1(LO), B1, and B2 modes. B
modes may be identified by means of a y′x′ polarized spec-
trum (Fig. 2(e), (f)). Remaining spectrum of x′z polariza-
tion contains lines related to E(TO) modes.
The most intense line (ν1) is observed in diagonal po-
larizations zz and x′x′. It demonstrates a so-called “invert-
ed” LO−TO splitting (see Table 3). Originally, in the frame
of Td symmetry of a free (VO4)3− complex, this mode is
nonpolar. It is in agreement with a small observed LO−TO
splitting. Inversion is a result of a fall of its energy into a
wide, forbidden gap of some strong dipolar mode. The
same “inversion”, but with smaller splitting is inherent in
the other intensive line (ν3) at 788 cm−1. Most probably
the dipole mode with great oscillator strength originates
from a polar ν3 mode of a (VO4)3– tetrahedron and pos-
sesses 778.2 (TO)–890.2 (LO) cm−1 splitting that covers the
greater part of discussed spectral range. As was mentioned
above, every internal degree of freedom, taking into account
its degeneracy, produces 4 different one-dimensional irreps
Fig. 2. (Color online) High-frequency Raman spectra of SrNi2V2O8 in the range of ν1(A1) and ν3(F2) vibrational modes of (VO4)3−
complex. Polarization and corresponding symmetry of the modes are marked. Intensity scales on left and right panels differ in 10 times.
1764 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 12
Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi2V2O8
(A1, A2, B1, B2) and 2 two-dimensional ones (E) in the crys-
tal. So, there are 4 groups of lines, each belongs to one de-
gree of freedom, and must be presented by A1+B1+B2+2E
symmetry. Figure 2 and Table 3 reveal detection of all 4 A1
lines, 6 B1+B2 lines versus 8 allowed, and 4 E lines versus 8
allowed.
3.3. Low-frequency Raman spectra of SrNi2V2O8
The low-frequency “lattice” range of Raman spectra
does not show noticeable anomalies in their temperature
dependence. Spectra in four polarizations belonging to
phonons of different symmetry are presented in Fig. 3. The
temperature dependences of the frequencies of all detected
lines are shown in Fig. 4. A list of all detected phonon lines
at lowest temperature with the indication of their symmetry
and related polarization rules are given in Table 4. The total
number of observed and detected low-temperature lines is
essentially smaller than the group theory predicts. Only 11
from 14 A1, 15 from 30 (B1+B2), and 16 from 31 E of al-
lowed phononic lines are detected. The cause of such a
deficit is probably the big number of formula units in the
crystal unit cell that leads to small Raman intensities of
some modes due to practically full interferential quench-
ing. These aspects are considered in the following section.
4. Symmetry aspects of the phonon excitations intensity
in the Raman spectrum of SrNi2V2O8
Intensity of the Raman scattering originates from a
polarizability induced by an appropriate mode in the crys-
tal. Group theoretical analysis gives the total number of the
modes based on the symmetry positions of the ions in the
structure. Symmetry of some complexes (dimensions, an-
gles, etc.) of a crystal structure sometimes appears higher
than their Wyckoff positions. It may lead to the extremely
weak intensity of some Raman signals. The following sec-
tions cover these issues.
Table 3. Frequencies, integral intensities and assignment of Raman lines observed in the spectral range of ν1(A1) and ν3(F2)
vibrational modes of (VO4)3− complex in SrNi2V2O8
Frequency, cm−1
Integral intensity,
arb. units
Irreps Polarization Mode
717.0 1991 A1(TO) zz
ν3
761.6 7832 A1(LO) x′x′
731.5
451 B1+B2 x′x′
201 B1+B2 y′x′
747.2 16606 E(TO) x′z
778.2 12734 A1(TO) zz
ν3
890.2 33888 A1(LO) x′x′
782.7 1271 E(TO) x′z
793.2 958 E(TO) x′z
793.4
7188 B1+B2 x′x′
1236 B1+B2 y′x′
788.0 80697 A1(LO) x′x′
ν3
788.4 138057 A1(TO) zz
817.9
14509 B1+B2 x′x′
17922 B1+B2 y′x′
821.7 387 E(TO) x′z
827.5
5594 B1+B2 x′x′
9116 B1+B2 y′x′
851.9 282998 A1(LO) x′x′
ν1
857.5 196273 A1(TO) zz
881.9
24959 B1+B2 x′x′
11177 B1+B2 y′x′
896.3
445 B1+B2 x′x′
1585 B1+B2 y′x′
914.0 2902 A1(TO) zz
two-particle
912.9 2241 A1(LO) x′x′
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 12 1765
V. Kurnosov, V. Gnezdilov, P. Lemmens, Yu. Pashkevich, A.K. Bera, A.T.M.N. Islam, and B. Lake
4.1. (VO4)3− modes
In the structure of SrNi2V2O8 the (VO4)3– complexes
occupy general positions, but their local second order axes
in the Td symmetry notation are oriented close to the prin-
cipal axes of the crystal. More precisely, there are two
groups of the tetrahedra whose second order axes are prac-
tically parallel to x and y crystallographic directions. Fur-
thermore, the tetrahedra are slightly rotated around these
preferred axes as can be seen in Fig. 5. We also consider
some uniaxial distortion of the tetrahedra along those pre-
ferred axes in order to include to their polarizability some
small parameters reflected the low symmetry of the po-
sition.
Fig. 3. (Color online) Temperature dependences of low-frequency range of SrNi2V2O8 Raman spectrum in: (a) x′z polarization corre-
sponding to E(TO) modes, (b) x′x′ polarization corresponding to A1(LO)+B1+B2 modes, (c) y′x′ polarization corresponding to B1+B2
modes, and (d) zz polarization corresponding to A1(TO) modes. Insets show some spectral peculiarities in detail.
1766 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 12
Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi2V2O8
Using such approach, the polarizabilities of an individual
VO4 tetrahedron related with its own modes in the crystal
are expressed in the following manner:
1
1mol ( )
a
A
a
A a
a
+ ∆
α =
, ( )1
mol
2
(1)A
b
E b
b
−
α =
,
( )1
mol
0
(2) 3
3
B
b
b
E b
b
α = δ
δ −
, ( )2 ( )
2mol ( ) ,B x
c
c
F x c
c
α = δ
−δ
( )( )
2mol ( )
d
E y
d
d
F y
d
δ
α = δ
, ( )( )
2mol ( ) ,
d
E z
d
d
F z d
−δ
α =
−δ
(3)
where term ∆a and difference between c and d are due to
an uniaxial distortion of the tetrahedron along x axis; terms
δb, δc, and δd are due to slight rotation around x axis. Us-
ing these assumptions and symmetry coordinates of
nondegenerated modes of the crystal, the polarizabilities
arising from A1, E, and F2 modes of the tetrahedra can be
expressed as follows:
___________________________________________________
1
1cryst
2
( ) 2 2
2
a
A
a
a
A a
a
+ ∆
α = + ∆
, 1
1cryst ( ) 2
0
a
B
aA
∆
α = −∆
,
( )1
cryst (1) 2
2
A
b
E b
b
−
α = −
, ( )1
cryst (1) 3 2
0
B
b
E b
−
α =
,
Fig. 4. (Color online) Temperature dependences of frequencies of
all detected Raman-active phonons in the low-frequency range in
SrNi2V2O8.
Table 4. Frequencies of observed Raman lines (in cm−1) of the
low-frequency spectral range in SrNi2V2O8 at a temperature 7 K.
A symmetry assignment is based on the polarization selection rules
A1(TO) A1(LO) B1+B2 E(TO)
zz x′x′ x′x′, y′x′ x′z
78.5 81.7
92.0 96.1
131.2 115.2
144.9 143.8
148.6
157.1
159.9
164.3 165.3
167.2 167.8
173.9
190.9 186.5
205.8 196.7
229.9 230.2 230.4
232.3
238.0
280.9 281.8 289.2
298.9
304.2
314.3 316.1
334.5 334.9 322.7
356.6 358.0
370.5 368.4 374.0
394.3 395.3 394.3
402.3 411.3 403.3
417.2
431.1 433.2
441.5 483.7 439.2
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 12 1767
V. Kurnosov, V. Gnezdilov, P. Lemmens, Yu. Pashkevich, A.K. Bera, A.T.M.N. Islam, and B. Lake
( )1
cryst (2) 6
2
A
b
E b
b
α =
−
, ( )1
cryst (2) 6
0
B
b
E b
α = −
,
( )1
2cryst ( ) 2
2
c
A
c
c
F x
δ
α = δ
− δ
, ( )1
2cryst ( ) 2
0
c
B
cF x
−δ
α = δ
,
( )2
2cryst ( ) 2 2
d
B
dF y
δ
α = δ
, ( )2
2cryst ( ) 2 2B
d
F z d
α =
.
(4)
Here the upper indices mark irreps of the crystal modes while symbols in parentheses belong to the internal modes of tet-
rahedron.
Twice-degenerated modes of the crystal have xz and yz components of polarizability tensor only. That is why they can on-
ly originate from those modes of an individual molecule, whose polarizabilities contain such components. It follows from (3)
that appreciable Raman intensity of twice degenerated modes in the crystal arises from the modes related to E(2), F2(x), F2(y),
and F2(z) molecular vibrations only. Theoretically these 4 degrees of freedom generate 8 crystal E modes, but only half of
them possess nonzero Raman polarizability. In order to understand why this happens we can consider the example of F2(x)
and F2(y) molecular degrees of freedom. These modes are dipolar that makes convenient their vector representation, as shown
in Fig. 5. The xz components of crystal polarizability for modes shown in Fig. 5 are expressed as follows according to (4):
( )cryst 1 2 3 5 871 4 6
1( ) 2( ),
2 2
yz yz yz yzxz xz xz xz xzS c dα = α +α +α +α +α +α +α +α = +
( )cryst 2 2 3 5 871 4 6
1( ) 2( ),
2 2
yz yz yz yzxz xz xz xz xzS c dα = α +α +α +α −α −α −α −α = −
( )cryst 3 2 3 5 871 4 6
1( ) 0,
2 2
yz yz yz yzxz xz xz xz xzSα = α −α −α +α +α −α −α +α =
( )cryst 4 2 3 5 871 4 6
1( ) 0.
2 2
yz yz yz yzxz xz xz xz xzSα = α −α −α +α −α +α +α −α = (5)
Fig. 5. (Color online) Patterns of y components of twice-degenerated modes in SrNi2V2O8 originating from F2 vibrational modes of
tetrahedral (VO4)3− complexes. Numeration of all tetrahedra belonging to primitive cell is used in expressions (5).
1768 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 12
Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi2V2O8
Modes S3 and S4 are silent due to orientation of one of
the second order axes of the tetrahedra along crystallo-
graphic direction in the crystal basal plane. Mode S2 is
also weak because c ≈ d. All nonzero polarizability ten-
sors of the crystal for twice-degenerated modes are pre-
sented below:
___________________________________________________
( )( )
cryst (2) 2
b
E x
b
E
δ
α =
δ
, ( )( )
cryst (2) 2E y
b
b
E
α = δ
δ
,
( )( )
2cryst ( ) 2
d
E x
d
F z
−δ
α =
−δ
, ( )( )
2cryst ( ) 2E y
d
d
F z
α = −δ
−δ
,
( )( )
2cryst ( , ) 2E x
d c
F x y
d c
+
α =
+
, ( )( )
2cryst ( , ) 2E y F x y d c
d c
α = +
+
,
( )( )
2cryst ( , ) 2E x
d c
F x y
d c
−
α =
−
, ( )( )
2cryst ( , ) 2E y F x y d c
d c
α = −
−
.
(6)
______________________________________________
Results of the analysis are collected in Table 5.
With regard to A1(ν1) and F2(ν3) modes of high-
frequency region, only one A1(ν1), one B2(ν3), and one
E(ν3) modes are expected to be intense if we assume that
their polarizability is originated purely from the molecular
polarizability. Taking into account small deviations from
ideal form and orientation of the tetrahedra the weak
A1(ν3), B1(ν1), B1(ν3), B2(ν3), and 2 E(ν3) can be added.
A comparison with experiment shows partial match. So,
in E spectrum one intense and three weak lines are ob-
served that differ from the prediction of one weak line. It is
remarkable that in the frequency range of ν1 mode no Ra-
man signal of E polarization is detected, that is in agree-
ment with the prediction. The analysis allows 4 B1,2 modes
Table 5. Raman tensor components calculated for A1, E and F2 modes of tetrahedral (VO4)3− complexes in SrNi2V2O8 crystal.
In the first column the symmetry of a free tetrahedron mode is indicated in parentheses
xx yy zz
A1(A1) (2a+∆a) 2 (2a+∆a) 2 2a 2
A1(F2(x)) δc 2 δc 2 −2δc 2
A1(E(1)) −b 2 −b 2 2b 2
A1(E(2)) b 6 b 6 −2b 6
B1(A1) ∆a 2 −∆a 2
B1(E(1)) −3b 2 3b 2
B1(E(2)) b 6 −b 6
B1(F2(x)) −δc 2 δc 2
xy=yx xz=zx yz=zy
B2(F2(z)) 2d 2
B2(F2(y)) 2δd 2
E(E(2)) 2δb 2δb
E(F2(x,y)) (d+c) 2 (d+c) 2
E(F2(x,y)) (d−c) 2 (d−c) 2
E(F2(z)) −2δd −2δd
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 12 1769
V. Kurnosov, V. Gnezdilov, P. Lemmens, Yu. Pashkevich, A.K. Bera, A.T.M.N. Islam, and B. Lake
with the most intense component in the frequency region
of the ν3 mode. Experimentally two intense and four weak
lines are detected. One of the intense lines is close to the ν1
frequency. It may mean that ∆a term of the molecular
polarizability is essential enough. In diagonal zz polariza-
tion (A1 modes) there are two intense enough lines close to
frequencies of ν1 and ν3 modes of free VO4 tetrahedron.
The analysis predicts less intense line due to δc term origi-
nated from the tetrahedra tilt. Its comparable with A1(ν1)
mode intensity can not be explained in the proposed simple
model where crystal polarizability is originated from the
molecular polarizability only. Real situation may be too
different from such a rough estimation. It means, for in-
stance, that some of these internal modes of the molecular
complexes may strongly polarize the crystal surrounding.
Nevertheless the model provides evidence that a large
number of (VO4)3– complexes situated in the crystal struc-
ture may lead to the interferential quenching of their
polarizability, resulting in a smaller number of intense
lines observed in the Raman spectra indeed.
As for E(ν2) and F2(ν4) modes of the tetrahedral
(VO4)3– complexes, the analysis predicts 3A1+5B1,2+4E
lines in the Raman spectrum of the crystal, including those
with small intensity. Remembering the group theory pre-
diction for these modes, 5A1+10B1,2+10E (Table 1), we get
about twice less detectable lines of this origin.
4.2. Modes related to Ni2+ and Sr2+ degrees of freedom
Sr2+ ions occupy positions with local symmetry C2 in
the crystal. Formally, 1A1+1A2+1B1+1B2+4E modes are
caused by their degrees of freedom (Table 1). The coordi-
nation of every Sr2+ ion consists of 8 oxygens. It turned
out that the surrounding ligands form approximately higher
symmetry, than C2 Wyckoff position for Sr2+. The sym-
metry is close to C2v with principal axis along z direction.
Figure 6 clearly shows permissibility of that approxima-
tion.
Polarizability tensors connected with the motions of
Sr2+ ions in their positions are the following:
___________________________________________________
,1,2 1( ) ,z
a
A b
c
α =
,1,2 1( ) ,x
e
B
e
α =
,1,2 2( )y B f
f
α =
,
,3,4 1( ) ,z
b
A a
c
α =
,3,4 1( ) ,x
f
B
f
α =
,3,4 2( )y B e
e
α =
,
(7)
______________________________________________
The numeration follows Fig. 6. Symbols in parentheses
relate to the C2v point group irreps. Results of summations
of expressions (7) through the normal modes originating
from Sr2+ degrees of freedom in the crystal are presented
in Table 6. As can be seen only 1A1+1B1+2E Sr2+ modes
are expected to be intense in Raman. A deficit contains
1B2+2E modes. Notably, tensors (7) do not contain xy com-
ponents at all, so there are no sources to produce Raman
intensity of B2 mode. This is a consequence of the actual
lack of rotation around the z axis of the oxygen polyhedron
surrounding the Sr2+ ion.
Fig. 6. (Color online) Structure of the Sr2+ coordination envi-
ronment (a), and their projection on the basal plane (b) in
SrNi2V2O8 according to Refs. 20, 23. Atoms numeration and
local coordinate systems are used in calculations.
Table 6. Raman tensor components calculated for Sr2+ and
Ni2+ degrees of freedom in the SrNi2V2O8 crystal. Labels x, y, z
in the first column represent directions of the ions shifts
xx yy zz
A1, z (a+b) 2 (a+b) 2 c2 2
B1, z (a−b) 2 −(a−b) 2
xy=yx xz=zx yz=zy
E, x (e+f) 2
E, y (e+f) 2
E, x (e−f) 2
E, y (e−f) 2
1770 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 12
Phonon excitations in the quasi-one-dimensional Haldane phase of SrNi2V2O8
Oxygen surroundings of Ni2+ in the structure of
SrNi2V2O8 looks like slightly distorted octahedron [20,23]
as shown in Fig. 7. Similarly to Sr2+ we will describe the
symmetry of the Ni2+ coordination environment as C2v in
the first approximation. Eight complexes are divided into
two groups 1, 4, 6, 7 and 2, 3, 5, 8 which possess
polarizability tensors analogous to (7). And the results are
obtained in the same manner as for Sr2+ degrees of free-
dom. In spite of twice greater number of Ni2+ ions in the
crystal structure, symmetry limitations in the described
model do reduce effectively this number, so the expected
number of intense Raman lines proves to be the same as
for the case of Sr2+ ions (Table 6). Effective symmetry rise
in this case leads to a bigger deficit of intense Raman lines.
It contains for Ni2+ degrees of freedom 2A1+2B1+3B2+4E.
Summing up the total proposed deficit of Raman lines in
the “lattice” frequency region, we obtain 4A1+11B1,2+12E.
This result is in a good agreement with experimental observa-
tions which estimate a lack of Raman lines in this region as
3A1+15B1,2+15E. Notice, that the proposed analysis does not
include exploration of the rotational and translational degrees
of freedom of VO4 tetrahedra which probably may produce
extremely weak Raman signals too.
5. Summary
Vibrational Raman spectra of SrNi2V2O8 are investigated
in the 10–1000 cm−1 frequency range at various temperatures
7–300 K. There is no evidence of a structural phase transition
in the investigated temperature range. Vibrational spectrum of
the crystal naturally divides into two frequency ranges, name-
ly “lattice” (50−500 cm−1) and internal ν1,3 modes of (VO4)3−
tetrahedral complex (700−900 cm−1). In the low-frequency
range 11A1+15B1,2+16E modes are detected versus
14A1+30B1,2+31E allowed by the symmetry. In the high-
frequency range there are 4A1+6B1,2+4E modes observed
versus 4A1+8B1,2+8E allowed. A big deficit of the observed
Raman lines is explained by a simple model which takes into
account the higher symmetry of the complexes in the crystal
structure than it is given by the position symmetry. Such
“symmetrization” leads to interferential quenching of certain
modes, which takes place due to big number of the identical
molecules and ions in the SrNi2V2O8 structure.
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1. Introduction
2. Experimental
3. Phonon spectra
3.1. Group theoretical analysis and polarization rules
3.2. Structure of the Raman spectrum and molecular vibrations of (VO4)3(
3.3. Low-frequency Raman spectra of SrNi2V2O8
4. Symmetry aspects of the phonon excitations intensity in the Raman spectrum of SrNi2V2O8
4.1. (VO4)3( modes
4.2. Modes related to Ni2+ and Sr2+ degrees of freedom
5. Summary
|