Raman scattering in LiNiPO₄ single crystal
The complete Raman spectra of a single crystal of LiNiPO₄ for a wide temperature range are reported. Among the 36 Raman-active modes predicted by group theory, 33 have been detected. The analysis of the spectra in terms of internal modes of the (PO₄)³⁻ group and of external modes is done with succes...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1301662018-02-09T03:03:46Z Raman scattering in LiNiPO₄ single crystal Fomin, V.I. Gnezdilov, V.P. Kurnosov, V.S. Peschanskii, A.V. Yeremenko, A.V. Schmid, H. Rivera, J.-P. Gentil, S. Низкотемпеpатуpный магнетизм The complete Raman spectra of a single crystal of LiNiPO₄ for a wide temperature range are reported. Among the 36 Raman-active modes predicted by group theory, 33 have been detected. The analysis of the spectra in terms of internal modes of the (PO₄)³⁻ group and of external modes is done with success. Besides, the multiphonon Raman scattering is discussed. Low-frequency lines, observed in the antiferromagnetic phase, are assigned to magnon scattering and are discussed briefly. 2002 Article Raman scattering in LiNiPO₄ single crystal / V.I. Fomin, V.P. Gnezdilov, V.S. Kurnosov, A.V. Peschanskii, A.V. Yeremenko, H.Schmid, J.-P. Rivera, S.Gentil // Физика низких температур. — 2002. — Т. 28, № 3. — С. 288-296. — Бібліогр.: 26 назв. — англ. 0132-6414 PACS: 78.30.Hv http://dspace.nbuv.gov.ua/handle/123456789/130166 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Низкотемпеpатуpный магнетизм Низкотемпеpатуpный магнетизм |
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Низкотемпеpатуpный магнетизм Низкотемпеpатуpный магнетизм Fomin, V.I. Gnezdilov, V.P. Kurnosov, V.S. Peschanskii, A.V. Yeremenko, A.V. Schmid, H. Rivera, J.-P. Gentil, S. Raman scattering in LiNiPO₄ single crystal Физика низких температур |
| description |
The complete Raman spectra of a single crystal of LiNiPO₄ for a wide temperature range are reported. Among the 36 Raman-active modes predicted by group theory, 33 have been detected. The analysis of the spectra in terms of internal modes of the (PO₄)³⁻ group and of external modes is done with success. Besides, the multiphonon Raman scattering is discussed. Low-frequency lines, observed in the antiferromagnetic phase, are assigned to magnon scattering and are discussed briefly. |
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Article |
| author |
Fomin, V.I. Gnezdilov, V.P. Kurnosov, V.S. Peschanskii, A.V. Yeremenko, A.V. Schmid, H. Rivera, J.-P. Gentil, S. |
| author_facet |
Fomin, V.I. Gnezdilov, V.P. Kurnosov, V.S. Peschanskii, A.V. Yeremenko, A.V. Schmid, H. Rivera, J.-P. Gentil, S. |
| author_sort |
Fomin, V.I. |
| title |
Raman scattering in LiNiPO₄ single crystal |
| title_short |
Raman scattering in LiNiPO₄ single crystal |
| title_full |
Raman scattering in LiNiPO₄ single crystal |
| title_fullStr |
Raman scattering in LiNiPO₄ single crystal |
| title_full_unstemmed |
Raman scattering in LiNiPO₄ single crystal |
| title_sort |
raman scattering in linipo₄ single crystal |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2002 |
| topic_facet |
Низкотемпеpатуpный магнетизм |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/130166 |
| citation_txt |
Raman scattering in LiNiPO₄ single crystal / V.I. Fomin, V.P. Gnezdilov, V.S. Kurnosov, A.V. Peschanskii, A.V. Yeremenko, H.Schmid, J.-P. Rivera, S.Gentil // Физика низких температур. — 2002. — Т. 28, № 3. — С. 288-296. — Бібліогр.: 26 назв. — англ. |
| series |
Физика низких температур |
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2025-07-09T13:00:24Z |
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| fulltext |
Fizika Nizkikh Temperatur, 2002, v. 28, No. 3, p. 288–296Fomin V. I., Gnezdilov V. P., Kurnosov V. S., Peschanskii A. V., Yeremenko A. V., Schmid H., Rivera J.-P., and Gentil S.Raman scattering in LiNiPO4 single crystalFomin V. I., Gnezdilov V. P., Kurnosov V. S., Peschanskii A. V., Yeremenko A. V., Schmid H., Rivera J.-P., and Gentil S.Raman scattering in LiNiPO4 single crystal
Raman scattering in LiNiPO4 single crystal
V. I. Fomin, V. P. Gnezdilov, V. S. Kurnosov,
A. V. Peschanskii, and A. V. Yeremenko
B. Verkin Institute for Low Temperature Physics and Engineering
of the National Academy of Sciences of Ukraine, 47 Lenin Ave., 61103, Kharkov, Ukraine
E-mail: gnezdilov@ilt.kharkov.ua
H. Schmid, J.-P. Rivera, and S. Gentil*
Department of Inorganic, Analytical and Applied Chemistry, University of Geneva
CH-1211 Geneva 4, Switzerland
Received November 1, 2001
The complete Raman spectra of a single crystal of LiNiPO4 for a wide temperature range
are reported. Among the 36 Raman-active modes predicted by group theory, 33 have been
detected. The analysis of the spectra in terms of internal modes of the (PO4)
3− group and of
external modes is done with success. Besides, the multiphonon Raman scattering is discussed.
Low-frequency lines, observed in the antiferromagnetic phase, are assigned to magnon
scattering and are discussed briefly.
PACS: 78.30.Hv
Introduction
The lithium orthophosphate of nickel belongs to
a family of antiferromagnets with the general for-
mula LiMPO4 (where M = Fe2+, Mn2+, Co2+, Ni2+)
and which are known to be magnetoelectrics [1,2].
In the paramagnetic phase these compounds have
the same orthorhombic space group Pnma, but the
magnetic groups in their antiferromagnetic phase
are partly different. All of them allow the occur-
rence of the linear magnetoelectric (ME) effect.
The mechanisms responsible for the ME effect in
LiMPO4 remain an open question.
The majority of experimental investigations of
the linear ME effect in LiMPO4 compounds real-
ized so far have been restricted to the study of the
quasistatic properties, i.e., to measurement of the
quasistatic magnetic (electric) moment induced by
an external quasistatic electric (magnetic) field.
Much less attention has been paid to the spectrum
of elementary excitations and to the influence of
ME interaction on excited states. The nature of the
large value of the ME coefficient in LiCoPO4 is not
yet clear. It may lie in the specific arrangement of
the low-energy electronic energy levels of the mag-
netic ion and their interaction with a vibrational
spectrum.
The motivation for the present study is manifold.
One of the objectives is to determine the frequency
and symmetry of the long-wavelength, or k = 0,
Raman-active phonons and to compare them with
the results of group theory analysis, based both on
the factor group and site symmetry methods.
At low temperature LiNiPO4 undergoes a transi-
tion to an antiferromagnetic (AF) phase, and thus
additional lines in consequence of the light scatter-
ing by spin waves, both first and second order, may
be observed in the Raman spectra.
Owing to the ME effect the Raman spectrum
may be more complicated in the AF phase due to an
additional mechanism of light scattering predicted
by Pradhan [3]. The origin of the mechanism re-
sides in the possibility (via ME) interaction of the
electrical (magnetic) vector of the incident light
* New address: Swiss Federal Institute of Technology Lausanne, Materials Department, Laboratory of Ceramics,
CH-1015 Lausanne, Switzerland.
© V. I. Fomin, V. P. Gnezdilov, V. S. Kurnosov, A. V. Peschanskii, A. V. Yeremenko, H. Schmid, J.-P. Rivera, and S. Gentil, 2002
with the magnetic (electric) vector of the scattered
light. The effect should be proportional at least to
the value of the ME coefficients at the frequency of
visible light, which are unknown. The «Pradhan»
lines in the spectrum may in principle be separated
via their difference given by the polarization selec-
tion rules.
Motivated by the above considerations, a Raman
scattering study of LiNiPO4 has been undertaken.
In this paper we are reporting spectra of the ob-
served elementary excitations in the frequency re-
gion from 4 to 1200 ñm−1 and at temperatures
between 5 and 300 K.
Synthesis of LiNiPO 4 single crystals and
experimental procedure
Single crystals of the orthophosphates LiMPO4
(M = Mn, Fe, Co, Ni) can be obtained by conven-
tional solution growth (see, e.g., [4] and [5]) in
LiCl flux. This high-temperature halide solvent is
advantageous as it consists partially of an element
present in the final compound and has rather low
viscosity in the molten phase, favoring stable
growth. Different experimental variants according
to the following reactions are possible for obtaining
the starting orthophosphate:
M(OH)2+NH4H2PO4+Li3PO4→LiMPO4+NH3+H2O ,
(1)
M3(PO4)2 + Li3PO4 → 3 LiMPO4 , (2)
MCl2 + Li3PO4 → LiMPO4 + 2 LiCl . (3)
For each of these reactions, a stoichiometric molar
ratio of reacting materials is required. Reaction (2)
was first used for the synthesis of LiMnPO4 crystals
by dissolving the starting reactants in LiCl, fol-
lowed by cooling [6]. The method was later modi-
fied slightly for the growth of LiFePO4 crystals [7]
and adapted for the growth of single crystals of the
entire series LiMPO4, with M = Mn, Fe, Co and
Ni [8].
In the present study, for growing LiNiPO4 single
crystals, reaction (3) was used and performed in a
LiCl flux, allowing us to obtain single crystals
large enough for physical experiments (∼ 1–
5 mm3). The molar ratio between LiNiPO4 and
LiCl in the starting mixture was optimized at 1:3.
Platinum crucibles of 30 ml volume were filled with
a maximum of 45 g of a stoichiometric mixture of
the powders, followed by a pre-melting at 800 °C.
Due to the high volatility of the solvent, the cruci-
bles were sealed by argon arc welding and a hole of
∼ 50 µm diameter was drilled through the lid in
order to equilibrate the pressure.
The growth temperature profile was as follows:
1) heating in 5 h to 890 °C, 2) soaking at 890 °C
for 4 h, 3) slow-cooling at 0.755 °C/h to 715 °C,
4) slow-cooling at 1.4 °C/h to 680 °C and 5)
crystal recovery at 680 °C. The crystal recovery
from the molten flux was the last critical problem
to be solved for obtaining weakly stressed crystals.
For this purpose the crucible was rapidly removed
from the furnace, two holes were pierced in the lid,
and the remaining liquid was quickly poured on a
porous ceramic.
The Raman spectra were measured on a
LiNiPO4 single crystal of high optical quality. The
sample was cut as a rectangular parallelepiped with
edges of 4.2, 3.0, and 2.4 mm length, parallel to the
crystallographic axes a, b, c of the orthorhombic
cell, respectively. Since the a, b, and c axes corre-
spond to the principal axes of the dielectric tensor,
this sample shape minimized errors due to birefrin-
gence in polarized Raman measurements. The sys-
tem of coordinates was chosen to be X || a, Y || b and
Z || c.
The Raman spectra were recorded with a Jobin-
Yvon U-1000 double monochromator equipped with
a cooled photomultiplier and photon counting elec-
tronics. The right-angle scattering geometry was
used. In order to reduce the beam-induced heating
of the sample and to enhance the scattered light
intensity, the 632.8 nm line of a He–Ne laser ope-
rating at powers up to 30 mW, was used in the
experiments. For the yellow-orange crystals of
LiNiPO4, the transmission window is centered in
the region of ∼ 573 nm [9,10]. The temperature
interval 4.2–300 K was covered by using a special
optical cryostat. The sample was kept in an ex-
change gas atmosphere.
Structural and magnetic features of LiNiPO 4
The lithium orthophosphates LiMPO4 (M =
= Co2+ or Ni2+) are isostructural with the minerals
lithiophilite (M = Mn) and triphilite (M = Fe),
which belong to the olivine family [1,11,12]. The
orthorhombic unit cell contains four formula units
and is described by space group Pnma (D2h
16) [12].
The crystal structure can be understood as a nearly
hexagonal close packing of oxygen atoms. Each
phosphorus atom in the crystal is surrounded by
four oxygen atoms, creating a distorted tetrahedral
(PO4)3− group with Cs (m ⊥ b) point symmetry. The
Raman scattering in LiNiPO4 single crystal
Fizika Nizkikh Temperatur, 2002, v. 28, No. 3 289
Ni2+ and Li2+ ions occupy the positions with site
symmetry Cs and Ci , respectively. They are sur-
rounded by distorted octahedra of oxygen atoms.
Nickel ions lie in puckered planes perpendicular to
the a axis. Adjacent planes are separated by PO4
tetrahedra sharing corners and edges with the
LiO6 octahedra.
Above TN = 19.1 K the crystal manifests para-
magnetic behavior [13]. Below TN a relatively strong
AF coupling between nearest-neighbor nickel ions is
occurring within the puckered plane via –Ni–O–Ni–
superexchange pathways [11,13,14]. However, there
is no direct or first-order superexchange (via one
common ion) coupling between the moments in
different planes, and only higher-order interactions
are possible, involving the phosphate groups as an
«exchange bridge». Each Ni2+ has a net of at least
four antiferromagnetic –Ni–O–P–O–Ni– links to
Ni2+ ions in adjacent planes. According to neutron
scattering data [13,14], the antiferromagnetic or-
dering takes place with preservation of the unit cell.
The spins of the nickel ions lie along the crystal axis
c and alternate up and down. Up to now the
magnetic space and point groups were considered to
be Pnm′a and mm′m, respectively [11]. Recent neu-
tron diffraction work has shown that a space-modu-
lated spin structure occurs in a narrow temperature
range close to TN with a magnetic incommen-
surate short range order persisting up to about
40 K [15,16].
The magnetic field dependence of the polariza-
tion induced via the ME effect in LiNiPO4 shows a
so-called «butterfly loop» feature both for the mag-
netic field H applied along the a axis, i.e. perpen-
dicular to the spin direction (c axis) [17], as well as
for H applied along the spin direction [18]. Usually
such behavior appears due to the presence of a
spontaneous magnetic moment in a compound (see,
e.g., [19,20]). Since such a small spontaneous mag-
netization was recently found for the related
LiCoPO4 [21], also showing «butterfly loops» [2],
the occurrence of a spontaneous magnetization in
LiNiPO4 can be expected, too. Thus a symmetry
lower than mm′m will be required.
In spite of the fact that the mm′m symmetry
forbids a spontaneous magnetic moment, it was
recently shown theoretically that a «butterfly loop»
can also be realized in 4-sublattice fully compen-
sated antiferromagnets with an «indirect cross»
magnetic structure [22]. In such a structure the
above-mentioned symmetry mm′m allows spin can-
ting in the pairs of adjacent sublattices, but the
resulting magnetic moment of a pair is «hidden»,
because another spin pair fully compensates it in the
unit cell. However, this mechanism does not seem
to apply to LiNiPO4 because, as stated above, it is
very likely that the «butterfly loops» are due to a
spontaneous magnetization.
Group theory analysis of fundamental
vibrations
The group theory analysis of the LiMPO4 family
compounds has been done in [23]. Let us summarize
the essential results. In all of them the unit cell
contains 4 formula units. The vibrational repre-
sentation Γvibr of the 84 normal modes at the center
of the Brillouin zone (k = 0) is distributed on the
irreducible representations of the D2h point group
as follows: Γvibr = 11Ag + 7B1g + 11B2g + 7B3g +
+ 10Au + 14B1u + 10B2u + 14B3u . Among them
there are 3 acoustic modes, 45 antisymmetrical
modes, active in IR absorption for the B1u , B2u ,
and B3u representations, and 36 symmetrical
Raman-active optical modes. The latter modes cor-
respond to the polarization of the excited and scat-
tered light in the chosen coordinate system as:
Ag–(XX), (YY), (ZZ), B1g–(XY), (YX), B2g–
(XZ), (ZX), and B3g–(YZ), (ZY).
In a first-order approximation, the vibrations can
be separated into internal vibrations (Γint) of the
(PO4)3− tetrahedra and external vibrations in which
they move and rotate as solid units. The external
vibrations are separated into the translational mo-
tions of the center of mass of (PO4)3−, Li+ and
Co2+ ions (Γtrans) and hindered rotations (libra-
tions) of the (PO4)3− ions (Γlibr). Such separation is
rather arbitrary and may be used in the group-the-
ory analysis for clarity only. In fact, they are not
completely independent. The analysis gives the fol-
lowing representation for the above-listed types of
vibration:
Γint = 6Ag + 3B1g + 6B2g + 3B3g +
+ 3Au + 6B1u + 3B2u + 6B3u ,
Γtrans = 4Ag + 2B1g + 4B2g + 2B3g +
+ 5Au + 6B1u + 4B2u + 6B3u ,
and
Γlibr = Ag + 2B1g + B2g + 2B3g +
+ 2Au + B1u + 2B2u + B3u .
V. I. Fomin et al.
290 Fizika Nizkikh Temperatur, 2002, v. 28, No. 3
Theoretically, a static splitting due to the Cs
crystal field symmetry and a dynamic splitting due
to the presence of 4 formula units in the unit cell
could take place for the frequencies of the internal
vibrations of (PO4)3− tetrahedra. Experimentally,
this may or may not be observed, depending on the
crystal field effects.
Experimental results and discussion
Polarized Raman spectra of a LiNiPO4 single
crystal, taken at 5 K for different orientations of
the sample sufficient to classify the symmetry types
of all the Raman-active modes, are shown in Fig. 1.
The intense lines which persist when the tempera-
ture rises from T < TN to room temperature are
identified here as first-order phonon excitations.
The symmetry assignments were made by means of
polarization measurements and are listed in Table.
Some «leak through» of forbidden lines in certain
polarization configurations is evident in these spec-
tra, arising from slight disorientation of the crystal
and/or the wide angle aperture optics which is
used in the experiments to collect scattered light.
The Raman spectra of LiNiPO4 are very similar to
those of LiCoPO4 [23].
Study of internal modes
Characteristic phonon lines with frequencies
higher than 400 ñm−1 are observed. The lines were
identified in accordance with their closeness to the
frequencies of the fundamental vibrational modes
of a free PO4 tetrahedron, which are 980 (ν1), 365
(ν2), 1082 (ν3), and 515 (ν4) ñm
−1 [24]. The redu-
cible vibrational representation of a free PO4 tetra-
hedron decomposes to A1 + E + F1 + 3F2 irredu-
cible representations of its Td symmetry group. The
internal modes are labeled using Herzberg’s nota-
tion [24] as: ν1 (A1 , symmetric P–O stretching),
the doubly degenerate ν2 (E, symmetric O–P–O
bond bending), the triply degenerate ν3 (F2 , anti-
symmetric P–O stretching), and the triply degene-
rate ν4 (F2 , antisymmetric O–P–O bond bending).
The remaining modes F1 and F2 are external and
correspond to rotation and translation of PO4 as a
whole unit, respectively.
In LiNiPO4 the point symmetry of (PO4)3− ions
is Cs , which is lower than the Td symmetry of the
free ion, hence the degeneracy of the free ion fre-
quencies must be lifted as: A1 → A′, E → A′ + A′′,
F1 → A′ + 2A′′, F2 → 2A′ + A′′. Since there are
four (PO4)3− ions within the primitive unit cell,
there are four times as many modes of each species.
They can be further related to the D2h factor
group symmetry of the crystal giving the rules:
4A′→ Ag+ B2g+ B1u+ B3u and 4A′′→ B1g+ B3g+
+ Au+ B2u . As a result, the internal phonons at
k = 0 in the LiNiPO4 crystal originate from the
fundamental vibrational modes of a free PO4 tet-
rahedron as shown in the following scheme:
ν1 → Ag + B2g + B1u + B3u , ν2 → Ag+ B1g+ B2g+
+ B3g+ Au+ B1u+ B2u+ B3u , ν3 and ν4 → 2Ag +
+ B1g+ 2B2g+ B3g+ Au+ 2B1u+ B2u+ 2B3u . The fre-
quencies of the phonons may be split due to a
dynamical effect.
Fig. 1. Low-temperature (5 K) polarized Raman spectra
of a LiNiPO4 single crystal. The spectral resolution is
2.0 ñm−1.
Raman scattering in LiNiPO4 single crystal
Fizika Nizkikh Temperatur, 2002, v. 28, No. 3 291
In the crystal, the value of frequency splitting
of the νi (i = 1–4) modes of the phosphate group is
an indicator of the strength of the coupling to an
environment. In the absence of interaction between
them, the modes in quartets Ag + B2g + B1u + B3u
and B1g + B3g + Au + B2u , which originate from
A′ and A′ ′ types of vibrations respectively, would
each have the same frequency. Unfortunately, to
the best of the authors’ knowledge, no IR work has
yet been done for this single crystal*. Hence we
Table
Experimentally observed frequencies (ñm−1) of vibrational excitations of the LiNiPO4 single crystal at 5 K (300 K)
and their classification
Type of vibrations
Symmetry of vibrations
Ag B1g B2g B3g
E
xt
er
na
l
114.0 (111.5)
122.0 (119.5)
—
172.0 (170.0)
175.5 (175.0)
182.0 (181.5)
193.5 (189.0)
199.0 (195.0)
242.5 (238.0)
255.5 (252.0)
258.0 (256.0)
262.0 (258.5)
287.5 (282.5)
308.0 (303.5)
313.0 (310.0)
325.0 (320.5)
329.0 (324.5)
329.5 (325.5)
In
te
rn
al
P
O
4
E(ν2)
∗
422.5 (417.5)
442.5 (437.0)
462.5 (459.0)
470.5 (467.5)
F2(ν4)
∗
581.5 (580.0)
592.0 (591.0)
592.5 (591.5)
603.0 (601.0)
642.0 (640.0)
—
A1(ν1)
∗ 948.5 (948.5)
—
F2(ν3)
∗
953.0 (952.0)
986.0 (987.5)
1011.5 (1010.5)
1023.0 (1022.5)
1074.5 (1072.0)
1090.0 (1088.0)
* Irreducible representations and the internal mode indexes of a free PO4 tetrahedron [24].
* The only published data [25] concern IR spectra of polycrystalline samples of Li1−3xFexNiPO4 (0 < x < 0.15).
V. I. Fomin et al.
292 Fizika Nizkikh Temperatur, 2002, v. 28, No. 3
have no experimental data about IR-active phonons
with B1u , B3u , and B2u symmetry (Au phonons are
neither IR nor Raman active), which belong to the
above-mentioned quartets, and so we have no possi-
bility to calculate the full range of frequency split-
ting of the νi modes in the crystal. Nevertheless, the
frequency separation of Ag and B2g , and of B1g and
B3g modes indicate that dynamical effects are far
from negligible (see Table). It should be noted that
the B2g component of the stretching mode ν1 is
weak and difficult to observe.
The separation of fundamental vibrations into
internal and external ones is valid in the case where
the respective vibration frequencies differ conside-
rably. Although the lowest Raman-active internal
modes at ∼ 420 ñm−1 are quite far from the highest
external modes at ∼ 330 ñm−1, the situation is not
so clear for antisymmetrical modes. For example,
the external antisymmetrical vibrations which in-
volve translational motions of light Li+ ions, are
expected to be higher in frequency. Nevertheless,
the internal–external modes approximation still re-
tains the merit of providing a good basis for under-
standing of k = 0 modes in the LiMPO4 compound.
Study of external modes
Following the scheme given above, all sharp
lines below 330 ñm−1 and above 100 ñm−1 are as-
signed to the external librational and translational
modes. An essential difference between the XX,
YY, and ZZ diagonal components of the scattering
tensor, belonging to Ag symmetry, reflects the con-
siderable anisotropy of the LiNiPO4 structure
(Fig. 1). It is evident from Table that the correct
number of bands with Ag , B2g , and B3g symmetry
is present, while the number of B1g peaks is defi-
cient. Only 3 peaks are clearly visible in the spectra
of appropriate polarization. Since the crystal under-
goes no structural phase transitions, the phonon
lines show only a weak frequency shift and broad-
ening with increasing temperature. The total shift
of all phonon lines in the temperature range from
4.2 to 300 K does not exceed 5 ñm−1 (Table).
An assignment of these lines to rotational and
translational modes is conditional, because they
have the same symmetry and, hence, may strongly
interact with one another. We can only say some-
thing about the specific contribution of rotation and
translation in each real mode in the crystal. It is
known [26] that the temperature dependence of the
phonon linewidth is determined mainly via two
mechanisms: (i) unharmonicity of the correspond-
ing vibrational mode and (ii) relaxation processes
which may be related to many-particle decay or
accidental reorientation, typical for atomic com-
plexes. The first mechanism provides a linear tem-
perature dependence of the spectral linewidth,
while the second one is represented as Arrhenius-
like contribution to the line broadening.
The reorientational motions in the LiMPO4 crys-
tals can be accomplished by the (PO4)3− tetrahedra
only during their hindered rotations. Hence the
B3g modes at 174.5 and 323 ñm−1 in the LiCoPO4
have been preferentially assigned to librations [23],
due to the essential contribution of the mechanism
(ii) to the temperature dependence of their widths.
It is interesting that only the B3g spectrum shows
an essential difference in the character of line
broadening (Fig. 2). In the frequency range of
external vibrations the B3g spectrum contains 2
translational and 2 librational modes. The first pair
may be described as translational motions of the
Ni2+ ions relative to the (PO4)3− ions parallel to the
crystal axis b. The second one is represented by
linear combinations of in-phase, around axis a, and
out-of-phase, around axis c, rotations of four
(PO4)3− tetrahedra in the unit cell. The experimen-
tal results for the temperature dependence of the
damping of the corresponding B3g modes at 193 and
329 ñm−1 in LiNiPO4 are found to be similar to
LiCoPO4 (Fig. 3). This supports our assignment of
these modes to ones of predominantly rotational
Fig. 2. Temperature behavior of the B3g external modes
in LiNiPO4 . The numbers indicate the temperature in
K: 300 (1), 250 (2), 200 (3), 150 (4), 90 (5), 25 (6), 5
(7). The spectral resolution is 2.0 ñm−1.
Raman scattering in LiNiPO4 single crystal
Fizika Nizkikh Temperatur, 2002, v. 28, No. 3 293
character. In the other polarizations the tempera-
ture behavior of linewidths does not show enough
difference to give priority to one of the two mecha-
nisms of broadening. Thus the classification of the
external modes remains, of course, qualitative.
Second order vibrational spectra
In addition to one-phonon peaks, there are weak
features around 750, 811, 887, and 919 ñm−1 in the
polarizations corresponding to the diagonal compo-
nents of the scattering tensor, which we assign to
two-phonon scattering (see Fig. 1). A more promi-
nent structure is evident in YY polarization. In the
off-diagonal Raman polarizations the second-order
spectrum is weak.
The bands at 887 and 919 ñm−1 can be assigned
to the two-phonon excitation and overtone of 442.5
and 462.5 ñm−1 bending modes, respectively. Of
course they can also be formed by combination of
other modes with approximately correct frequen-
cies, such as: (581.5 + 308), (592.5 + 325), and
(582 + 329) ñm−1.
The broad bands at 750 and 811 ñm−1 are very
likely the combination of O–P–O bond bending
vibrations ν2 and ν4 and some external modes, for
example: (462 + 287.5), (581.5 + 242.5), (422.5 + 325),
(470.5 + 329.5), (442.5 + 329) ñm−1. In contrast to
overtones the combined bands arise from two-parti-
cle processes, which involve pairs of phonons with
the only restriction that the sum wave vector must
be zero. If phonons in the pair have some frequency
dispersion, they produce broad bands in a second-
order Raman spectrum.
Low-frequency excitations in AF phase
In the low-frequency Raman spectra of LiNiPO4
a set of lines appears at T < TN . Representative
spectra in three experimental geometries, recorded
at temperatures above and below TN and covering
the frequency range 0–210 ñm−1, are shown in
Fig. 4. Well below TN the YY spectrum comprises
a peak at 60 ñm−1, accompanied by a broad asym-
metric band which shows a maximum intensity at
66.5 ñm−1, and the cutoff frequency is about
130 ñm−1. There is a peak at 58.5 ñm−1 in the ZY
spectrum and a peak at 56.5 ñm−1 with a shoulder
on the low-frequency side of the YX spectrum. No
visible features were observed in the XZ spectrum,
and so it is not reproduced here. The observed peaks
are attributed to magnon scattering, because they
vanish above TN = 19.1 K. However, a definite as-
signment of the lines to distinct excitations modes
is not possible at the present stage of investigation.
There are no data on the magnon dispersion curves
nor results of antiferromagnetic resonance experi-
ments from which the energy of a zone-center
(k = 0) magnon at T = 0 K may be estimated. For
the time being we can only note that the number of
Fig. 3. Temperature dependence of the width Γ at half
the height of the phonon lines in the low-frequency B3g
spectrum (see Fig. 2).
Fig. 4. Low-frequency spectra of LiNiPO4 at 25 (1) and
5 (2) K. The sharp lines at 122, 177.5, 193.5, and
199 ñm−1 are the vibrational modes. The spectral resolu-
tion is 2.0 ñm−1.
V. I. Fomin et al.
294 Fizika Nizkikh Temperatur, 2002, v. 28, No. 3
observed lines in the Raman spectra of LiNiPO4 at
T << TN exceeds the number that may be predicted
by the square two-dimensional model of the antifer-
romagnet used in [13].
Conclusion
Finally, we summarize the present results and
the remaining problems. The Raman spectrum of
LiNiPO4 displays reasonable agreement with group
theory predictions. The internal–external modes ap-
proximation is satisfactory for the lattice dynamics
of LiMPO4 compounds. The vibrations of the
(PO4)3− ions may be treated by the site group
method. The observed splitting of the ν2 , ν3 , and
ν4 modes of the «free» tetrahedral complex indicate
that in LiNiPO4 the host-lattice phosphate interac-
tion and the dynamic coupling between (PO4)3−
complexes is not weak.
Due to the anharmonicity of the vibrational
modes, overtones, and two-phonon excitations,
which are combinations of the external and the
bending vibrations of the (PO4)3− complexes, are
observed in the Raman spectra.
We have revealed no violations of the polariza-
tion selection rules below the Ne′el temperature of
LiNiPO4 which may be connected with the Pradhan
mechanism of light scattering in ME crystals [3].
Thus the effect is considered to be weak [1] and
hence it will be difficult to observe it in this
compound. The static values of the ME susceptibi-
lity in LiNiPO4 are considerably smaller than in
LiCoPO4 , as experiments [2] have shown. By as-
suming that the magnetoelectric coefficients are not
much changed at optical frequencies from their
static values, there is a chance to observe them in
LiCoPO4 . In addition, detailed investigations of
phonons by infrared absorption are necessary. To
the best of the authors’ knowledge, no IR work has
yet been done on these single crystals, and such
experiments would be very helpful in the discussion
of this new effect in Raman scattering.
The evidence of long-range antiferromagnetic
order is observed in the form of the appearance of
additional lines at 56.5, 58.5, 60 ñm−1 and of a
broad asymmetric band at 66.5 ñm−1 at tempera-
tures below TN . Their frequencies and behavior
with changing temperature allow them to be identi-
fied as the Raman scattering on spin-wave excita-
tions. A definite assignment of the lines to distinct
excitations is not possible at the present stage of
investigation. Detailed experimental data on the
temperature and magnetic field dependence of the
low-frequency Raman spectrum of LiNiPO4 remain
a topic for future study.
Acknowledgments
The authors thank Prof. N. F. Kharchenko for
helpful discussions and steady interest in the work.
1. M. Mercier, J. Gareyte, and E. F. Bertaut, C. R.
Acad. Sc. Paris B264, 979 (1967).
2. J.-P. Rivera, Ferroelectrics 161, 147 (1994).
3. T. Pradhan, Phys. Scripta 45, 86 (1992).
4. H. J. Scheel and D. Elwell, Crystal Growth from
High-Temperature Solutions, Academic Press, Lon-
don (1975).
5. W. Tolksdorf, in: Handbook of Crystal Growth.
Vol. 2: Bulk Crystal Growth, D. T. J. Hurle (ed.),
North-Holland Elsevier Science Publishers, Amster-
dam (1994), Part 2a, Chapt. 10, p. 563.
6. F. Zambonini and L. Malossi, Z. Kristallogr. 80,
442 (1931).
7. R. E. Newnham, R. P. Santoro, and M. J. Redman,
J. Phys. Chem. Solids 26, 445 (1965).
8. M. Mercier, These de doctorat d’Etat, Faculte des
Sciences, Universite de Grenoble, France (1969).
9. G. E. Rossman, R. D. Shannon, and R. K. Waring,
J. Solid State Chem. 39, 277 (1981).
10. A. Belletti, R. Borromei, R. Cammi, and E. Cavalli,
Phys. Status Solidi B163, 281 (1991).
11. R. P. Santoro, D. J. Segal, and R. E. Newnham, J.
Phys. Chem. Solids 27, 1192 (1966).
12. I. Abrahams and K. S. Easson, Acta Crystallogr.
C49, 925 (1993).
13. D. Vaknin, J. L. Zarestky, J. E. Ostenson, B. C.
Chakoumakos, A. Goni, P. J. Pagliuso, T. Rojo, and
G. E. Barberis, Phys. Rev. B60, 1100 (1999).
14. R. P. Santoro, R. E. Newnham, and S. Nomura, J.
Phys. Chem. Solids 27, 655 (1966).
15. D. Vaknin and J. L. Zarestky, Abstract [24.006], in:
The 2000 March Meeting of the American Physical
Society, Minneapolis, March 23, 2000.
16. D. Vaknin et al., to be published.
17. I. Kornev, M. Bichurin, J.-P. Rivera, S. Gentil, H.
Schmid, A. G. M. Jansen, and P. Wider, Phys. Rev.
B62, 12247 (2000).
18. I. Kornev et al., to be published.
19. E. Ascher, H. Rieder, H. Schmid, and H. Stossel, J.
Appl. Phys. 37, 1404 (1966).
20. M. Senthil Kumar, J.-P. Rivera, Z. G. Ye, S. D.
Gentil, and H. Schmid, Ferroelectrics 204, 57
(1997).
21. N. F. Kharchenko, Yu. N. Kharchenko, R. Szym-
chak, M. Baran, and H. Schmid, Fiz. Nizk. Temp.
27, 1208 (2001) [Low Temp. Phys. 27, 895 (2001)].
22. I. E. Chupis, Fiz. Nizk. Temp. 26, 574 (2000) [Low
Temp. Phys. 26, 422 (2000)].
23. V. I. Fomin, V. P. Gnezdilov, V. S. Kurnosov,
A. V. Peschanskii, V. V. Eremenko, S. Gentil, and
J.-P. Rivera, Fiz. Nizk. Temp. 25, 1107 (1999)
[Low. Temp. Phys. 25, 829 (1999)].
Raman scattering in LiNiPO4 single crystal
Fizika Nizkikh Temperatur, 2002, v. 28, No. 3 295
24. G. Herzberg, Infrared and Raman Spectra of Polya-
tomic Molecules, Van Nostrand, New York (1975).
25. A. Goni, L. Lezama, M. I. Arriortua, G. E. Bar-
beris, and T. Rojo, J. Mater. Chem. 10, 423 (2000).
26. M. M. Suschinsky, Raman Scattering Spectra of
Molecules and Crystals, Nauka, Moscow (1969) (in
Russian).
V. I. Fomin et al.
296 Fizika Nizkikh Temperatur, 2002, v. 28, No. 3
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