Light scattering on phonons in quasi-one-dimensional antiferromagnet CsFeCl₃·2H₂O induced by magnetic ordering
The appearance of new phonon lines in the Raman spectrum of the quasi-one-dimensional antiferromagnet CsFeCl₃·2H₂O as a consequence of magnetic ordering with a change of the unit cell volume was detected experimentally. An analysis of the possible mechanisms that might lead to the observed spectral...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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| Цитувати: | Light scattering on phonons in quasi-one-dimensional antiferromagnet CsFeCl₃·2H₂O induced by magnetic ordering / V.S. Kurnosov, Yu.G. Pashkevich, A.V. Peschanskii, V.I. Fomin, A.V. Yeremenko // Физика низких температур. — 2002. — Т. 28, № 7. — С. 724-732. — Бібліогр.: 14 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1302272025-02-09T14:42:49Z Light scattering on phonons in quasi-one-dimensional antiferromagnet CsFeCl₃·2H₂O induced by magnetic ordering Kurnosov, V.S. Pashkevich, Yu. G. Peschanskii, A.V. Fomin, V.I. Yeremenko, A.V. Магнетизм The appearance of new phonon lines in the Raman spectrum of the quasi-one-dimensional antiferromagnet CsFeCl₃·2H₂O as a consequence of magnetic ordering with a change of the unit cell volume was detected experimentally. An analysis of the possible mechanisms that might lead to the observed spectral features is done. A new mechanism of inducing Raman scattering on phonons from the boundary of the paramagnetic Brillouin zone is hypothesized. The authors are very grateful to Prof. V.V. Eremenko for his constant interest in this research and for helpful discussion. 2002 Article Light scattering on phonons in quasi-one-dimensional antiferromagnet CsFeCl₃·2H₂O induced by magnetic ordering / V.S. Kurnosov, Yu.G. Pashkevich, A.V. Peschanskii, V.I. Fomin, A.V. Yeremenko // Физика низких температур. — 2002. — Т. 28, № 7. — С. 724-732. — Бібліогр.: 14 назв. — англ. 0132-6414 PACS: 71.45.-d, 78.30.-j https://nasplib.isofts.kiev.ua/handle/123456789/130227 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Магнетизм Магнетизм |
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Магнетизм Магнетизм Kurnosov, V.S. Pashkevich, Yu. G. Peschanskii, A.V. Fomin, V.I. Yeremenko, A.V. Light scattering on phonons in quasi-one-dimensional antiferromagnet CsFeCl₃·2H₂O induced by magnetic ordering Физика низких температур |
| description |
The appearance of new phonon lines in the Raman spectrum of the quasi-one-dimensional antiferromagnet CsFeCl₃·2H₂O as a consequence of magnetic ordering with a change of the unit cell volume was detected experimentally. An analysis of the possible mechanisms that might lead to the observed spectral features is done. A new mechanism of inducing Raman scattering on phonons from the boundary of the paramagnetic Brillouin zone is hypothesized. |
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Article |
| author |
Kurnosov, V.S. Pashkevich, Yu. G. Peschanskii, A.V. Fomin, V.I. Yeremenko, A.V. |
| author_facet |
Kurnosov, V.S. Pashkevich, Yu. G. Peschanskii, A.V. Fomin, V.I. Yeremenko, A.V. |
| author_sort |
Kurnosov, V.S. |
| title |
Light scattering on phonons in quasi-one-dimensional antiferromagnet CsFeCl₃·2H₂O induced by magnetic ordering |
| title_short |
Light scattering on phonons in quasi-one-dimensional antiferromagnet CsFeCl₃·2H₂O induced by magnetic ordering |
| title_full |
Light scattering on phonons in quasi-one-dimensional antiferromagnet CsFeCl₃·2H₂O induced by magnetic ordering |
| title_fullStr |
Light scattering on phonons in quasi-one-dimensional antiferromagnet CsFeCl₃·2H₂O induced by magnetic ordering |
| title_full_unstemmed |
Light scattering on phonons in quasi-one-dimensional antiferromagnet CsFeCl₃·2H₂O induced by magnetic ordering |
| title_sort |
light scattering on phonons in quasi-one-dimensional antiferromagnet csfecl₃·2h₂o induced by magnetic ordering |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2002 |
| topic_facet |
Магнетизм |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/130227 |
| citation_txt |
Light scattering on phonons in quasi-one-dimensional antiferromagnet CsFeCl₃·2H₂O induced by magnetic ordering / V.S. Kurnosov, Yu.G. Pashkevich, A.V. Peschanskii, V.I. Fomin, A.V. Yeremenko // Физика низких температур. — 2002. — Т. 28, № 7. — С. 724-732. — Бібліогр.: 14 назв. — англ. |
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Физика низких температур |
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| fulltext |
Fizika Nizkikh Temperatur, 2002, v. 28, No. 7, p. 724–732
Light scattering on phonons in quasi-one-dimensional
antiferromagnet
CsFeCl3·2H2O induced by magnetic ordering
V. S. Kurnosov1, Yu. G. Pashkevich2, A. V. Peschanskii1, V. I. Fomin1,
and A. V. Yeremenko1
1B.Verkin Institute for Low Temperature Physics and Engineering National Academy of Sciences
of the Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine
2A.Galkin Donetsk Physical and Technical Institute of the National Academy of Sciences of the
Ukraine, 72 R.Luxemburg Str., Donetsk 83114, Ukraine
E-mail:Kurnosov@ilt.kharkov.ua
Received February 1, 2002
The appearance of new phonon lines in the Raman spectrum of the quasi-one-dimensional
antiferromagnet CsFeCl3·2H2O as a consequence of magnetic ordering with a change of the
unit cell volume was detected experimentally. An analysis of the possible mechanisms that
might lead to the observed spectral features is done. A new mechanism of inducing Raman
scattering on phonons from the boundary of the paramagnetic Brillouin zone is hypothesized.
PACS: 71.45.-d, 78.30.–j
Introduction
The compound CsFeCl3·2H2O under considera-
tion is a representative of a family of quasi-one-di-
mensional chained orthorhombic magnets with a
general chemical formula AMX3·2H2O, where
A = Cs, Rb, M = Mn, Fe, Co and X = Cl, Br. All
these crystals have D h2
8 (Pcca) symmetry in the
paramagnetic phase [1–3]. The magnetically ordered
phases of crystals of this series are described by dif-
ferent magnetic space groups. The magnetic cell is
commonly doubled along the crystallographic direc-
tion b compared to the paramagnetic one [1,4,5].
The CsFeCl3·2H2O and RbFeCl3·2H2O crystals are
attracting interest because they are an Ising type of
antiferromagnet, unlike the Heisenberg type ob-
served in CsMnCl3·2H2O [1]. Moreover, the
Dzyaloshinski–Moriya interaction produces a con-
siderable canting of the spins in the antiferro-
magnetic phase (AF) of CsFeCl3·2H2O and
RbFeCl3·2H2O, resulting in an uncompensated
magnetic moment within each of the paramagnetic
ion chains. The total momentum of the crystals re-
mains zero because of the alternating direction of the
moments in neighboring chains. The magnetic mo-
ments of the chains are oriented in parallel with the
crystallographic axis c of the crystals, and there-
fore, application of an external field along this di-
rection can induce a first-order phase transition
(PT) to a weak ferromagnetic (WF) phase [1]. A
specific feature of this PT is the fact that the
flip–flop of all the spins of the paramagnetic ions
in each separate chain occurs through the motion of
a magnetic soliton along the chain. Besides, this PT
occurs with the passage of the crystal through a
number of metastable intermediate phases which
are characterized by different ratios between the
numbers of chains with the ferromagnetic moment
oriented along and opposite to the applied field
[1,6,7].
Despite the great number of experimental stu-
dies of CsFeCl3·2H2O motivated by its interesting
magnetic properties, very few of them were carried
out using optical methods. Among the experiments
known to the authors, only the experiments on
excitonic absorption of light in the visible range
have been performed in high magnetic fields (up to
those of the metamagnetic transition) [8–10]. Since
not all the crystals of the above family undergo
© V. S. Kurnosov, Yu. G. Pashkevich, A. V. Peschanskii, V. I. Fomin, and A. V. Yeremenko, 2002
structure phase transitions, while their structures
are almost similar, Raman and IR spectroscopy
measurements of their vibrational spectra have not
aroused particular interest. Moreover, the vibra-
tional spectra of one of the earliest representatives
of the family, namely, CsMnCl3·2H2O, have been
previously studied comprehensively, including by
the authors of the present paper [11–13]. The ex-
periments reported here were motivated by the au-
thors’ interest in the specific features of the Raman
scattering in the magnetically ordered phase of
CsFeCl3·2H2O (referred to below as CFC). Fore-
most among these is light scattering by magnons,
quite possibly by solitons. Besides, the fact that an
Fe2+ ion has low-energy electron levels generated
due to the splitting of its ground term 5T2 in a
low-symmetry crystal field suggests the occurrence
of electronic transitions active in the Raman scat-
tering in the low-frequency spectrum.
The experiment performed demonstrated that
at the temperatures below the Néel point
(TN = 12.75 K [7]) the Raman spectrum of the
crystalwas much richer than that of CsMnCl3·2H2O
(CMC). But at temperatures much above the mag-
netic ordering points in CMC and CFC these
spectra are quite similar. The low-temperature
Raman spectrum of CFC displays additional
lines as against the spectrum of CMC, the lines
being differently sensitive to variations in tem-
perature of the crystal and external magnetic
field. Some of the lines have intensity comparable
to the intensity of the strongest lines of the original
phonon spectrum of CFC, which disappear on tran-
sition of the crystal to a paramagnetic (PM) (in
temperature) or a WF (in field) phase. The present
paper concerns mainly the nature of these lines and
the physical reasons for their occurrence in the
Raman spectrum.
Experimental procedure
The transparent pale brown single crystals of
CFC were grown from an aqueous solution of CsCl
and FeCl2·4H2O by slow evaporation at T = 37° C
in a nitrogen atmosphere to prevent Fe2+ oxidation
[1,9]. The single crystals keep well in oxygen-free
gaseous atmospheres. The adjustment of the crys-
tallographic directions was made according to a
well-defined habit, similar to that of CMC [4].
Samples in the form of rectangular parallelepipeds
with dimensions of 6�5�2 mm were cut from the
single crystals and polished up to optical quality of
the surface. The sample faces were oriented in
parallel with the principal crystallographic
planes of the crystal. The Cartesian coordinate
system used was related to the crystallographic di-
rections as x || a, y || b, z || c.
The measurements were carried out in two types
of optical cryostats: (i) one type permitted the ex-
periments to be done in a wide temperature range
of 4.2 to 300 K, and (ii) the other one had a
two-section Helmholtz superconducting solenoid
for performing the measurements in an exchange
gas of liquid helium at ~4.2 K at magnetic field
strengths up to 30 kOe. The Raman scattering was
excited by He–Ne and Ar+ laser radiation (wave-
length 6328 Å, power 40 mW, and wavelength
4880 Å, power 120 mW). The 90° scattered light
was analyzed with a computerized Raman spec-
trometer based on a Jobin Yvon U-1000 double
monochromator which was equipped with a cooled
photomultiplier and a photon counting system. The
signal–noise ratio was improved by the spectrum
acquisition method with a multiple scanning of the
frequency range studied.
The use of the two light sources was dictated by
several reasons. In experiments with Raman scat-
tering the illumination of a sample by a focused la-
ser beam produces a higher overheating in the laser
beam zone, relative to the sample surface, the
higher the absorption at the laser wavelength.
Since the crystal optical transmission at the He–Ne
laser wavelength of 6328 Å is higher, that source
appeared to be more attractive for the experiments.
Despite the fact that the argon laser produces a
much more intense overheating of the sample, it
was used for the measurements in magnetic field
because the solenoid drastically confines the angu-
lar aperture of the scattered light and hence, de-
creases significantly the intensity of the signal de-
tected. In that case the benefit that permitted us to
compensate the aperture loss consisted of two com-
ponents: first, a high radiation power, and, second,
the Rayleigh 1/�4 law for the Raman scattering in-
tensity.
Experimental results
The Raman scattering spectrum of the CFC crys-
tal studied at temperatures below TN revealed two
intense (182 and 501 cm–1) and four weak (125,
130, 140, and 607 cm–1) lines, with polarization
corresponding to the diagonal components of the
scattering tensor. The distinguishing feature of
these lines is the fact that their intensities de-
crease rather fast with increasing temperature in
the immediate vicinity of TN and that they al-
most disappear at higher temperatures (Fig. 1).
But the «additional» lines undergo no noticeable
variations in frequency and width. It should be
Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 725
Light scattering on phonons in quasi-one-dimensional antiferromagnet
noted that lines «additional» to the original
phonon spectrum can be also observed in the spec-
trum with off-diagonal components of the Raman
tensor at temperatures below TN . Those lines, how-
ever, are all of low intensity compared to the lines of
the original phonon spectrum and do not exhibit dis-
tinctly the above-mentioned temperature dependence*.
The temperature evolution of the most intense
lines, of frequencies 182 and 501 cm–1, is shown in
Figs. 2 and 3. The 488 and 177 cm–1 lines in the
spectra correspond to the phonons of the original
vibrational spectrum of the crystal and show no
anomalous behavior in the temperature range
given in the figures. The temperature dependence
of the 182 cm–1 line area correlates well with the
Néel temperature (Fig. 4). The temperature in
these experiments was determined by the ratio of
intensities of Stokes and anti-Stokes scattering at
the lowest-frequency phonon (~30 cm–1) in the
crystal. This ratio satisfies the relation:
I
I
s
a kT
� exp
��
,
726 Fizika Nizkikh Temperatur, 2002, v. 28, No. 7
V. S. Kurnosov, Yu. G. Pashkevich, A. V. Peschanskii, V. I. Fomin, and A. V. Yeremenko
Fig. 1. Parts of the Raman spectrum of CsFeCl3·2H2O
corresponding to scattering tensor components yy (a)
and zz (b) at temperatures, K: 5 (1), 25 (2), and 80
(3). The «additional» lines (see the text) are marked by
arrows. The spectral resolution is 2 cm–1.
Fig. 2. The temperature evolution of part of the Raman
spectrum with scattering tensor component zz for
CsFeCl3·2H2O.
* The nature of these exitations will be considered in a separate paper.
where Is and Ia are the Stokes and anti-Stokes
components of the scattering on a phonon of energy
��; T is the temperature, and k is the Boltzmann
constant.
The measurements with the magnetic field di-
rected along the crystal axis c show that the 182 cm–1
line intensity decreases rapidly as the magnetic field
strength approaches a critical value, at which one can
observe a PT to a new magnetic phase [1,6] (Fig. 5).
The relation between intensity of the line and cy-
clic variations in intensity of the applied magnetic
field is illustrated in Fig. 6.
Discussion of the experimental results
To account for the experimental results, some
specific features of the crystallographic and mag-
netic structures of CFC should be considered.
Magnetism of CFC
In the magnetically ordered phase of CFC an
octasublattice structure (Fig. 7,a), the symmetry of
which is described by magnetic space group
P2bcca’, is realized [1]. The available literature
data [1,6,7] suggest that the magnetic structure of
CFC is formed under the action of dominant
antiferromagnetic superexchange interaction along
the chains consisting of cis-octahedra of FeCl4O2
bound together by common apical ions Cl–. The
chains in the structure of the crystal are oriented
along the a direction. The orbital and spin degene-
racies of the ground state 5T2 of the Fe2+ ion are
completely lifted theby crystal-field effect of low
symmetry C2 and the spin–orbit interaction.
The three-dimensional ordering of the magnetic mo-
ments (antiferromagnetic in all directions to nearest
neighbors) is brought about by the interchain
superexchange, which is at least two orders of magni-
tude weaker than the intrachain one [1]. As a result,
the magnetic cell appears to be doubled along the
crystallographic direction b as compared to the
paramagnetic one. Also noteworthy is the high
value of the Dzyaloshinski–Moriya interaction,
which causes the spins to be canted from the a di-
rection by an angle of 15° in the ac plane [1]. This
Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 727
Light scattering on phonons in quasi-one-dimensional antiferromagnet
Fig. 3. The temperature evolution of part of the Raman
spectrum with scattering tensor component yy for
CsFeCl3·2H2O.
Fig. 4. The temperature dependence of relative area of
the 182 cm–1 line in CsFeCl3·2H2O. To make the figure
more pictorial, the dashed line is plotted by eye.
canting results in a ferromagnetic moment of each
individual chain in the crystal which is directed
collinearly with the c axis. The moments of all
chains in the crystal compensate each other due to
antiferromagnetic ordering of nearest spins of
neighboring chains, so that the total magnetic mo-
ment of the crystal is zero.
On application of an external magnetic field of
intensity ~9.5 kOe along the c axis, the crystal un-
dergoes a PT at temperatures below TN [1,6,7]. As
a result, the ferromagnetic moments of all chains
become oriented along the field direction
(Fig. 7,b). It should be emphasized that in the
new phase the neighboring chains along the b di-
rection are found to be translationally equivalent
once again, and the magnetic cell volume reverts to
the volume of the paramagnetic cell. The WF
phase symmetry is described by space group
728 Fizika Nizkikh Temperatur, 2002, v. 28, No. 7
V. S. Kurnosov, Yu. G. Pashkevich, A. V. Peschanskii, V. I. Fomin, and A. V. Yeremenko
Fig. 5. The part of the Raman spectrum with scattering
tensor component yy as a function of the external
magnetic field HZ in CsFeCl3·2H2O. The sample
temperature is ~11 K. The spectral resolution is ~ 3 cm–1.
Fig. 6. The plot of the area ratio of the 182 and 177 cm–1
lines shown in Fig. 5 versus magnetic field. The branches
with increasing and decreasing field are denoted by squares
and triangles, respectively.
Fig. 7. The magnetic structure of CsFeCl3·2H2O in
antiferromagnetic (a) and weak ferromagnetic (b)
phases.
Pc′c′a. During «magnetization» the crystal actu-
ally undergoes a number of transitions through the
multitude of intermediate phases with a different
specific number of chains with «inverted» (com-
pared to the normal AF phase) ferromagnetic mo-
ments [7]. The moderate intensity of the magnetic
field at which this PT occurs is accounted for by
the small values of the interchain exchange interac-
tion integrals along the c and b directions. As for
the magnetic structure inside the chain, it remains
almost unchanged in such weak fields, because it is
stabilized by the high single-ion anisotropy and
intrachain exchange.
In terms of the Heisenberg approximation, the
magnetic parameters can be described by the following
values of exchange integral Ja/k = 6.0 ± 0.5 K and
single-ion anisotropy constant D/k = –40 ± 20 K
with total spin S = 2 [6]. With these relations of the
model parameters, the magnet at low temperatures
may be approximated by the Ising model with effective
spin Seff = 1/2 and effective exchange integral
Jeff /k = 42 ± 5 K [6].
Analysis of the Raman spectrum
The specific features of the Raman spectrum of
CFC, manifesting themselves as additional (to the
original phonon spectrum) lines in the magnetic
phase, may be brought about by different mecha-
nisms.
First, it should be noted that according to all
the available published data, CFC, along with
other representatives of this family of crystals, un-
dergoes no structural PT. The fact is evidenced by
the authors’ observations. No peculiarities in the
temperature behavior of the Raman spectrum which
are accounted for by a structural phase transition
followed by a multiplication of the unit cell volume
were found. The soft mode usual at such PTs is not
observed in the low-temperature phase. In the fol-
lowing, the authors will proceed from the fact that
there are no phase transitions in CFC.
As mentioned in the Introduction, aside from the
phonon excitations, the low-frequency Raman spec-
trum of CFC can contain lines caused by a scatter-
ing owing to the transition between crystal-field-
split levels of the ground state term of the Fe2+ ion,
and scattering by magnons. Turning back to the
main point of the present paper, namely, to the
treatment of the anomalous behavior of the addi-
tional scattering lines of frequencies 125, 130, 140,
182, and 501 cm−1 (Fig. 1), we should consider
some possible mechanisms. To do this, we should
first estimate the energy range within which the
magnon scattering may be observed.
In terms of the Heisenberg approach for a
one-dimensional chain of spins, the magnon energy
dispersion within the one-dimensional Brillouin
zone (BZ) can be given as follows:
� �
� �
E JS
D
JS
� ��
�
��
�
�� �
�
�
�
�
�
�
�
�
2 1
2
2
2
1
2
cos ,
where � is the spatial phase of a spin wave in the a
direction. Using this equation, one can obtain the
following estimates of magnon energies at the
center and at the boundary of the one-dimensional
BZ: E(0) = 42 cm
–1, E(�/2) = 46 cm–1. In terms
of the Ising model, the magnon energy at the BZ
boundary, E(�/2) = 4JeffSeff, is estimated as being
equal to 58 cm–1. Besides the energy of the optical
magnon, the transition from the lowest component
of the electron pseudo-doublet, with a total
momentum projection of �1, to the first excited
singlet level, with a projection of 0, is estimated to
be 80 cm–1 [10]. All these simple estimates are
rather rough, but they make it possible to place an
upper limit on the energy range in which the
magnon spectrum may manifest itself: to 100 cm–1.
Therefore, it is hardly probable that additional
lines disappearing from the scattering spectrum at
temperatures above TN are accounted for by the
magnon scattering. The two-magnon scattering,
which may fall just within the frequency range
studied, rarely, if ever, is of high intensity in the
diagonal components of the scattering tensor.
Besides, it is primary conditioned on the strong
exchange along the chains which is essentially un
affected by the magnetic field applied in our
experiments (see above).
The electron transitions also evident in the Raman
spectrum of CFC exhibit a somewhat different (com-
pared to the lines considered) evolution with increas-
ing temperature. The electron lines in the Raman
spectrum also show the decrease in area with increas-
ing temperature, but this occurs at much higher tem-
peratures (above 70 K in CFC) and is followed by a
drastic broadening of the lines. The latter fact does not
allow the suggestion that the lines are unobservable
because the integral intensity vanishes. Thus the addi-
tional lines under consideration cannot be ascribed to
scattering by electron transitions either.
Another feature of the magnetic structure of
CFC mentioned above is the double volume of the
unit cell compared to the paramagnetic one. This
doubling, determined by neutron scattering [1], is
solely of a magnetic nature without any structural
distortion. A double-unit-cell crystal is thought to
exhibit a larger number of phonon modes in the
Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 729
Light scattering on phonons in quasi-one-dimensional antiferromagnet
Raman spectrum, the additional lines appearing at
the magnetic BZ center from the paramagnetic BZ
boundary. Despite this formal concept, there are
very few experimental works on Raman scattering
by phonons generated from the paramagnetic BZ
boundary under magnetic ordering with a unit cell
multiplication.
In the case of CFC two facts have permitted
the authors to suggest that the additional lines
under consideration are indeed related to scatter-
ing by phonons generated from the paramagnetic
BZ boundary. These are, first, the temperature
dependence, showing a fast decrease in intensity
of the lines in the vicinity of TN and their absence
at higher temperatures, and, second, the field de-
pendence of the intensity of these lines. The latter
for the most intense line of frequency 177 cm–1
demonstrates a behavior similar to the tempera-
ture dependence. When the unit cell volume re-
turns to the paramagnetic volume, either as a re-
sult of the temperature increasing or as a result of
a PT in an external magnetic field, the additional
lines disappear from the Raman spectrum.
A formal increase in the number of Raman-ac-
tive phonons resulting from the doubling of the
unit cell volume in the magnetically ordered phase
cannot explain the physical mechanisms which are
responsible for the additional phonon lines in the
Raman spectrum. There must be a reason causing
nonequivalence of the polarizabilities associated
with vibrations of the same ions from neighboring
cells along the doubling direction. Otherwise, be-
cause the vibrations of identical ions in the modes
from the BZ boundary are opposite in phase, the in-
tensity of Raman scattering by them should be zero
due to the complete interference damping. As a mat-
ter of fact, this is an example of the wave-vector k
selection rule for light scattering or absorption (the
k = 0 rule).
730 Fizika Nizkikh Temperatur, 2002, v. 28, No. 7
V. S. Kurnosov, Yu. G. Pashkevich, A. V. Peschanskii, V. I. Fomin, and A. V. Yeremenko
Fig. 8. The trajectory ellipticity of identical ions from
neighboring-in-direction b cells in local magnetic
fields H1 and H2. U1 and U2 are antiphase displacement
components for the mode from the paramagnetic BZ
boundary, V1 and V2 are in-phase displacement components
induced by the Lorentz force.
Table
Irreducible spin combinations (ISC) in CFC at points k19 = (0,0,0) and k21 = (0,�/b,0) of the paramagnetic BZ and
at the center of antiferromagnetic BZ reduced along b (the symbols are taken from [14] and spin numbers from Fig. 7).
ISC PM phase AF phase
F(0) S
1
(0)+S
2
(0)+S
3
(0)+S
4
(0) S
1
+S
2
+S
3
+S
4
+S
5
+S
6
+S
7
+S
8
L
1
(0) S
1
(0)+S
2
(0)–S
3
(0)–S
4
(0) S
1
+S
2
–S
3
–S
4
+S
5
+S
6
–S
7
–S
8
L
2
(0) S
1
(0)–S
2
(0)+S
3
(0)–S
4
(0) S
1
–S
2
+S
3
–S
4
+S
5
–S
6
+S
7
–S
8
L
3
(0) S
1
(0)–S
2
(0)–S
3
(0)+S
4
(0) S
1
–S
2
–S
3
+S
4
+S
5
–S
6
–S
7
+S
8
F(k
21
) S
1
(k
21
)+S
2
(k
21
)+S
3
(k
21
)+S
4
(k
21
) S
1
+S
2
+S
3
+S
4
–S
5
–S
6
–S
7
–S
8
L
1
(k
21
) S
1
(k
21
)+S
2
(k
21
)–S
3
(k
21
)–S
4
(k
21
) S
1
+S
2
–S
3
–S
4
–S
5
–S
6
+S
7
+S
8
L
2
(k
21
) S
1
(k
21
)–S
2
(k
21
)+S
3
(k
21
)–S
4
(k
21
) S
1
–S
2
+S
3
–S
4
–S
5
+S
6
–S
7
+S
8
L
3
(k
21
) S
1
(k
21
)–S
2
(k
21
)–S
3
(k
21
)+S
4
(k
21
) S
1
–S
2
–S
3
+S
4
–S
5
+S
6
+S
7
–S
8
Symmetry analysis of polarizability
The phase transition to a magnetically ordered
phase P2bcca′ (see Table) occurs at the point k21 of
the paramagnetic BZ and is described by the order
parameter L3x(k21) or L1z(k21) which transforms
according to the irreducible representation �3(k21).
For the required polarizability ��
ij to be obtained,
the dielectric permittivity tensor �ij should be ex-
panded in normal coordinates of the vibrational
modes U
�
at the paramagnetic BZ point k21 and in
the magnetic vector η� corresponding to the order
parameter. The latter describes the static perturba-
tion of the medium due to the PT. The so-called
«Faraday» (linear in magnetic vector) term in the
expansion is of the following form at k19 = 0:
� � � ��
�
�
�
� �ij
ij
U
U�
�
� �
�
2
21 21η k k ,
where � � � �η� �k k k21 3 21 21 L x( ) / .
The nonzero polarizability tensors correspond
only to the vibrational modes transforming accord-
ing to the irreducible representations �6(k21) and
�7(k21) and are of the forms:
� �� �� �6 21 7 21k k� �
�
�
�
�
�
�
�
�
�
�
�
�
. .
. .
. . .
,
. .
. . .
. .
( )
d
d
f
f
�
�
�
�
�
�
.
As is evident from the above analysis, under mag-
netic ordering the paramagnetic BZ boundary may in-
duce only those lines which in the low-temperature
phase are related to phonons of symmetries B1g and
B2g, while the observed additional lines show sym-
metry Ag and occur in the diagonal components of
the scattering tensor. Hence, the first order of per-
turbation theory cannot explain the anomalies un-
der consideration.
Another mechanism that permits one to derive
the required polarization selection rules for
phonon modes generated from the paramagnetic
BZ boundary under magnetic ordering can be il-
lustrated as follows.
Since there exists a nonzero local magnetic field
on ligands surrounding the paramagnetic ion, then
during motion in the vibrational mode there may
occur a Lorentz force perpendicular to the direction
of the ion displacement. Hence, the linear trajec-
tory of the ion motion transforms to an elliptical
one. In this case the directions of traversing the el-
lipse are opposite because the identical ions from
neighboring unit cells along the direction of dou-
bling in the magnetic cell are connected by the
antitranslation operation. Thus, for the phonon
mode originating from the paramagnetic BZ
boundary, where the displacements, of ions with
no local magnetic field are opposite in phase, the
perpendicular components of the displacements,
generated by the Lorentz force, appear to be
in-phase. This mechanism is illustrated schemati-
cally in Fig. 8.
As the Lorentz force is of relativistic origin it is
hard to suggest that it may produce a sufficient de-
gree of ellipticity to induce intense lines of light
scattering comparable with those of the original
spectrum. This hypothesis, however, does have
meaning if it is remembered that the mixing of dif-
ferent-symmetry vibrational modes corresponding
to the paramagnetic BZ boundary and center occurs
just in this way. If the modes are close in fre-
quency, this channel may enhance the intensity of
the additional lines at the expense of the original
ones. At least, this mechanism appears to be appro-
priate for description of the 177 and 182 cm–1
modes. They have close frequencies, and the 177
cm–1 line of the original phonon spectrum is
sufficiently wide, even at low temperatures, to
overlap 182 cm–1 line resonantly (Fig. 3). The reso-
nance effects are also supported by the asymmetric
complex shape of the 177 cm–1 line at low tempera-
tures, which becomes symmetric in the PM and WF
phase in external magnetic fields (Figs. 3 and 5).
At the moment the authors propose the above
mechanism as a possibility. Verification of its ade-
quacy requires a further, more comprehensive study
into the anomalies of the scattering spectrum of
CFC and a development of microscopic theoretical
models which would enable the above spectral fea-
tures arising upon magnetic ordering to be esti-
mated numerically.
Conclusions
The experiments with the quasi-one-dimensional
chained antiferromagnet CsFeCl3·2H2O revealed
additional, quite intense lines in the Raman spec-
trum at the phase transition to a magnetically or-
dered phase, followed by changes in the volume of
the crystal magnetic cell.
It is found that in an external magnetic field the
most intense additional line of 182 cm–1 disappears
at the phase transition to a weak ferromagnetic
phase.
Analysis of the symmetry of the paramagnetic,
antiferromagnetic, and weak ferromagnetic struc-
tures of the crystal suggests that the new lines re-
sult from the magnetic-ordering-induced light scat-
tering by phonons originating from the
paramagnetic BZ boundary.
Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 731
Light scattering on phonons in quasi-one-dimensional antiferromagnet
Analysis of the magnetic contribution to the
phonon polarizability of the crystal made in the
first order of perturbation theory showed no corre-
lation with the experimental polarization selection
rules for the additional lines.
A new mechanism of inducing light scattering by
vibrational modes corresponding to the phonons
from the paramagnetic BZ boundary is hipothesized.
It is based on the mixing of different-symmetry
modes from the BZ center and boundary due to the
ellipticity of the ion trajectory of vibrations in their
local magnetic field.
The authors are very grateful to Prof. V.V.
Eremenko for his constant interest in this re-
search and for helpful discussion.
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