arXiv:cond-mat/0005096v1 [cond-mat.str-el] 4 May 2000
Optical Properties of the Spin-Ladder Compound Sr14Cu24O41
Z. V. Popovi´ ca, M. J. Konstantinovi´ cb, V. A. Ivanova, O. P.
Khuonga, R. Gaji´ cc, A. Vietkindand V. V. Moshchalkova
aLaboratorium voor Vaste-Stoffysica en Magnetisme,
K. U. Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium
bMax-Planck-Institut f¨ ur Festk¨ orperforschung,
Heisenbergstrasse 1,D-70569 Stuttgart, Germany
cInstitute of Physics, P.O.Box 68, 11080 Belgrade, Yugoslavia and
dPhysics Department, Moscow State University, 119899 Moscow, Russia
We report the measurements of the pseudodielectric function, far-infrared reflectivity and Raman
scattering spectra in Sr14Cu24O41single crystal. We study the lattice and the spin dynamics of
the Cu2O3 spin ladders and CuO2chains of this compound. The ellipsometric and the optical
reflectivity measurements yield the gap values of 1.4 eV, 1.86 eV, 2.34 eV (2.5 eV) for the ladders
(chains) along the c-axis and 2.4 eV along the a-axis. The electronic structure of the Cu2O3ladders
is analyzed using tight-binding approach for the correlated electron systems. The correlation gap
value of 1.4 eV is calculated with the transfer energy (hopping) parameters t = t0=0.26 eV,
along and perpendicular to legs, txy=0.026 eV (interladder hopping) and U=2.1 eV, as a Coulomb
repulsion. The optical parameters of the infrared active phonons and plasmons are obtained by
oscillator fitting procedure of the reflectivity spectra. Raman scattering spectra are measured at
different temperatures using different laser line energies. The two-magnon peak is observed at
about 2880 cm−1. At temperatures below 150 K the new infrared and Raman modes appear due
to the charge ordering.
PACS numbers: 78.30.Hv; 78.20.Ci; 71.27.+a; 74.72.Jt
The Sr14Cu24O41compound is one of the three stable phases in the Sr-Cu-O system which
can be synthesized under ambient pressure. The other two stable phases are Sr2CuO3,
which has simple chains of Cu ions, and SrCuO2 with zigzag chains of Cu ions. This
oxide has unique crystal structure based on two sublattices; one of them consists of Cu2O3
two-leg ladders and the second one is formed by CuO2chains. These two sublattices are
incompatible along one crystallographic direction, thus resulting in an 1D incommensurate
structure . According to the structural analysis , the ladder sublattice is face-centered-
orthorhombic (space group Fmmm) with a lattice parameters a=1.1459 nm, b=1.3368 nm
and cLadder=0.3931 nm. There are two ladder layers with two ladders per unit cell, Fig.
1. The chain sublattice is A-centered orthorhombic (space group Amma), with nearly the
same a and b axes but different c axis, cChain=0.2749 nm. However, Sr14Cu24O41can be
considered as nearly commensurate structure at 7xcLadder=2.7372 nm and 10xcChain=2.7534
nm. The schematic illustration of Sr14Cu24O41crystal structure is given in Fig. 1.
The physical properties of Sr14Cu24O41have attracted a lot of attention recently [2, 3,
4, 5, 6, 7, 8, 9, 10, 11, 12], in connection with the rich physics associated with the S=1/2
Heisenberg antiferromagnetic quasi one-dimensional (1D) structures and the discovery of
superconductivity in Sr0.4Ca13.6Cu24O41under high pressure . The progress in this field
has been summarized in Ref. . Various magnetic [3, 4, 5], NMR [6, 7] and neutron
scattering [8, 9] measurements, showed that Sr14Cu24O41has two kinds of magnetic gaps.
The first one, ∆L= 32.5 meV, is attributed to the singlet-triplet excitation in the Cu2O3
spin-ladders, with the exchange energies along the legs (J=130 meV) and the rungs (J0=72
meV) . The second one, ∆C= 11.5 meV, is argued to arise from the spin dimer formation
in the CuO2chains , with an antiferromagnetic intradimer coupling J1=11.2 meV. Similar
ratio of the superexchange interaction energies, J0/J ∼ 0.5, as well as the magnitude of
J0=(950±300) K, is found in the17O and63Cu NMR measurements .
The Raman spectra of Sr14Cu24O41were measured previously [14, 15]. From the com-
parison between Raman spectra of the various layered tetragonal cuprates, Abrashev et al..
 concluded that the main contribution to the spectra comes from the Raman forbidden-
infrared active LO phonons and the two-magnon scattering. Furthermore, Sugai et al. 
argued that, besides strong two-magnon features, some low-frequency modes in the Ra-
man spectra are also magnetic in origin, since they have similar energies to those found
in the neutron scattering experiments . Still, for the proper identification of the mag-
netic modes, the temperature dependent Raman spectra, as well as the spectra in magnetic
field, are required. Also, detailed analysis of the lattice dynamics and comparison between
Raman and infrared (IR) spectra are indispensable due to the incommensurability of the
structure. Therefore, we present here the Raman and IR spectra at various temperatures
between 5 and 300 K in order to make more complete assignment of the vibrational modes in
Sr14Cu24O41. The Raman spectra are also measured under resonant conditions, with a laser
light energy close to gap values. The correlated electron tight-binding model of electronic
structure is used to estimate the hopping parameters, in fact adjusted to the measured gaps
and exchange energies.
The present work was performed on (010) oriented single crystal plates with dimensions
typically about 5 x 1 x 6 mm3in the a, b and c axes, respectively. The infrared measurements
were carried out with a BOMEM DA-8 FIR spectrometer. A DTGS pyroelectric detector
was used to cover the wave number region from 100 to 700 cm−1; a liquid nitrogen cooled
HgCdTe detector was used from 500 to 1500 cm−1. The spectra were collected with the
2 cm−1resolution. The low temperature reflectivity spectra in the range from 30 to 5000
cm−1were measured using Bruker IFS 133v FIR-spectrometer with Oxford-Cryostat. The
Raman spectra were recorded in the backscattering configuration using micro- and macro-
Raman systems with Dilor triple monochromator including liquid nitrogen cooled CCD-
detector. An Ar- and Kr -ion lasers were used as an excitation source. We measured the
pseudodielectric function with a help of a rotating-analyzer ellipsometer. We used a Xe-
lamp as a light source, a double monochromator with 1200 lines/mm gratings and an S20
photomultiplier tube as a detector. The polarizer and analyzer were Rochon prisms. The
measurements were performed in the 1.6-5.6 eV energy range. Optical reflectivity spectra
were measured at room temperature in the 200-2000 nm spectral range using Perkin-Elmer
Lambda 19 spectrophotometer.
The electronic structure of Sr14Cu24O41is calculated using the tight-binding method for
correlated electrons . Recent exact diagonalization and a variational Monte Carlo sim-
ulations revealed that electronic structure of Sr14Cu24O41is well described by single ladder
energy spectrum . It means that electron energy dispersions are governed mainly by
electrons in the ladder. According to the ARPES measurements , the chains contribute
to the electronic structure of Sr14Cu24O41with a dispersionless band. Without entering any
lengthy discussions about the substance nonstoichiometry and the carrier transport between
chains and ladders, we assume further on that the ladder unit Cu1+n
has total charge
−2. In other words, there is one hole, n = 1, per copper ion in the ladder for negligibly
small hybridization of its dx2−y2−orbitals with the py−orbital of intermediate oxygens. The
angle between Cu atoms of neighboring ladders is near right angle (88.7◦), Fig. 1. In our
consideration of the electronic structure we assumed that the directions between the nearest
neighbor Cu ions form an ideal right angle.
The Hamiltonian for the correlated copper holes in the ladder with two rungs, a −b and
c − d, per a unit cell can be written as
H = −2t
σ(p)aσ(p) + b+
σ(p)bσ(p) + c+
σ(p)cσ(p) + d+
σ(p)bσ(p) + c+
σ(p)dσ(p) + H.c.
1 + e−ipy??
σ(p)dσ(p) + H.c.
σ(p)cσ(p) + H.c.
where a,b,c,d represent chains, (see Fig.1.(a)), t (t0) are the values of the carrier hopping
along legs (rungs), txyis a hopping amplitude between ladders, U is the Anderson-Hubbard
repulsion, and µ is the chemical potential and other notations as usual. The x and y axis of
the reference system are taken along the a and the c crystallographic directions, respectively.
Applying the X−operator machinery , the correlation split energy bands are governed by
zeros of the inverse Green’s function in the first perturbation order with respect to tunneling
p (ω) =
C C 0 0
+ r r−t0
+ r −t0
+ r r
0 0 D D
0 0 D D
C C 0 0
with r = −2tcospy,C = −txy
1 + e−ipy?
,D = −txy
Here the correlation factors f0+, f−2are determined by fermion occupation n per site.
Namely, for the considered paramagnetic phase they are f0+= 1 − n/2, f−2= n/2 and all
equal to 1/2 (n = 1). After an analytical continuation, iωn→ ξ + iδ, in Eq.
one can find the bonding /antibonding correlation energy dispersions as follows:
??? = 0
p = −2tcospy±
For derivation of these energy dispersions from the eight-by-eight fold secular equation
(see Eq.(2)) it was useful to apply the theorem about the decomposition of determinant
with respect to diagonal elements (see Appendix A in Ref. ). The subbands ξ−
are completely occupied by carriers with concentration n = 1 per copper site of ladder for
the chosen chemical potential µ = U/2. The nearest unoccupied energy band is ξ+
correlation gap in electronic structure can be estimated as
∆corr = minξ+
B(p) − maxξ−
(t0+ 2t − 2txy)2+ U2+
(t0+ 2t)2+ U2
− (t0+ 2t + txy).
For the dimensionless energies, ω+,−
p/2t, τ0= t0/2t,τ = txy/2t, the non-correlated
electron density of states per spin, ρ(ε)=
p)], for the unit cell volume,
is defined analytically as follows
0(−1 − 2τ + ατ0≤ ε ≤ −1 + 2τ − τ0) =
−1 + 2τ + ατ0≤ ε ≤1
2+ τ + ατ0
0(−1 + 2τ + ατ0≤ ε ≤ 1 + ατ0) =
Eqs.(6) representtheanalytical expressions forthe electrondensity of states
viaelliptic integralsF andK ofthe 1-stkindin theLegendrenormal
2τ (τ + kα) + 1 − (ε + ατ0)2?
τ2+ 2(1 − ε − ατ0) and α = ±.
The electron-electron repulsion, U, splits the density of the non-correlated electronic
2τ (τ + kα) + 1 − (ε + ατ0)2?
/[(1 + ε + ατ0)(τ + kα)kα],
states ρ0. The correlated electron density of states is
and S =
(1 + 2τ + τ0)2+
(1 + τ0)2+
are expressed via dimensionless correlated energies ξ±≡ ξ±(p)/2t. With the help of Eq.(7)
and Eqs.(6) one can calculate the correlated electron density of states for corresponding
energy ranges. Its explicit form naturally includes the first kind elliptic integrals. The
results of the calculations are plotted in Fig. 2.
The overlap of the energy ranges for the electronic dispersions, Eq.(3), leads to the
special features of the correlated electronic structure at L5 = 1/2(−1 − 2τ + τ0) − S −
(1 + 2τ + τ0)2+ (U/t)2and L7= 1/2(1/2 + τ + τ0)−S−1/2
(1/2 + τ + τ0)2+ (U/t)2
in the lower correlated band.Logarithmic divergencies inside the band at L2
(−1 + 2τ − τ0)2+ (U/t)2, L4
1/2(−1 + 2τ − τ0) − S − 1/2
1/2 (1 − τ0)2+ (U/t)2, L6= 1/2(−1 + 2τ + τ0) − S − 1/2
at the correlated band edge L8 = 1/2(1 + τ0) − S − 1/2
manifestations of the 2D electronic structure of Sr14Cu24O41 compound. We would like
=1/2(1 − τ0) − S −
(−1 + 2τ + τ0)2+ (U/t)2and
(1 + τ0)2+ (U/t)2are clear
to emphasize that in the one-dimensional case (txy→ 0) the electron density of states
is taking features of a single spin-ladder without any logarithmic peaks, then the di-
vergencies become square-root like and they are located at the band edges, ε = ±1:
ρ(ε) = 8K (0)/π2√1 − ε2= 4/π√1 − ε2.
The dielectric function ǫ2of Sr14Cu24O41is shown in Fig.3 in the spectral region from
1.6 eV to 5.5 eV. These spectra were computed from the measured Fourier coefficients using
the equations for an isotropic case. Consequently, ǫ2represents a complicated average of the
projections of the dielectric tensor on the sample surface. We presented the spectra of the
(010) surface taken with the a-axis, Fig. 3(a) and c axis, Fig. 3(b), in the plane of incidence
(PI). According to the prescription given by Aspnes , we attribute these components to
the components of the dielectric tensor ǫaa
2. The bands with the energies of 2.4, 4.1,
and 4.7 eV for the a-axis and at about 1.86, 2.34, 2.5, and 4.3 eV are found for the c axis
in the plane of incidence, respectively.
Inset (a) in Fig. 3 shows reflectivity spectra of Sr14Cu24O41. These spectra are calculated
from measured dielectric functions ǫ1and ǫ2. Inset (b) in Fig. 3 represents the unpolarized
optical reflectivity of Sr14Cu24O41 measured at room temperature. In addition to peaks,
previously observed in ellipsometric measurements, a new peak at about 1.4 eV appears.
The room temperature polarized far-infrared reflectivity spectra of Sr14Cu24O41are given
in Fig. 4. The open circles are the experimental data and the solid lines represent the
spectra computed using a four-parameter model for the dielectric constant:
ǫ(ω) = ǫ∞(
LO,j− ω2+ ıγLO,jω
TO,j− ω2+ ıγTO,jω−
ω(ω − ıτ−1)), (8)
where ωLO,j and ωTO,j are longitudinal and transverse frequencies of the jthoscillator,
γLO,j and γTO,j are their corresponding dampings, ωp is the plasma frequency, τ is the
free-carrier relaxation time and ǫ∞is the high-frequency dielectric constant.
The best fit parameters are given in Table I. The agreement between observed and cal-
culated reflectivity spectra is rather good. For the E||a polarization, eight oscillators with
TO frequencies at about 164, 194, 219, 249, 283.5, 310.4, 554 and 623 cm−1are clearly seen.
In the E||c polarization, Fig. 4(b), nine oscillators at 135, 148, 253, 293, 345, 486, 540,
596 and 620 cm−1are observed. Besides phonons, our model includes the Drude expression
for light scattering on free carriers. We obtained the plasma frequency at about 4000 cm−1
(1000 cm−1) for the E||c (E||a) polarizations.
The room temperature Raman spectra of Sr14Cu24O41, for (aa) and (cc) polarized con-
figurations are presented in Figs. 5(a) and 5(b). These spectra consist of only Agsymmetry
modes. Four modes at 246, 302, 548, and 582 cm−1are clearly seen. The low temperature
(cc) Raman spectra are given in Figs. 5(c)-(g). By lowering temperature below 200 K, the
modes narrow and in addition the new modes appear. We will discuss them later on. The
Raman spectra of Sr14Cu24O41, excited by different lines of Ar and Kr lasers at 8 K, are
shown in Fig. 6 for the (cc) and (aa) polarized configurations in the spectral ranges: (a) from
700 to 1400 cm−1, (b) from 1675 to 1975 cm−1and (c) from 2600 to 3300 cm−1. Anticipating
our conclusions, we divide the Raman spectra in three different energy regions: one phonon
(0-700 cm−1), two-phonon (700-1400 cm−1) and two-magnon region (above 1500 cm−1). The
mode at about 2900 cm−1and a broad structure at about 1900 cm−1are magnetic in origin,
according to their intensity and frequency dependence as a function of the temperature, see
The average unit cell of Sr14Cu24O41consists of four formula units with 316 atoms in all.
Since there is a large number of atoms in the unit cell, we can expect a very large number
of optically active modes. Consequently, the lattice dynamical calculation is practically
impossible. All atoms have 4(e) position symmetry of Pcc2 (C3
2v) space group . Factor-
group-analysis (FGA) yields the following distribution of vibrational modes:
ΓSr14Cu24O41= 237A1(E||c,aa,bb,cc) + 237A2(ab) + 237B1(E||a,ac) + 237B2(E||b,bc) (9)
According to this representation one can expect 948 modes which are both Raman and
infrared active. Experimentally, the number of observed modes is less then ten for each
polarization. Because of that, we consider separately the contribution of each sublattice
unit. As mentioned earlier, the space group of ladder sublattice is Fmmn (D23
2h). The site
symmetries of Sr, Cu, O1 and O2atoms are (8h), (8g), (8g) and (4b), respectively. The
FGA for the ladder structure (Sr2Cu2O3) yields :
ΓLadder= 3Ag+ 3B1g+ 2B2g+ B3g+ 4B1u+ 4B2u+ 4B3u
The space group of a chain sublattice is Amma (D17
2h). The site symmetries of Cu and O
atoms are (4c) and (8f). The FGA gives for the chain structure:
ΓChain= 3Ag+ 3B1g+ 2B2g+ B3g+ Au+ 2B1u+ 3B2u+ 3B3u,
Since Amma is not a standard setting for D17
2hspace group (Cmcm) we use Cxy
symmetry for oxygen atoms and Cx
2vsymmetry for Cu atoms in above representations.
Thus, the total number of vibrational modes from both sub-units is:
Γ = 6Ag(aa,bb,cc)+6B1g(ab)+4B2g(ac)+2B3g(bc)+Au+6B1u(E||c)+7B2u(E||b)+7B3u(E||a)
According to this analysis we should expect 6Agmodes; one mode from vibrations of the Sr
atoms, two modes which originate from vibrations of Cu atoms and other three Agmodes
are due to oxygen vibrations. In order to assign the observed Agmodes we compare our
spectra with the corresponding spectra of the Cu-O based materials with similar structural
units as in Sr14Cu24O41. For example, in SrCuO2 and YBa2Cu4O8 the Cu-O double
layers exist and resemble the one leg of the ladder structure in Sr14Cu24O41. The Cu-O
chains, formed from copper oxide squares with the common edges, as in Sr14Cu24O41, are
also present in CuO  and CuGeO3. Thus, the lowest frequency mode in Fig. 5(a)
at 246 cm−1can be assigned to vibrations of the Cu ladder atoms (see Fig. 1). The
corresponding Agmode of copper vibrations in YBa2Cu4O8(SrCuO2) appears at 250 (263)
cm−1. The next mode is found at 302 cm−1. This mode represents the vibrations of the
chain oxygen atoms along the a-axis and appears in CuO at the same frequency . The
mode at 548 cm−1is breathing mode of O1oxygen ladder atoms. Similar mode appears in
SrCuO2at 543 cm−1. The second oxygen ladder atom (O2), Fig. 1, is situated in the center
of inversion (D2hsite symmetry) and has no Raman activity. The highest frequency Raman
mode in Figs. 5(a)-(b), at about 582 cm−1, is caused by the chain oxygen vibrations along
the c-axis. Corresponding mode appears in CuO at 633 cm−1 and in CuGeO3at 594
cm−1. The vibrations of Sr atoms, with frequency of 188 cm−1as in SrCuO2, are not
observed in the spectra. Finally, the Agmode at 153 cm−1, see Fig. 8, originates from the
vibrations of the Cu atom in chains. Again, similar mode is found in YBa2Cu4O8at 153
By lowering temperature Raman peaks narrow and at about T=150 K the new modes
appear (Fig. 5 and Table II). Similar effects are found in the IR spectra as well. This temper-
ature coincides with the charge ordering temperature established in the NMR and neutron
scattering experiments [7, 9]. NMR study  showed the splitting of signal from Cu3+ions
into two peaks below 200K suggesting the occurrence of the charge ordering. This effect is
confirmed by Cox et al. . They measured synchrotron x-ray scattering on Sr14Cu24O41
single crystals and showed the appearance of the satellite peaks at (00l) positions. The
results are interpreted in terms of a charge-ordered model involving both dimerization be-
tween two-nearest-neighbors of Cu2+ions surrounding a Cu3+ion on a Zhang-Rice singlet
site, and dimerization between nearest-neighbors of Cu2+ions.
Fig. 8(a) shows the (cc) polarized low temperature (T=10 K) Raman spectra of
Sr14Cu24O41 in the 125 - 750 cm−1spectral region, excited with 647.1 nm (1.91 eV) and
488 nm (2.54 eV) energies. There are a remarkable difference between Raman spectra for
these excitation lines which appears due to resonance effects. Namely, both lines are very
close to gap energies for polarization along c-axis, see Fig. 3. The reflectivity spectra mea-
sured at 10 K for the E||c and the E||a polarizations are given in Figs. 8(b) and 8(c),
respectively. In order to compare Raman with IR data we shown in the same figure the
ǫ2(ω) and the −Im[1/ǫ(ω)] spectra. These spectra are obtained using Kramers-Kronig anal-
ysis of reflectivity data. The TO and LO mode frequencies are obtained as peak positions of
the ǫ2(ω) and the −Im[1/ǫ(ω)], respectively. For most of all Raman active modes we found
theirs infrared counterparts (some of them are denoted by vertical lines) either for the E||a
or the E||c polarizations. The appearance of similar lines in IR and Raman spectra, if not
being the consequence of the symmetry, may also be attributed to the resonant conditions.
It is well documented [26, 27] that Raman forbidden IR active LO modes appear in the
Raman spectra of the insulating Cu-O based materials for the laser line energies close to
gap values. The appearance of these modes in the Raman spectra is explained by Fr¨ ohlich
interaction . Here, since the 647.1 nm line is very close to the gap values (1.86 eV, see
Fig. 3) one can expected that the IR LO modes appear in the Raman spectra of Sr14Cu24O41
as well. Such effect is usually accompanied by the observation of the strong phonon over-
tones, as we shown in Fig. 6(a). All modes with energies higher then 700 cm−1are in fact
the second order combinations (overtones) of the low-energy modes. The assignment and
the frequencies of these modes are given in Table III. Therefore, the properties of the modes
observed in our spectra may be understood in terms of the available symmetry combined
with resonant effects, thus making proper identification of the low-temperature phonons
practically impossible without detailed structural analysis.
Now we focus on magnetic properties. As it is mentioned earlier, the neutron scattering
and NMR measurements estimated the spin-ladder gap value to be at ∆L= 32.5 meV (268
cm−1)  or at 40.5 meV (326 cm−1) , respectively. Because of that, we paid special
attention to the 200-350 cm−1spectral range, Fig. 5 (left panel). By lowering temperature
we observe the appearance of the new modes at 262, 293, and 317 cm−1. At the same time
we find the modes with the same energy in the low-temperature IR spectra, Figs. 8(b)-(c).
The 262 cm−1mode is very close in energy to the magnetic gap, thus possibly one-magnon
excitation, as proposed by Sugai et al.. However, the origin of the one-magnon excitation
in the light scattering process usually comes from the spin-orbit interaction, which is found to
be very small in transition metal oxides due to quenched orbital momentum of the transition
metal ions. Moreover, below 100 K, this mode has nearly the same temperature dependency
of the frequency and intensity, like all other low-temperature modes and we identify them
as zone edge phonons, which become Raman active due to the zone folding effect caused by
the charge ordering transition . Yet another type of magnetic excitations is expected to
appear in the Raman spectra of two-leg-ladders at energies close to 2∆L∼ 534 cm−1.
The mode at 498 cm−1(see Fig. 5 (g), right panel) shows a typical asymmetric shape with
a tail towards high-frequencies, as expected for the onset of the two-magnon continuum. Its
energy difference from 2∆Lcould be the magnon binding energy. However, as it is shown in
Fig. 8(b), this mode is positioned between TO and LO frequencies of very strong IR active
mode in the E||c spectra. This mode also shows a strong resonant enhancement, see Fig. 8
(a). Therefore, at this stage, it is hard to make definite conclusions about the origin of this
mode and further experiments are needed to clarify this issue. Similar discussion holds for
the spectral range around the twice the spin-gap value associated with a chains, 2∆C∼180
cm−1, where continuum-like feature is also found in the Raman spectra.
Finally, we discuss the modes in the spectral range above 1500 cm−1. The strongest
mode in the spectra is centered at about 2840 cm−1for the 488 nm excitation and at about
2880 cm−1for the 514.5 nm excitation line. This feature decrease in intensity and shifts to
lower energies at higher temperatures, Fig. 7. The same structure is already observed in
many copper oxides at similar frequencies [27, 29]. Thus, all observed effects indicate the
two-magnon origin of this mode. The energy of the two-magnon mode, associated with a
top of the magnon brunch, in copper oxide insulators is about 3J, where J represents the
In the case of the two-leg-ladders, its energy position for different polarized configurations
in the Raman spectra may be used to estimate the exchange parameters parallel (J) and
perpendicular (J0) to the ladders . Since the energy position of the two-magnon peak is
the same for (cc) and (aa) polarizations, Fig. 6(c), such an analysis suggests that J = J0.
This conclusion is fully in agreement with Raman scattering data of Ref. and recent
high-energy neutron scattering measurements, but inconsistent with previous neutron
, NMR and magnetization measurements, which estimated J0/J ratio to be between
0.5 and 0.8. The discrepancy may be related to the fact that in the previous measurements,
the high-energy magnetic excitations were not observed directly, but estimated indirectly
from the low-energy spin gap measurements assuming an ideal model . Thus, the Raman
scattering is more direct method to obtain J0/J ratio. The two-magnon mode at 2880 cm−1
gives exchange energy J=119 meV, very close to the neutron scattering value J=130 meV
It is also interesting to note that the two-magnon mode is asymmetric with the spectral
weight shifted to higher frequencies. Such a spectral shape of the two-magnon mode can be
a consequence of the resonance , or it can be related to the bound-hole-pair effects .
Still, further experiments on the hole doped crystals are necessary to clarify this point.
Let us consider Fig. 6(b), where a weak structure appears in (cc) spectra at about 1920
cm−1. Its energy is exactly equal to 2J and varies with a laser line frequency in a similar
way as the two-magnon mode at 2880 cm−1. The energy shift of this mode as a function of
temperature was not seen because of its very low intensity, thus leaving the origin of this
mode as an open question. In addition to the 1920 cm−1mode, we found a weak structure
at about 1700 cm−1, as well. This mode does not possess any noticeable temperature
dependencies of energy and intensity. We concluded that this mode is an overtone phonon
mode. Its frequency can be represented as the third order of the 568 cm−1mode (3c3, see
Finally, we discuss the electron energy dispersions and density of states, which are cal-
culated using the model described in Sect. III. First, we analyze the influence of the en-
ergy transfer (hopping) to the correlation gap. Fig. 9 shows the correlation gap ∆corrvs.
the Anderson-Hubbard parameter U. The plotted curves are calculated using Eq.(5) and
J = 4t2/U=0.13 eV for different hopping energy ratios txy/t and t0/t. From Fig. 9 we con-
clude that the main influence to the correlation gap value comes from the Anderson-Hubbard
parameter U. Because of that, by knowing the electronic gap from the ellipsometric or optical
absorption measurements and the exchange energy J from the Raman spectroscopy we can
determine the hopping parameters and the onsite electron-electron repulsion U. However,
relative ratio of the hopping energies perpendicular and parallel to the legs as well as the
interladder hopping, does not influence much the correlation gap . Namely, a decrease of the
transfer energy along the rungs from t0/t=1 to t0/t=0.5 increases ∆corrfor about 6%. Also,
an increase of the interladder hopping txyfrom 0 to 10% of the hoping value t along the legs,
produces a decrease of ∆corrfor about 2.5%. Therefore, the interladder effects on electronic
structure of Sr14Cu24O41are found to be negligibly small even though the distance between
the neighboring ladders is short (see Fig. 1). The correlation gap is observed at 1.4 eV.
This value is determined as a maximum of dielectric function ǫ2(ω) obtained from KKA of
the unpolarized reflectivity data, see Inset (b) of Fig. 3(b). Using this value and the fact
that t0/t = 1 (comes form J0/J = 1), txy= 0 we obtained U=2.1 eV. Similar values for the
correlation gap and U has been also found in SrCuO2.
Energy dispersion, shown in Inset of Fig. 2, allows us to assign the 1.86 eV peak in Fig.
3(a) to the gap value (∆1=1.87 eV) between bonding and antibonding bands at the Z-point.
Also, 2.4 eV peak from the ellipsometric measurements corresponds to the gap from the
lowest occupied band (L6, Fig. 2) to the highest empty band at Z-point of Brillouine zone
(∆2=2.4 eV). By comparison of our measured and calculated gap values, with previously
published results [17, 35], we found that our t0/t ratio is close to the ratio determined in
. Mizuno et al., , calculated the optical conductivity for small clusters, simulating
the ladders and the chains. They obtained the gap for the ladder at about 1.7 eV while the
contribution from the chains mainly emerges at a higher energy showing the large spectral
weight at around 2.6 eV. These values are very close to our experimental results. Therefore,
the peaks at 1.86, 2.4 and 2.5 eV, see Fig. 3(b), may correspond to the ladders and the
In conclusion, we studied the optical properties of the Sr14Cu24O41single crystal. The
lattice vibrations are analyzed using the far-infrared reflectivity and Raman scattering mea-
surements in the wide frequency and temperature range. At temperatures below 150 K the
new IR and Raman modes appear, presumably due to the charge ordering. The two-magnon
excitations are found in the Raman spectra which could be related to minimal (2∆) and
maximal (twice the top of the magnon brunch) magnon energy. The exchange constants
along the legs and rungs of the ladders are found to be the same, J = J0 ∼ 120 meV.
The optical reflectivity and the ellipsometric measurements are used to study the charge
dynamics. The gap values of 1.4 eV, 1.86 eV (2.5 eV) for the ladders (chains) along the
c-axis and 2.4 eV along the a-axis are found. These results are analyzed using tight-binding
approach for the correlated electrons. The correlation gap value of 1.4 eV is calculated with
the transfer energy (hopping) parameters t=t0=0.26 eV, along and perpendicular to the
legs, and U=2.1 eV, as a Coulomb repulsion.
We thank W. K¨ onig for low-temperature infrared measurements.Z.V.P., V.A.I and
O.P.K acknowledge support from the Research Council of the K.U. Leuven and DWTC.
The work at the K.U. Leuven is supported by the Belgian IUAP and Flemish FWO and
GOA Programs. M.J.K thanks Roman Herzog - AvH for partial financial support.
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