Optical properties of the spin-ladder compound Sr14Cu24O41
ABSTRACT We report the measurements of the pseudodielectric function, far-infrared reflectivity, and Raman scattering spectra in Sr14Cu24O41 single crystal. We study the lattice and the spin dynamics of the Cu2O3 spin ladders and CuO2 chains of this compound. The ellipsometric and the optical reflectivity measurements yield the gap values of 1.4, 1.86, 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 Cu2O3 ladders is analyzed using the 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 an 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.
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−