# 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.

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**ABSTRACT:**An unified picture for the Raman response of magnetic excitations in cuprate spin-ladder compounds is obtained by comparing calculated two-triplon Raman line-shapes with those of the prototypical compounds SrCu2O3 (Sr123), Sr14Cu24O41 (Sr14), and La6Ca8Cu24O41 (La6Ca8). The theoretical model for the two-leg ladder contains Heisenberg exchange couplings J_parallel and J_perp plus an additional four-spin interaction J_cyc. Within this model Sr123 and Sr14 can be described by x:=J_parallel/J_perp=1.5, x_cyc:=J_cyc/J_perp=0.2, J_perp^Sr123=1130 cm^-1 and J_perp^Sr14=1080 cm^-1. The couplings found for La6Ca8 are x=1.2, x_cyc=0.2, and J_perp^La6Ca8=1130 cm^-1. The unexpected sharp two-triplon peak in the ladder materials compared to the undoped two-dimensional cuprates can be traced back to the anisotropy of the magnetic exchange in rung and leg direction. With the results obtained for the isotropic ladder we calculate the Raman line-shape of a two-dimensional square lattice using a toy model consisting of a vertical and a horizontal ladder. A direct comparison of these results with Raman experiments for the two-dimensional cuprates R2CuO4 (R=La,Nd), Sr2CuO2Cl2, and YBa2Cu3O(6+delta) yields a good agreement for the dominating two-triplon peak. We conclude that short range quantum fluctuations are dominating the magnetic Raman response in both, ladders and planes. We discuss possible scenarios responsible for the high-energy spectral weight of the Raman line-shape, i.e. phonons, the triple-resonance and multi-particle contributions. Comment: 10 pages, 6 figuresPhysical Review B 03/2005; · 3.66 Impact Factor - SourceAvailable from: arxiv.org[Show abstract] [Hide abstract]

**ABSTRACT:**The Raman response in the antiferromagnetic 2-leg S = 1/2 Heisenberg ladder is calculated for various couplings by continuous unitary transformations. For leg couplings above 80% of the rung coupling a characteristic 2-peak structure occurs with a point of zero intensity within the continuum. Experimental data for CaV2O5 and La y Ca 14 − y Cu24O41 are analyzed and the coupling constants are determined. Evidence is found that the Heisenberg model is not sufficient to describe cuprate ladders. We argue that a cyclic exchange term is the appropriate extension.EPL (Europhysics Letters) 01/2007; 56(6):877. · 2.26 Impact Factor - SourceAvailable from: Dong Qian[Show abstract] [Hide abstract]

**ABSTRACT:**We report measurement of collective charge modes of insulating Sr14Cu24O41 using inelastic resonant x-ray scattering over the complete Brillouin zone. Our results show that the intense excitation modes at the charge gap edge predominantly originate from ladder-containing planar substructures. The observed modes are found to be dispersive for momentum transfers along the “legs” (ℏQ⃗‖ĉ) but nearly localized along the “rungs” (ℏQ⃗‖â). We show that the dispersion and peak width characteristics of the modes can be understood in the strong-coupling quantum limit (Hubbard U⪢tladder>tchain, where t is the hopping parameter). Quite generally, we demonstrate that the momentum tunability (Q⃗ resolution) of inelastic x-ray scattering can be utilized to resolve mode contributions in multicomponent incommensurate quantum electron systems.Physical review. B, Condensed matter 01/2007; 76(10). · 3.77 Impact Factor

Page 1

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

Abstract

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

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Page 2

I. INTRODUCTION

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 [1]. According to the structural analysis [1], 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 [2]. The progress in this field

has been summarized in Ref. [13]. 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) [8]. The second one, ∆C= 11.5 meV, is argued to arise from the spin dimer formation

in the CuO2chains [8], 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 [6].

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..

[14] 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. [15]

argued that, besides strong two-magnon features, some low-frequency modes in the Ra-

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man spectra are also magnetic in origin, since they have similar energies to those found

in the neutron scattering experiments [8]. 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.

II.EXPERIMENTAL DETAILS

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.

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Page 4

III.ELECTRONIC STRUCTURE

The electronic structure of Sr14Cu24O41is calculated using the tight-binding method for

correlated electrons [16]. Recent exact diagonalization and a variational Monte Carlo sim-

ulations revealed that electronic structure of Sr14Cu24O41is well described by single ladder

energy spectrum [17]. It means that electron energy dispersions are governed mainly by

electrons in the ladder. According to the ARPES measurements [10], 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

2

O2−

3

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

?

?

?

?

p,σ

cospy

?

a+

σ(p)aσ(p) + b+

σ(p)bσ(p) + c+

σ(p)cσ(p) + d+

σ(p)dσ(p)

?

−t0

p,σ

?

a+

σ(p)bσ(p) + c+

σ(p)dσ(p) + H.c.

?

−txy

p,σ

?

?

e−i√2px+ e−i(√2px+py)??

1 + e−ipy??

a+

σ(p)dσ(p) + H.c.

?

nj

−txy

p,σ

b+

σ(p)cσ(p) + H.c.

?

+ U

?

i=a,b,c,d

↑inj

↓i− µ

?

i=a,b,c,d

nj

i,

(1)

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 [18], the correlation split energy bands are governed by

zeros of the inverse Green’s function in the first perturbation order with respect to tunneling

4

Page 5

matrix:

?

D−1

p (ω) =

Aa−bB

B∗

Ac−d

,

(2)

where

?Aa−b =

a {0+

-2

b {0+

C C 0 0

-2

−iωn−µ

f0+

r

+ r r−t0

−t0

−t0

−iωn−µ+U

f−2

−t0

−t0

+ r −t0

−t0

−t0

−iωn−µ

f0+

r

+ r r

−iωn−µ+U

f−2

+ r

,

?B =

0 0 D D

0 0 D D

C C 0 0

with r = −2tcospy,C = −txy

?

1 + e−ipy?

,D = −txy

?

e−i√2px+ e−i(√2px+py)?

.

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:

????

D−1

p (ω)

??? = 0

ξ±

B(p) =1

2

?

ε1,2

p +

??

ε1,2

p

?2+ U2

?

,(3)

ξ±

A(p) =1

2

?

ε1,2

p −

??

ε1,2

p

?2+ U2

?

,(4)

where ε1,2

p = −2tcospy±

For derivation of these energy dispersions from the eight-by-eight fold secular equation

?

t2

0+

?

2txycospy

2

?2± 4t0txycospy

2cos

√2px

2.

(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. [19]). The subbands ξ−

Band ξ−

A

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+

Band the

correlation gap in electronic structure can be estimated as

∆corr = minξ+

B(p) − maxξ−

A(p) =(5)

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Page 6

1

2

??

(t0+ 2t − 2txy)2+ U2+

?

(t0+ 2t)2+ U2

?

− (t0+ 2t + txy).

For the dimensionless energies, ω+,−

p

= ε1,2

p/2t, τ0= t0/2t,τ = txy/2t, the non-correlated

?

electron density of states per spin, ρ(ε)=

px,py[δ(ε−ω+

p)+δ(ε−ω−

p)], for the unit cell volume,

is defined analytically as follows

ρα

0(−1 − 2τ + ατ0≤ ε ≤ −1 + 2τ − τ0) =

?

4

π2√kατK (qα),

4

π2qα

4

π2qα

ρα

0

−1 + 2τ + ατ0≤ ε ≤1

2+ τ + ατ0

?

=

√kατF

?

?1

arcsinaα;1

qα

?

,(6)

ρα

0(−1 + 2τ + ατ0≤ ε ≤ 1 + ατ0) =

√kατK

qα

?

.

Eqs.(6)representtheanalyticalexpressionsfortheelectrondensityofstates

viaellipticintegralsFandKofthe1-st kindintheLegendrenormal

form withmodulus

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

qα

=

??

2τ (τ + kα) + 1 − (ε + ατ0)2?

/[(1 + ε + ατ0)(τ + kα)kα],

/kατ/2,argument

aα

?

=

??

wherekα

=

states ρ0. The correlated electron density of states is

ρ(ε) =

2

1 +

ξ′

+

?

(ξ′

?U

ξ±

?

+)

?2

2+(U

2t)

2

ρ0

?

ξ

′

+

?

+

2

1 −

ξ′

−

?

(ξ′

−)

2+(U

2t)

2

ρ0

?

ξ

′

−

?

,where(7)

ξ

′

±=

ξ

2

±−

2t

+ S

and S =

1

4

(1 + 2τ + τ0)2+

?U

t

?2

−

?

(1 + τ0)2+

?U

t

?2

− 2τ

,

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 −

1/2

(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

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Page 7

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.

IV.EXPERIMENTAL RESULTS

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 [20], we attribute these components to

the components of the dielectric tensor ǫaa

2and ǫcc

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∞(

n

?

j=1

ω2

ω2

LO,j− ω2+ ıγLO,jω

TO,j− ω2+ ıγTO,jω−

ω2

p

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

7

Page 8

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

Fig. 7.

V.DISCUSSION

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 [1]. 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)

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Page 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 [21]:

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

s

site

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)

(10)

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[22] and YBa2Cu4O8[23] 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 [24] and CuGeO3[25]. 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 [24]. 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

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Page 10

the c-axis. Corresponding mode appears in CuO at 633 cm−1[24] and in CuGeO3at 594

cm−1[25]. 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

cm−1.

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 [7] 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. [11]. 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 [26]. Here, since the 647.1 nm line is very close to the gap values (1.86 eV, see

10

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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) [8] or at 40.5 meV (326 cm−1) [28], 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.[15]. 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 [7]. 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[29].

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[8], where continuum-like feature is also found in the Raman spectra.

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Page 12

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

exchange interaction.

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 [30]. 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.[15] and recent

high-energy neutron scattering measurements[31], but inconsistent with previous neutron

[8], NMR[6] 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 [32]. 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

[8].

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 [30], or it can be related to the bound-hole-pair effects [15].

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

12

Page 13

mode. Its frequency can be represented as the third order of the 568 cm−1mode (3c3, see

Table II).

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[34].

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

[17]. Mizuno et al., [35], 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,

13

Page 14

the peaks at 1.86, 2.4 and 2.5 eV, see Fig. 3(b), may correspond to the ladders and the

chains, respectively.

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.

VI. ACKNOWLEDGMENT

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.

14

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[1] E. M. Mc.Carron, M. A. Subramanian, J. C. Calabrese, and R. L. Harlow, Mat. Ress. Bull.

23, 1355 (1988).

[2] M.Uehara, T Nagata, J. Akimitsu, H. Takahashi, N. Mori, and K. Kinoshita, J. Phys. Soc.

Jpn. 65, 2764 (1996).

[3] N. Motoyama, T. Osafune, T. Kakeshita, H. Eisaki, and S Uchida, Phys. Rev. B 55, R3386

(1997).

[4] S. A. Carter, B. Batlogg, R. J. Cava, J. J. Krajewski, W. F. Peck, Jr, and T. M. Rice, Phys.

Rev. Lett. 77, 1378 (1996).

[5] Z. Hiroi, S. Amelinckx, G. Van Tendeloo, and N. Kobayashi, Phys. Rev. B 54, 15849 (1996).

[6] T. Imai, K. R. Thurber, K. M. Shen, A. W. Hunt, and F. C. Chou, Phys. Rev. Lett. 81, 220

(1998).

[7] M. Takigawa, N. Motoyama, H. Eisaki, and S. Uchida, Phys. Rev. B 57, 1124 (1998).

[8] R. S. Eccleston, M. Uehara, J. Akimitsu, H. Eisaki, N. Motoyama, and S. Uchida, Phys. Rev.

Lett. 81, 1702 (1998).

[9] M. Matsuda, K. Katsumata, H. Eisaki, N. Motoyama, S. Uchida, S. M. Shapiro, and G.

Shirane, Phys. Rev. B 54, 12199 (1996).

[10] T. Takahashi, T. Yokoya, A. Ashihara, O. Akaki, H. Fujisawa, A. Chainani, M. Uehara, T.

Nagata, J. Akimitsu and H. Tsunetsuga, Phys. Rev. B 56, 7870 (1997).

[11] D. E. Cox, T. Iglesias, K. Hirota, G. Shirane, M. Matsuda, N. Motoyama, H. Eisaki, and S.

Uchida, Phys. Rev. B 57, 10750 (1998).

[12] T. Osafune, N. Motoyama, H. Eisaki, and S. Uchida, Phys. Rev. Lett. 78, 1980 (1997).

[13] E. Dagotto, Rep. Prog. Phys, 62, 1527 (1999).

[14] M. V. Abrashev, C. Thomsen, and M. Surtchev, Physica C 280, 297 (1997).

[15] S. Sugai and M. Suzuki, Phys. Stat. Sol. (b) 215, 653 (1999).

[16] V. A. Ivanov, J. Phys.: Cond. Matter 6, 2065 (1994).

[17] S. Koike, K. Yamaji and T. Yanagisawa, J. Phys. Soc. Jpn. 68, 1657 (1999).

[18] V. A. Ivanov, Physica B 186-188, 921 (1993).

[19] V. A. Ivanov, K. Yukushi, E. Ugolkova, Physica C 275, 26 (1997).

[20] D. E. Aspnes, J. Opt. Soc. Am. 70, 1275 (1980).

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