Physica C 357±360 (2001) 265±268
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Separation of electronic and phononic components in
Raman spectra of YBa2…Cu1 x Znx †3O7 d
M. Limonov a,*,1, D. Shantsev a,1, S. Tajima a, A. Yamanaka b
b
a
SRL-ISTEC, 10-13, Shinonome 1-Chome, Koto-ku, Tokyo 135-0062, Japan
Chitose Institute of Science and Technology, Chitose, Hokkaido 066-8655, Japan
Received 16 October 2000; accepted 15 January 2001
Abstract
The B1g -Raman scattering spectra of twin-free YBa2 …Cu1 x Znx †3 O7 d single crystals have been analyzed by using a
phenomenological function of the electronic response v…x† ˆ R…x† ‡ iq…x†. We found a low-frequency shift of the 2Dpeak in the q…x† with Zn-doping, consistent with the changes in R…x† and the phonon parameters. Ó 2001 Elsevier
Science B.V. All rights reserved.
PACS: 74.25.Gz; 74.25.Kc; 74.72.Bk
Keywords: YBa2 Cu3 O7 d ; Raman spectra; Electronic response function
1. Introduction
Electronic and phononic Raman scattering
has been commonly used as a tool to investigate
various high-Tc superconductors. Since the scattering by the phonon states interferes with that
by the electronic continuum in high-Tc superconductors, a proper separation of electronic and
phononic components in Raman scattering spectra is of great importance. Particularly for
YBa2 Cu3 O7 d there are many strong phonon lines
*
Corresponding author. Tel.: +81-3-3536-0618; fax: +81-33536-5717.
E-mail address: limonov@istec.or.jp (M. Limonov).
1
Permanent address: A.F. Io€e Physical-Technical Institute,
Russian Academy of Sciences, Politeknicheskaya, 26, 194021
St. Petersburg, Russia.
even near the 2D-peak, which makes it dicult to
extract phononic or electronic components correctly.
There are two main approaches for the extraction of the electronic background from
Raman spectrum. The ®rst one is the widely used
``standard Fano procedure'' [1]. The second approach is based on the Green functions [2] and
enables us to treat the interference e€ect explicitly
[3±5]. In this paper, to extract uncoupled phonon
parameters and interference e€ects we improve our
Green functions approach [5], assuming an appropriate electronic response function in which
real and imaginary parts are connected via a
Kramers±Kronig relation. Applying this model
for analysis of the B1g -spectra of YBa2 …Cu1 x Znx †3 O7 d single crystals, we were also able to
demonstrate the Zn-substitution e€ects on the
behavior of the 2D-peak as well as on the phonon
self-energy.
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 0 2 2 7 - 1
266
M. Limonov et al. / Physica C 357±360 (2001) 265±268
2. Results and discussion
In this paper, precise temperature dependences
of the Raman spectra have been investigated for
optimally doped twin-free YBa2 …Cu1 x Znx †3 O7 d
single crystals. These crystals were grown by a topseeded pulling technique and oxygenated under
uniaxial pressure in order to obtain the orthorhombic twin-free samples as described previously
[6]. The Zn-free crystal show the maximum Tc of
93 K, while it decreases down to 85 K in the 0.4%
Zn-doped sample with optimal oxygen content.
The Raman spectra were studied using a T64000
Jobin±Ivon triple spectrometer with a liquidnitrogen cooled CCD detector. A typical spectral
resolution was 3 cm 1 . The 514.5 nm line of an
Ar±Kr laser was used for the excitation. The
power density was about 1 W/cm2 on the sample
surface, and, as a result, the overheating was
suppressed down to less than 5 K in all experiments.
The Raman spectra in the X 0 Y 0 -polarization
(B1g symmetry in a tetragonal D4h notation) consist of electronic continuum and the B1g -like phonon line at about 340 cm 1 . Additionally, several
weak A1g -like phonon lines appear in the spectra.
Fig. 1 shows an example of the X 0 Y 0 -spectra for the
YBa2 …Cu0:996 Zn0:004 †3 O7 d crystal after subtraction
of all A1g -like phonons. This subtraction was
performed using A1g -like Raman spectra (XX- and
YY-polarizations) from our previous paper [7].
Below Tc the electronic spectrum exhibits a superconducting response with a broad 2D-peak. To
extract the phononic and electronic parameters
correctly, we use formula obtained on a basis of
the Green's function approach for description of
the coupled electron±phonon Raman spectrum [2]:
1
F …x† ˆ B…x† q…x† ‡
C…1 ‡ e2 †
2
S
2
2
x†V
‡
2q…x†eS
q
;
1†
V2
where B…x† ˆ 1 ‡ n…x; T † is the Bose factor, e ˆ
x X†=C, S ˆ S0 ‡ V 2 R…x†. The renormalized
frequency X and the line width C of the phonon
are represented as X ˆ X0 ‡ V 2 R…x† and C ˆ C0 ‡
V 2 q…x†, where V is the electron±phonon cou-
Fig. 1. The Raman spectra of the YBa2 …Cu0:996 Zn0:004 †3 O7 d
crystal at T ˆ 10 K in the X 0 Y 0 -polarization after subtraction of
A1g -like phonons. The thick solid curve is the results of the
®tting procedure using Eq. (1). The thin solid curve shows q…x†
function. In the inset both real and imaginary parts of the
electronic response v…x† ˆ R…x† ‡ iq…x† are presented.
pling constant, X0 and C0 are uncoupled values,
q…x† and R…x† are the imaginary and real parts
of the electronic response v…x†. Four parameters
X0 , C0 , S0 , and V were set x-independent in the
®tting.
The key point of the present treatment is a
proper description of the electronic response
function v…x† ˆ R…x† ‡ iq…x†. In the paper by
Bock et al. [3], the phenomenological expression
I1 tanh…x=xT † was proposed to describe the incoherent electronic background. We examined
several another formulae for qn …x†, and the good
®tting was obtained with the following expression:
x
qn …x† ˆ Cn p ;
2†
x2 ‡ x2T
where Cn and xT are the ®tting parameters. This
function ®ts successfully the conventional behavior
of the normal electronic response function, i.e.
q…x† ! const at high frequencies and q…x† / x at
low x.
The real part R…x† is directly linked to the
imaginary part q…x† via the Kramers±Kronig
relation. For a certain cuto€ frequency xcut
(xcut X) for qn …x†, Hilbert transformation of
Eq. (2) gives
M. Limonov et al. / Physica C 357±360 (2001) 265±268
2
267
For temperatures below Tc , it is convenient to
write down the total electronic response as a sum
of the normal and superconducting contributions,
q…x† ˆ qn …x† ‡ qs …x†. The superconducting contribution qs …x† should re¯ect the appearance of
the superconducting gap leading to a 2D-peak
which is accompanied by a suppression of q…x† at
lower frequencies. Both the peak and the suppression are described by Lorentzians with opposite signs similar to those proposed in Ref. [3].
As can be seen in Fig. 1, the ®tting of the experimental Raman spectrum is perfect. To extract
the Zn-doping dependence of the superconducting
gap, we investigated the temperature dependence
of the electronic response function q…x†. We have
found a pronounced low-frequency shift of the
peak in q…x† with Zn-doping (Fig. 2). This result
suggests that the gap amplitude D …T ˆ 0† de-
creases by 30 cm 1 owing to a small amount
of Zn-doping (x ˆ 0:4%). Although in¯uence of
Zn-doping on the Raman scattering of YBa2 …Cu1 x Znx †3 O7 d single crystals have been investigated before [8], such a decrease of the gap energy
in B1g -polarization was not reported in Ref. [8]
probably because the spectra were analyzed simply
by mutual subtraction without taking into account
any interference e€ect.
The ®tting procedure taking into account both
q…x† and R…x† explicitly, also allows us to extract
the uncoupled phonon parameters X0 , C0 , and S0 .
A complete picture of Raman scattering in the
YBa2 …Cu1 x Znx †3 O7 d crystals will be discussed
in a separate paper [9]. As an example, the temperature dependences of both uncoupled X0 and
renormalized X ˆ X0 ‡ V 2 R frequencies of the
340 cm 1 line are shown in Fig. 3. The uncoupled
frequencies X0 show a smooth temperature dependence, without any anomaly in the superconducting state. Even in the normal state, we can see
a small softening (V 2 R 2 cm 1 ) of renormalized
frequencies X due to interaction with the electronic
background. The superconductivity induced e€ect
manifests itself in a rapid decrease of the renormalized frequencies below Tc . The magnitude
of softening of the 340 cm 1 line in the Zn-free
Fig. 2. The temperature dependences of the maximums of the
electronic response functions q…x† in the X 0 Y 0 -polarization for
the pure and Zn-doped YBa2 …Cu1 x Znx †3 O7 d crystals. The
solid lines are guides to the eye.
Fig. 3. Temperature dependences of the uncoupled X0 and
renormalized X ˆ X0 ‡ V 2 R frequencies of the 340 cm 1 phonon line for the Zn-free and Zn-doped YBa2 …Cu1 x Znx †3 O7 d
single crystals.
R…x† ˆ
p
x2T ‡ x2cut ‡ xcut
Cn 6
x
‡ p
4 ln p
p
x2T ‡ x2cut xcut
x2 ‡ x2T
0
13
q
2
2
2
2 ‡ x2 †
x
xx
‡
x
‡
x
x
cut
T
T
T
cut
x
x
B cut
C7
q
ln @
A5 :
xcut ‡ x x2 ‡ xx ‡
x2T ‡ x2cut …x2 ‡ x2T †
cut
T
3†
268
M. Limonov et al. / Physica C 357±360 (2001) 265±268
and Zn-doped YBa2 …Cu1 x Znx †3 O7 d crystals is
essentially di€erent, re¯ecting a di€erence in R…x†
between the two crystals.
Acknowledgements
The authors are thankful to A.I. Rykov for
preparation of the samples and to J. Quilty for
helpful discussions. This work is supported by
New Energy and Industrial Technology Development Organization (NEDO) as Collaborative
Research and Development of Fundamental Technologies for Superconductivity Applications. One
of us (DS) was supported by STA fellowship.
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