Physica C 408–410 (2004) 834–836 www.elsevier.com/locate/physc
Far infrared c-axis optical conductivity in an oriented Bi2Sr2Ca2Cu3O10 polycrystal Vinh Ta Phuoc a
a,*
, Vincent Garnier b, Isabelle Monot-Laffez a, Francßois Gervais
a
LEMA UMR 6157, CNRS-CEA, Universite Francßois Rabelais, Parc de Grandmont, 37200 Tours, France b CRISMAT, UMR 6508, CNRS, 6 Bd Marechal Juin, 14050 Caen, France
Abstract Polarized reflectivity measurements were performed on an oriented Bi2 Sr2 Ca2 Cu3 O10 polycrystal. We found that FIR c-axis optical response exhibits similarities with other multilayer compounds such as YBa2 Cu3 Ox or Bi2 Sr2 Ca1 Cu2 O8 . As temperature is decreased, a broad band developing around 450 cmÿ1 and nearby phonon anomalies are observed. Moreover, two oxygen bond-bending modes are evidenced at 362 and 392 cmÿ1 . This latter grows in intensity as temperature decreases, contrary to bilayer superconductors. The appearance of the 450 cmÿ1 broad band is well described by the model of Munzar in which the superconductor is considered as stacked superconducting layers with non equivalent intra-trilayer and interlayer Josephson coupling constants. Our results show that oriented polycrystals are useful to investigate c-axis optical properties of high Tc superconductors. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction One of the main features in c-axis optical conductivity of multilayer high Tc superconductors is the appearance of a broad band around 450 cmÿ1 as temperature is decreased [1–5]. Van der Marel and Tsvetkov [6] suggested that this peak is due to a transverse Josephson plasma resonance (TJPR). In their model, the dielectric function eðxÞ results in contributions of the different conduction channels added in serie, contrary to a homogeneous medium in which contributions are added in parallel. This model was extended by Munzar et al. [3] to describe phonon anomalies by taking into account local fields acting on different ions involved in a vibration mode, and it was successfully used to investigate c-axis optical response of bilayer compounds [3– 5,7]. The aim of this work is to show how the c-axis optical conductivity of trilayer Bi2 Sr2 Ca2 Cu3 O10 can be interpreted in the framework of the Munzar model. Note however that important questions remain opened.
*
Corresponding author. E-mail address:
[email protected] (V.T. Phuoc).
Although the model well fits the experiments, it is difficult to interpret the increase of the 450 cmÿ1 peak far above Tc in YBa2 Cu3 Ox in term of Josephson currents as pointed out by Timusk and Homes [8]. Another key point of the c-axis properties is the change of the c-axis kinetic energy below Tc , and its contribution to the condensation energy [9,10].
2. Results and discussion Sample preparation and characterisation are described elsewhere [11]. Polarized reflectivity measurements were performed in the range 40–8000 cmÿ1 between 300 and 4 K. Optical conductivity was obtained by the Kramers–Kronig analysis of the reflectance. The real part c-axis optical conductivity rðxÞ ¼ r1 ðxÞ þ ir2 ðxÞ is shown in Fig. 1 as a function of temperature. The main phonon modes are located at 95, 130, 170, 210, 253, 305, 362, 392, 605 cmÿ1 . Note that the two modes at 362 and 392 cmÿ1 are assigned to oxygen bond-bending modes [10], while only one is evidenced in Bi-2212 [7]. As illustrated in Fig. 1(a), the 450 cmÿ1 peak does not depend on temperature above Tc , in agreement with previous works on Bi2212 [7] and Bi2223 [10].
0921-4534/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.03.213
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Fig. 1. (a) Real optical conductivity vs. frequency for 5, 20, 60, 80, 100, 120, 140, 160, 180 K and (b) Dr1 ðT Þ ¼ r1 ð5KÞ ÿ r1 ðT Þ for 20, 60, 80, 100, 120, 180 K.
Moreover, oxygen bond-bending and 605 cmÿ1 modes are strongly renormalized in the superconducting state. Fig. 1(b) shows that, while the 362 cmÿ1 mode does not show any significant change, the 392 cmÿ1 mode drastically increases below Tc , contrary to a strong suppression of the 366 cmÿ1 peak observed in Bi2212 [7]. This behaviour has also been recently reported by Boris et al. [10]. To explain both growth of the 400 cmÿ1 mode and loss of intensity of the 360 cmÿ1 peak (which does not change in our spectra), the authors invoke the relative agreement between phonon eigenvector pattern and local field pattern calculated within the Munzar model. Finally, we find that the 600 cmÿ1 phonon assigned to the vibration of apical oxygen strongly decreases below Tc , due to change in interlayer local field [3]. To fit our data, we simplify the Munzar model as follows: (i) we assume that the interlayer region is insulating so that its susceptibility vint ¼ 0, (ii) the electric field renormalization due to the displacements of the ions is neglected, (iii) except for the oxygen bondbending modes, 1 the field acting on the ions involved in phonon modes is assumed to be Eint , (iv) the intratrilayer susceptibility vbl includes a London term and a Drude term which represents the electronic background:
1 As pointed out by Boris et al. [10], the spectral weight of the oxygen bond-bending modes is determined by both local field and eigenvector patterns. For simplicity, we fit these two modes regardless of local field effects. The anomalies are then taken into account by changing the oscillator strength and damping.
Fig. 2. Experimental data (thin lines) and fits (thick gray lines) of r1 and r2 for 5 and 180 K.
vbl ðxÞ ¼ ÿx2bl =x2 ÿ X2bl =½xðx þ icbl Þ. Note that a midinfrared contribution is also added in parallel. Fig. 2 shows the very good agreement between experimental data and the model above and below Tc . 2 This indicates that our simplified model captures the main physics of the system, namely, the appearance of the 450 cmÿ1 mode related to the TJPR. In summary, we show that the temperature dependence of the fir c-axis conductivity of Bi2223 is quite similar to bilayer superconductors. The 450 cmÿ1 peak and phonon anomalies are evidenced, and their temperature dependence are studied. But contrary to bilayer compounds, one of the oxygen bond-bending mode increases below Tc . Experimental data well agree with a simplified Munzar model. Thus, the 450 cmÿ1 bump can be attributed to a transverse Josephson plasma resonance, and phonon anomalies are due intra-trilayer and interlayer local field effects. Moreover, data show that oriented polycrystals well reproduce c-axis properties of layered superconductors.
2
Fit frequencies x and dampings c are in cmÿ1 , S are oscillator strengths (dimensionless): e1 ¼ 4:15, xbl ¼ 0, Xbl ¼ 1200, cbl ¼ 275, Smir ¼ 2:7, xmir ¼ 2500, cmir ¼ 5000, S1 ¼ 0:2, S2 ¼ 0:3, S3 ¼ 0:3, S4 ¼ 0:5, S5 ¼ 2, S6 ¼ 0:75, S7 ¼ 0:38, S8 ¼ 0:6, x1 ¼ 130, x2 ¼ 170, x3 ¼ 210, x4 ¼ 253, x5 ¼ 305, x6 ¼ 362, x7 ¼ 392, x8 ¼ 605, c1 ¼ 7, c2 ¼ 15, c3 ¼ 35, c4 ¼ 30, c5 ¼ 48, c6 ¼ 38, c7 ¼ 25, c8 ¼ 40 at 180 K; e1 ¼ 4:15, xbl ¼ 1100, Xbl ¼ 1060, cbl ¼ 1040, Smir ¼ 2:7, xmir ¼ 2500, cmir ¼ 5000, S1 ¼ 0:4, S2 ¼ 0:67, S3 ¼ 0:9, S4 ¼ 0:954, S5 ¼ 2:1, S6 ¼ 0:75, S7 ¼ 0:58, S8 ¼ 0:6, x1 ¼ 134, x2 ¼ 172, x3 ¼ 210, x4 ¼ 255, x5 ¼ 300, x6 ¼ 368, x7 ¼ 392, x8 ¼ 608, c1 ¼ 9, c2 ¼ 21, c3 ¼ 29, c4 ¼ 35, c5 ¼ 53, c6 ¼ 35, c7 ¼ 22, c8 ¼ 60 at 5 K.
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References [1] C. Homes et al., Phys. Rev. Lett. 71 (1993) 1645. [2] S. Tajima et al., Phys. Rev. B 55 (1997) 6051. [3] D. Munzar et al., Solid State Commun. 112 (1999) 365. [4] M. Gr€ uningen et al., Phys. Rev. Lett. 84 (2000) 1575. [5] C. Bernhard et al., Phys. Rev. B 61 (2000) 618.
[6] D. van der Marel, A. Tsvetkov, Czech. J. Phys. 46 (1996) 3165. [7] V. Zelezny et al., Phys. Rev. B 63 (2001) 060502. [8] T. Timusk, C. Homes, Solid State Commun. 126 (2003) 63. [9] D. Munzar, T. Holden, C. Bernhard, Phys. Rev. B 67 (2003) 020501. [10] A. Boris et al., Phys. Rev. Lett. 89 (2002) 277001. [11] N. Petit et al., Eur. Phys. J. B 25 (2002) 423.
