Anomalies of the infrared-active phonons in underdoped YBa2Cu3Oy as evidence for the intra-bilayer Josephson effect

SSC 4918

PERGAMON

Solid State Communications 112 (1999) 365–369 www.elsevier.com/locate/ssc

Anomalies of the infrared-active phonons in underdoped YBa2 Cu3 Oy as evidence for the intra-bilayer Josephson effect D. Munzar a,b,*, C. Bernhard a, A. Golnik a,1, J. Humlı´cˇek b, M. Cardona a a

b

Max-Planck-Institut fu¨r Festko¨rperforschung, Heisenbergstraße 1, D-70569 Stuttgart, Germany Department of Solid State Physics and Laboratory of Thin Films and Nanostructures, Faculty of Science, Masaryk University, Kotla´rˇska´ 2, CZ-61137 Brno, Czech Republic Received 22 July 1999; accepted 12 August 1999 by J. Kuhl

Abstract The spectra of the far-infrared c-axis conductivity of underdoped YBCO crystals exhibit dramatic changes of some of the phonon peaks when going from the normal to the superconducting state. We show that the most striking of these anomalies can be naturally explained by changes of the local fields acting on the ions arising from the onset of inter- and intra-bilayer Josephson effects. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. High-Tc superconductors; D. Dielectric response; D. Phonons; E. Light absorption and reflection

The essential structural elements of the high-Tc superconductors are the copper–oxygen planes which host the superconducting condensate. Many experiments, and also some theoretical considerations, suggest that these planes are only weakly (Josephson) coupled along the c-direction. Studies of the c-axis transport [1,2] and those of the microwave absorption [3], and the far-infrared c-axis conductivity [4–6] revealing Josephson plasma resonances, have established that Josephson coupling indeed takes place for planes (or pairs of planes) separated by insulating layers wider than the in-plane lattice constant. It is not fully understood why the coupling is so weak and it is debated whether this is related to the unconventional ground state of the electronic system of the planes causing a charge confinement [7,8] and/or to the properties of the insulating layers. In this context, it is of interest to ascertain whether the closely-spaced copper-oxygen planes of the so-called bilayer compounds, like YBa2 Cu3 Oy , are also weakly (Josephson) coupled. In this paper, we show that the far-infrared spectra of the c-axis conductivity of underdoped YBa2 Cu3 Oy with 6:4 # y # 6:8 may provide a key for resolving this important issue. The spectra exhibit, beside a spectral gap that shows * Corresponding author. 1 Permanent address: IFD, Warsaw University, Hoza, 69, PL-00681 Warsaw, Poland.

up already at temperatures much higher than Tc [9–13], two pronounced anomalous features [9–13]. Firstly, at low temperatures a new broad absorption peak appears in the frequency region between 350 cm21 and 550 cm21 . The frequency of its maximum increases with increasing doping; for optimally doped samples this feature seems to disappear. Secondly, at the same time as the peak forms, the infraredactive phonons in the frequency region between 300 cm21 and 700 cm21 are strongly renormalized. This effect is most spectacular for the oxygen bond-bending mode at 320 cm21 , which involves the in-phase vibration of the plane oxygens against the Y-ion and the chain ions. For strongly underdoped YBa2 Cu3 O6:55 with Tc < 50 K, this mode loses most of its spectral weight and softens by almost 20 cm21 . Although the additional peak and the related changes of the phonon peaks (phonon anomalies) start to develop above Tc , there is always a sharp increase of the peak magnitude below Tc [14]. Similar effects have also been reported for several other underdoped bilayer-compounds (see, e.g. Refs. [15,16]) and for hole-doped ladders in Sr142x Cax Cu24 O41 [17]. Van der Marel et al. have suggested [18] that the additional peak around 450 cm21 could be explained using a phenomenological model [19] of the dielectric response of superlattices with two superconducting layers (a bilayer) per unit cell. The model involves two kinds of Josephson

0038-1098/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved. PII: S0038-109 8(99)00377-4

366

D. Munzar et al. / Solid State Communications 112 (1999) 365–369

150

(a) σ( Ω-1 cm-1)

100

300K 75K 4K

(b)

T=300K

(c)

T=75K

(d)

T=4K

50 0 -50

-100

300K 75K 4K 200

ν(cm-1)

700 200

ν(cm-1)

700 200

ν(cm-1)

700 200

ν(cm-1)

700

Fig. 1. (a) Experimental spectra of the c-axis conductivity, s ˆ s1 1 is2 , of YBa2 Cu3 O6:55 with Tc ˆ 53 K. The thick and thin lines correspond to s1 and s2 , respectively. Experimental data (open circles) together with the fits obtained by using the present model (solid lines) for (b) T ˆ 300 K, (c) T ˆ 75 K, and (d) T ˆ 4 K. The dotted lines in (b), (c), and (d) represent the electronic contributions.

junctions: inter-bilayer and intra-bilayer. As a consequence, the model dielectric function exhibits two zero crossings corresponding to two longitudinal plasmons: the interbilayer and the intra-bilayer one. In addition, it exhibits a pole corresponding to a transverse plasmon which may be associated with the additional peak. Such an assignment has been recently confirmed by more quantitative considerations regarding the doping dependence of the peak position [20]. Nevertheless, the model in its original form fails to explain the spectacular anomaly of the 320 cm21 phonon mode (the loss of the spectral weight and the softening). In this article, we present an extension of the original model of van der Marel et al. [19] which allows us to explain not only the occurence of the additional peak but also the related phonon anomalies. The important new feature is that we take into account local electric fields acting on the ions participating in the phonon modes. As we show below, the phonon anomalies are then simply due to dramatic changes of these local fields as the system becomes superconducting. Let us introduce the model. The dielectric functionP is written as 1…v† ˆ 11 …v† 1 i12 …v† ˆ 1∞ 1 …i=v10 † k kjk …v†l=E…v†, where 1∞ is the interband dielectric function, jk are the induced currents, kl means the volume average, and E is the average electric field along the c-axis. The following currents have to be taken into account: the Josephson current between the planes of a bilayer, jbl ˆ 2i v 10 xbl Ebl , the Josephson current between the bilayers, jint ˆ 2i v 10 xint Eint , the current due to the oxygen bending mode at 320 cm21 , jP ˆ 2i v 10 xP Eloc P , and the current due to the other three infrared-active modes (at 280, 560, and 630 cm21 ) involving vibrations of apical oxygens and chain atoms, jA ˆ 2i v 10 xA Eloc A . Here xbl ˆ 2…v2bl =v2 † 1 Sbl v2b =…v2b 2 v2 2 ivgb †, xint ˆ 2 2 2 2 2…v2int =v2 † 1 Sint v2b =… Pvb 2 v 2 ivgb †, xP ˆ SP vP =…vP 2 v2 2 ivgP †, xA ˆ 3nˆ1 Sn v2n =…v2n 2 v2 2 ivgn † are the susceptibilities that enter the model. The plasma frequencies of the intra-bilayer and the inter-bilayer Josephson plasmons

are denoted as vbl and vint , respectively. We do not attribute any physical interpretation to the parameters vb and gb of the Lorentzian terms in the equations for xbl and xint that are designed solely to reproduce the featureless residual electronic background—including its pseudogap like suppression at low temperatures—in the narrow frequency-range of interest in a Kramers–Kronig consistent way. The response of the phonons is described by Lorentzian oscillators. Further, Ebl is the average electric field inside a bilayer, Eint is the average field between neighbouring bilayers, Eloc P is the local field acting on the plane oxygens (whose contribution to the 320 cm21 mode is known to be dominant [21]) and Eloc A is the local field acting on the ions located between the bilayers. The fields Ebl , Eint , Eloc P , and Eloc A can be obtained using the following set of equations: Ebl ˆ E 0 1

k axP Eloc P 2 10 1∞ 1∞

…1†

Eint ˆ E 0 2

bxP Eloc P 1 gxA Eloc A 1∞

…2†

Eloc P ˆ E 0 1

k ; Eloc A ˆ E 0 ; 210 1∞

…3†

2ivk ˆ jint 2 jbl , E…dbl 1 dint † ˆ Ebl dbl 1 Eint dint containing two additional variables, k and E 0 . The former represents the surface charge density of the copper–oxygen planes which alternates from one plane to the other whereas E 0 is the part of the average internal field E that is not due to the effects of k, xP and xA . The terms in Eqs. (1) and (3) containing k represent the fields generated by charge fluctuations between the planes. The terms in Eqs. (1) and (2) containing xP and xA represent the fields generated by the displacements of the ions. The values of the numerical factors a, b, and g (1.8, 0.8, 1.4) have been obtained using an electrostatical model [22]. The distances between

D. Munzar et al. / Solid State Communications 112 (1999) 365–369

367

Table 1 Values of the parameters used in the present computation. The temperatures are given in K, the frequencies and the broadening parameters in cm21 y

T

1∞

vbl

vint

Sbl

Sint

vb

gb

SP

S1

S2

S3

vP

v1

v2

v3

gP

g1

g2

g3

6.55 6.55 6.55

300 75 4

5.15 5.15 5.15

0 994 1205

0 0 220

1280 450 8.2

1000 170 2.7

680 810 6000

250000 140000 180000

1.3 1.3 1.3

0.056 0.056 0.056

0.087 0.087 0.087

0.32 0.32 0.32

390 390 390

290 285 284

553 563 564

647 655 656

21 9 9

22 14 12

29 20 15

16 7 3

6.75 6.75

260 4

5.15 5.15

0 1779

0 450

1700 13.8

1700 4.8

700 2400

220000 15000

1.3 1.3

0.056 0.056

0.200 0.200

0.30 0.30

390 390

296 288

582 589

631 646

13 2.5

20 16

15 25

25 20

6.45 6.45

250 4

5.15 5.15

0 949

0 150

310 560

240 480

860 520

120000 120000

1.3 1.3

0.060 0.060

0.100 0.100

0.42 0.42

400 400

286 280

553 556

650 654

34 42

24 24

30 20

15 5

corresponding to the apical oxygen modes at 560 cm21 and 630 cm21 and the increase of their asymmetry. The dotted lines in Figs. 1(b), (c), and (d) represent the results obtained after omitting the phonons in the fitted expresions (SP ˆ S1 ˆ S2 ˆ S3 ˆ 0:0). It appears that the plasmon peak collects the lost part of the normal-state spectral weight of the phonons. The remaining part (Spl ), however, belongs to the superconducting condensate. In the absence of the phonons and for Sbl ˆ Sint ˆ 0, the spectral weight of the d 2 peak at v ˆ 0 is Sd ˆ …p=2†10 …dbl 1 dint †v2bl v2int =…dbl v2int 1 dint v2bl † and Spl ˆ …p=2†10 …dbl dint =…dbl 1 dint ††…v2bl 2 v2int †2 =…dbl v2int 1 dint v2bl †. For vbl and vint as given in Table 1, we obtain Sd ˆ 1700 V21 cm22 and Spl ˆ 10000 V21 cm22 . This example demonstrates that the effects certainly should be taken into account in discussing the sum rules which have recently obtained renewed interest in the context of a possible change of the c-axis kinetic energy when the system becomes superconducting [24,25]. Our model allows us to explain the spectral weight anomalies by using simple qualitative arguments. Neglecting the feedback effects of the phonons and the residual electronic background, the electric fields Ebl and Eint are given by: Ebl ˆ …dbl 1 dint †1int E=…dbl 1int 1 dint 1bl †,

12

εint

εbl

8

0 4 -6 0

ν(cm-1)

|Eloc P/E|

6 εbl , εint

the planes of a bilayer and between the neighbouring  and dint bilayers are denoted by dbl (dbl ˆ 3:3 A)  (dint ˆ 8:4 A), respectively. Fig. 1 shows our experimental spectra of the c-axis conductivity of YBa2 Cu3 O6:55 with Tc ˆ 53 K which have been obtained by ellipsometric measurements. The technique of ellipsometry [12,13] provides significant advantages over conventional reflection methods in that (i) it is selfnormalizing and does not require reference measurements and (ii) 11 …v† and 12 …v† are obtained directly without a Kramers-Kronig transformation. Experimental details will be presented in a subsequent publication [14]. Also shown in Fig. 1 are the fits obtained by using the model explained above. The values of the parameters used are summarized in Table 1. Those used in computing the room-temperature spectrum have been obtained by fitting the experimental data (with vbl ˆ 0:0 and vint ˆ 0:0). Those used in calculating the 4 K spectrum have also been obtained by fitting the data, except for 1∞ , vP , and the oscillator strengths of the phonons (SP , S1 , S2 , S3 ) which have been fixed at the room-temperature values. The appearance of the additional peak and the anomalies already at temperatures higher than Tc may be caused by pairing fluctuations within the bilayers. Motivated by this idea, we have fitted the 75K spectra in the same way as the 4K ones allowing only the upper plasma frequency (vbl ) to acquire a nonzero value. We shall comment on this point below. Note that the values of the phonon frequencies are somewhat different from those obtained from a usual fit of the data (such as in Refs. [9– 13,21]) since the phonon susceptibilities represent response functions with respect to the local fields instead of the average field [23]. Fig. 1 demonstrates that our model is capable of providing a good fit of both the normal- and the superconducting-state data without any changes of the oscillator strengths of the phonons and without any change of vP . It reproduces successfully: (i) the appearance of the additional peak, its position, broadening and magnitude; (ii) the loss of the spectral weight of the peak corresponding to the oxygen-bending mode and the pronounced softening of this mode; (iii) the loss of the spectral weight of the peaks

0 700

Fig. 2. The approximate dielectric functions of the intra-bilayer and the inter-bilayer regions, 1bl and 1int defined in the text (solid lines). The room- and low-temperature spectra of the local field Eloc P acting on the plane oxygens (dashed and dotted lines).

368

D. Munzar et al. / Solid State Communications 112 (1999) 365–369

σ1( Ω-1 cm-1)

140 (a)

Tc=25K

(c)

Tc=25K

fit

exp.

σ1( Ω-1 cm-1)

0 250 (b)

Tc=80K

(d)

exp.

fit

0 200

ν(cm-1)

Tc=80K

700 200

ν(cm-1)

700

Fig. 3. Our experimental spectra of the c-axis conductivity of YBa2 Cu3 Oy with (a) y < 6:45 (Tc ˆ 25 K) and (b) y < 6:75 (Tc ˆ 80 K). (c) and (d) Fits of these spectra obtained by using the present model. The solid and dotted lines correspond to T ˆ 4 K and T ˆ 250 K, respectively.

Eint ˆ …dbl 1 dint †1bl E=…dbl 1int 1 dint 1bl †, where 1bl ˆ 1∞ 2 v2bl =v2 and 1int ˆ 1∞ 2 v2int =v2 . The low-temperature spectra of 1bl and 1int are shown in Fig. 2. In the frequency range of the oxygen bending mode, 1bl and 1int have opposite signs and similar magnitudes and the same holds for Eint and Ebl . As a consequence, the local field acting on the plane oxygens, which equals the average of the two fields Eint and Ebl (cf. Eqs. (1), (2), and (3)), can become rather small. The frequency range of the modes of the apical oxygen is close to the zero crossing of 1bl . Consequently, the local field acting on the apical oxygens, Eint , is rather small in this frequency region. It is the decrease of the local fields when going from the normal to the superconducting state which is responsible for the decrease of the spectral weight of the phonons. The room- and low-temperature spectra of Eloc P shown in Fig. 2 illustrate the above considerations. As the doping increases, the additional peak shifts towards higher frequencies due to the progressive increase of the plasma frequencies and it becomes broader and less pronounced since the residual background conductivities increase (see Figs. 3 and 1(a)). The anomaly of the oxygen bending mode is clearly linked to the formation of the additional peak. It is most striking for y < 6:55 (see Fig. 1(a)) while it is less pronounced for the y < 6:75 sample (see Fig. 3(b)). For the most strongly underdoped sample (y < 6:45), the additional peak and the phonon merge together forming a single highly-asymmetric structure (see Fig. 3(a)). These trends can be understood using arguments similar to those presented above (see the discussion related to Fig. 2) and are well reproduced by our model as demonstrated in Fig. 3.

Finally, we note that we do not find any indication for the additional peak in optimum doped and overdoped samples [12,13]. The proximity of the onset temperature of the anomalies and the onset temperature of the spin gap (T p ) observed in nuclear magnetic resonance experiments has provoked several speculations [11,16] that the anomalies are due to the coupling of the phonons to spin excitations. The success of our model in describing the data for Tc , T , T p rather indicates that in this temperature-range the intra-bilayer plasmon is already developed. This suggests that many of the electronic and possibly also structural anomalies starting below T p (see, e.g., Ref. [26]) may be caused by pairing fluctuations within the bilayers. In summary, we have extended the phenomenological model of van der Marel et al. involving inter-bilayer and intra-bilayer Josephson junctions by including phonons and local-field effects. Our model allows us to explain not only the additional broad peak around 450 cm21 but also the phonon anomalies, in particular the spectacular anomaly of the oxygen bending mode at 320 cm21 . Our results indicate that even the closely spaced copper-oxygen planes of underdoped bilayer cuprates are only weakly (Josephson) coupled in agreement with the “confinement” hypothesis of P.W. Anderson [7]. In addition, our results will be important for quantitative estimates of interlayer effects in the high-Tc cuprates. We suggest that the onset of the anomalies above Tc may be caused by pairing fluctuations within the bilayers. Our treatment of the local-field effects may find applications in studies of phonons in other layered systems with correlated electronic ground state. Acknowledgements We thank G.P. Williams and L. Carr for technical support at the U4IR beamline at NSLS and E. Bru¨cher and R. Kremer for SQUID measurements. We acknowledge discussions with M. Gru¨ninger, D. van der Marel, R. Zeyher, T. Strohm, and A. Wittlin. D.M. gratefully acknowledges support by the AvH Foundation.

References [1] M. Rapp et al., Phys. Rev. Lett. 77 (1996) 928. [2] K. Schlenga et al., Phys. Rev. B 57 (1998) 14518 and references therein. [3] Y. Matsuda et al., Phys. Rev. Lett. 75 (1995) 4512. [4] K. Tamasaku, Y. Nakamura, S. Uchida, Phys. Rev. Lett. 69 (1992) 1455. [5] P.J.M. van Bentum et al., Physica B 211 (1995) 260. [6] H. Shibata, T. Yamada, Phys. Rev. Lett 81 (1998) 3519. [7] P.W. Anderson, The Theory of Superconductivity in the HighTc Cuprates, Princeton University Press, Princeton, NJ, 1997. [8] V.J. Emery, S.A. Kivelson, O. Zachar, Physica C 282–287 (1997) 174 and references therein.

D. Munzar et al. / Solid State Communications 112 (1999) 365–369 [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]

C.C. Homes et al., Physica C 254 (1995) 265. J. Schu¨tzmann et al., Phys. Rev. B 52 (1995) 13665. R. Hauff et al., Phys. Rev. Lett. 77 (1996) 4620. C. Bernhard et al., Phys. Rev. B 59 (1999) 6631. C. Berhard et al., Phys. Rev. Lett. 80 (1998) 1762 and references therein. C. Bernhard et al., unpublished. T. Zetterer et al., Phys. Rev. B 41 (1990) 9499. A.P. Litvinchuk et al., Z. Phys. B 92 (1993) 9. T. Osafune et al., Phys. Rev. Lett. 82 (1999) 1313. D. van der Marel et al., private communication. D. van der Marel, A. Tsvetkov, Czech. Journ. of Phys. 46 (1996) 3165. M. Gru¨ninger et al., cond-mat/9903352. R. Henn et al., Phys. Rev. B 55 (1997) 3285. We have represented the ions by uniformly charged planes perpendicular to the c-axis and expressed the additional

[23]

[24] [25] [26]

369

electrical fields generated by the phonon displacements. The electrostatical calculations lead to expressions for the parameters a, b, g. The values of the charge densities of the planes have been estimated using the values of the effective ionic charges presented in Ref. [21]. In order to express the fields Ebl and Eint , the boundaries between the intra- and interbilayer regions have to be specified. We have identified them with the charged planes corresponding to the oxygens. In the absence of interlayer currents, the input frequencies would correspond to the LO-frequencies while the frequencies renormalized according to the model equations would correspond to the TO-ones. D.N. Basov et al., Science 283 (1999) 49. S. Chakrabarty, H. Kee, E. Abrahams, Phys. Rev. Lett. 82 (1999) 2366. D. Mihailovic, T. Mertelj, K.A. Mu¨ller, Phys. Rev. B 57 (1998) 6116.