- Email: [email protected]
Zone centre phonons in high Tc CaBi2Sr2Cu2O8
Solid State Communications, Vol. 68, No. 2, pp. 255-257, 1988. Printed in Great Britain.
0038-1098/88 $3.00 + .00 Pergamon Press plc
Z O N E C E N T R E P H O N O N S IN H I G H T,. CaBizSr2Cu208 H.C. Gupta* Department of Physics and Astronomy and Center for Fundamental Materials Research, Michigan State University, East Lansing, MI 48824, USA
(Received 27 May 1988 by S. Amelinckx) The zone centre phonons have been investigated in CaBi2Sr2Cu208 using radial and tangential force constants. It is found that the phonons due to Bi-O layers do not play an important role from the point of view of superconductivity. The calculation provides an information on the phonons which may be important for explaining the high temperature superconductivity. S U P E R C O N D U C T I V I T Y has been reported above 100K in C a - B i - S r - C u - O and T 1 - C a - B a - C u - O systems [1-4]. An important step in understanding the possible mechanism responsible for such a high superconducting transition temperature is the study of various phonons in these compounds. The C a - B i - S r Cu oxide system forms a new class of structure containing more than just corner sharing C u - O polyhedra. The key structural elements are a double layer of edge-sharing Bi-O octahedra with a 2-fold perovskitelike layer of copper oxide. Therefore, the interesting question addressed here is that the phonons associated with Bi-O octahedra are important for superconductivity or not, since the band structure calculations [5] indicate the presence of a conducting reservoir of carriers in the Bi-O planes, which themselves do not exhibit strong correlation effects. The crystal structure of high T, superconducting phase of CaBi 2Sr2Cu208 has been found to be consisting of a superlattice of orthorhombic subunits [6-8]. This orthorhombic subunit has a somewhat tetragonal symmetry with lattice parameters b ~ a = 3.83A ° and c = 30.89A ° [6]. Hybertsen and Mattheiss [5] approximated this pseudotetragonal subunit by a body-centered tetragonal structure for their electronic band structure calculations of CaBi 2S r z C u 2 0 8 . In the present work, therefore, the same body-centered tetragonal structure has been considered for the investigation of zone centre phonons whose primitive cell is shown in Fig. 1. The crystal structure as shown in Fig. 1 consists of 15 different kind of atoms. This has been necessitated to retain the Hermitian character of the developed
45 x 45 matrix, in which the various interatomic interactions accounted are given in Table 1. The choice of Cu-O (3) radial force constant is based on the average of the following values. Firstly, the strongest bond [9] in La 2. ,(Ba, Sr)xCuO 4 [Planer Cu-O(2)] has a bond stretching force constant lying between 120 and 176Kdyncm ~ whereas B r u n e t al. [10] found the Cu-O~ stretch force constant to be 85 Kdyn cm 1in La,.ssSr0.tsCuO 4. Further, the Cu(1)O(i) bond stretching force constant was 120Kdyn
* Permanent Address: Physics Department, Indian Institute of Technology, Hauz Khas, New Delhi! 10016, India.
Fig. 1. Primitive cell for body centered tetragonal CaBi2Sr2Cu208. O(1), 0(2) and 0(3) represent oxygens in the Bi, Sr and Cu planes respectively.
!
ca @ sr 0 8i @ cu 0 o
255
0
256
Z O N E C E N T R E P H O N O N S IN H I G H T,. CaBi2Sr2Cu208
Table 1. Force constants in the primitive unit cell
(F(g. 1) Atom pairs
Radial force constant (Kdyncm ~)
Cu-O(3) Bi O(1) Ca-O(3) Sr 0(3) Sr-O(2) Cu-O(2) Bi-O(2) Sr O(1) 0(3) 0(3)
125 125 50 50 50 40 30 25 20
cm ~ in the study of Cu-O vibrations of YBa2Cu30~ by Stavola et al. [1 l]. The Bi-O(1) radial force constant has been evaluated on the information that the breathing modes of BiO6 in BaPb~ ,Bi,O3 are in the range 560-600cm I [12]. The Ca-O(3), Sr-O(3) and St-O(2) radial force constants have been taken to be equal to La-On force constant [10]. The Cu-O(2) radial force constant has been taken on the lines of Cu(2)-O(1) bond stretching force constant as used by Stavola et al. [11]. The Bi-O(2) and Sr-O(l) radial i\3rce constants are scaled properly whereas 0(3) 0(3) radial force constant has been again taken equal to O~ O~ force constant [10]. The tangential force constants for each interatomic interaction has been deduced by dividing by 5 the corresponding radial t\)rce constants. The factor 5 has been estimated on the radial and tangential force constants ratio being equal to interatomic distance/Born Meyer parameter (0.345 A °). LJsing the force constants as described above, the zone centre phonons have been calculated. The fourteen degenerate values in order of magnitude are 25.14, 39.61, 81.79, 155.4, 163.8, 247, 401.4, 402.2, 495.5, 515.8, 587.2, 587.2, 645.2, 645.2cm t whereas the other fourteen values for which the atoms vibrate along z-axis are 41.4, 80.27, 111, 188.8, 188.9, 246.8, 351.7, 354.3, 373.7, 374.3, 434.2, 449.8, 449.8, 469.9cm ~ An agreement with the recent Raman scattering results [13] on superconducting crystals of Bi2(Srl ,Ca,.)~Cu20r can be observed. The eigen vector analysis of the frequencies indicate that the frequency 587.2cm ~ is due to the phonons in Bi O(1) plane only whereas the frequencies 373.7 and 374.3cm ~ are associated with the vibrations of Bi-O(l) plane with 0(2) oxygens [Bi-O6 octahedra]. It was found by changing the various force constants (other than those associated with BiO(1) and Bi-O(2)) that these modes remain almost unaffected, indicating that they do not play any impor-
Vol. 68, No. 2
tant role in the phonon dynamics of CaBi2Sr2Cu20 s system. This was further strengthened by a preliminary investigation of the finite wave vector phonon calculation where these modes did not exhibit much of a dispersion also. Therefore, this is very unlikely that the phonons due to Bi-O planes are important from the viewpoint of superconductivity. The eigen vector calculation corresponding to the degenerate frequency 449.8 cm ~indicated only the oxygen (0(3)-0(3)) displacements. Weber [9] and I [14] have earlier pointed out that large electron-phonon coupling is caused by O p orbitals of the conduction band involving specific O vibrations. This inference should be on a firm footing now when high Tc systems have been found without copper atoms [15] in Ba0.6K0aBiO~. Therefore, a common mechanism of superconductivity for both the bismuth and copper oxides could be postulated [16] if the oxide valley consisting of oxygen network is considered mainly responsible for the high superconducting transition temperature. Acknowledgements -- The author is grateful to Prof.
S.A. Solin and Prof. S.D. Mahanti for their encouragement. This work was supported by the NSF M R G under grant D M R 85-14154 and in part by the Center for Fundamental Materials Research of Michigan State University.
1. 2. 3. 4. 5. 6.
7. 8.
9. 10.
REFERENCES H. Maeda, Y. Tanaka, M. Fukutomi & T. Asano, Japan J. Appl. Phys. 27, L209 (1988). C.W. Chu, J. Bechtold, L. Gao, P.H. Hot, Z.J. Huang, R.L. Meng, Y.Y. Sun, Y.Q. Wang & Y.Y. Xue, Phys. Rev. Lett. 60, 941 (1988). Z.Z. Sheng, A.M. Hermann, A. El Ali, C. Almasan, J. Estrada, T. Datta & R.J. Matson, Phys. Rev. Lett. 60, 937 (1988). Z.Z. Sheng & A.M. Hermann, Nature 332, 138 (1988). M.S. Hybertsen & L.F. Mattheiss, Phys. Rev. Lett. 60, 1661 (1988). S.A. Shunshine, T. Siegrist, L.F. Schneemeyr, D.W. Murphy, R.J. Cava, B. Batlogg, R.B. von Dover, R.M. Fleming, S.H. Glarum, S. Nakahara, R. Farrow, J.J. Krajewski, S.M. Zahurak, J.V. Waszczak, J.H. Marshall, P. Marsh, L.W. Rupp, Jr. & W.F. Peck (to be published). J.B. Torrance, Y. Tokura, S.J. LaPlaca, T.C. Huang, R.J. Savoy & A.I. Nazzal (to be published). J.M. Tarascon, Y. Le Page, P. Barboux, B.G. Bagley, L.H. Greene, W.R. McKinnon, G.W. Hull, M. Giroud & D.M. Hwang (to be published). W. Weber, Phys. Rev. Lett. 58, 1371 (1987). T. Brun, M. Grimsditch, K.E. Gray, R. Bhadra, V. Maroni & C.-K. Loong, Phys. Rev. B35, 8837 (1987).
Vol. 68, No. 2 11.
12. 13.
ZONE CENTRE PHONONS IN HIGH T,. CaBi 2SrzCu20 8
M. Stavola, D.M. Krol, W. Weber, S.A. Shunshine, A. Jayaraman, G.A. Kourouklis, R.J. Cava & E.A. Rietman, Phys. Rev. B36, 850 (1987). S. Sugai, Japan J. Appl. Phys. 26 (Supplement 26-3) 1123 (1987). M. Cardona, C. Thomsen, R. Liu, H.G. von Schnering, M. Hartweg, Y.F. Yan& Z.X. Zhao, Solid State Commun. 66, 1225 (1988).
14. 15.
16.
257
H.C. Gupta, Solid State Commun. 65, 495 (1988). R.J. Cava, B. Batlogg, J.J. Krajewski, R. Farrow, L.W. Rupp, Jr., A.E. White, K. Short, W.F. Peck & T. Kometani, Nature 332, 814 (1988). T.M. Rice, Nature 332, 780 (1988).
0038-1098/88 $3.00 + .00 Pergamon Press plc
Z O N E C E N T R E P H O N O N S IN H I G H T,. CaBizSr2Cu208 H.C. Gupta* Department of Physics and Astronomy and Center for Fundamental Materials Research, Michigan State University, East Lansing, MI 48824, USA
(Received 27 May 1988 by S. Amelinckx) The zone centre phonons have been investigated in CaBi2Sr2Cu208 using radial and tangential force constants. It is found that the phonons due to Bi-O layers do not play an important role from the point of view of superconductivity. The calculation provides an information on the phonons which may be important for explaining the high temperature superconductivity. S U P E R C O N D U C T I V I T Y has been reported above 100K in C a - B i - S r - C u - O and T 1 - C a - B a - C u - O systems [1-4]. An important step in understanding the possible mechanism responsible for such a high superconducting transition temperature is the study of various phonons in these compounds. The C a - B i - S r Cu oxide system forms a new class of structure containing more than just corner sharing C u - O polyhedra. The key structural elements are a double layer of edge-sharing Bi-O octahedra with a 2-fold perovskitelike layer of copper oxide. Therefore, the interesting question addressed here is that the phonons associated with Bi-O octahedra are important for superconductivity or not, since the band structure calculations [5] indicate the presence of a conducting reservoir of carriers in the Bi-O planes, which themselves do not exhibit strong correlation effects. The crystal structure of high T, superconducting phase of CaBi 2Sr2Cu208 has been found to be consisting of a superlattice of orthorhombic subunits [6-8]. This orthorhombic subunit has a somewhat tetragonal symmetry with lattice parameters b ~ a = 3.83A ° and c = 30.89A ° [6]. Hybertsen and Mattheiss [5] approximated this pseudotetragonal subunit by a body-centered tetragonal structure for their electronic band structure calculations of CaBi 2S r z C u 2 0 8 . In the present work, therefore, the same body-centered tetragonal structure has been considered for the investigation of zone centre phonons whose primitive cell is shown in Fig. 1. The crystal structure as shown in Fig. 1 consists of 15 different kind of atoms. This has been necessitated to retain the Hermitian character of the developed
45 x 45 matrix, in which the various interatomic interactions accounted are given in Table 1. The choice of Cu-O (3) radial force constant is based on the average of the following values. Firstly, the strongest bond [9] in La 2. ,(Ba, Sr)xCuO 4 [Planer Cu-O(2)] has a bond stretching force constant lying between 120 and 176Kdyncm ~ whereas B r u n e t al. [10] found the Cu-O~ stretch force constant to be 85 Kdyn cm 1in La,.ssSr0.tsCuO 4. Further, the Cu(1)O(i) bond stretching force constant was 120Kdyn
* Permanent Address: Physics Department, Indian Institute of Technology, Hauz Khas, New Delhi! 10016, India.
Fig. 1. Primitive cell for body centered tetragonal CaBi2Sr2Cu208. O(1), 0(2) and 0(3) represent oxygens in the Bi, Sr and Cu planes respectively.
!
ca @ sr 0 8i @ cu 0 o
255
0
256
Z O N E C E N T R E P H O N O N S IN H I G H T,. CaBi2Sr2Cu208
Table 1. Force constants in the primitive unit cell
(F(g. 1) Atom pairs
Radial force constant (Kdyncm ~)
Cu-O(3) Bi O(1) Ca-O(3) Sr 0(3) Sr-O(2) Cu-O(2) Bi-O(2) Sr O(1) 0(3) 0(3)
125 125 50 50 50 40 30 25 20
cm ~ in the study of Cu-O vibrations of YBa2Cu30~ by Stavola et al. [1 l]. The Bi-O(1) radial force constant has been evaluated on the information that the breathing modes of BiO6 in BaPb~ ,Bi,O3 are in the range 560-600cm I [12]. The Ca-O(3), Sr-O(3) and St-O(2) radial force constants have been taken to be equal to La-On force constant [10]. The Cu-O(2) radial force constant has been taken on the lines of Cu(2)-O(1) bond stretching force constant as used by Stavola et al. [11]. The Bi-O(2) and Sr-O(l) radial i\3rce constants are scaled properly whereas 0(3) 0(3) radial force constant has been again taken equal to O~ O~ force constant [10]. The tangential force constants for each interatomic interaction has been deduced by dividing by 5 the corresponding radial t\)rce constants. The factor 5 has been estimated on the radial and tangential force constants ratio being equal to interatomic distance/Born Meyer parameter (0.345 A °). LJsing the force constants as described above, the zone centre phonons have been calculated. The fourteen degenerate values in order of magnitude are 25.14, 39.61, 81.79, 155.4, 163.8, 247, 401.4, 402.2, 495.5, 515.8, 587.2, 587.2, 645.2, 645.2cm t whereas the other fourteen values for which the atoms vibrate along z-axis are 41.4, 80.27, 111, 188.8, 188.9, 246.8, 351.7, 354.3, 373.7, 374.3, 434.2, 449.8, 449.8, 469.9cm ~ An agreement with the recent Raman scattering results [13] on superconducting crystals of Bi2(Srl ,Ca,.)~Cu20r can be observed. The eigen vector analysis of the frequencies indicate that the frequency 587.2cm ~ is due to the phonons in Bi O(1) plane only whereas the frequencies 373.7 and 374.3cm ~ are associated with the vibrations of Bi-O(l) plane with 0(2) oxygens [Bi-O6 octahedra]. It was found by changing the various force constants (other than those associated with BiO(1) and Bi-O(2)) that these modes remain almost unaffected, indicating that they do not play any impor-
Vol. 68, No. 2
tant role in the phonon dynamics of CaBi2Sr2Cu20 s system. This was further strengthened by a preliminary investigation of the finite wave vector phonon calculation where these modes did not exhibit much of a dispersion also. Therefore, this is very unlikely that the phonons due to Bi-O planes are important from the viewpoint of superconductivity. The eigen vector calculation corresponding to the degenerate frequency 449.8 cm ~indicated only the oxygen (0(3)-0(3)) displacements. Weber [9] and I [14] have earlier pointed out that large electron-phonon coupling is caused by O p orbitals of the conduction band involving specific O vibrations. This inference should be on a firm footing now when high Tc systems have been found without copper atoms [15] in Ba0.6K0aBiO~. Therefore, a common mechanism of superconductivity for both the bismuth and copper oxides could be postulated [16] if the oxide valley consisting of oxygen network is considered mainly responsible for the high superconducting transition temperature. Acknowledgements -- The author is grateful to Prof.
S.A. Solin and Prof. S.D. Mahanti for their encouragement. This work was supported by the NSF M R G under grant D M R 85-14154 and in part by the Center for Fundamental Materials Research of Michigan State University.
1. 2. 3. 4. 5. 6.
7. 8.
9. 10.
REFERENCES H. Maeda, Y. Tanaka, M. Fukutomi & T. Asano, Japan J. Appl. Phys. 27, L209 (1988). C.W. Chu, J. Bechtold, L. Gao, P.H. Hot, Z.J. Huang, R.L. Meng, Y.Y. Sun, Y.Q. Wang & Y.Y. Xue, Phys. Rev. Lett. 60, 941 (1988). Z.Z. Sheng, A.M. Hermann, A. El Ali, C. Almasan, J. Estrada, T. Datta & R.J. Matson, Phys. Rev. Lett. 60, 937 (1988). Z.Z. Sheng & A.M. Hermann, Nature 332, 138 (1988). M.S. Hybertsen & L.F. Mattheiss, Phys. Rev. Lett. 60, 1661 (1988). S.A. Shunshine, T. Siegrist, L.F. Schneemeyr, D.W. Murphy, R.J. Cava, B. Batlogg, R.B. von Dover, R.M. Fleming, S.H. Glarum, S. Nakahara, R. Farrow, J.J. Krajewski, S.M. Zahurak, J.V. Waszczak, J.H. Marshall, P. Marsh, L.W. Rupp, Jr. & W.F. Peck (to be published). J.B. Torrance, Y. Tokura, S.J. LaPlaca, T.C. Huang, R.J. Savoy & A.I. Nazzal (to be published). J.M. Tarascon, Y. Le Page, P. Barboux, B.G. Bagley, L.H. Greene, W.R. McKinnon, G.W. Hull, M. Giroud & D.M. Hwang (to be published). W. Weber, Phys. Rev. Lett. 58, 1371 (1987). T. Brun, M. Grimsditch, K.E. Gray, R. Bhadra, V. Maroni & C.-K. Loong, Phys. Rev. B35, 8837 (1987).
Vol. 68, No. 2 11.
12. 13.
ZONE CENTRE PHONONS IN HIGH T,. CaBi 2SrzCu20 8
M. Stavola, D.M. Krol, W. Weber, S.A. Shunshine, A. Jayaraman, G.A. Kourouklis, R.J. Cava & E.A. Rietman, Phys. Rev. B36, 850 (1987). S. Sugai, Japan J. Appl. Phys. 26 (Supplement 26-3) 1123 (1987). M. Cardona, C. Thomsen, R. Liu, H.G. von Schnering, M. Hartweg, Y.F. Yan& Z.X. Zhao, Solid State Commun. 66, 1225 (1988).
14. 15.
16.
257
H.C. Gupta, Solid State Commun. 65, 495 (1988). R.J. Cava, B. Batlogg, J.J. Krajewski, R. Farrow, L.W. Rupp, Jr., A.E. White, K. Short, W.F. Peck & T. Kometani, Nature 332, 814 (1988). T.M. Rice, Nature 332, 780 (1988).