VOLUME 59 Nos.10-12 ISSN 0022-3697

1998 OCTOBER-DECEMBER

EDITORS

Arun Bansil

Boston

Yasuhiko Fujii

Tokyo

Robert N. Shelton

Davis

...........iaI.,!.l.....;9~!~~~§) SPECIAL ISSUE

Spectroscopies in Novel Superconductors

GUEST EDITORS

.-\ . BX,\SIL R. MARKIEWICZ, S. SRIDHAR, D. LlEBENBERG

~ PERGAMON

-J. Phys. Oelll Solids Vol 59, No. 10-12, pp. 1831 -1 834, 1998

0022-3697/98/$ - see fronl maller ~ Pergamon PH: 80022-3697(98)00121-8 © 1998 Elsevier Science LId. All righlS reserved

MICROSCOPIC THEORY OF THE LOCAL DYNAtvIICS IN 2-1-4 HIGH-Tc SCPERCO~DUCTORS

\1. D_ K..-\PL a, b.", and G. O. ZIMMERMAN" 'Ph) 0; Dep:mrnenl. Bosto n Ln iversity. 590 Commonwealth Ave.. Boston. MA 02215, SA

' Chemt tr) Depar!ment. Simmons College, 300 The Fenway, Boston, MA 02115 , USA

Abstract-Tile local Jahn-Teller dynamics of the CU06 octahedra are explored using the conventional Jahn - T ell eT effe t approach. The vibronic interaction of the symmetrized and hybridized electronic states with the J ubI : degenerate vibrations leads to four local minima of monoclinic symmetry. These results are in agreemen t with experimental neutron scattering data. While the obtained local minima and their combinations could be used to represent the overall crystal structure, they are different from the previously calculated free­ene rgy minima of the crystal. © 1998 Elsevier Science Ltd . All rights reserved

Keywords: D . superconductivity, local dynamics, Jahn-Teller effects

Several investigations have centered on the micro­

scopic theory of structural phase transitions in the 2-1-4

high-Tc superconductors [1-7]. The investigations, based

on the cooperative pseudo-Jahn-Teller effect theory

taking into account experimental data and symmetry

group analysis, answered the following questions: (1)

what is the symmetry and structure of local di stortions

around the Cu ion. and how they are connected to the

"tilting" -mode and other crystal lattice modes; (2) how

does the soft "tilting" -mode affect the electronic states;

(3) how are the electronic states involved in the mechan­

ism of the structural transitions?

Very important experimental data about the the local

structure of the systems under consideration ha ve become

available [8). Using the pair distribution function data

obtained in the experiments on neutron powder diffrac­

tion for La2_,Ba,Cu04 , Billinge et al. [8) showed that in

contrast to the predictions ofthe crystal structure models,

the CuO 6 octahedra do not change their ti It direction in

different crystal phases. The long-range structure of the

high temperature phases can be considered as linear

superpositions of the [11 D)-direction tilts. (The [110]

designation may change depending on the authors'

choice of the principal axes.)

We show below that the experimental data are in

agreement with the earlier developed microscopic

theory. Our numerical calculations confirm that the

local adiabatic Cu06 potential does have four minima

phenomenologically suggested in Ref. [8]. The symmetry

of each of the minima is monoclinic, however, the

increase in the temperature leads to the tunneling aver­

aging between nearest-neighbor minima [at the phase

transition from low temperature tetragonal (LIT) phase

to the low temperature orthorhombic (LTO) phase] and

"Corresponding author.

then between all four minima [at the phase transition from

the LTO phase to the high temperature tetragonal (HIT)

phase]. The long range structures are the combinations of

these averaged local distortions.

The crystal Hamiltonian considered earlier [5-7] can

be written as:

(I)

where the first term describes the elastic energy of the

crysta1 strained in the structurally ordered phase and the

electron-strain interaction, H ph is the phonon energy, and

the next two terms are the electron-phonon interaction

and the crystal field energy splitting.

Because we are interested in the local dynamics of the

CU06 octahedra, we will initially ignore the crystal phonon

dispersion, and in terms of the electron-vibration interac­

tion, we will deal with the local distortions Qm instead of

using the creation and annihilation phonon operators. With

this approach, the second and third terms are:

Hill = ~K (Qm2 + Q1Il2) + V(E',"QIn + E"'r>'")2.3 2 E E, E,. x E, y ':.!E,.

+ G (J1Il(n"12 _ Q1II2) +G (J11In"I QIII (2)I z 'L.£s Ey 2 x 'L.E:, E,.

where the first term is the elastic energy of the CU06

clus1er, and the last three terms correspond to the linear

and quadratic electron-vibration interaction, KE is the

elastic constant of the E g(D 4") di stortions, V, Gland G 2

are the linear and quadratic vibronic constants. The

electronic operators E~:Y' 0';' and 0'; are represented by

the matrices:

(3)

1831

1832 M. D. KAPLAN and G. O. ZIMMERMAN

Fig. 1. Perspective view of the four lowest adiabatic potentials as a function of Q, and Q,.with KE = 3, G 1= 0.5, G 2 = 1.5, V = 3, ~ = 1 and ~ I = 0.5. .

Fig. 2. Perspective view of the four lowest adiabatic potentials as a function of Q,. and Q)' with KE = 3, G 1= 1.5, G 2 ':" 0.5, V = 3, ~ = I and ~ I =0.5. Note the 45° rotation of the minima with respect to Fig. I.

1833 Microscopic theory of the loca l dynamics in 2- 1-4 high-T, superconductors

-2 . 5

Fig. 3. View along the Q,-ax is of the fi rs t excited adiabatic potential with "t' = 3, G I = 0.5, Gz = 1.5, V = 3, D, = I and D,I =0.5.

of elec tronic func tions

where the ground 'lr8" -state is separated by a D, I-gap

from the firs t excited 'lr tI ,,, -state, above which is the next

The Hamiltonia n (2) a nd operators (3) are written as a set excited sta te 'lri:' separated from 'lrtI,., by a 2Ll-gap. (Fo r

- 2

-2 .5

Fig. 4. View along the Q,.-axis of the first excited adiabatic potential with "E =3, G I = 1.5 , Gz = 0.5, V = 3, D, = I and D, I =0.5.

1834 M. D. KAPLAJ"l and G. O. ZIl\llvIERMAN

simplicity, we ignore here the 'Ii B,., -excited statr; betw 'en

'Ii A" and 'Ii E, because the results and conclusions are

virtually unchanged by thi s omission. Thi s can be

confirmed qualitatively and quantitati'ely by direct

calculations.)

Samples of the calculations are ho\\n in Figs l--l

which show the adiabatic potentials. The ,·alue of the

parameters was chosen so . s to illustrate the existence

of the four minima III the adiabatic potential ,

although those parameters will have to be adjusted to

describe a real crystal. These figures clearly support our

conc lu~ ion s .

REFERENCES

I. Pic 'c • \\ .. E .. Cohen, R. E. and Krakauer, H., Phys. Rev. LeI/. . 991. 67. 228 .

2. :-'!ark.ie,-\ icz . R. S .. Ph,sica C, 1993,210, 235. 3. :-'!arkie \\ icz. R. S .. Ph.'"-licu C. 1992,200, 65. -1. Flach. S .. Plakida. )i . M. and Aksenov, V. L., Int. J. Mod.

Ph.'·s. 8.1 990.4.1955 . · 5. Kaplan , ?vl. D .. iVlaterials Theory and Modelling, MRS,

1'.291 , 1993, p. 223. 6. Kaplan, M. D. , in Modern Problems, ed . A. A. Kiselev .

Leningrad University, 1989, pp. 184-217 . 7 . Kaplan , M. D., Physica C, 1991 , 180, 351. 8. Billinge, S. 1. L.. Kwei , G. H. and Takagi , H., Phys. Rev.

Lett., 1994, 72, 2282.

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