- Email: [email protected]
Pyroelectric and piezoelectric effects in single crystals of YBa2Cu3O7-δ
~Solid State Communications, Vol. 75, No. 4, PP. 319-323, 1 9 9 0 . Printed in Great Britain.
0038-1098/9053.00+.00 Pergamon Press plc
PYROELECTRIC AND PIEZOELECTRIC EFFECTS IN SINGLE CRYSTALS OF YBa2Cu307-8 D. Mih~ovi6 Institut Josef Stefan Jamova 39, 61111 Ljubljana, Yugoslavia and Institute for Polymers and Organic Solids University of California, Santa Barbara, CA 93106 and Alan J. I-leeger Institute for Polymers and Organic Solids University of California, Santa Barbara, CA 93106 (Received 12 April 1990 by A.A. Maradudin) A transient voltage is observed between c-axis contacts of a YBa2Cu3OT-8 (~)=0.1) single crystal upon application of a heat pulse (either generated thermally or by laser absorption). A similar transient voltage appears when stress is applied to tl2_esample. We have not been able to observe either effect in insulating YBa2Cu307-6 (~-0.7). We suggest that the thermally-induced voltage is a pyroelectric effect and that the stress-induced voltage is a piezoelectric effect, implying the existence of a macroscopic polarization in the material. We discuss possible mechanisms for charge symmetry breaking (involving the apex 0(4) oxygen atom) which would giverise to a macroscopic polarization along z in the YBa2Cu307 structure.
a)
The possibility of ferroelectric (or antiferroelectric) behavior in high-Te materials is suggested by the wellknown tendency of the perovskite structure to distort and form such ordered phases. Moreover, the connection between incipient (anti)ferroelectricity and superconductivity has been made by a number of authors. I-3 However, the crystal structure of YBa2Cu307 as determined by X-ray and neutron diffraction measurements has been reported to be centrosymmetric and, therefore, not ferroelectric. Recently, there have been a number of suggestions that carrier injection leads to local distortions such that both microscopic and macroscopic symmetry breaking might be observed in these materials. 4-7 In this paper, we report the observation of a transient voltage across the z-axis of a YBa2Cu3OT-5 (~=0.1) single crystal upon heating with thermal or laser pulses as well as a transient voltage across the z-axis resulting from the application of mechanical stress. We conclude that the measured voltages can be explained as resulting from a change in macroscopic polarization as a result of the application of a heat pulse, AV-(~P/~I')AT, or a stress pulse, AV-(3P/~Z)AZ, where T is the temperature and Z is the stress; i.e. the pyroelectric and piezoelectric effects, respectively. The experimental results, therefore, imply the existence of a macroscopic polarization in YBa2Cu307. The geometry of the heating experiment is shown in Figure 1. The sample was a single crystal of YBa2Cu307-5 (5=0.1), with dimensions approximately 0.5x0.5x0.5 mm; the crystal was superconducting with Tc=90K and ATe =0.3K, as determined by 4-probe resistance measurements. We measured both the voltages between c-axis contacts perpendicular to the CuO2 planes (V12 and V34) and the
VI
_I
Laserspot
1 3 b)
X Y
4 I_ Vl LI / ~ Heater
1 3
Iv2
,, / /
/
4
Figure 1: Sample geometry used in the experiments; the z axis corresponds to the c-axis of the crystal: a) laser beam incident on the y-z (or x-z) surface; b) a nichrome heater is mounted near the sample surface. 319
320
PYROELECTRIC AND PIEZOELECTRIC
voltages between a-axis (or b-axis) contacts (Vt3 and V24). The two-probe resistance, measured at room temperature across the c-axis of the sample, was approximately lf~. The laser heating experiment (514.5 rim) was performed either by focussing the beam into a spot much smaller (30gin diameter) than the sample or by exposing the sample to an expanded beam with diameter larger than the sample dimensions (Figure la). Alternatively, the heat pulse was generated by a thin, small nichrome heater wire placed near, but not in contact with, the sample (Figure lb). The latter method of direct heating was used to demonstrate that the induced voltages are not photovoltaie in origin, but thermal. The voltage was measured with a high-impedance nanovoltmeter or a digital oscilloscope. The contacts were made using gold paste with gold wires connecting to the gold-coated leads of a semiconductor device package. The YBCO crystal was attached to the package with GE varnish. Figure 2 shows that when the 30gin diameter laser beam was turned on or off (Figure 2a), a transient voltage
a)
l
10s -100 pv _
#/--\
b) A
Time
~
c)
o ;>
EFFECTS IN SINGLE CRYSTALS
Vol. 75, No. 4
was observed (Figure 2b) across the z-axis contacts, VT = V12 - 1001.tV; the voltage is negative when the laser is turned on and positive when the laser is turned off. If the laser beam was not focussed exactly in the center between the two contacts, we also measured a steady thermopower voltage due to the temperature difference, TI - T2, between the two Au-YBa2Cu307-5 contact junctions in addition to the transient voltage. As expected, when scanning the focussed spot across the sample along the z-direction, the thermoelectric voltage varied linearly with distance across the sample and was zero with the beam focused precisely in the middle. A similar voltage was measured across all z-axis contacts (V34,V23 and V14). However, neither the sign nor the magnitude of the transient signal change with the position of the laser beam along in the x-z surface. Thus, the transient voltage along the z-axis results from a temperature change and not from a thermal gradient. Although steady thermoelectric voltages V13 or V24 were measured (corresponding to temperature differences AT 13=T l-T3 and AT24=T2-T4, respectively), no transient voltage was observed between contacts I and 3 or 2 and 4 along the x (or y) direction. The latter observation is
particularly important for it demonstrates that the signal does not arise from the contacts. It also demonstrates that the thermally-induced voltage appears only along the c-axis direction. Additional evidence of the different origins of the transient voltage and the thermoelectric voltage comes from the laser intensity dependence shown in Figure 3. With the laser focused near one contact (such that there is a temperature difference AT12 between contacts 1 and 2) the thermoelectric voltage shows superlinear dependence with AT12 proportional to IL(1"7+0"l), whereas the transient voltage is sub-linear, VT proportional to IL(0.7(~-0'I). From the time dependence of the transient signal (Figure 2b), we conclude that the voltage is proportional to the temperature derivative, +3/3T, of a macroscopic 35O
Time
i i t
'
IOOO
400 s
30O
i
''''1
....
.....
r-
I'' -
' ' I ' ' ' ' I ' I'[ 2' ]' [] 'I' ''' ''' '
~.]oo
250 - ; 200 o b J3
_~ ~5o
,6"
10
/."'a / I0
1oo
0 J
Figure 2: Voltage appearing across the sample (between contacts separated along z) upon exposure to the laser beam: a) the timing diagram of the laser; b) the transient voltage V12; c) thermoelectric voltage, St3, as a function of time measured with a focussed laser spot midway between contacts 1 and 2; d) derivative of the thermopower, S13 with respect to time; e) heater current timing; f) transient voltage due to thermal pulse from the heater wire (note the difference in time scale).
JD h
100
./Of
,/
50
/ ".-'O Dj
Laser intensity (roW)
-e/
J ~ e
,/~gl U"
¢
d D"
0 0
5
10
15
20
25
30
35
Laser intensity (roW) Figure 3: The thermoelectric and transient voltages as a function of laser intensity; solid dots represent the transient pyroelectric voltage; open squares represent the thermoelectric voltage. The inset shows a log-log plot of the same data.
Vol. 75, NO. 4
PYROELECTRIC AND PIEZOELECTRIC
thermodynamic variable, such as the polarization per unit volume, t'. "l'nis is demonstrated by comparing the calculated derivative of the thermoelectric voltage V13 (which is proportional to ATI3) shown in Figure 2d with the measured transient voltage VT=V12 shown in Figure 2b. The rise and fall decay times of the transient voltage signal are determined by the thermal response of the crystal. The data shown in Figure 2 were obtained with the sample at room temperature. When the sample is cooled, the time constant of the pyroelectric voltage changes since the thermal conductivity and specific heat change the thermal time constant of the system. Cooling the sample below T o we observe only the thermoelectric voltage due to the gold contacts since the thermopower of the supereonductior is zero. As expected, the sign of the thermoelectric voltage is reversed below To, since in the normal state the thermopower of YBa2Cu307 is opposite in sign and larger in magnitude than that of gold. When we laser-heated the sample with sufficient power to raise the temperature above To the pyroelectric voltage reappeared. Figure 2f shows the transient voltage measured when using the nichrome wire heater as the heat source. The principal difference between direct heating and laser pulse heating is the time-constant: the thermally-induced voltage shows no characteristic time scale for the decay of the transient voltage since the time scale is dominated by the thermal cooling characteristic of the heater wire. The observation of a transient voltage using the wire heater also excludes artifacts originating from the photoelectric effect (which cannot be eliminated with laser excitation), and unambiguously links the induced voltage to the temperature derivative, 0/0T. Having eliminated possible artifacts due to contacts and photo-effects, we suggest that the general characteristics of the transient voltage imply the existence of the pyroelectric effect in YBa2Cu307-8: an induced voltage VT ~ c~ 0~/0T where i~ is the macroscopic polarization per unit volume which is directed along ~ (the unit vector along the c-axis). Since observation of a pyroelectric effect in a high T c metal is of special interest and since such an effect would be symmetry forbidden if the structure were truly centrosymmetric, we present additional evidence for the existence of a macroscopic polarization; specifically, we fred that YBa2Cu307 is piezoelectric. To attempt to detect a piezoelectric response, we mounted a single crystal of YBa2Cu307 in a press between two metal dies. The contacts to the sample were made with indium so as to exclude possible transient voltages due to contact slippage when a mechanical shock is applied. Upon giving one of the dies a sharp shock, we observed a piezoelectric voltage between the two c-axis contacts, as shown in Figure 4. No such voltage was observed from either a YBa2Cu306.1 ceramic sample or from a YBa2Cu306.3 single crystal. The sign of the voltage changed, depending on whether pressure was applied to the sample (decrease in volume) or relieved (increase in volume). This observation of both a piezoelectric response and a pyroelectric response provide evidence for the existence of a macroscopic polarization along the c-axis in YBa2Cu3OT. A similar effect, although on a different time scale, was recently reported by Kennedy at al7, who stressed pellets of
EFFECTS IN SINGLE CRYSTALS
4
-
> E o
3
>O
1 -
2
321
-
JaLJ,JJal,..~,d,u,, LId,~,,
0 ~ =l
'[ Ij'"111'v"ll"[r'[IWTt~'~l]')'~'TIl"~rI'T'lP~. ,
0
,
,
I
200
,
,
,
]
400
,
,
,
I
,
,
,
600
I
800
,
,
I000
Time (ms) Figure 4: The transient voltage between surfaces normal to the c-axis obtained when a single crystal of YBa2Cu307 is given a mechanical shock. ceramic YBa2Cu307 using a piezoelectric transducer. Although possible artifacts which could give rise to the observed voltage were considered, they could not find a satisfactory explanation for the origin of the effect based on the proposed centrosymmetric structureof the material. Because the sample is conducting, the magnitude of the polarization is difficultto estimate with accuracy. The thermally induced voltage across a pyroelcctric (piezoelectric)insulator would be of the form AV
= d A P = (d/co)ACt
where d is the sample thickness, eo is the permittivity of free space, AP is the change in the polarization and Aa is the corresponding change in the surface charge density resulting from the change in temperature (or stress). When the material is a conductor with resistivity p and dielectric constant ~, the pyroelectric (piezoelectric) capacitor is shunted by the low sample resistance. As a result, the external voltage is decreased by the ratio Zp/'CT where Xp=reop (i.e. the time needed for relaxation of a nonuniform charge distribution in a conductor) and '~Tis the characteristic time over which the temperature (or the stress) is changing: AVext = ('Cp/X,r)d.AP = (Xp/'r,.r)d(Ac/eo) For YBa2Cu307, the c-axis resistivity is of order 1 ~-cm [10 "12 esu], so that Xp<10-10s (corresponding to K-100). Since the characteristic time for AT is of order 1 second (see Figure 2), Ao > 2x10 -7 Coulombs/cm 2 = 1012 electron charges per cm2, and AP>Ao/eo = 2x10 -2 cm -2 [4~Ao (esu) - 6xl03 esu] along ~. This relatively large value for AP (which is presumably still small compared to P) is consistent with ferroelectfic ordering; e.g.in BaTiO3, P=l.6xl0-1cm-2, [7.8x104 esu cm-2]. The smaller p along ~or 5 crystal axes will reduce AVext proportionately, and may explain why we don't observe an effect in these two directions. In order to observe the pyro- and (piezo-)electric effects, the distortions which lead to the polarization must be static with the following features:
322
PYROELECTRIC AND PIEZOELECTRIC
(i) an electric dipole moment directed along the c-axis within the unit cell; (ii) long-range order of the dipole moments to give a macroscopic polarization. Fluctuations involving a large number of individual dipole moments (or clusters of dipole moments) would lead to thermally induced and stress induced voltage noise. To create a dipole moment along the c-axis, random oxygen disorder in the Cu-O chains of YBa2Cu307-8 would not be sufficient. An extra oxygen in an "unoccupied chain site" (an O(5) site defect) would create a local dipole moment along g (or B) but not along ~. A number of recent experiments6, 8-10 suggest an anharmonic potential for the apex 0(4) site. This suggests that a possible symmetry breaking displacement of the two 0(4) ions within the unit cell could occur, perhaps in conjunction with such an 0(5) site defect. The asymmetric displacement of the 0(4) ions would break the inversion symmetry and, thereby, create a microscopic dipole moment with a component along ~. Since ordering of such defect sites occurs naturally along twin boundaries in YBa2Cu307, a macroscopic polarization could result. However, the absence of an observed transient voltage along the x (or y) direction in our experiments, and the relatively large value inferred for AP (<
Vol. 75, NO. 4
EFFECTS IN SINGLE CRYSTALS
holes in the new unit cell are on opposite planes and on opposite corners of the new cell, their sites related by a (1,1,1) vector (in the notation of the undistorted cell). As a result, the dipole moments add; this alternation also favors ordering of the successive CuO2 planes so as to obtain a macroscopic polarization directed along ~. The resulting smacture can be thought of as a lattice of hole-bipolarons (a polaron on each of the two planes in the enlarged unit cell) modulating the CuO2 plane slructure, with the hole density approximately equal to the optimal value of 0.25 holes per
e.~T'-~ 4 •
a)
0
•
0
_
~ : •
4 •
•
0
•
0
~ d 0
• •
0
~-CuO planes ~
CuO Chains
~....--g--._..~._~.. ~ _
• I
~
-
-
•
0
4 CuO Planes
2a
=
b)
-
T 0
A
•
0
V •
~
~ -
0
•
0
A
y
~
A
[I--
CuO
~
ClIO
V •
i
0
~
_/-'=---~-
Chains
"~- CuO
-- I 2a
~
Planes
-I
,0(2)
X'
c)
X
~..~- -~y, Y Figure 5: Schematic structural diagrams (the arrows designate the direction of distortion of the apex oxygen): a) In-plane anti-distortions with correlated hole occupancy and asymmetric 0(4) (with respect to the CuO2 planes) displacement so as to give a caxis polarization; the phase of the distortion is such that the nodes are on the Cu sites (designated as open circles), corresponding to holes predominantly on oxygen sites (designated as flied circles); b) Same as a) except the holes are on Cu sites and the nodes are on O sites; c) Schematic diagram of two planes with correlated hole occupancy so as to give dipole moments (arrows) associated with hole-occupied sites (solid circles) which add to yield a macroscopic polarization. The sites without arrows (open circles) may in fact have reduced charge density and a smaller reversed dipole moment. (Note the rotation of axes.)
Vol. 75, NO. 4
PYROELECTRIC
AND PIEZOELECTRIC
plakette. More generally, the holes would be expected to delocalize with partial occupancy on the "unoccupied" sites in Figure 5c. This model of strongly correlated holes coupled to intra-plane anti-distortions is, of course, not the only way to construct a macroscopic polarization. One could start with an essentially uniform hole charge density in the CuO2 planes and invoke a uniform ferroeleetric asymmetric displacement of the apex oxygens. Although X-ray and neutron diffraction studies have concluded that the YBa2Cu307 structure is cenmasymmetric, the pyroelectric and piezoelectric phenomena reported here imply the existence of small symmetry breaking distortions. Since there are a number of recent experiments 6,12 which are sensitive to local deformations of the lattice and which show local symmetry breaking upon the introduction of holes, it would be interesting to re-examine the YBa2Cu307 structure in finer detail.
EFFECTS
IN SINGLE CRYSTALS
323
We conclude that YBa2Cu307 appears to be both pyroeleetric and piezoelectric, implying the existence of a macroscopic polarization per unit volume (ferroelectrie) directed along the e-axis. We have proposed a model in which the small symmetry breaking distortions which lead to the macroscopic polarization can be thought of as a lattice of hole-bipolarons modulating the CuO2 plane structure; it would seem that ff correct, the implied hole-bipolaron lattice might be relevant to pairing in the superconducting state. Acknowledgement: We would like to thank G. Collin for kindly providing the YBa2Cu3OT-6 crystals and C. Foster, K. Voss and L. Forro for many stimulating discussions. This research was supported in part by a grant from the Office of Naval Research, N00014-83-K-0450. D.M. would like to acknowledge support from the Fulbright Program and from CEC grant no. CII 0568-C.
References 1. 2. 3. 4. 5.
6. 7.
A.R. Bishop, R.L. Martin, K.A. Muller and Z. Tesanovic, Zeitsehrift fuer Physik B 76, 17 (1989). A. Bussmann-Holder, A. Simon and H. Buttner, Physical Review B ~ 207 (1989). J. Schreiber and P. Haertwich (to be published). Y.H. Kim, C.M. Foster, A.J. Heeger, S. Cox and G. Stucky, Physical Review B ~ 6478 (1988). C. Taliani, R. Zamboni, G. Ruani, F.C. Matacotta and K.I. Pokhodnya, Solid State Communications, ~ 487 (1988). D. Mihailovi6 and C.M. Foster, Solid State Communications 74. 753 (1990). R.J. Kennedy, W.G. Jenks and L.R. Testardi, Bulletin of the American Physical Society 35, No. 3, 424 (1990), Phase Transitions, (in press, 1990).
8.
H. Ritschel, L. Pintschovius and W. Reichardt, Physica C, 1~2-164, 17-5 (1989). S.D. Conradson and I.D. Raistrick, Science, 243, 9. 1340 (1989). 10. S.L. Drechsler, N.M. Plakida, V.L. Aksenov, T. Galbaatar, R. Rakauskas, and S. Stamenkovic, Proceedings of the International Conference on HighTc Thin Films and Single Crystals, Wonu Scientific (,o be published). 11. a. J.B. Torrance, A. Bezinge, A.L Nazzal and S.S.P. Parkin, Physica C, 162-164, 291 (1989). b. Y. Tokura, J.B. Torrance, T.C. Huang and A.L Nazzal, Physical Review B ~ , 7156 (1988). 12. T. Egami in Oxygen Disorder Effects in High-Tc Superconductors, Ed. by J.L. Mran-Lopez and I.K. Sc huller (Plenum, 1990).
0038-1098/9053.00+.00 Pergamon Press plc
PYROELECTRIC AND PIEZOELECTRIC EFFECTS IN SINGLE CRYSTALS OF YBa2Cu307-8 D. Mih~ovi6 Institut Josef Stefan Jamova 39, 61111 Ljubljana, Yugoslavia and Institute for Polymers and Organic Solids University of California, Santa Barbara, CA 93106 and Alan J. I-leeger Institute for Polymers and Organic Solids University of California, Santa Barbara, CA 93106 (Received 12 April 1990 by A.A. Maradudin) A transient voltage is observed between c-axis contacts of a YBa2Cu3OT-8 (~)=0.1) single crystal upon application of a heat pulse (either generated thermally or by laser absorption). A similar transient voltage appears when stress is applied to tl2_esample. We have not been able to observe either effect in insulating YBa2Cu307-6 (~-0.7). We suggest that the thermally-induced voltage is a pyroelectric effect and that the stress-induced voltage is a piezoelectric effect, implying the existence of a macroscopic polarization in the material. We discuss possible mechanisms for charge symmetry breaking (involving the apex 0(4) oxygen atom) which would giverise to a macroscopic polarization along z in the YBa2Cu307 structure.
a)
The possibility of ferroelectric (or antiferroelectric) behavior in high-Te materials is suggested by the wellknown tendency of the perovskite structure to distort and form such ordered phases. Moreover, the connection between incipient (anti)ferroelectricity and superconductivity has been made by a number of authors. I-3 However, the crystal structure of YBa2Cu307 as determined by X-ray and neutron diffraction measurements has been reported to be centrosymmetric and, therefore, not ferroelectric. Recently, there have been a number of suggestions that carrier injection leads to local distortions such that both microscopic and macroscopic symmetry breaking might be observed in these materials. 4-7 In this paper, we report the observation of a transient voltage across the z-axis of a YBa2Cu3OT-5 (~=0.1) single crystal upon heating with thermal or laser pulses as well as a transient voltage across the z-axis resulting from the application of mechanical stress. We conclude that the measured voltages can be explained as resulting from a change in macroscopic polarization as a result of the application of a heat pulse, AV-(~P/~I')AT, or a stress pulse, AV-(3P/~Z)AZ, where T is the temperature and Z is the stress; i.e. the pyroelectric and piezoelectric effects, respectively. The experimental results, therefore, imply the existence of a macroscopic polarization in YBa2Cu307. The geometry of the heating experiment is shown in Figure 1. The sample was a single crystal of YBa2Cu307-5 (5=0.1), with dimensions approximately 0.5x0.5x0.5 mm; the crystal was superconducting with Tc=90K and ATe =0.3K, as determined by 4-probe resistance measurements. We measured both the voltages between c-axis contacts perpendicular to the CuO2 planes (V12 and V34) and the
VI
_I
Laserspot
1 3 b)
X Y
4 I_ Vl LI / ~ Heater
1 3
Iv2
,, / /
/
4
Figure 1: Sample geometry used in the experiments; the z axis corresponds to the c-axis of the crystal: a) laser beam incident on the y-z (or x-z) surface; b) a nichrome heater is mounted near the sample surface. 319
320
PYROELECTRIC AND PIEZOELECTRIC
voltages between a-axis (or b-axis) contacts (Vt3 and V24). The two-probe resistance, measured at room temperature across the c-axis of the sample, was approximately lf~. The laser heating experiment (514.5 rim) was performed either by focussing the beam into a spot much smaller (30gin diameter) than the sample or by exposing the sample to an expanded beam with diameter larger than the sample dimensions (Figure la). Alternatively, the heat pulse was generated by a thin, small nichrome heater wire placed near, but not in contact with, the sample (Figure lb). The latter method of direct heating was used to demonstrate that the induced voltages are not photovoltaie in origin, but thermal. The voltage was measured with a high-impedance nanovoltmeter or a digital oscilloscope. The contacts were made using gold paste with gold wires connecting to the gold-coated leads of a semiconductor device package. The YBCO crystal was attached to the package with GE varnish. Figure 2 shows that when the 30gin diameter laser beam was turned on or off (Figure 2a), a transient voltage
a)
l
10s -100 pv _
#/--\
b) A
Time
~
c)
o ;>
EFFECTS IN SINGLE CRYSTALS
Vol. 75, No. 4
was observed (Figure 2b) across the z-axis contacts, VT = V12 - 1001.tV; the voltage is negative when the laser is turned on and positive when the laser is turned off. If the laser beam was not focussed exactly in the center between the two contacts, we also measured a steady thermopower voltage due to the temperature difference, TI - T2, between the two Au-YBa2Cu307-5 contact junctions in addition to the transient voltage. As expected, when scanning the focussed spot across the sample along the z-direction, the thermoelectric voltage varied linearly with distance across the sample and was zero with the beam focused precisely in the middle. A similar voltage was measured across all z-axis contacts (V34,V23 and V14). However, neither the sign nor the magnitude of the transient signal change with the position of the laser beam along in the x-z surface. Thus, the transient voltage along the z-axis results from a temperature change and not from a thermal gradient. Although steady thermoelectric voltages V13 or V24 were measured (corresponding to temperature differences AT 13=T l-T3 and AT24=T2-T4, respectively), no transient voltage was observed between contacts I and 3 or 2 and 4 along the x (or y) direction. The latter observation is
particularly important for it demonstrates that the signal does not arise from the contacts. It also demonstrates that the thermally-induced voltage appears only along the c-axis direction. Additional evidence of the different origins of the transient voltage and the thermoelectric voltage comes from the laser intensity dependence shown in Figure 3. With the laser focused near one contact (such that there is a temperature difference AT12 between contacts 1 and 2) the thermoelectric voltage shows superlinear dependence with AT12 proportional to IL(1"7+0"l), whereas the transient voltage is sub-linear, VT proportional to IL(0.7(~-0'I). From the time dependence of the transient signal (Figure 2b), we conclude that the voltage is proportional to the temperature derivative, +3/3T, of a macroscopic 35O
Time
i i t
'
IOOO
400 s
30O
i
''''1
....
.....
r-
I'' -
' ' I ' ' ' ' I ' I'[ 2' ]' [] 'I' ''' ''' '
~.]oo
250 - ; 200 o b J3
_~ ~5o
,6"
10
/."'a / I0
1oo
0 J
Figure 2: Voltage appearing across the sample (between contacts separated along z) upon exposure to the laser beam: a) the timing diagram of the laser; b) the transient voltage V12; c) thermoelectric voltage, St3, as a function of time measured with a focussed laser spot midway between contacts 1 and 2; d) derivative of the thermopower, S13 with respect to time; e) heater current timing; f) transient voltage due to thermal pulse from the heater wire (note the difference in time scale).
JD h
100
./Of
,/
50
/ ".-'O Dj
Laser intensity (roW)
-e/
J ~ e
,/~gl U"
¢
d D"
0 0
5
10
15
20
25
30
35
Laser intensity (roW) Figure 3: The thermoelectric and transient voltages as a function of laser intensity; solid dots represent the transient pyroelectric voltage; open squares represent the thermoelectric voltage. The inset shows a log-log plot of the same data.
Vol. 75, NO. 4
PYROELECTRIC AND PIEZOELECTRIC
thermodynamic variable, such as the polarization per unit volume, t'. "l'nis is demonstrated by comparing the calculated derivative of the thermoelectric voltage V13 (which is proportional to ATI3) shown in Figure 2d with the measured transient voltage VT=V12 shown in Figure 2b. The rise and fall decay times of the transient voltage signal are determined by the thermal response of the crystal. The data shown in Figure 2 were obtained with the sample at room temperature. When the sample is cooled, the time constant of the pyroelectric voltage changes since the thermal conductivity and specific heat change the thermal time constant of the system. Cooling the sample below T o we observe only the thermoelectric voltage due to the gold contacts since the thermopower of the supereonductior is zero. As expected, the sign of the thermoelectric voltage is reversed below To, since in the normal state the thermopower of YBa2Cu307 is opposite in sign and larger in magnitude than that of gold. When we laser-heated the sample with sufficient power to raise the temperature above To the pyroelectric voltage reappeared. Figure 2f shows the transient voltage measured when using the nichrome wire heater as the heat source. The principal difference between direct heating and laser pulse heating is the time-constant: the thermally-induced voltage shows no characteristic time scale for the decay of the transient voltage since the time scale is dominated by the thermal cooling characteristic of the heater wire. The observation of a transient voltage using the wire heater also excludes artifacts originating from the photoelectric effect (which cannot be eliminated with laser excitation), and unambiguously links the induced voltage to the temperature derivative, 0/0T. Having eliminated possible artifacts due to contacts and photo-effects, we suggest that the general characteristics of the transient voltage imply the existence of the pyroelectric effect in YBa2Cu307-8: an induced voltage VT ~ c~ 0~/0T where i~ is the macroscopic polarization per unit volume which is directed along ~ (the unit vector along the c-axis). Since observation of a pyroelectric effect in a high T c metal is of special interest and since such an effect would be symmetry forbidden if the structure were truly centrosymmetric, we present additional evidence for the existence of a macroscopic polarization; specifically, we fred that YBa2Cu307 is piezoelectric. To attempt to detect a piezoelectric response, we mounted a single crystal of YBa2Cu307 in a press between two metal dies. The contacts to the sample were made with indium so as to exclude possible transient voltages due to contact slippage when a mechanical shock is applied. Upon giving one of the dies a sharp shock, we observed a piezoelectric voltage between the two c-axis contacts, as shown in Figure 4. No such voltage was observed from either a YBa2Cu306.1 ceramic sample or from a YBa2Cu306.3 single crystal. The sign of the voltage changed, depending on whether pressure was applied to the sample (decrease in volume) or relieved (increase in volume). This observation of both a piezoelectric response and a pyroelectric response provide evidence for the existence of a macroscopic polarization along the c-axis in YBa2Cu3OT. A similar effect, although on a different time scale, was recently reported by Kennedy at al7, who stressed pellets of
EFFECTS IN SINGLE CRYSTALS
4
-
> E o
3
>O
1 -
2
321
-
JaLJ,JJal,..~,d,u,, LId,~,,
0 ~ =l
'[ Ij'"111'v"ll"[r'[IWTt~'~l]')'~'TIl"~rI'T'lP~. ,
0
,
,
I
200
,
,
,
]
400
,
,
,
I
,
,
,
600
I
800
,
,
I000
Time (ms) Figure 4: The transient voltage between surfaces normal to the c-axis obtained when a single crystal of YBa2Cu307 is given a mechanical shock. ceramic YBa2Cu307 using a piezoelectric transducer. Although possible artifacts which could give rise to the observed voltage were considered, they could not find a satisfactory explanation for the origin of the effect based on the proposed centrosymmetric structureof the material. Because the sample is conducting, the magnitude of the polarization is difficultto estimate with accuracy. The thermally induced voltage across a pyroelcctric (piezoelectric)insulator would be of the form AV
= d A P = (d/co)ACt
where d is the sample thickness, eo is the permittivity of free space, AP is the change in the polarization and Aa is the corresponding change in the surface charge density resulting from the change in temperature (or stress). When the material is a conductor with resistivity p and dielectric constant ~, the pyroelectric (piezoelectric) capacitor is shunted by the low sample resistance. As a result, the external voltage is decreased by the ratio Zp/'CT where Xp=reop (i.e. the time needed for relaxation of a nonuniform charge distribution in a conductor) and '~Tis the characteristic time over which the temperature (or the stress) is changing: AVext = ('Cp/X,r)d.AP = (Xp/'r,.r)d(Ac/eo) For YBa2Cu307, the c-axis resistivity is of order 1 ~-cm [10 "12 esu], so that Xp<10-10s (corresponding to K-100). Since the characteristic time for AT is of order 1 second (see Figure 2), Ao > 2x10 -7 Coulombs/cm 2 = 1012 electron charges per cm2, and AP>Ao/eo = 2x10 -2 cm -2 [4~Ao (esu) - 6xl03 esu] along ~. This relatively large value for AP (which is presumably still small compared to P) is consistent with ferroelectfic ordering; e.g.in BaTiO3, P=l.6xl0-1cm-2, [7.8x104 esu cm-2]. The smaller p along ~or 5 crystal axes will reduce AVext proportionately, and may explain why we don't observe an effect in these two directions. In order to observe the pyro- and (piezo-)electric effects, the distortions which lead to the polarization must be static with the following features:
322
PYROELECTRIC AND PIEZOELECTRIC
(i) an electric dipole moment directed along the c-axis within the unit cell; (ii) long-range order of the dipole moments to give a macroscopic polarization. Fluctuations involving a large number of individual dipole moments (or clusters of dipole moments) would lead to thermally induced and stress induced voltage noise. To create a dipole moment along the c-axis, random oxygen disorder in the Cu-O chains of YBa2Cu307-8 would not be sufficient. An extra oxygen in an "unoccupied chain site" (an O(5) site defect) would create a local dipole moment along g (or B) but not along ~. A number of recent experiments6, 8-10 suggest an anharmonic potential for the apex 0(4) site. This suggests that a possible symmetry breaking displacement of the two 0(4) ions within the unit cell could occur, perhaps in conjunction with such an 0(5) site defect. The asymmetric displacement of the 0(4) ions would break the inversion symmetry and, thereby, create a microscopic dipole moment with a component along ~. Since ordering of such defect sites occurs naturally along twin boundaries in YBa2Cu307, a macroscopic polarization could result. However, the absence of an observed transient voltage along the x (or y) direction in our experiments, and the relatively large value inferred for AP (<
Vol. 75, NO. 4
EFFECTS IN SINGLE CRYSTALS
holes in the new unit cell are on opposite planes and on opposite corners of the new cell, their sites related by a (1,1,1) vector (in the notation of the undistorted cell). As a result, the dipole moments add; this alternation also favors ordering of the successive CuO2 planes so as to obtain a macroscopic polarization directed along ~. The resulting smacture can be thought of as a lattice of hole-bipolarons (a polaron on each of the two planes in the enlarged unit cell) modulating the CuO2 plane slructure, with the hole density approximately equal to the optimal value of 0.25 holes per
e.~T'-~ 4 •
a)
0
•
0
_
~ : •
4 •
•
0
•
0
~ d 0
• •
0
~-CuO planes ~
CuO Chains
~....--g--._..~._~.. ~ _
• I
~
-
-
•
0
4 CuO Planes
2a
=
b)
-
T 0
A
•
0
V •
~
~ -
0
•
0
A
y
~
A
[I--
CuO
~
ClIO
V •
i
0
~
_/-'=---~-
Chains
"~- CuO
-- I 2a
~
Planes
-I
,0(2)
X'
c)
X
~..~- -~y, Y Figure 5: Schematic structural diagrams (the arrows designate the direction of distortion of the apex oxygen): a) In-plane anti-distortions with correlated hole occupancy and asymmetric 0(4) (with respect to the CuO2 planes) displacement so as to give a caxis polarization; the phase of the distortion is such that the nodes are on the Cu sites (designated as open circles), corresponding to holes predominantly on oxygen sites (designated as flied circles); b) Same as a) except the holes are on Cu sites and the nodes are on O sites; c) Schematic diagram of two planes with correlated hole occupancy so as to give dipole moments (arrows) associated with hole-occupied sites (solid circles) which add to yield a macroscopic polarization. The sites without arrows (open circles) may in fact have reduced charge density and a smaller reversed dipole moment. (Note the rotation of axes.)
Vol. 75, NO. 4
PYROELECTRIC
AND PIEZOELECTRIC
plakette. More generally, the holes would be expected to delocalize with partial occupancy on the "unoccupied" sites in Figure 5c. This model of strongly correlated holes coupled to intra-plane anti-distortions is, of course, not the only way to construct a macroscopic polarization. One could start with an essentially uniform hole charge density in the CuO2 planes and invoke a uniform ferroeleetric asymmetric displacement of the apex oxygens. Although X-ray and neutron diffraction studies have concluded that the YBa2Cu307 structure is cenmasymmetric, the pyroelectric and piezoelectric phenomena reported here imply the existence of small symmetry breaking distortions. Since there are a number of recent experiments 6,12 which are sensitive to local deformations of the lattice and which show local symmetry breaking upon the introduction of holes, it would be interesting to re-examine the YBa2Cu307 structure in finer detail.
EFFECTS
IN SINGLE CRYSTALS
323
We conclude that YBa2Cu307 appears to be both pyroeleetric and piezoelectric, implying the existence of a macroscopic polarization per unit volume (ferroelectrie) directed along the e-axis. We have proposed a model in which the small symmetry breaking distortions which lead to the macroscopic polarization can be thought of as a lattice of hole-bipolarons modulating the CuO2 plane structure; it would seem that ff correct, the implied hole-bipolaron lattice might be relevant to pairing in the superconducting state. Acknowledgement: We would like to thank G. Collin for kindly providing the YBa2Cu3OT-6 crystals and C. Foster, K. Voss and L. Forro for many stimulating discussions. This research was supported in part by a grant from the Office of Naval Research, N00014-83-K-0450. D.M. would like to acknowledge support from the Fulbright Program and from CEC grant no. CII 0568-C.
References 1. 2. 3. 4. 5.
6. 7.
A.R. Bishop, R.L. Martin, K.A. Muller and Z. Tesanovic, Zeitsehrift fuer Physik B 76, 17 (1989). A. Bussmann-Holder, A. Simon and H. Buttner, Physical Review B ~ 207 (1989). J. Schreiber and P. Haertwich (to be published). Y.H. Kim, C.M. Foster, A.J. Heeger, S. Cox and G. Stucky, Physical Review B ~ 6478 (1988). C. Taliani, R. Zamboni, G. Ruani, F.C. Matacotta and K.I. Pokhodnya, Solid State Communications, ~ 487 (1988). D. Mihailovi6 and C.M. Foster, Solid State Communications 74. 753 (1990). R.J. Kennedy, W.G. Jenks and L.R. Testardi, Bulletin of the American Physical Society 35, No. 3, 424 (1990), Phase Transitions, (in press, 1990).
8.
H. Ritschel, L. Pintschovius and W. Reichardt, Physica C, 1~2-164, 17-5 (1989). S.D. Conradson and I.D. Raistrick, Science, 243, 9. 1340 (1989). 10. S.L. Drechsler, N.M. Plakida, V.L. Aksenov, T. Galbaatar, R. Rakauskas, and S. Stamenkovic, Proceedings of the International Conference on HighTc Thin Films and Single Crystals, Wonu Scientific (,o be published). 11. a. J.B. Torrance, A. Bezinge, A.L Nazzal and S.S.P. Parkin, Physica C, 162-164, 291 (1989). b. Y. Tokura, J.B. Torrance, T.C. Huang and A.L Nazzal, Physical Review B ~ , 7156 (1988). 12. T. Egami in Oxygen Disorder Effects in High-Tc Superconductors, Ed. by J.L. Mran-Lopez and I.K. Sc huller (Plenum, 1990).