~ Solid State Communications, Vol. 76, No. 4, pp. 511-516, 1990. Printed in Great Britain.

0038-1098/9053.00+.00 Pergamon Press plc

EVD£NCE FOR BROKEN TIME REVERSAL SYMMETRY IN CUPRATE SUPERCONDUCTORS

H . J . Weber! a) D. Weitbrecht} a) D. Brach! a)

A.L.ShelarLkov} a'b) H. Keiter! a) W. Weber! a)

Th. Wolf! c] J. c~erk! dl G. Linker! dl G. Roth! dl P.C. Splittgerber-Hunnekes (e) and G. G~ntherodt (e)

(a) Institut f6r Physik, Universit~t Dortmund, D-4600 Dortmund 50, FRG (b) Ioffe Physico-Technical Institute, Leningrad 194021, USSR (c) Kernforschungszentrum Karlsruhe, ITP, D-7500 Karlsruhe I, FRG (d) Kernforschungszentrum Karlsruhe, INFP, D-7500 Karlsruhe i, FRG (e) II. Physikalisches Institut, RWTH Aachen, D-5100 Aachen, FRG

(Received 23 July 1990 by M. Cardona, revised manuscript received 16 August 1990)

Evidence for Broken Time Reversal Symmetry in Cuprate Superconductors

Reflection measurements on a one-domain single crystal of YBa2Cu307_ 8 and

transmission measurements on single crystals of Bi2Sr2CaCu208 are reported

which indicate optical circular effects Delow temperatures T$ somewhat above the respective superconducting temperatures T¢. The signs of rotation can be controlled by an external magnetic field. We interpret these results as strong evidence for a state with broken time reversal symna~try below T=, as predicted by the theories of anyon or flux phase superconductivity.

1.Introduction

Some of the models for high temperature superconductivity in the cuprates predict that time reversal symmetry ~ and also two- dimensional reflection 'symmetry P are broken in the superconducting state. These models include the "flux phases" of the two-dimensional t-J model [1-3], and in particular the "anyon" models [4,5], where the charge carriers can be described as quasi-particles confined to two dimensions and obeying fractional statistics - similar to the quasi-particles in the fractional quantum Hall effect. The ~ and ~ symmetries are presumed to be broken below a certain critical temperature larger than or equal to the superconducting transition temperature Tc. As one of the experimental consequences of broken and ~ symmetries [6,7], circular dichroism and circular birefringence should occur; i.e. an effect analogous to the Faraday rotation - yet without any extrinsic magnetic field.

Recently two experiments have been published, presenting conflicting results. The first one, by Lyons et al [8], reports attempts to measure circular dichroic reflections from various cuprate superconductors, including single crystals and films of YBa2Cu307_ ~ (the

films on MgO substrate) as well as single crystals of Bi2Sr2CaCu208. The onset tempera-

511

tures for circular dichroism are reported to lie between 150 and 300 K, with much lower values for the films than for the crystals.

The second paper, by Spielman et al [9],reports that no "non-reciprocal" circular birefringence has been observed in a variety of high quality YBa2Cu307_ 6 films (also on MgO

substrate). These films have been measured in transmission, using a novel fiber-optic gyroscope to reject any "reciprocal" circular birefringence due to optical activity in the samples.

In this publication, we report reflection measurements of circular dichroism on a one-domain single crystal of YBa2Cu307_ 6 as well

as transmission measurements of circular birefringence on single crystals of Bi2Sr2CaCu208. The data indicate a state of

spontaneously broken symmetry below certain transition temperatures Ts > T¢, with T$ - T¢ 20, 40 K, for YBa2Cu307_ ~ and Bi2Sr2CaCu208, respectively. Furthermore, temperature cyclings of the samples in an external static magnetic field of alternating directions have resulted in controlled switching of the sign of the rotation.

2.Samples

Single crystals of YBa2Cu307_6: Growth was

512 BROKEN TIME REVERSAL SYMMETRY IN CUPRA'Lr~ SUPERCONDUCTORS

carried out as described in [10]. A ZrO 2

crucible was used, lined by a Au foil. A mixture of 3 at% Y203 , 28 at% ~aCO 3 and 69 at% CuO was

melted at 10OO°C (4Oh) and 1010°C (5Oh). Crystal growth occured during slow cooling at a rate of 0.30 K/h down to 966.8°C, applying the accelerated crucible rotation technique. At the end of the growth process, the melt was decanted intc a porcelain capsule placed inside the furnace. Then the furnace was cooled down to room temperature during 125 h. Additional Oxygen loading was carried out in pure oxygen atmosphere at various temperatures and times between 600°C and 430°C, and 50 to iOO h, respectively. Comparable single crystals contain typically 6-8 at % Au impurities on the Cu(1) position. No Au atoms could be found on the Cu(2) positions. Tc = 92.5 K was measured inductively. Some of the crystals e~hibited untwinned domains with areas ~ (300 ~m)-. X-ray analysis of such untwinned domains contained less than I0 % fraction of twins.

Films of YBa2Cu307_ 6 (for details see

[ii]): i00 to 300 run films were deposited by inverted cylindrical magnetron sputtering onto (iOO) MgO substrates. Complete e-axis growth was achieved, and T¢ ~ 89 K, with critical currents j¢ ~ 2.106 [A/cm 2 at 77 K. The size of twinned domains was - 30 rum, with typical grain sizes of

200 nm. Single crystals of Bi2Sr2CaCu208 (for

details see [12]): Stoichiometric mixtures of Bi203, SrCO 3, CaCO 3 and CuO were melted for 2 h

at I050°C in AI203 crucibles. The melt was

rapidly cooled to 950°C, then further cooled to 800°C and to 5OO°C with cooling rates of 1 K/h and I0 K/h, respectively. Thereafter the batch was quenched to room temperature. Pl~telet-like crystals (sizes up to 5 x i0 x 1 ~m) were ob- tained, oriented normal to the bottom of the crucible. Wavelength dispersive X-ray anal~%is did not show any traces of A1 in the crystals and confirmed the nearly ideal stoichiometric composition. Using secondary neutral particle mass spectroscopy, the depth profiles of atomic distributions were analysed and found to be very homogeneous. Scanning tunneling microscopy showed atomic resolution and the 2.65 nm incom- mensurate superstructure. Values of Tc ~ 87 K were found by dc-susceptibility measurements.

3.Reflection experiments

The experimental sot-up is shown in Fig. i. The light source is a linearly polarized He-Ne laser (633 nm). Normal incidence is obtained by a wedge made from a birefringent crystal. It serves both as a polarizer and as an analyzer. One axis of its optical indicatrix is nearly parallel to the polarization direction of the laser, being the y direction in Fig. i. If the sample or another optical component mounted in the beam path changes the polarization, the reflected light wave contains x components of the field, which are differently deflected and can be detected. The azimuthal orientation and the ellipticity of the light wave is varied by the A/2 -plate and by the A/4 plate,

Vol. 76, NO. 4

Detector ! (vl) l (v2)

) x

EH (vz)

k/2

Lens Somple Au -Hirror

Eryostot

Fig. 1= The optical apparatus used for reflection measurements. The birefringent wedge BW transmits x- and y-polarized light waves~ The azimuthal orientation of the A/4- and A/2-plate is referred to these directions. The Faraday cell FC and the electro-optical modulator EM will produce the signals I(vl) and l(uz) as described in the text.

respectively. Both elements are rotated in steps of I0 rad. The Faraday cell, driven at the frequency ul ~ 400 Hz, serves as an intensity modulator. The electro-optical modulator induces ellipticity at the frequency vZ ~ 700 Hz. The signals I(vl) and I(v2) of both modulators are detected by lock-in techniques. The sample is mounted on a Au mirror. Shifting the cryostat, the light is reflected by the isotropic Au mirror. In this position the A/4 plate is adjusted and the influence of spurious effects arising from imperfections of the optical elements are controlled. The adjustment of the A/4 plate is checked before and after each run and also during the runs.

At room temperature, the YBa2Cu307_ ~ sample

was oriented so that its crystallographic u axis nearly coincided with the x axis of the optical system (misalignment angle 2~o). The A/2 plate provides an accurate adjustment of the sample

VOl. 76, NO. 4 BROKEN TIME REVERSAL SYMMETRY IN CUPRATE SUPERCONDUCTORS 513

axis with the incident light polarization. The positions of the A/4 and A/25 plates were measured with an accuracy of 3.10 tad.

For a homogeneou~ sam pl~ with an ideal surface, the relation E' =: ~ ~ between the in- cident electric field (E~,Ey) and the reflected field JEI,E#) is determined by the reflectivity matrix r which can be written as

= r [1 + P l ~ l + iP2~ 2 + (~1 + i~2)~y ] (1)

^

~1,2 = ~x sin(2~l,2) + ~z C°S(2~i,2)

with ~ being the Pauli matrices. All the x,y,z

parameters in eq. (I) can be chosen as real numbers. Circular dichroism is caused by a finite ~1, while circular birefringence originates from ~2.

In general, the angles ~i and %2 are arbi-

trary. However, they must coincide when a symmetry element of the sample is a mirror plane

normal to the surface. For orthorhombic YBa2Cu307_ 6 the angles ~i,2 are zero, when

counted from one of the crystal axes (the choice of u or b changes only the signs of Pl,2 ) .

Non-zero ~2 - ~I indicates lost ~ symmetry. The

term in eq. (i) leads to an asymmetry in the conversion of right-to-left and left-to-right polarized light. It can be finite only if the sample is in a state with broken ~ symmetry [6].

If both ~ and S symmetries are broken but is conserved, we believe that the angles

~i and ~2 should be equal: ~i and ~2 enter the

symmetric combination (r)12 + (r)21 of the

matrix elements of r and are expected to be even by the same arguments which allow to conclude that the symmetric part (Cik + Cki) of

the dielectric tensor (or any other linear response matrix) is a # even quantity. A finite (92 - ~i )' which was ~ odd but # even, would

violate ~ symmetry. Due to broken ~, ~i = ~2 =

~o z 0, but ~o should be # even. The ~ term, as in the Faraday effect is odd in both # and and conserves ~.

For the determination of ~i' ~2 and ~ we

use the following procedure: For ~ = 0 (see Fig. I) we rotate the A/2 plate and find CA where I(v2) = 0. Rotating both the A/2 and the A/4 plates, we find ~A and Co where simultaneously I(v2) = 0 and I(vl) has a minimum. For small angles ~ and ~ one can show that

4~^ = - ~I/p2 + 2~2 (2)

4~s = ~I + (I + p2 ) ~Z/pl

2P2{~ 2 - ~i ) + 2~ 1 (3)

2~A = ~I + P2 ~2/Pl - 2P2(~2 - ~i )" (4)

As B^ is linearly dependent on (C^ - ~e), its measurement provides a consistency check of the experimental results.

For temperatures T from 300K to - IIOK, the measurements yield ~A - (a = ~A = 0 within experimental uncertainty (see also Sect. 5). In this T region we have ~ = 0 and ~i ~ ~2 • 2~o.

Nowev~[ below T - IIOK the angles C = CA - ~o and C = C0 - Co are non-zero and strongly T dependent (see Fig. 2). The different signs of the angles can only be understood by an onset of

and/or of (~2 - ~i ) . This means that the

sample looses either t symmetry or both ~ and 7 symmetries below T ~ IIOK.

Thermocycling results in different sign@ ~f C~ but in the same sign~ for the product ~ C • The average~alue for i~ i ,~n the different runs is 1.7"i0- tad and C /C = -0.gz± 0.3. For different positions on the,(300 Inn) surface of the sample the values of C for a light spot of (90 pm) varies by only 30%, indicating that in a single crystal the observed effect is rather uniform.

Analysing the intensities I(vl) and I(~Z) as functions of ~ and C, we find Pl and P2 of

eq. {i). These quantities do not show any pronounced T dependences in the range of 50 to 300K. For T = 100K we found ~= -0.ii ± 0.04 and P2 = -0.24 ± 0.02. The corregponding anisotropy o2 the reflectivity agrees with the values given in other studies [13].

6

x 10 -2

0

- 6

• • • • i l I i

• • - &

$

t •

I L I I ] , I ,

20 40 60 80 100 120K

FIG. 2: Typical temperature dependence of circular dichroism for YBa2Cu307_ 6 obtained in

reflection measurements. The angles C" and C** (given in rad) are proportional to circular dichroism as described in the text. Circles are values for the reference position of the ^/4-plate.

514

4.Transmission

Due to the perfect cleavage of Bi2Sr2CaCu208 it is rather easy to prepare

samples which are sufficiently thin for measurements in transmission. Thickness homogeneity is controlled under a polarizing microscope; only that part of a sample is used which does not show any variation of the interference color between crossed Nicols. The samples are carried by an optical glass. They exhibit ~ 60% absorption, indicating thicknesses of = 100 nm (absolute values could not be measured). As shown in Fig. 3, the opticai components for the transmission measurements are similar to those described above. The electro-optical modulator induces ellipticity in the linearly polarized laser light (l = 633 nm), while the Faraday cell modulates its azimuthal orientation. The I/4 plate then transforms ellipticity into rotation and vice versa. The frequencies and the technique for detecting signals are the same as above.

The structureof the transmission matrix is identical to that of r in eq. (I). At room temperature, {I = ~2 = 0 and ~i = ~2 = ~o. The

polarization direction of the laser and one principal axis of the I/4 plate are adjusted parallel to ~o, Then the signals produced by both modulators vanish and the analyzer is in the extinction position 8o. As shown in Fig. 3, the value of 80 without sample may vary slightly due to strain birefringence of the cryostat windows (x) and of the sample substrate (+). Due to an onset of ~ and/or (~2 - ~I ) the sample may

cause a rotation by an angle es of the polarization. 8s is measured by rotating the analyzer until the signal of the electro-optical modulator vanishes. As shown in Fig. 4, the onsets of 8s are observed near 130K. Again~ different temperature cyclings lead to different signs and magnitudes of 8s.

5.Discussion

BROKEN TIME REVERSAL SYMMETRY IN CUPRATE SUPERCONDUCTORS Vol. 76 No. 4

Laser EH FC XI~, 5ample Analyzer

Lens Cryostot Detector

Fig. 3: Optical apparatus used in transmission experiments. The modulators EM and FC are the same as in Fig. i.

2 ~-~

x10-3i

1

0 ! ~ I

i t- 1

-2 !

I

_, L

, , • • • 11 l•

• % • el -=~-w

60 100 140 180 K

Flg. 4: Results for circular birefringence of Bi2Sr2CaCu208 obtained for two temperature

cycles. Angles 8s are given in rad. (x) and (+) are reference values as. described in the text.

Both optical experiments indicate that at certain temperatures Ts a transition-like change occurs in the optical properties of the samples. If intrinsic symmetry properties of the crystals cause the transition, two alternatives are possible below Ts: either the crystals are no longer symmetric with respect to mirror trans- formations ~ in the uc or bc planes, but time reversal symmetry ~ is still valid, or the crystals are in a state of broken ~ and symmetries.

The first case would correspond to a structural transition with ~ symmetry lost, such as a crystal structure with monoclinic symmetry. Then, a finite value of {~2 ~i ) is allowed,

and the present reflection experiment would yield values of (~2 - ~l ) as big as ~ 0.15 - 0.3

rad. Similarly, the transmission experiment can be interpreted by optical activity in a low symmetry crystal structure. Usually however, structural transitions also modify the optical anisotropy p of the crystal, and in view of the large values for (~2 - ~i ) one would also expect

observable changes in P2 and/or Pl" Furthermore,

domain formation should occur, with alternating signs of (~2 - ~i ) in different domains, No such

features are observed, The large value of (~2 - ~i ) should also imply a substantial struc-

tural change, observable by X-ray or neutron spectroscopy. Yet to the best of our knowledge, there have been no reports on a monoclinic or gyrotropic transition near i00 - 14OK.

Because of additional measurements in an external magnetic field, described below, we interpret our data as a strong evidence for a transition to a state with broken ~ and symmetries. Such a state (where ~ is conserved as a "minimum" hypothesis) can be characterized by a pseudo-vector, odd in 9, as if the system has a built-in magnetic "field" ~. From symmetry arguments one. should expect a "Zeemann" interaction "~ between the built-in "field" and an external magnetic field ~. Therefore, an applied magnetic field is expected to orient the internal "field". The orientation of the built-in "field" and thus the signs of ~ or es are expected to be controlled by the direction of a magnetic field in the process of cooling below Ts.

VOl. 76, NO. 4 BROKEN TIME REVERSAL SYMMETRY IN CUPRATE SUPERCONDUCTORS 515

To investigate such an effect, we have carried out the following cycling experiments: at T = 180 K, a static magnetic field of - 200-500 Gauss parallel to the c-axis of the sample was switched on, the sample was cooled below Ts, and the magnetic field was switched off (above Tc to prevent possible flux freezing). Then the sample was again heated to 180 K, and the magnetic field was reversed. The cooling cycle was then carried out %s before. In each of these cycles the angles ~ or 8s were monitored after switching the magnetic field off below Ts. In all cycles - three were carried out for the reflection, seven for t~e transmission experiment - the signs of O, or ~ changed when- ever the direction of the applie~ magnetic field was altered, but the signs of ~ or 6s did not change, when ~ was kept the same. Similar cycles without magnetic field resulted in a statistical

distribution of the signs of angles 8s or ~ (ii events, 5 positive, 6 negative signs).

* t*

From the data of ~ and ~ in Fig.l, and using the measured value of P2' eqs. 2 and 3

with ~I = ~2 = ~o allow to determine the value

of (~I + (2 p2/Pl ) = -0.13 +0.03 at T = 20K. If

the value of ~o is not 2changed by any ~ field "magnetostriction" ( ~ ~] ), we obtain ~I = -0.05 ± 0.02 and ~2 = - 0.04 + 0.02. Note that only the relative signs of ~I and ~2 are meaningful, their absolute signs change whenever the "field" changes sign. We should mention that the values for I~I and thus for I~ decreased to some extent over a period of several weeks, we attri- bute this degradation of the YBa2Cu307_ 6 sample

to some loss of oxygen in the surface layers. It was a surprise for us that such a weak

magnetic field of 200 - 500 Gauss is able to orient the internal "field". This is the more so, as the myon spin rotation (~SR) data of [14] give a very restrictive upper limit for the strength of the "Zeemann" interaction (per unit volume). Our magnetic field data can only be understood if we assume that the mechanism of orientation involves the motion of macroscopic domains with different orientations of the internal "field". In this picture, the driving force is proportional to the macroscopically large volumes of the domain walls. Then, if pinning forces due to sample imperfections are not too large in our high quality single crystals, the orientation of the internal "field" is possible even if the "Zeemann" interaction is small as it follows from the ~SR results. A weak "Zeemann" interaction, or in other words a small magnetic moment related to the ~ field, also follows from the fact that we do not observe any domain structure typical for ferromagnets. A model without any direct relation between ~ breaking effects and magnetic moments is discussed in [7].

We consider the magnetic field experiment as a direct test of the symmetry of the state below Ts and as a direct proof that the state exhibits broken ~ and • symmetries. As a consequence, a built-in "field" arises below Ts, with probably a "ferromagnetic" alignment in different CuO layers. Any further conclusions concerning its nature or even more concerning the statistics of the charge carriers cannot be drawn from the present macroscopic experiment.

Furthermore, the present data do not show unambiguously that • symmetry is conserved - this is only the simplest assumption consistent with the data.

Let uS now discuss the possibility that our results are caused by spurious effects due to imperfect samples, such as the presence of a certain number of misoriented domains. The observed rotation of the light might then be caused by these domains and the specific T dependence of the data might originate from specific optical properties of the domains, of other imperfections and of a superposition of all these effects. Indeed, sample imperfections are present, as we observe finite values of A~ = ~^ - ~s for T > Ts, while for perfect samples we expect A~ = 0 when ~I = ~2 = ~ = 0

(see_~qs. 2,3). The observed values for A~%,~ 2.10 -- rad, almost two orders of magnitude smaller than A~ at low T. It is hard to imagine that a strong enhancement of A~%,~ can occur below Ts, even harder to conceive that the signs of A~,m change for different runs and, moreover, are controlled by an external magnetic field. Similar arguments allow to reject other spurious effects like T dependent strains, imperfections of the optical system etc. Another possibility is that there exist sample regions with much higher T¢ values. Flux trapping in these regions may then.lead to a Faraday effect in the magnetic field experiments. Yet the magnitude of the signal is the same in the experiments with and without magnetic field, which is in contradiction to the above assumptions.

Our results might be considered as a qualitative confirmation of the data of [8], although our Ts values are much lower. However, our results are in disagreement with the conclusions of [9]. At the early stage of this study we have also investigated c-axis oriented YBa2Cu307_ ~ films on MgO substrate, using the

same optical set-up. These films had very similar characteristics as those used in [9]. The films did not exhibit any optical anisotropy in the ub plane. In our film experiments we did not see any clear indications of ~ breaking effects.

From our single crystal data we estimate the nonreciprocal rotation - i0 - i00 ~rad/CuO layer (or - 20 200 rad/rmn, values almost comparable to those obtained for Faraday rotation in ferromagnetic insulators such as EuS [15]). The upper limit of rotation deduced from the film data of [9] is 5 ~rad/CuO layer for the case of "ferromegnetically" ordered CuO layers (beam size s = 15 l~m, domain size d = 50 nm). Presently it is not clear to us, whether the difference in these numbers indicates an essential discrepancy of the two studies. It ls possible that the values of rotation are frequency dependent (1.06 vs 0.63 jJm), or that the effect is more difficult to detect in films, because of a more efficient averaging than assumed in [9]. In any case, their gyroscope experiment carried out on single crystals should result in observable S breaking effects.

6.Conclusion

In conclusion, we have measured optical circular effects in single crystals of the high

516 BROKEN TIME REVERSAL SYMMETRY IN CUPRATE SUPERCONDUCTORS Vol. 76, No. 4

T¢ cuprates YBa2Cu307_6 and Bi2Sr2CaCu208, and

have found a transition-like change in the opti- cal properties at Ts which is ~ 20K above T¢ in YBa2Cu307_ 6 and ~ 40K above T¢ in Bi2Sr2CaCu208.

The magnetic field measurements strongly support the interpretation that, at T$, a phase transition occurs to a state with broken time reversal symmetry.

Acknowledgments - One of us (ALS) acknowledges helpful discussions with A. Schmid and X. Zotos. This work has been supported by the Minister f~r Wissenschaft und Forschung des Landes Nordrhein- Westfalen, by the Bundesminister f~r Forschung und Technologie, and by the European Community ESPRIT program, project No. 3041-MESH.

References

B. Baskaran, Z. Zou, and P.W. Anderson, Solid State Commun. 63, 973 (1987) 87) I. Affleck and B. Marston, Phys. Rev. B37, 3774 (1988) P. Lederer, D. Poilblanc, and T.M. Rice, Phys. Rev. Left. 63, 1519 (1989) V. Kalmeyer and. R.B. Laughlin, Phys. Rev. Lett. 59, 2095 (1988) Y.H. Chen, B. I. Halperin, F. Wilczek, and E. Witten, Int. J. Mod. Phys. B3, 1001 (1989) B. I. Halperin, Proc. Int. Seminar on Theory of High Temperature Superconductivi- ty, Dubna, USSR (1990), to be published A.G. Aronov and A.L. Shelankov, Proc. Int. Conf. Low Temp. Physics 19, to be published K.B. Lyons, J. Kwo, J.F. Dillon, G.P. Espinosa, M. "McGlashan-Powell, A.P. Ramirez, and L.F. Schneemeyer, Phys. Rev. Left. 64, 2949 (1990) S. Spielman, K. Fesler, C.B. Eom, T.H. Geballe, M.M. Fejer, and A. Kapitulnik, Phys. Rev. Lett. 65, 123 (1990)

I0 Th. Wolf, W. Goldacker, B. Obst, G. Roth, and R. Fl6kiger, J. Crystal Growth 96, I010 (1989)

II X.X. Xi, G. Linker, O. Meyer, E. Nold, B. Obst, F. Ratzel, R. Smithey, B. Stehlau, F. Weschenfelder, and J. Geerk, Z. Phys. B74, 13 (1989) ~

12 P.C. Splittgerber-H~nnekes, C. Quit~nann, W. Albrecht, C. Valder, and G. G~ntherodt, Verh. DPO (VI) 25, 1255 (1990), and to be published

13 M.P. Petrov et al, Solid State Co~mun. 67, 1197 (1988), B. Koch, H. P. Geserich and Th. Wolf, Solid State Commun. 71, 495 (1989)

14 R. F. Kiefl et al, Phys. Rev. Lett. 64, 2082 (1990)

15 J. Schoenes, P. Wachter, and F. Rys, Solid State Commun. 15, 1891 (1974)