Physica B 180 & 181 (1992) 383-388

North-Holland PHYSICA ir(

Spin dynamics in the high-T, system YBa,Cu,O,+,

J. Rossat-Mignod”,b, L.P. Regnault”, C. Vettiercvd, P. Bourgesb, P. Burlet”, J. Bossy’, J.Y. Henrya and G. Lapertot” “Centre d’Etudes Nucltaires de Grenoble, DRFMCISPSMSIMDN, 85 X, 38041 Grenoble Cedex, France hLaboratoire Lton Brillouin, CEN-Saclay, 91191 Gif-Sur-Yvette Cedex, France ‘Institut Laue-Langevin, 1.56 X, 38042 Grenoble Cedex, France “European Synchrotron Research Facility, BP 220, 38043 Grenoble Cedex. France

We report on inelastic neutron scattering experiments carried out on single crystals of the YBaZCu,O,+, system. The

spin dynamics has been systematically investigated in five typical regimes: the pure and doped AF states (x = 0.15, 0.37),

the weakly doped (X = 0.45, 0.51, 0.53) and the heavily doped (X = 0.69, 0.92) metallic states which all exhibit a

superconducting ground state. The hole doping strongly affects the AF order, dynamical AF correlations remain in the

metallic state which, surprisingly, involves only in-plane spin components. An energy gap has been found in the spin

excitation spectrum of any superconducting samples, however, it becomes weaker close to the I-M transition. A quite

unusual T dependence of the spin excitation spectra was found.

1. Introduction

The knowledge of the wave vector and energy dependences of the spin excitation spectrum is of crucial importance in building up an appropriate theory of high-T, superconductivity. We have focused our interest on the YBa,Cu,O,+, system because the availability of large single crystals (-0.3 cm’), in which the oxygen content can be changed from 0, to 0, with good accuracy and homogeneity, has allowed us to undertake inelastic neutron scattering experi- ments. The spin dynamics has been successively inves- tigated in the five characteristic regimes of the phase diagram determined by neutron diffraction [l] (see fig.

IO

2 0' c

Oxygen content : Y

Fig. 1. Phase diagram of the YBa,Cu,O,+, system as a function of the oxygen content.

1): the pure (X = 0.15) and doped (x = 0.37) AF states [l-3], the weakly doped metallic state (x = 0.45 and 0.51) [3,4], the heavily doped metallic state which develops superconductivity below T = 60 K (x = 0.69) [3,4] or T, = 90 K (X = 0.92) [3,4]. In this paper we shall summarize the results with a special emphasis on the superconducting samples, especially those for oxy- gen content of x = 0.53 and 0.92, which have been investigated quite recently and are reported here for the first time. For any composition, a magnetic scatter- ing was clearly identified for the first time using the triple-axis spectrometer IN8 at ILL. However, more accurate results were obtained recently on the high flux triple-axis spectrometer 2T at the Laboratoire L&on Brillouin. In all experiments, the single crystal was oriented with the [l 1 0) and [0 0 l] axes within the horizontal scattering plane and placed into a conven- tional ILL cryostat.

2. The pure and doped AF states

Up to x = 0.20, the AF ordering (T, = 415 K, m,, = 0.64~~) is not affected by the oxygen doping, indicat- ing that no holes are transferred from Cu(l) to Cu(2) planes. The magnetic excitation spectrum, well de- scribed by spin wave theory, yields a large in-plane

spin wave velocity c,, = 1 eV A (see fig. 2) (J,., c‘u = 0.15 eV) and a large AF coupling between the two Cu(2) layers (J,=10~2-10~’ J). This AF coupling persists in the metallic and superconducting state. However, the coupling between bilayers is weak (J’ = lo-‘J), as well as the planar anisotropy (AJi.! = 10m4).

For x > 0.20, T, and m,, decrease abruptly above x = 0.35, and the 3d-AF order disappears around x, = 0.41 because a critical concentration ni = 2%, of oxy- gen p-holes is transferred into Cu(2) planes. These

0921-4526/92/$05.00 0 1992 -El sevier Science Publishers B.V. All rights reserved

384 .I. Rossat-Mignod et al. / Spin dynamics in YBaZCu,O, +=

‘“c YBi2Cu3b6+x &

q (r.1.u.)

Fig. 2. Excitation energies of in-plane and out-of-plane spin

components in the pure (X = 0.15) and the doped (x = 0.37)

AF states.

holes give rise to some disorder in the spin direction within the basal plane, yielding a strong damping of in-plane spin excitation and a renormalization of the spin wave velocity (c = 0.45 eV A for x = 0.37, see fig. 2). The renormalization is found to be q dependent and decreases as q becomes larger than r, (l/t). Such a behaviour was explained recently by numerical cal- culations of the ground state energy and spin wave dynamics of a disordered 2d-XY model [5]. Another striking result is the low T reentrant behaviour of the AF order parameter which could be explained by the concept of magnetic two level systems induced by hole doping [6,7].

3. The weakly doped metallic state

For x > x, = 0.41, an insulating-metal (I-M) transi- tion occurs due to a sudden transfer of a large amount of p-holes (lo-12%) from Cu(1) into Cu(2) planes which suppresses the 3d-AF ordering and leads to a superconducting ground state at low temperatures. Experiments carried out on samples with oxygen con- tents of x = 0.45 (T< = 37 K) and 0.51 (T, = 47 K) [8] have proved that dynamical AF correlations persist in the metallic state (Aq = 0.10 * 0.01 r.l.u., [,Ja = 2.2 for both samples). A more accurate investigation has been performed quite recently on a sample with x = 0.53 and typical high energy scans at increasing tem- peratures are reported in fig. 3. Q-scans across and along the (112, 112, I) AF ridge have allowed us to define the nuclear contribution and to extract the AF correlated magnetic contribution. The small peaks at ho = 42 meV and 20 meV are phonon and local mode contributions, respectively, as we shall see later in a comparison with the sample x = 0.92. As was already pointed out for the sample with x = 0.51 [3,4], we confirmed that the q-widths at both JLw = 10 and 26 meV show no measurable (less than 10%) T depen- dence up to T= 287 K, in agreement also with recent measurements by Bourges et al. [9]. Moreover, a quite

1 1 1 1 I s 1 I ,

J,JOO Y ~a,CU,O,,,, a’ q ( l/2 , l/2 , 5.2 )

800

600 Cu (III) / PG (00

; LOO T = 207 K

& 200 ‘;

:

----~ 0

-0

- 800

; 600

5 LOO T

* 200 z ---_ 2 0

0 10 20 30 LO 50

Energy ( meV 1

Fig. 3. Energy scans performed at Q = (l/2. l/2,5.2) for

Y%Cu,O,, 57 as a function of temperature. Above the back-

ground (BG), the nuclear contribution is indicated (Cl).

new and important result is that the AF coupling between the two Cu(2) layers remains unaffected up to T= 287 K, therefore the strong decrease of the magnetic signal around lo-30 meV when T increases is due to intra plane effects. In order to have a better representation of the influence of temperature on the magnetic scattering we have plotted, in fig. 4, the imaginary part of the dynamical susceptibility

Energy ( meV 1

Fig. 4. Im{X(q, hw)} as a function of the energy for

YBaZ%O, 5J for increasing temperatures.

J. Rossat-Mignod et al. I Spin dynamics in YB~,CU,O,,~ 385

Energy (meV)

Fig. 5. Low energy part of the spin excitation spectrum of Im{X(q, fiw)} for YBa,Cu,O, 5, below (T= 1.75 K) and above (T = 50,150 K) the superconducting transition (T, = 47 K). An energy gap (E, = 4 meV) is clearly observed.

,y(Q, ho) which is related to the dynamical structure factor by the relation S(Q, hw):

At low temperatures the spectrum exhibits a broad maximum, defining a characteristic energy r_ = 18 meV, and falls off at high energies much faster than a simple Lorentzian function, the scattering above 50 meV being quite small. By increasing the tempera- ture, the low energy part of the spectrum is strongly depressed in a non-trivial manner, as for example a continuous increase of rW with T. From T= 200- 287 K, the maximum is not changed but the total AF correlated scattering is reduced. A more detailed anal- ysis of the T dependence is reported in the discussion.

The low energy part of the spectrum (see fig. 5) clearly shows that an energy gap is opening in the spin excitation spectrum as the temperature is decreased (E, = 3 meV and 4 meV for x = 0.45 and 0.51, respec- tively). Then the low energy spectral weight is trans- ferred to higher energies (see fig. 5) giving an explana- tion for the slight increase of the scattering below 12 meV (see fig. 4). It must be noted that the spin gap (E,) has a quite small value in comparison with the BCS prediction (-3.5TJ which indicates a gapless superconductivity on approaching the I-M transition (see fig. 13).

4. The 60 K superconducting phase

A sample with an oxygen content x = 0.69 (T, = 59 K [8]), at the end of the T, = 60 K plateau has been investigated and results were reported for the first time a year ago at the LT-19 Conference [3,4]. A magnetic scattering has been clearly identified, and the energy spectra obtained as a function of temperature are reported in fig. 6 in the form of Im X. Q scans show an increase of the q width by 40% (Aq =

yBa2cu306.69 6=(1/2,1/2,1.6)

‘0 5 10 15 20 25

Energy (meV)

Fig. 6. Low energy part of the spin excitation spectrum of Im{ x( q, ho)} for YBa&u,O, 69 below (T = 5 K) and above (T = 75,150,250 K) the superconducting transition (T, = 59 K). An energy gap (E, = 16 meV) clearly persists above T

0.14 * 0.02 r.l.u., l/a = 1.5) indicating that doping in Cu(2) layers is still increasing plateau. The broad energy spectrum is around r, = 28 ? 2 meV.

the p-hole in the T,

maximum

Below T, a measurable scattering is found only above 12 meV, indicating a larger energy gap in the spin excitation spectrum E, = 16 meV, defined by the inflexion point (see fig. 6). A quite important result is the persistence of a pseudo gap well above T,, Im x recovers a linear energy dependence only above 150- 200 K. This unusual behaviour is illustrated in the insert of fig. 6 which shows the T dependence of the slope of Im x. This demonstrates that a pseudo-gap starts to open below 150 K, explaining the unusual T dependence of the li TIT NMR results [lo-141.

5. The 90 K superconducting phase

Inelastic neutron scattering experiments on a heavi- ly doped sample with an oxygen content x = 0.92 were reported, for the first time, at the High T, Conference in Kanazawa [4]. This composition was chosen to have a high T, value (T, = 91 K [S]) but not yet a metallic character along the c-axis, as it is the case for x = 1, the next composition which we shall investigate in the near future. Energy scans, performed at increasing temperatures (see fig. 7), exhibit a rather complex lineshape. However, q-scans, across or along the (112 112 I) ridge, clearly show evidence of a magnetic scattering contribution and allow us to define the nuclear contribution. The latter can be explained by assuming three contributions on top of a flat back- ground: a contamination from the (006) Bragg peak at

386 .l. Rossat-Mignod et al. i Spin dynamics in YBa,Cu,O, + I

lsoo - Y Ba2 CuA 92

1000 - Cu /lll)/PGf0021‘

500 -

E

000

Energy (meV)

Fig. 7. Energy scans performed at Q = (l/2,1/2,5.2) for

YBa,Cu,O, y2, as a function of temperature. Above the

background (BG) the nuclear contribution is indicated (0).

24 meV, a peaked contribution at 20 meV arising from a local mode due to oxygen atoms in Cu chains (see fig. 9) and a broad response well accounted for by a damped harmonic oscillator (fro, = 21.5 meV, rW = 26 meV) which may arise from large positional fluctua- tions of apical oxygen atoms.

The magnetic contribution can now be determined at any temperatures (see fig. 7); the results, reported in fig. 8 in the form of Im x exhibit many unusual features. At T = 5 K, there is no measurable scattering below 25 meV giving evidence for a sharp energy gap in the spin excitation spectrum at E, = 28 +- 1 meV. More surprising is the sharp drop of the signal above 45 meV and the existence of a sharp peak at 41 meV (resolution limited in energy and a narrower q width, 0.18 r.1.u. instead of 0.27 r.1.u.) which could appear as a collective excitation through the superconducting

gap.

_ KOO L y Ba2CU306.92 a= (l/2 l/2 5.2)

20 30

Energy (meV 1 Fig. 8. Im{x( y. r’tw)} as a function of the energy for

YBaZCu,O, 92 and increasing temperatures below and above

T, = 91 K. An energy gap (E,, = 28 meV) is clearly seen

together with a collective excitation at fiw = 41 meV.

At T = 81 K (T < T, = 91 K), the magnetic scatter- ing remains unchanged except for an energy shift of

the coherent peak at 41 meV towards a lower energy of -25 meV which may reflect the T dependence of

the superconducting energy gap. At higher temperatures, the magnetic scattering is

strongly depressed. However, it must be emphasized that the energy scale, r_ = = 30? 2 meV, does not change with temperature, nor does the AF correlation length (Aq=0.25t0.02r.l.u., </a=0.84?0.08). This decrease of the AF correlated scattering intensity occurs over the whole energy range which may indi- cate a transfer to a q independent scattering related to single site quantum fluctuations. Moreover, even at T = 283 K, Im x is far from a Lorentzian shape; it falls off much faster at high energies.

6. Discussion and concluding remarks

The above results have revealed that the spin excita- tion spectrum of high T, superconductors exhibits quite unusual features which have to be emphasized.

(i) The spin excitation spectrum is strongly aniso- tropic for both weakly and heavily doped samples. This means that only the in-plane spin components are AF correlated. Such a conclusion follows from a com- parison of energy scans performed at Q = (l/2, li 2,5.2) and Q = (3/2,3/2,2.2) for which in-plane and out-of-plane spin components have different weights.

For Q = (112, l/2,5.2),

S(Q, hw) = 0.15 S”(Q, ho) + 1.85

x ~[Y(Q, hw) + S’“(Q, ho)].

For Q = (312,3/2,2.2),

S(Q, hw) = 0.90 S”(Q, hw) + 1.10

x ;[.Y(Q, ho) + S”(Q, ho)].

Typical energy scans performed at Q = (312, 312.

.I. Rossat-Mignod et al. I Spin dynamics in YBa,Cu,O, +i 387

1600

E 1600 x 1Lou

l.. 1200

1 1000

g 600

E 600

$ 400

g 200

- s. 0

.yj 1000

5 600

" 600

E 100 s g 200

0

?i = ( 3/2 , 3/2 , 2.2 11 _’

------

1 _l-

--------- l I I I I I 1 I I I

10 20 30 40 50

Energy ( meV 1

Fig. 9. Energy scans performed at Q = (3/2,3/2,2.2) for

YBa$u,O, 53 and O,,, at T = 10 K. Above the background (BG) the nuclear contribution is indicated (0). The magnetic contribution involves only in-plane spin components.

2.2) are reported in fig. 9 for both oxygen contents x = 0.53 and 0.92; experiments being carried out under the same conditions, data can be compared on an absolute scale. The first remark concerns the nu- clear contribution. The broad contribution is similar in both samples whereas the extra peaks at 21 meV and 36 meV are twice as strong in 0, 92 than in O,,,, Then the latter must involve oxygen atoms in Cu chains whereas the former is more likely due to oxygen atoms in the apex position. The remaining contribution is the magnetic response which can be accounted for quan- titatively (see dotted line in fig. 9) only be assuming a contribution of in-plane spin components, i.e. a scal- ing factor of 1.7 between measurements at the two scattering wave vectors.

(ii) The slope Im ~/ho exhibits an anomalous T

dependence due to the opening of a pseudo-gap well above T,, as shown in fig. 10 where the energies were chosen to be smaller than the spin excitation gap (hw = 2meV for x =0.53 and 10meV for x =0.92). The data have been calibrated to get an absolute comparison. This slope is nothing but the value 1 /T, T

measured by NMR. A stronger T dependence is found for weakly doped samples, the behaviour for x = 0.53 is actually similar to that found in the (LaSr),CuO, system [14]. For x = 0.92, Im xihw exhibits a maxi- mum around 120-130 K in excellent agreement with NMR results on the same sample [ll]. Thus the decrease of Im xlhw (l/T,T) below 130 K is due to the opening of a pseudo gap in the spin excitation

160, I I I

0 x = 0.51 ,)1w = 2 meV A x=O.92,&w=lOmeV

0 100 200 300

Temperature ( K 1

Fig. 10. Slope Im{x( 4, LJ)} /ho, as a function of tempera-

ture, taken for an energy smaller than the spin gap, for

YBa,CuP, 5L ((Co = 2 meV) and 0, 92 (hw = 10 meV). The

dotted line is the value taken at f20 = 10 meV for 0, 5,. For a

quantitative comparison, the values for 0, 92 have been

multiplied by the ratio of the square of the 4 widths; there-

fore the CJ integrated values are actually plotted.

spectrum. A similar behaviour occurs for the sample x = 0.69 whereas for weakly doped samples, the ener- gy gap is not so robust and disappears just above T,.

The origin of this energy gap is not yet clear. It may result either from some superconductivity pairing or from fermiology effects due to the special shape of the quasi-particle Fermi surfaces, as shown by recent theoretical investigations [lS-171.

(iii) the T dependence of the excitation spectrum is not trivial, the simple w/T behaviour predicted by the marginal Fermi liquid theory [18] is not obeyed. As an example, we plotted, in fig. 11, IiIm x, normalized to the low T value, as a function of T for different energy transfers. To our surprise, above 150 K a Curie-Weiss- type law is followed:

1 - = &- (1 + (Y(T- e,)), Imx (1

with 0, = +117 K and lieu = ad” (1 /(Y = 23.5 K at 10 meV). Im x0 is the value at T = 0.

A similar behaviour was found by NMR in the (LaSr),CuO, system [14]. Below 150 K a crossover occurs towards a T independent value for T < 50 K. This behaviour may reflect some interaction between quasi-particles.

(iv) The strong increase of T, from 60 K to 90 K is associated with an increase by a factor of two of the in-plane 9 width indicating a large increase of hole doping (see fig. 12). However, the characteristic ener- gy, r_ exhibits only a slight change, the important change occurring at the I-M transition (see fig. 12).