High temperature NQR studies of Sr-doped La2CuO4

PHYSICAI ELSEVIER

Physica B 199&200 11994~ 230 -234

High temperature NQR studies of Sr-doped La2CuO, T. Imai "'¢'d, C.P. Slichter "'b'¢'d'*, K. Yoshimura

M. Katoh ¢, K. Kosuge

"Department of Physics, Unit,ersiO" of Illinois at Urbana-Champaign, Loomis Laboratoo' o.f Physics. 11 I0 West Green St., Urbana. IL 61801-3080, USA bDepartment ~#"Chemistry. University 01"illinois at Urbana-Champaign, Loomis Laboratory t?f Physics. 1110 West Green St.. Urbana. IL 61801-3080, USA "Frederick Seit: Materials Research Laboratory, UniversiO' of Illinois at Urbmta-Champaign, Loomis Laboratory of Physics, I110 West Green St.. Urbana. IL 61801-3080. USA aScience and Technology Center.]'or Supereomhtetirity ~Department t~f Chemistry, Faculty t?f Science. l~roto Universio'. Kyoto 606. Japan

Abstract We report measurements of ~'3Cu spin lattice relaxation rates l/Tt, in La2_xSr.,CuO for 0 < x < 0.15, and the Gaussian component, I/T2c., of the transverse decay rate for x = 0 at temperatures up to 900 K. For x = 0, the results test and confirm the current theories of LazCuO,, as a quantum antiferromagnet and determine the correlation length as a function of temperature. The product TI T/T2c, is independent of temperature from 450 to 900 K, giving clear evidence for quantum critical scaling. For x > 0, the high temperature T~ is nearly independent of x, showing that even the doped materials at high temperature maintain essential characteristics of the x = 0 antiferromagnet,

1. Introduction A striking feature of the high-temperature cuprate supercond,~ctors is that they may be thought of as being derived from parent compounds which are antiferromagnetic insulators. The simplest parent compound is La2CuO,~. In 1989, Chakravarty, Halperin, and Nelson (CHN) [1] published a notable paper on the theory of a two-dimensional quantum Heisenberg antiferromagnet at low temperatures. Subsequently, Chakravany and Orbach [2] analyzed the effect of the spin fluctuations ott the nuclear and electron spin-lattice relaxation times T1. Pure La2CuO, orders antiferromagnetically for temDerature below 308 K. Although NMR studies of the

*Corresponding amhor.

ordered state have been made, until recently no one has observed the resonance in the unordered or paramagnetic state owing to the short transverse relaxation time, T 2, and the diminished signals resulting from elevated temperatures. We have now succeeded in measuring T t and T 2 in the paramagnetic state of La2CuO,, [3, 4] from about 400 to 900K, and have measured T1 in La2-,Sr~CuO.~ from even lower low-temperature limits to similar upper temperature limits. The data are collected by means of nuclear quadrupole resonance (NQR) on unoricnted powders. Vor La2CuO4, the sample was kept in a sealed container since we found that otherwise the sample properties changed irreversibly at the highest temperatures as u result of interaction with atmospheric oxygen. It is useful to think of our studies as probing the high-energy excitations of these systems. It is known that

0921-4526 94507.00 C: 1994 Elsevier Science B V All rights reserved SSDIO921-4526(93}EO267.K

T. Itnai ct cal./ Plysicu B 199&200 ( I994 ) 230-234

the nearest neighbor exchange interaction J is about 1600 K, so our highest temperatures are still well below J. However, as we point out below, another important temperature is 2p,, where y, is the stiffness coetfcient for spin waves. Since 2rcp, z J z 500 K. We therefore acquire data for temperatures both above and below

231

Quanlum

Critical

2Ps.

2. Theoretical background

In their classic paper, CHN discuss the various theoretical possibilities of the two-dimensional quantum Heisenberg antiferromagnet in terms of a phase diagram. Figure 1 shows a somewhat simplified version of their diagram. The quantity g is a type of coupling constant which subsumes a variety of physical variables (for example, the spin of the individual magnetic atoms, or the relative size of second neighbor versus first neighbor exchange coupling). A general proof has been given that the two-dimensional quantum Heisenberg antiferromagnet (2D-QHAF) does not order for temperatures T > 0. Only at T = 0 is there a possibility of order. However, if the coupling constant g exceeds a critical value, gc, the zero-point fluctuations characteristic of quantum mechanical systems prevent establishment af order even at T = 0. This state has been labeled quanfum disordered. The corresponding phase exists up to temperatures above absolute zero for all values of g in excess of gF. For .(Ic g,, the ordered state exists only at T = 0. CHN point out that regardless of the size of g, for temperatures below J, quantum critical fluctuations are important in determining the correlation length, 6. of antiferromagnetic spin fluctuations. They denote this as the quantm crirical regime. As one lowers the temperature from T = J, 5 gets progressively longer. If g < gE, there is a further theoretical simplification for temperatures below 2p, which enables them to describe the model in purely classical terms. They denote this regime as the renormaiized classical region. As T approaches zero, 4’ goes to infinity roughly as exp(27cpJ T). On the other hand, if the coupling constant y exceeds the critical value, the correlation length saturates when the temperature is lowered, preventing ordering at T = 0. In the process, a gap develops in the energy excitation spectrum. This is the regime CH’V labeled as quantum disordered on their phase didgram. The fact that La,CuO, has an ordering temperature of 308 K rather than 7ero is explained by CHN as arising from a small interplanar exchange coupling J’. To account for T, of 308 K. J’ ne:d only be about IO-’ of J! CHN point out that as long as ont is only a modest temperature above T: !!+z system shouii’; be weii aescribed by the two-dimensional model.

s - exP(~P*~T)

I

,2d-Neel

Line Coupllng Constant “g”

Fig. 1. Proposed

phase diagram

berg antifcrromagnct

to two-dimensional

Hciscn-

(after Ref. [I]).

The three different phase regions are characterized by different forms of temperature dependence of ,f. CHN propose that one can determine an appropriate value of g to describe a particular material by examination of its low-temperature (T < Zy,) behavior of <. If one is headed towards ordering. f will behave exponentially with l/T; if one is not, < should show signs of saturating. CHN apply this reasoning to the neutron scattering data to conclude that for LaJuO,. y < gE. so that the system would order at T = 0 even without interlayer coupling. Recently. Sokol and Pines [S] have suggested that doping the cuprates has an effect similar to increasing the coupling constant g. making possible materials which at low temperatures are in the quantum disordered phase. They propose that the spin gap thereby expected gives rise to the experimentally observed rapid fall-off of spin susceptibility at low temperatures.

3. Detailed comparison of t eory with experiment for La,CuO, We report two types ofmrasurcments. TI and TzG. the Gaussian component of the transverse nuclear relaxation time T, of 63Cu nuclei. Both T, and T,, arise from the hyperfine coupling of the b3C~ nuclear spins to electron spins on the Cu atoms. Moriya [16] showed that T, gives information abour l”, the imaginary part of the electron spin susceptibility. Pennington and Slichter (f’s) [7] showed that Tzc gives icformation about x’. the real part of the electron spin susceptibility.

232

T. Imai et al. / Physica B 199&200 (1994) 230-234

For NQR, Moriya's result is

i

T--~ = ~l:/dh:

E

-~U:lO0 "

fx(ql'

~'(q'(o.t°")

(1)

'O m

.m.

O

% where &(q) = Ax + 2B [cos (q a) + cos (q).a)] is the hypertine coupling interaction of the nuclei with the electrons, A± is the a(b)-axis on-site hyperfine constant, and B the isotropic nearest neighbor coupling. PS showed that the Gaussian component of the transverse decay arose from a coupling between copper nuclei which went via their coupling to the electron spins (another manifestation of the indirect coupling of nuclear spins discovered in high-resolution N M R of liquids). They calculated this in terms of the real part of the non-local electron spin susceptibility, X(r,r') or its Fourier transform, the q-dependent real part x'(q). (We follow a convention that x(q) means ~(q, w = 0).) lmai et al. [8] have extended the original experimental results from 100 to 300 K for YBazCu307 using the technique of low-field NMR. Recently, Thelen and Pines [7] have reexpressed the PS results as

O

10

D

*O

Q

•Q .

.

.

1o.1 .

.

.

.

.

.

•

.

.

.

.

.

2 1000/T

.

.

.

.

e

3 [K" ~]

4

Fig. 2. Temperature dependence of I/TtT I''~ for x - 0 (Ok x = 0.02 (©) and x = 0.04 (121)and l/TzGTfor x -- 0 (m). Solid curves are the best fit to the rigorous expression of I/Tm given in Ref. [2] with d = 0.135eV and I/T:G given in Ref. [4] with 3 = 0.132 eV. so that from Eq. (4), i / ( T t / T ~'s) varies exponentially with I/T. As Sokol and Pines [5] have shown, in this same region,

(T-~--~2~):'= 0~ . 6 9 1 1 ~ . 1 , - (q) ~,z(q) , 2 q

1 Tzra T '

~: ~

(2) Since both ,((q) and X"(q, (o) depend on the correlation length ~, both T~ and T2~ do likewise. Both T t and T2G can be calculated, if one has a theoretical expression for the corresponding ;(' or Z'. Chakravarty and Orbach [2] find 1 ( T/27tp,)t. s T---~t~" HIQ)Z (1 + T/2np~) 2 ~'

(3)

where H(Q) is the hyperfine field at the antiferromagnetic wave vector.

so that likewise I/T,,GT should go exponentially with ~/T. Figure 2 shows In(I/Tt Tl~) and Inll/T2~ T) versus I/T. Utilizing Eqs. 15) and (6), Fig. 2 shows that in this temperature regime the correlation length varies exponentially with temperature. The T t fit gives d = 0.138 -/- 0.!5 eV and the Tzc fit gives J = 0.132 + 0.05 eV in good agreement with the neutron scattering experiments by Hayden et al. [9] which give 3' = 0.132 eV, 3.2. Quantum critical region ( 2p~ < T < J)

Chubukov and Sachdev [ i 0 ] and subsequently Sokol ~md Pines [5] have used scaling arguments to show that

3.1. Renormolized classical region ( T < 2p~ ) f " l - | ' N l ,:|.~,-,vt, rl-,.,~

exp ~2r~t,,~T) x~ I + 0.5 (T/2n,o,}

(6)

i F v constant expl2r~p,/TL

14)

1 - - ~ constant, TI

(7b)

Then I

Ti T

t '~ "

(51

-

1

T2(,

~" ~

(7c}

T. bnai et al./ Physica B 199&200 (1994) 230-234 U.I~

|

I

m

I

I

ii

10

u

233

.........

, ....

, ....

, ....

, ....

, ....

5

0.5

o 0.4

T TIT ° %

%

~'0.3m

~,o % 0 e',.

0.2

0.1 0

a99

300

400

, 500

,

,

600

700

, 800

, 900

- - 1

0 300

100

i

i

.

.

I

i

i

.

400

Fig. 3. Temperature dependence of the inverse correlation length a/~ in La~CuO, estimated from the results of I/T2~ presented in Fig. 2 ( e ) compared with the results of neutron scattering experiments by Keimer et al. (O).

Tt T Tzc~

- constant.

~9)

Figure 4 shows clearly that this scaling law is satisfied to a high degree of precision from 450 to 900 K. Also shown in Fig. 4 is the result of a calculation of l/Tt by Sokol et al. [12] and of I/T2G by Sokol et ai. [13] using high-temperature expansions.

.

.

.

.

I

x=O.02 o

"x=O.04 O

'0

.

.

• .

I

e

e-f.o_

. . . .

-

. . . .

I

I

. . . .

0

8oo 0 0 0 1 0 0 0

'

'

'

e

"

-

'

l

'

v

"

x--O o

¢ 0 ¢

W

The result is shown in Fig. 3 together with measured values of a/~ obtained by Keimer et al. [11]. The data not only extend our knowledge of ~ to much higher temperatures, but also confirm the scaling result of Eq. (Ta) relating ~ to temperature. The strong contrast between the temperature dependence of ~ below and above 500 K as seen in Figs. 2 and 3 shows clearly that one has gone from one regime to another as one crosses this temperature. We believe we are observing the transition predicted by C H N from the renormalized classical at low temperatures to the quantum critical at high temperatures. A further test of the high-temperature regime has been provided by S,~kol and Pines [5], who point out that scaling arguments based on the fundamental equations (1) and (2) regime that when T > 2p~:

.

•( , ) , ,

0

m,,-,-ql

(8)

I

~"

Fig. 4. Temperature dependence of i/Tt and l/Tzc, observed for LazCuO,~. Dashed and dotted curves indicate the theoretical prediction for I/T t and I/TaG based on the 2d-Heisenberg model after Refs. [12] and [13], respectively. Note that there is no adjustable parameter in these theoretical calculations.

If one assumes a specific q and ~ dependence for X', one can calculate ~/a from the measured T2c's. We have performed such a calculati~,,i using Eq. 18) to obtian a/~ from our Tz~ data:

X'(q)

.

G

soo 6 0 0 7 0 0 T [K]

T [K]

T2~ 2 I "-F q2~2

0

. . . o o"oo'~,"'"

lit

oo~O,:,¢{'

0

ltT 1

¢

%

0

0 0

x=0.075

@ 0

o

0

n

.

e

0

I'-'-" -"~! ®

X=0.15

• ml il I'~

,~m

o

•

!

2o0

.

.

.

-

400

=

~oo

.

n

coo

-

=

.

1000

T [K]

Fig. 5. Temperature dependence of i.Tt for various doping levels of La2 - ~,Sr, CuO,,.

4. Sr--doped La2CuO,~

L'~2CuO4 [3] to higher temperatures. The results are shown m Fig. 5 for a variety of Sr dopings (La2 - xSrxCuO4). The x = 0.02 and 0.04 samples are insulators at low temperatures. The x = 0.075 and 0.15 samples are conductors and, at low enough temperatures, superconductors. Indeed, x = 0.15 gives the highest superconducting transition temperature obtainable by Sr doping.

234

T. lmai et a!./ Physica B 199&200 (1994) 230-234

The striking aspect of Fig. 5 is that the samples have identical Tt's at high temperatures. The data presented in the earlier portion of this paper and the great success of theorists in predicting or explaining it leave no doubt that LazCuO4 is a two-dimensional Heisenberg quantum antiferromagnet. We must therefore conclude that the doped samples behave at high temperalures like Heisenberg antiferromagnets. As their temperature is lowered, their correlation length grows, but evidently the presence of the mobile holes limits its growth.

Acknowledgement The authors would like to thank L.P. Gor'kov, A. Sokol, D. Pine~, M. Gelfand, S. Chakravarty, R. Birgeneau, M. Kastner, A. Chubukov, P.A. Lee, D. Thelen, M. Klein, M. Salamon, T. Moriya, J.P. Lu, D.E. MacLaughlin, and F. Borsa for their helpful discussions and communicatior~s. This work was supported by the US National Science Foundation through the Science and Technology Center for Superconductivity Grant Number DMR-91-,!0000 (C.P.S. and T.I.) and under Grant Number DEF'GO2-91ER45439 to the University of Illinois at Urbana-Champaign, Frederick Seitz Materials Research Laboratory (C.P.S. and T.I.). The work in Japan was supported by a Grant-in-Aid for Scientific

Research on Priority Areas, "Chemistry of New Superconductors" (01645004 and 02227102) from the Ministry of Education, Science and Culture of Japan.

References [1] S. Chakravarty, B.I. Halperin and D.R. Nelson, Phys. Rev. B 39 (1989) 2344; S. TS'c, B.i. Halperin and S. Chakravarty, Phys. Rev. Lett. 62 (1989) 835. [2] S. Chakravarty and R. Orbach, Phys. Rev. Lett. 64 {1990) 224. [3] T. Imai, C.P. Slichter, K. Yoshimura and K. Kosuge, Phys. Rev. Lett. 70 (1993) 1002. [4] T. Imai, C.P. Slichter, K. Yoshimura, M. Katoh and K. Kosuge, Phys. Rev, Lett. 71 (1993) 1254. [5] A. Sokol and D. Pines, Phys. Rev. Lett. 71 (1993) 2813. [6] T. Moriya, J. Phys. Soc. Japan 18 {1963) 516. [7] C.H. Pennington et al., Phys. Rev. B 39 (4) (1989) 27; C.H. Pennington and C.P. Slichter, Phys. Rev. Lett. 66 (1991) 381. Also, see D. Thelen and D. Pines, preprint. [8] T. Imai, C.P. Slitter, A.P. Paulikas and B. Veal, Phys. Rev. B 47 {1993) 9158. [9] S.M. Hayden et al., Phys. Rev. Lett. 67 (1991} 3022. [10] A.V. Chubukov and S. Sachdev, Phys. Rev. Lett. 71 (1993) 169 I l l ] B. Keimer et al., Phys. Rev. B 46 {1992) 14034. [12] A. Sokol, E, Gagliano and S. Bacci, Phys. Rev. B 47 (1993) 14646. [13] A. Sokol, R. Gienister and R.P.P. Singh, preprint.