Magnetostriction and thermal expansion of high-Tc magnetic superconductors REBa2Cu3O7−x (RE = Sm, Eu, Gd, Dy, Ho, Er, Tm and Y)

Physica C 161 (1989) 48-58 North-Holland, Amsterdam

MAGNETOSTRICTION AND THERMAL EXPANSION OF HIGH-To MAGNETIC S U P E R C O N D U C T O R S REBa2Cu307_x ( R E - - S m , Eu, Gd, Dy, Ho, Er, Tm A N D Y) A. del M O R A L , M.R. IBARRA, P.A. A L G A R A B E L and J.I. A R N A U D A S Laboratorio de Magnetismo de S61idos, Dpto Fisica de Materia Condensada and Instituto de Ciencia de Materiales de Arag6n, Facultad de Ciencias, Universidad de Zaragoza & CSIC, 50009 Zaragoza, Spain

Received 1 May 1989 Revised manuscript received 21 July 1989

The magnetostriction, parallel (2,) and perpendicular (A± ) to the applied magnetic field, has been measured in the HTC magnetic superconductors REBa2Cu307-x (RE = Sm, Eu, Gd, Dy, Ho, Er, Tm and Y), between 3.8 K up to above To,with applied magnetic fields up to 2.45 T. The anisotropic magnetostriction, 2t=A m--A.L,is very weak ( < 10-6) (except for Dy and Ho compounds, where it is large, around - 120× 10-6 at 4.2 K and 2.45 T), indicative, for anisotropic ions, of weak effective field penetration at the RE sites. Besides At is of single-ion origin for Dy and Ho compounds, where performing such a test is feasible. The volume striction, to= Am+22 ±, is of the same order of magnitude (around 20 × 10-6) for most of the systems, indicative of a diamagnetic effect. The thermal expansion (th.e.) has been measured for this series, showing a Griineisen T 3 regime at low temperatures, and the Debye temperatures (in the range of ~ 345-391 K) have been obtained. Noticeable, is that th.e. strains collapse to a universal temperature dependence over most of the range of temperatures explored (between around 25-200 K), indicative of a common anharmonie phonon lattice origin, that of YBa2Cu307-x compound.

1. Introduction After the a n n o u n c e m e n t o f high t e m p e r a t u r e superconductivity ( H T C ) in the ceramic material YBa2Cu3OT_x by Wu et al. [ l ], m a n y magnetic [ 2 3 ], thermal a n d specific heat [ 14-18 ], t r a n s p o r t [ 1 9 - 2 5 ] a n d elastic properties [ 2 6 - 2 7 ] , a m o n g m a n y others, have been investigated in this system a n d in those o b t a i n e d by substitution o f Y by a rare earth ( R E ) partner. Surprisingly, substitution o f Y by RE magnetic ions does not destroy superconductivity, Tc r e m a i n i n g at 9 2 - 9 3 K . Only the comp o u n d s with R E = C e , P r a n d Tb are known not to present a superconductive phase. This is so inasmuch that for RE = Sm, Gd, Dy, H o a n d Er the systems seem to o r d e r antiferromagnetically ( A F ) at N6el t e m p e r a t u r e s TN=0.60, 2.2, 0.95, 0.17 a n d 0.59 K respectively [ 16,28,29 ], although in the present work we are not interested in this very low temperature regime. As shown a n d p o i n t e d out by T h o m p s o n et al. [ 3 ] a n d other authors [2,6,9], in the REBa2Cu3OT_x compounds, the RE ions retain their local m o m e n t 0921-4534/89/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland)

a n d can be magnetized within the SC state. In fact, it has been repeatedly shown [3,6,9,10,11,13] that the magnetic susceptibility above To, a n d even below Tc for H > 1 T, follows a C u r i e - W e i s s law, X= C~ (TO), where 0 is negative, indicative o f negative exchange interactions. Also shown is the general t r e n d that, at the virgen state, when the a p p l i e d field first increases there appears a low field d i a m a g n e t i c mini m u m , at a r o u n d 0.2 T (as in type II superconduct o r s ) , followed by a superposed p a r a m a g n e t i c ( P ) c o n t r i b u t i o n that, usually, makes magnetization positive. Besides, when the field is reversed a large hysteresis appears, the final state keeping (at 4.2 K ) substantial r e m a n e n t magnetizations. This practically means that above a certain a p p l i e d field, Hp, m a g n e t i z a t i o n changes sign and the system behaves as an effective paramagnet. This field Hp is sometimes quite large (see table I ) a n d it has not been experimentally attained. A n o t h e r result relevant to o u r work is the observ a t i o n [ 30,31 ] that a strong m o d u l a t i o n o f magnetic field takes place inside the lattice. This conclusion comes out from the result ( o b t a i n e d in the D y a n d

A. del Moral et al. / HTC superconductors magnetostriction

Table I Field, Hp, at whichthe diamagneticand paramagnetic contributions to magnetizationcancelout, and anisotropic magnetostriction, At, measured at 4.2 K and H= 2.05T, for the REBa2Cu3OT_x series Compound

T(K)

Hp(T)

2,( × 10-6)

Y Sm Eu Gd Dy Ho Er Tm

4.3 " 2.3 4.2 '" " " "

>6.0 >6.0 > 4.0 0.52 0.42 0.69 1.4 8.9

5 ~0 ~0 ~0 - 84 - 66 - 5 ~0

Gd compounds) that the regions constituted by the RE planes sandwiched between the CuO layers (of~ 4 A of thickness) behave as superconductive sheets, yet those RE containing sheets are only partially shielded from the applied magnetic field. In fact, the internal field sensed by the RE ions only attains a reduced fraction ( < 50%) of it, the full penetration being only attained when H ~ 2 T. Therefore, the main flux penetration takes place within the regions between such sheets, which indeed exclude the RE sites. In front of the above mentioned facts, magnetostriction can also be a useful probe to decide whether the RE layers have been effectively field penetrated [ 32 ]. In fact, even in the paramagnetic state, RE lattices undergo large magnetostrictions when subjected even to moderate fields, much larger than usual SC matrices [33,34]. Therefore, for those REBaCuO systems where RE sites are effectively field penetrated, we should observe a sizeable anisotropic magnetostriction, which it will turn out negligible under the lack of penetration. This effective field penetration must be the combined result of the amount of material becoming normal and of the degree of shielding at the RE sites. To test those ideas we have performed magnetostriction measurements on polycrystalline samples of RE Ba2Cu3OT_x ( R E = Sm, Eu, Gd, Dy, Ho, Er, Tm and Y) at the larger available field of 2.45 T and temperatures above the AF regime (above 3.8 K). We will make now some comments about the thermal expansion (th.e.) behaviour in such materials which are relevant to our work. To our knowledge,

49

th.e. measurements have been already performed on the Y [35-37] and Gd systems [38]. In the Y system no sizeable anomaly was detected in the th.e. coefficient ot ( = ( 1/l) (Ol/OT)), at the critical temperature T¢( =90.6 K) [35,36], but in the Gd one a "jump" otn-ots----7X 10 -s was indeed observed [38]. This very weak anomaly must be in correspondence with one in the specific heat, Cv, as expected from the simple relationship or=7 C v / 3 B (where B is the bulk modulus and 7, the Grtineisen parameter), and in fact a jump in specific heat A C , _ s ~ - 4 . 4 J / m o l K has been observed in YBa2Cu3OT_x [ 39 ].

2. Experimental techniques The REBa2CuaO7_x compounds were prepared using one of the usual routes in those ceramics. The samples were prepared from stoichiometric amounts of RE203, BaCO3 and Cu(NO3). 3H20. The nitrates were decomposed at 600 ° C, followed by solid state reaction of the powder at 950°C in 02 stream, during ~ 72 h. Afterwards, the samples were cooled down to ~ 2 0 0 ° C within the furnace. Then, they were crushed and encapsuled (at ~ 8 kbar) and sintered at 800°C in 02 stream, being finally cooled down slowly in the 02 atmosphere within the furnace. Some minor variations of such procedure have been followed also. The sample densities were around 5 g/ cm 3 (the theoretical density is, e.g. for ErBa2Cu3OT_x, 7.12 g/cm3), the compaction being of around 70%. The samples were powder X-ray analyzed, the SC orthorhombic structure being checked (e.g., the Er compound has a = 3 . 8 0 6 ( 1 ) A , b = 3 . 8 7 5 ( 2 ) A and c = 11.658(3)~, as lattice constants), and the possible presence of other phases being estimated within the confidence interval of the X-ray powder method, i.e. less than 5% ( ~ 10% for the Er sample, which turns out to be the less pure). Measurements of AC low field susceptibility, XAC, were performed [ 24,40 ] in order to ascertain whether our samples were good HTC superconductors. The real part of ZAC, measured at a frequency of 120 Hz and with a peak magnetic field value of ~, 100 mOe, shows a well defined diamagnetic shielding, starting at about Tc = 91-92 K. Only in the Eu and Gd com-

50

A. del Moralet al. /HTCsuperconductors

pounds the complete shielding is not attained until x 70 K and w 78 K, respectively. The thermal expansion and magnetostriction measurements were carried out using the well known strain gauge technique, which determines strains above z 5 x 1O-’ reliably. Magnetostriction was measured both parallel, A,,, and perpendicular, AI, to the applied magnetic field (up to 2.45 T), between 3.8K and well above T,. Such measurements allow one to determine both the anisotropic, &=I,,-A Ir and volume, o=A,, + 2A*, strictions . The main limitation of this technique is the gauge magnetoresistante, which for our gauges (Micromeasurements SK350) is typically of the order of 25 X 10e6 equivalent strain at 3.9 K and 2.45 T (gauge factor, gc2.04). However, magnetoresistance was carefully compensated (within ? 4%) using a dummy gauge, glued on a silica disk, this gauge and the active one constituting the arms of a sensitive DC bridge. The th.e. and magnetostriction apparatus is fully auto-

,,5x lo-”

,

I

I

magnetostriction

mated and controlled by a microcomputer, the readings of temperature, field and strain being taken simultaneously via a multiplexer.

Y

2.5-

i

29-

;

15

8

IO-

! 0.5 -

TEMPERATURE

(K )

Fig. 1. Temperature dependence of the thermal expansion for the REBa2Cu307_, series of compounds (the meaning of the symbols is in insert).

1

O*O

I

I

I

I

I

50

loo

l50

200

250

TEMPERATURE

300

(K)

l,5x lo-’ I

I

:Y

I

-

ir 6

5 G

l.O-

k @.I 6 0.5-

.l 0” o.o-

0

I

I

50

loo

I

150 TEMPERAME

I

200 CK)

250

300

i o.oo

. I

50

I

loo

150 TEWERAWfK)

200

250

Fig. 2. (a) Temperature dependence of the linear thermal expansion coefficient, (Y= ( 1/I) (allaT) for the REBa2Cu307_, compounds (RE=Sm, [3; RE=Y, +). (b) The same as for fig. 2a for RE=Eu(iJ), RE=Tm(+). (c) The same as for fig. 2a for RE=Gd(Cl), RE=Er(+). (d) Thesameasforfig. 2aforRE=Ho(O),RE=Dy(+).

A. de/Moral et al. / HTC superconductors magnetostriction 3. Experimental results and discussion

40

3. I. Thermal expansion

{ 12~4"~

)n

kB,(T)

-0-;.

i

i

i

o

'

0.0 0.0

where K c = ( n 4 / 5 ) ( n ~ k B / B ) . In specific heat measurement [ 14 ], a linear contribution, FT, has been also observed (although its physical origin is yet unclear), which should contribute to the strain AI/I as a term proportional to T 2. In figs. 3a-b, we show that for this series of compounds, eq. (2) GriJneisen law is well accomplished within an interval of temperature above around 20 K. An attempt to fit our resuits to a law which included a F T 2 contribution to AI/I failed. However, such a linear term has been found [ 37 ] for ot in the lower temperature interval 2 . 2 - 8 K for Y B a 2 C u 3 0 7 _ x . Griineisen law eq. (2) also allows one to determine the Debye temperatures, 0D, from the slopes of the straight lines of fig. 3. However, calculation of the constant Ko is diffi-

G5

1.0

ZO xlOs

15

T 4 (K 4 )

40 xlO. a

'

,

~

'

/ / . / o

•

3.C o

x

"'2.0

o

_1

o

•

1.0

0£

(1)

T4

v

x w

3

where ~ is the average, over the phonon Ik> states, of the Griineisen parameters 7k, 0D is the Debye temperature, n is the number of RE ions per unit of volume and B is the bulk modulus; kB is the Boltzmann constant. Therefore from the definition of or= (1/ l) (8l/8T), it follows immediately from ( 1 ) that AI

xlO 4

~ao

In fig. 1 we show the temperature variation of the th.e. strain, Al/l, for the present series, and in figs. 2a-d, the linear th.e. coefficients, a. The observation is that no anomaly at T¢, i.e. an ot,-as difference, is observed in any of these series of compounds within our experimental accuracy (better than _+0.5X10-6K-I). However, measurements on YBaECU307_x, with degrees of accuracy of ~ 0 . 5 X I 0 - 7 K -1 [35] and ~ 0 . 4 X I 0 - 6 K - 1 [36], did not detect any anomalous change as well. Besides, no other anomaly is observed between 3.8 K and ~ 300 K, which could be indicative of a crystallographic phase transition. Accordingly with the simple standard DebyeGriineisen model [ 41 ], for low enough temperatures the anharmonic phonon contribution to the th.e. coefficient has the variation

=

51

LO ( K41

D.O

T 4

xlO"62"0

Fig. 3. (a) Thermal expansion strain vs. the fourth power of temperature for the REBa2Cu307_x series (RE = Gd:[]; Dy: 0; T m : ~ ; y : A ); the straight lines are least squares fits. (b) The same as for fig. 3a for: R E = S m ( [ ] ) , H o ( 0 ) , E u ( l l ) , E r ( ~ ) .

cult, and therefore we have assumed it constant, and determined 0D for the series taking the specific heat determined value for YBa2Cu307_x (0D= 391 K) as ref. [ 14 ]. The values of 0D SO obtained are quoted in table II. Table II Debye temperatures, 0D, scaling constants, k (see section 3.1 for details), and th.e. linear coefficient, a, at ~ 2 5 0 K , for REBazCu3OT_x compounds Compound

0D(K)

k

o~( X 10 -61

Y Sm Eu Gd Dy Ho Er Tm

391" 374+4 382+4 338+4 345 + 4 367+4 352+_4 377+_7

1.0 0.70 0.78 0.80 0.62 0.59 0.66 0.68

10.0 11.6 11.6 11.2 13.8 11.6 13.9 13.3

• From ref. [ 14].

A. de/Moral et al. / HTC superconductors magnetostriction

52

At higher t e m p e r a t u r e s the Debye m o d e l gives a m o r e c o m p l i c a t e d t e m p e r a t u r e d e p e n d e n c e for O~ph [41 ], i.e.

3 n T k B ( T ) 3°°//r aPh--

B

~

2.0

i

]

i

i

ii

< 1.5

x4e x

!

i xlO-3

(fl

(eX_l)------~dx.

(3)

x~ I.C §

II

II

o B

Most revealing is that the th.e. strain t e m p e r a t u r e variations for the whole series collapse to a universal curve over most o f the entire t e m p e r a t u r e range studied (up to about 300 K ) (see fig. 4), if we scale Al/l for YBaECuaO7_ x with constant n u m b e r s k, given in table II. This result constitutes a strong indication o f a c o m m o n p h o n o n lattice origin for the th.e. in the whole series o f H T C superconductors studied, i.e. a universal f ( T / O D ) function in the Debye model eq. ( 3 ) h a p p e n s to be the case. The dif450

xlO-6

-140 ..~ ~'-120

'

~

n ii

0.~

e e !1

_ . O,(I i~ e t O I p

O.0

50

~

,~o TEMPERATURE

~o

2;0

3OO

(K)

Fig. 4. The collapse of the thermal expansion vs. temperature dependence of the REBa2Cu3OT_xseries, starting from the Y compound with normalizing constants k given in table II. k is defined as the low temperature quotient of the RE compound th.e. with the Y one.

'

~

~

'

a

/ a a K Dy Bo2Cu 3 O7_x

~.0SK

F--

F~-~oo ~j-B0

~

SgSK

Z

~

8.05K

-60

lo K

~-Z,0

13.0SK 16,5K 2005K

I

0 5C

x lO-6

5

'

3o.,o~

E 3c

2

=0if..%. 10 5,, '

~2C

"

1.500K

I

20

25

'

~--

~7~"

'

z"

'

b

J'~/-n''na^ru^nx

H=2,5,

~

.

j ?

8.05K 13.05K 16.5 K

-

1 0

0

1 20

10

. . . . .

-lC

"

I

15 H (kOe)

0

:E

lC

"

'

z~C

o

"

10

~ 30

T(K)--

I 5

40

50

~

. ~...~__~J~"~~ ~

~

....

I 10

I 15 H(kOe)

I 20

~...~)-20.05K - 250K" 30~05K

i 25

Fig. 5. (a) Isotherms of magnetostriction parallel to the field, 20, against the applied magnetic field, H, for DyBa2Cu3OT_xcompound. (b) Isotherms of magnetostriction perpendicular to the field, 2 ±, against the applied magnetic field, H, for DyBa2Cu307_x compound. In the insert, the thermal dependence of2 ± at H= 2.45 T.

A. del Moral et al. / HTC superconductors magnetostriction

ferences observed in the normalizing constants k among the diverse RE partners (see table II) likely derive from different lattice cell masses and bond strengths. Although the collapse differs by as much as around 10% among the different RE at the higher temperatures studied (above -~ 200 K), the general above mentioned trend cannot be ruled out. However, perhaps more precise th.e. measurements are needed to confirm clearly such a statement. 3.2. Magnetostriction

We will divide the study of magnetostriction of these series into the anisotropic and volume contributions.

3.2.1. Anisotropic magnetostriction

In figs. 5a-b, 6a-b and 7a-b, we show the isotherms of the parallel to the field, 211, and perpendicular, 2 . , magnetostrictions for some compounds. Noteworthy, as it can be seen from the inserts in figs. 5b and 6b for Dy and Ho compounds, respectively, is that 2 ± clearly shows up the beginning of the paramagnetic (P)-antiferromagnetic (AF) transition within the RE sublattice. In figs. 8a-b we show the scaling of Rt with H 2 for Dy and Ho compounds, respectively; the good linearity found is a indication that in fact the RE sublattices are behaving paramagnetically. In figs. 9a-b we show the thermal variations of 2, and 2 ±, at the maximum applied field of 2.45 T, for

MAGNETFELD, IC15 H(kOe)20 5 APPLIED 10 z ~-2o

l

~3

53

t

25

I

~61K

I

I!aK

a

~<-r~

-70xlO6 I z-25 _o

xlO- 6

20

3{;~

I-0

/

xi0-6

,

~I ,

)

~I i

H° B ° 2 Cu 3 OT -x

~

~

/~0 16.1K 38K / / 7 S0K I12.6K O.OK

b

m 15

_J

o

Z U.I

5

•

,

I ~

22.0K

n- 0

W

5

10 15 20 APPLIED MAGNETIC FIELD, H(kOe)

25

Fig. 6. (a) The same as for fig. 5a, for HoBa2Cu3OT_x compound. (b) The same as for fig. 5b, for HoBa2Cu3OT_xcompound.

20

x

I0 -6 ,

~

i

,<~25

,

x I0-11 '

I

'

i

]

I

'

I

3.11 K

3.8K

15

Er Ba2CusOT-z

aS-

5.3K 6.OK

5.3 K QK

Er Ba2Cu.~07..

ZSK 9.OK

~ m

7.5K

L~

9.OK It.OK

~ 5

II .OK 13. OK

13.OK

15.11K

1§.SK

IS,OK

Ill.OK

~2

~o -%

5

I0

15

~0

w ~ -5_

25

'

H (kOe)

,b

;

,~

2'o

25

H (kOe)

Fig. 7. (a) The same as for fig. 5a, for ErBa2Cu3Ov_x compound. (b) The same as for fig. 5b, for ErBazCu3OT_x compound. 5~0, 40.OK 30.05 K 211.0K

a

20.~K

~ , -50

16.5K

IOK 13.05K

I

&05 K ~.95K

I0~11

I

,oo

I

,

I

I

H 2 (kOe 2) 0

100

200

l

3.8K 4.5K

,

,oo H z (KOe 2 )

,oo

>

300

L,00

500

600

I

I

I

I

,,~

b 32.0K 270K

~-25 O rY

20.0K

15.0K

~ ~

-50

t3 0

12.0K

HoBa2Cu307x_

~

o l0K

~

8.OK

(1~

6.1K

<

-75

3.8K

-100

xlO-6

i

~

I

t

J

r

Fig. 8. (a) Isotherms of anisotropic magnetostriction, 2 , against the square of the applied magnetic field, H 2, for DyBa2Cu3OT_x. (b) The same as for fig. 8a, for HoBa2Cu3OT_x compound.

55

A. del Moral et al. /HTC superconductors magnetostriction

0

IO

30

20

40

I

50

T(K)

IO

0

20

30

T(K)

I

15

2

x 10-S

I.,, thermal depenwith RE=Dy( A),

b much that for Eu3+, J= 0 in the ground state. Nevertheless the mixing-in of the next excited multiplet J= 1, separated by around a few hundred K from the ground state [ 421, can give rise to substantial magnetostriction, regarding the non null magnetic moment found for this ion, of z 1.5 ug for TI 100 K

IO

2 5

0

Fig. 10. The anisotropic magnetostriction, dence for the REBa2Cu307_, compounds, Ho(o)andEr(v).

20

Fig. 9. (a) Temperature dependence of the parallel, A,, ( A, v, A symbols), and perpendicular, i, (., X, CI symbols), for REBaZCu307_x compounds (RE=Y, Eu, Tm, Er), at the applied field H~2.45 T. (b) The same as for fig. 9a for the compounds with RE = Sm,Gd ( O,A symbols for A,,; x, o, for A I ).

these series (except for Dy and Ho compounds ) . The observation is that those systems behave very isotropically, i.e. ;i ,,z I I, and therefore the anisotropic striction is essentially zero, A,=: 0. On the other hand, magnetostriction is large in Dy and Ho compounds (fig. 10). These results can be phenomenologically understood considering table I. There we can observe that for Dy and Ho compounds the applied field (2.45 T) is much larger than HP, whereas for the remaining compounds, where A, is weak or practically zero, the applied field is much smaller than Hp. Weak magnetostriction is not surprising either for the Gd compound, inasmuch that Gd3+ is an S state ion, or for the Y one. However for the other compounds of the series the null magnetostriction observed calls for a weak or null penetration at the RE sites by the applied magnetic field. Therefore these RE sites look quite well shielded. Perhaps one could also expect weak magnetostriction for the Eu compound, inas-

1101. Unfortunately, the shielding precludes a comparison of the ground state magnetostriction among the different RE probes. At 0 K, n,(O) -cr.& )J(Jl/ 2), where crJ is the Stevens factor, (r:,) is the quadratic average radius of the 4f shell and J is the total angular momentum. Where comparison is feasible, i.e. with the Dy3+ and Ho3+ ions, we notice that &(Dy)/l,(Ho)x0.78 at 4.2K and for the maximum applied field of 2.45 T; this ratio compares remarkably well with the predicted one from the above formula: 0.75. The agreement indicates that we are, in fact, in the presence of single-ion crystal field magnetostriction. For the Er3+ ion such a comparison cannot be made at this time as far as an applied field of 2.45 T is quite close to HP (see table I> and therefore A, should be far from saturation. Measurements using strong fields (up to 18 T) are currently envisaged in order to come closer to the saturation strictions of the RE3+ ions within these superconducting matrices. In fig. 11 we show the scaling of A,, at H~2.45 T, against the reduced magnetization m =M( T, 2.45 ) / M(0, 2.45) (refs. [3,9] ) for the Dy and Ho compounds. As we can observe, for temperatures well above TN, A,( T, 2.45) N ma, with CYnot very far from 2, that indicates a paramagnetic crystal field single-

56

A. del Moral et al. / HTC superconductors magnetostriction

6C

I

I

I

I

I

3.2.2. V o l u m e magnetostriction

I I I

xi0-6 L,0

20

~

.5

~=2.4/ 10

0.1

I

~

.2

i

.3

l.

I

I

,

,

.5 .6 .7 B .9

m ----ib

Fig. l 1. Double logarithmic plot for the scaling of the anisotropic magnetostriction, 2t, with the reduced magnetization, m, for REBa2Cu3OT_xcompounds (RE=Dy: ,~; Ho: o ). The slopes of the least squares fitted lines are represented by or. ion magnetostriction as well [43]. Such parastriction should be developed inside the normal conducting material, i.e. within the superconducting vortices, where there exists, indeed, field penetration. Outside the vortices, 2t must be weak, as for a superconducting diamagnetic system (i.e. o f the order of 0.5 × 10 -6 [33 ], as happens in YBa2Cu307_x (see fig. 9a) ), and this is what it is observed in most o f the present compounds. We should finally stress that no measurable magnetostriction (smaller than ~ 0 . 5 X 10 -6) has been observed around T¢, for the present series.

I

30

I

E)-6

Volume magnetostrictive strains in paramagnetic RE lattices can have, in principle, two possible origins: the dependence o f exchange with the distortion (exchange striction) and the modulation o f the CEF levels with the strain, yet in this case the symmetry o f the CEF contribution to the strain must be of high order (higher or equal to fourth-order in angular m o m e n t u m Stevens operators) [44]. Therefore volume magnetrostriction could provide, in principle, additional information about the interactions underlying the RE sublattice in the present series. In fig. 12 we show the thermal variation o f the volume magnetostriction, o9=2, + 2 2 . , at the maxim u m applied field o f 2.45 T, for the present series. Quite noticeable is that (except for the Dy, Er and Y compounds, where co is larger) all 09 are o f the same order o f magnitude and also become negligible at similar temperatures. These results again call strongly for a volume striction produced by the superconducting diamagnetic "host" lattice, with little intervention of the RE ions. This is so inasmuch that the Y c o m p o u n d shows the same volume striction thermal behaviour and the same thing happens for the Eu c o m p o u n d with J - - 0 ground state, as discussed

,

,

,

• Y o Tm ~, Sm

3

g

• +

150

3 z" Q

x Gd

ov Eu Er

x10-6

H=2.4 T

I--

Dy Ho

100 ~:

I--

Lo

t.u z Od

50 u 2~

talC

.._1

..J

o

9 1

10

2O

30

I

i

40

50

60

T(K)

Fig. 12. Thermal dependence of the volume magnetostriction, co, at H=2.45 T for the REBazCu3OT_xseries. (for Y, Dy and Er compounds the right hand vertical scale applies).

A. del Moral et al. / H T C superconductors magnetostriction

before. The volume striction of YBa2Cu307_x seems too large for a closed shells y3+ ion, a n d therefore one could speculate whether the large o9 is related to the magnetic m o m e n t ascribed to the copper ions, between a r o u n d 0.1 a n d 0.6 ~tB [ 2,3,6,13,22 ], which besides display a complex squared AF lattice [45 ]. If this is the case, volume magnetostriction could be of exchange a n d single ion crystal field origins. These considerations could be extended, in general, to the rest of the series. Another explanation has been advanced by Zieglowski et al. [46], based on the distortion produced u p o n the lattice by the magnetic Laplace forces a m o n g SC parallel shielding currents, assumed to exist along cylindrical paths within the C u - O chains disposed above and below the RE ion layers. The origin of the m a x i m a of 09 observed (see fig. 12) could be correlated with the precursors of the P AF transition (within the RE sublattice), as observed in the c o m p o u n d s with S m , G d , D y , H o and Er [ 15-17 ], and with the elastic moduli hardening observed at relatively low temperature in YBa2Cu307_x [ 2 6 - 2 7 ] and La2_xSrxCuO 4 [47], as well.

Acknowledgements We are most grateful to members of Departam e n t o de Q u i m i c a Inorg~inica, U n i v e r s i d a d Complutense ( M a d r i d ) : M.A. Alario, U. Amador, N. Barahona, F. Fern~indez, E. Garcia, J. Gonzalez-Calvet, E. Mor~in, R. S~iez-Puche and N. Vallet for the preparation and characterization of the samples, and to J. Bartolom6, F. Lera and C. Rillo (ICMA, U n i v ersidad de Zaragoza) for additional information concerning the SC diamagnetic effect and for useful discussions. We also acknowledge the financial support of the European C o m m u n i t i e s , u n d e r Contract no. S C 1 - 0 0 3 6 F (Superconductors Project).

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