Trapping and relaxation of inter- and intragrain vortices in YBa2Cu3O7−δ

PHYSICA

Physica C 199 (1992) 201-206 North-Holland

Trapping and relaxation of inter- and intragrain vortices in YBaECU3OT_ E.V. B l i n o v b, E. L~ihderanta a, R. L a i h o a a n d Yu.P. S t e p a n o v b a Wihuri Physical Laboratory, University of Turku, 20500 Turku, Finland b A.F. loffe Physico-Technical Institute, Academy of Sciences of Russia, St.-Petersburg, 194021, Russian Federation

Received 20 May 1992 Revised manuscript received 15 June 1992

Isothermoremanent magnetization and its relaxation with time have been investigated in ceramics and powders of YBa2Cu3OT_,~ at different temperatures after magnetizing the sample in a field ofnex t < 600 Oe. From the results for powder samples we obtained for intragranular vortices the value of the effective pinning energy Ucff~0.7 eV, independent of H ext. In the ceramic material Uefr was found to depend strongly on the applied field reaching a value of 5 eV at 10 Oe and decreasing steeply when the magnetizing field was increased, The field dependence is discussed by using a model which takes into account the interaction between vortices.

1. Introduction

Magnetization o f type-II superconductors, including high-To metal oxides, has a metastable nature. Consequently, time dependent measurements can be used to investigate high-T~ superconductors [ 1-5 ], especially the flux-dynamics and flux trapping phen o m e n a [ 6 - 8 ] . In addition to the basic properties such information is important for applications o f these materials [ 9,10 ]. The magnetic flux structure in ceramic high-Tc superconductors was shown [ 1 1-13 ] to be very complex. In a wide range o f experimental conditions different kind o f vortices m a y exist in these materials, i.e. ( 1 ) intragranular Abrikosov vortices and (2) Josephson and hypervortices in weak links formed by contacts between grains. Moreover, it should be noted that powders also may contain weak links, as pointed out for example in ref. [ 14 ]. In ceramic materials all these vortices can be divided practically into two groups: intragrain and intergrain vortices. The critical magnetic field o f the material in the grains, H~I, is higher than that o f the intergranular weak link H¢~ [ 15 ]. When the magnetic field is increased starting from zero the inter-

grain vortices start to be trapped in weak links at H > HcWt and at H > H d the intragrain vortices appear. The effects due to trapping o f these two kinds o f vortices can be distinguished by comparing the properties o f sintered and powdered samples in different magnetic fields. It is obvious that the effective pinning energy and the relaxation rate for inter- and intragrain vortices may be different due to their structural differences and conditions o f occurrence. The motion of the vortices is usually analyzed in terms o f the energy barrier parameter Uo [ 16 ]. For single crystals o f YBaaCu307_~ the values of Uo, determined from magnetic measurements, are in the range of U~ ~ 0.02-0.1 eV and U~b ~ 0.15-0.6 eV when the field (30 O e < H < 30 kOe) is applied parallel or perpendicular to the c-axis, respectively [ 17 ]. Xu et al. [ 18] have investigated c-axis-oriented YBa2Cu3OT_~ powder in an applied field o f 1.0 T, obtaining values of Uo from g 20 meV at 5 K to ~ 1 3 0 meV at 35 K. Kes et al. [19] have reported the value of Uo~ 1 eV determined from AC-resistance measurements of a thin film. From DC-resistivity of Y B a 2 C u 3 0 7 _ ~ single crystals Uo has been found to range from 0,87 eV in the field o f 12 T to 17 eV in the field of 0.1 T [ 20 ]. The grain boundaries of ceramic superconductors can be regarded as extreme local inhomogeneities o f

0921-4534/92/$05.00 © 1992 Elsevier Science Publishers B.V. All fights reserved.

202

E. V. Blinov et al. I Trapping and relaxation of vortices in YBaeCus07_~

the material. Therefore they can provide an effective system for pinning of the magnetic flux vortices. Nikolo and Goldfarb [ 21 ] have used the imaginary part of the AC-susceptibility, Z~c, to determine Uo at the grain boundaries. From the Arrhenius expression for the frequency dependence of the temperature shift of the maximum of Z ~ c ( T ) they found Uo= 12 eV in the zero field limit (H=0.01 Oe). Above a decoupling field ( 13-25 Oe) the energy barrier was found to disappear. In this paper we report measurements of the isothermoremanent magnetization (IRM) and its time dependence in ceramic and powder samples of YBa2Cu307_a. It is demonstrated that comparing the remanent magnetization and its relaxation rate we can distinguish the behaviour of the intergrain and intragrain vortices. From the results obtained at different temperatures and magnetizing fields, H~x~,the values of the effective pinning energy U~ff are calculated by using the Anderson-Kim flux creep model [ 16 ]. The conception of vortex interaction is used to interpret the dependence of/Jeff on the magnetic field in ceramic samples.

controlled with flowing He gas and measured with an accuracy of 0.2% using a carbon-glass thermometer. The field Hext is produced by a copper solenoid (Hext<220 Oe) or by a superconducting magnet (Hext> 220 Oe). Before every measurement the remanent field of the sample space (usually 1-2 Oe) was determined with a small Pb test sample and compensated after observing the field at which the plot of M versus H changes its sign. The values of IRM were determined as follows. At first the sample was warmed to a temperature above 130 K and then cooled in zero external field down to the measuring temperature (ZFC process). The magnetizing field was applied during a waiting time tw of 10-20 s. An increase of tw of 5 min had no observable influence on the results. The measurements of IRM and the time dependence of IRM were made in zero external field after switching off Hext. By using the Cu solenoid for the generation of H~xt the time dependence measurements could be started from small time values.

3. Results and discussion 2. Experimental

3. I. E x p e r i m e n t a l results

The samples were prepared from sintered pellets of YBa2Cu307_a annealed for 17.5 h at 940°C, 20 h at 907°C, 2 h at 600°C and for 7 h at 400°C. After these treatments the grain size of the material, dg, was 5 ~tm. By using a longer annealing time at 940 ° C (73 h instead of 17.5 h) dg could be increased to 20 ~tm. The powdered samples were prepared from the latter material by using the methods described in ref. [22]. In this way we obtained samples with a larger volume-to-surface ratio reducing hence the relative significance of the surface effects [ 23 ] in the measurement. All our samples exhibited a sharp resistive transition at 92 K. The magnetic measurements were made with a SQUID magnetometer. In this equipment the sample passes through two counterwound pick-up coils connected to an RF-SQUID. For time dependent measurements the sample is placed inside one of the pick-up coils and the SQUID output voltage is recorded as a function of time after removing the magnetizing field//ext. The temperature of the sample is

In fig. 1 the typical time dependence of IRM (at 78 K) is presented for ceramic YBa2Cu307_ a after magnetizing the sample in the field of 10 Oe. From this plot we can estimate the relaxation rate dM/dln t.

.,

0

1~ of IRM "o,.

o I

5 - 1

-2

¸

.....

,

10

. . . . . . . .

,

time10 ~s)

. . . . . . . .

,

1000

Fig. 1. Time dependence of the SQUID output signal measured in zero field at 78 K, after magnetization the ceramic YBa2Cu307_6 sample (ds=20 ~tm) in the field of 10 Oe. The vertical line correspondsto 1% of the isothermoremanentmagnetization (IRM).

E. V. Blinov et a L / Trapping and relaxation o f vortices in YBa2Cu3Oz_~

The dependences of IRM on the magnetizing field are shown in fig. 2 ( a ) and (b) and (c) and (d) for the ceramic and the powdered samples, respectively. The measurements were made at 78 K. In a ceramic sample nonzero values of IRM could be observed only for H~x,->HeWl( ~ 2 - 3 0 e ) . In the case of Hex~= 10-30 Oe the isothermoremanent magnetization is approximately constant. In the powdered material IRM is observable only when H~xt is above 30 Oe ( ~H¢] ). It is known that He, is anisotropic, i.e. H ae~ b i-~,-¢~. " I4c Because the grains in our powder specimens were not aligned, the critical field H~ ~ 30-40 Oe at 78 K, as estimated from fig. 2, is determined by the grains oriented so that the value of the penetrating field is lowest. This agrees well with the value of the critical magnetic field H~ b ~ 37 Oe, calculated from the data for single crystals at the same temperature [24 ]. In fig. 2 ( b ) and (d) the IRM is presented as a function of H~xt up to 600 Oe. In both ceramic and powdered samples the increase of IRM above Hd can be attributed to the intragrain vortices. In addition to the low-field saturation of IRM observed in the ceramic material (fig. 2 ( a ) ) a second saturation ( ~ 8 X 10 -8 A m 2 / m g ) is found in both type of samples when H~xt> 150 Oe. In fig. 3 the relaxation rate dM/dln t is presented as a function of/-/ext. It is obvious that in addition

(a)

t . '(~)..... 0,4

,%-.

!

~ 0

O0 10

~ ©

O.8

~

° 40

60

80

N "~

0.0

L

0,8

20 o,~

6o ~L

oo o o o o

1.o

o

°o°

~ ~

(o) o

0.02

o m

#

0.01

a

D

&

0.00

"

:

13

:

:

:

:

:

:

:

:

(b) o

0.02 o

0.01 o a o

0.00 0

~ ..... o ~o

6'o ' 8'o

H,,t (Oe)

Fig. 3. The time constant dM/dln t for ceramic (a) and powdered (b) YBa2Cu307_~ measured in zero field at 78 K after magnetizing the sample in the field Hc,,.

to the remanent magnetization also the relaxation rate for the ceramic and powder samples differ for H~,t< 40 Oe. In the ceramic material dM/dln t is almost constant between Hex, = 10-40 Oe. In the powdered material the time dependence is observed only above Hext comparable to He]. By using the formula

(1)

0.2

0.2 q:D

0.03

1 dM kT S = M d l n t - Ueff'

o3

203

o

O.6

O.4

C12 0.2

0.2 ~100

200 300 400 500

Ho~t (0°)

0.0

o

2 ~o, 2?0,39o . 4?0,5o0,

He,t (Oe)

Fig. 2. Plots of IRM as a function of the magnetizing field HCxt between 0 - 5 0 0 Oe for a ceramic, (a) and (b), and a powdered, (c) and (d), sample of YBa2Cu3OT_~. The magnetic moment is normalized to the saturation value (next> 150 Oe). The measurements are made at T = 78 K.

based on the Anderson-Kim flux creep model [ 16 ], we determined the values of Ucff from the experimental data measured as a function of H~x,. In fig. 4 Ueff(H~x,) is presented for the ceramic sample with dg ~ 5 ~tm (triangles) and for a powder sample (circles). These data were obtained at 78 K. As can be seen from figs. 2 (a) and 3 (a) the behaviour of IRM and dM/dln t for the ceramic sample seem to be rather similar. Nevertheless, a close examination of the data shows that the effective pinning energy Ueff, obtained from these results, decreases with increasing magnetic field for H~x, > 10 Oe. For the powder sample the value of Ucff~0.7 eV is obtained independently of the magnetization field. The depen-

E. V. Blinov et al. / Trapping and relaxation of vortices in YBa2Cu307_,~

204

4

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>

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8

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. . . .

0

° i

. . . .

50

8

8 i

8" . . . .

oi

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,

,

150

He×t (Oe) Fig. 4. Dependence of the effective pinning energy Ucff on the magnetic field at 78 K in ceramic (triangles) and powder samples (circles).

6 • . (o) T = 41 K

(c)

T =

71

K

5 4 3

2:3 5 5 4 3 2 1 0

19o ~

2~

Ho,,t (Oe) Fig. 5. Effective pinning energy Ueffvs. magnetic field for a ceramic sample at temperatures 41 K (a), 5 8 K ( b ), 71 K (c), and 7 8 K (d). Solid lines are fits to eq. ( 12 ).

dences of U~ffon HCxt at four different temperatures (41 K, 58 K, 71 K and 78 K), are shown in fig. 5. 3.2. Magnetic flux structure and relaxation of different kind of vortices

As was sown in fig. 2 the dependence of the remanent magnetization on the magnetization field is different in ceramic and powder samples. For the powder the increase of the remanent magnetization with increasing magnetic field is due to intragrain

vortices which start to penetrate into the particles at Hex,>Hc~. As evident from fig. 2(c) in our powder sample Hc~ is 30-40 Oe at 78 K. In ceramic materials the magnetic flux structure is more complex. In addition to grains, the flux can be trapped in this case also in the network of the weak links. This is possible in the range of fields H~W~< Hext < H¢~2, where H~'2 is the upper critical field of the weak link [ 15 ]. Within this limit the field penetrates between the grains within a distance cHext/4rJ~w [ 5 ] leaving the grains as partially diamagnetic inclusions. Here J~w is the critical current of weak links in the approximation that they are equal. When the field exceeds Hc~ the fluxons enter the grains with penetration depth determined by J~g instead of J~w. So we can find a range of magnetizing fields ( H ~ 40 Oe, when also intragranular vortices appear in the grains, the decrease of U~frcan be explained by the interaction between inter- and intragrain vortices [ 26 ]. That interaction decreases the critical current density through the intergrain contacts leading to the decrease of the remanent magnetization due to intergrain vortices. At HHc] but also at H < Hc]. For these low magnetic fields a quantitative approach based on the interaction between intergrain vortices can be proposed. The interaction energy U]2 between two filaments can be written as [27] • g

(r]2\

(2)

where q~o=h2e=2.07× 10 - 7 Mx is the flux quantum. Here r12 is the distance between two vortex lines and Ko(x) is is the zeroth order Bessel function of the second kind [28]. Ko(x) can be approximated by a logarithmic function

E. V. Bfinov et aL / Trapping and relaxation of vortices in YBa2Cu307_6

Ko(x) ~ _ -Iln(~)+

?1,

(3)

K o ( X ) "" (2zx) -1/2 e x p ( - x ) ,

(4)

when x is large• Here ? is the Euler's constant (?=0.577). The distance between two vortex lines can be written as [29] r12 =

,

(5)

where H is the applied magnetic field• With high field values eqs. (2), (3) and (5) give U t 2 = U ' (2) [ l n ( 2 H 1 / 2 ) - ? ] ,

(6)

where a = ( ~ o / n ) ~ / 2 / 2 . The coefficient function U' (2) describes the strength of the interaction. It has the unit of energy and is proportional to 2 -2 . According to the BCS theory [ 27 ], the temperature dependence of 2 is 2 ( T ) = 2 o [ 1 - (~c)4] -1/2

(7)

Hence U' (2) depends on temperature as u'~:l-

~

.

(8)

Using eqs. ( 2 ), (4) and ( 5 ), we can write for small field values UI2 = U" (2) H~/4 exp( - a l l

-~/2) ,

In

H~xt -7

,

when H~xt is high and

Ueff= U0 - U " (2)H,xt I/4 e x p ( - a H ~ l / 2 ) ,

(12)

when H~xt is low. The fields used in our experiments represent rather the low than the high field limit of the vortex interaction model presented above. This is also reflected by the fact that with the conceivable values of o~ (i.e. 2 0 = (22ab2c)1/3=0.20 ~tm [24]) U12 determined from eq. (6) becomes negative in fields of Hext < 100 Oe. This leads to an unphysical situation where the interaction between the vortex lines is attractive instead of repulsive. The change of the sing of U,2 is due to the approximation of K o ( x ) by the logarithmic function (see eq. ( 3 ) ) which exaggerates its decrease in small fields. In fig. 5 the values of U~ff, determined from the experimental data, are compared with eq. (12) as a function of H~xt (solid lines), and in fig. 6 as a function of H~xt ~/4 exp ( -- aH~x~/2 ). In the latter case, U~ff must give a straight line if one chooses a correct value of a (i.e. correct 2). At the limit of ,g~/4• ~xt e x p ( aH~/2)~O we obtain the value of U o - 6 + 1 eV. This is clearly larger than those reported for single crystal specimens [ 17-19 ] and about half of the result obtained from the AC-susceptibility measurements for intergranular weak links in ceramic sam-

(9)

where U" (2) is proportional to 2 -3/2. The repulsion energy U~2 between the vortex lines decreases the energy barrier of the flux motion to an effective value U~fr= Uo - U,2 - F V X ,

during tw before the measurement. Therefore the field dependence of Uefr can be written as Ue~=Uo-U'(2)

when x is small and by an exponential function

205

(10)

where Uo is the (microscopic) energy barrier which does not depend on experimental conditions. F V X is the energy resulting from the Lorenz force F o c B V B , V is the activation volume and X is the width of the barrier [ 18 ]. In a measurement of the remanent moment we have BIn0 and the term F V X can be ignored. The magnetic field in eqs. (5), (6) and (9) is essentially the field H, xt applied on the sample

(c) T - 71 K 5 4

•li'l 2

o.r~ l.p 1..5 zp . ~ T b" )58 K

~

•

1.p

1.~ 2,p

"L"

)T

-

78 K

.

2.,~

H1/4exp( - ctH-~/2) Fig• 6. Dependence of U~r on H~/r4 exp( -o~H~x~/2) at temperatures of 41 K (a), 58 K (b), 71 K (c) and 78 K (d). Solid lines are fits to eq. (12).

206

E. V. Blinov et al. / Trapping and relaxation o f vortices in YBa2Cu3Oz_~

pies [21 ]. It is also f o u n d that Uo does n o t d e p e n d o n t e m p e r a t u r e w i t h i n the range c o n s i d e r e d in o u r m e a s u r e m e n t s , 41 K < T < 7 8 K. As can be seen f r o m fig. 5 a good a g r e e m e n t between the calculated a n d e x p e r i m e n t a l d e p e n d e n c e o f Ueff o n HCxt is o b t a i n e d i n the range o f low magnetic fields b y using the s i m p l e vortex i n t e r a c t i o n m o d e l d e s c r i b e d above. It s h o u l d be n o t e d , however, that the vortex glass m o d e l [30 ] m a y p r o v i d e a n alt e r n a t i v e a p p r o a c h to this p r o b l e m . F u r t h e r investigations o f this q u e s t ! o n are i n progress.

4. Summary I s o t h e r m o r e m a n e n t m a g n e t i z a t i o n ( I R M ) a n d its t i m e d e p e n d e n c e h a v e b e e n i n v e s t i g a t e d in low magnetic fields for c e r a m i c a n d p o w d e r e d s a m p l e s o f YBa2Cu307_~ at different t e m p e r a t u r e s . C o m p a r i son o f the r e m a n e n t m a g n e t i z a t i o n a n d its r e l a x a t i o n rate allows us to d i s t i n g u i s h the b e h a v i o u r o f the intergrain vortices, t r a p p e d in a c e r a m i c s a m p l e f r o m the b e h a v i o u r o f the i n t r a g r a i n vortices in powders. I n p o w d e r s the effective energy b a r r i e r Uefr does n o t d e p e n d o n the m a g n e t i c field. I n the c e r a m i c samples Ueff shows a m a x i m u m a r o u n d 10 Oe w h e n pres e n t e d as a f u n c t i o n o f the m a g n e t i z i n g field. T h e decrease o f Ueff i n the range OfHext > 10 Oe is e x p l a i n e d by i n t e r a c t i o n b e t w e e n vortices.

Acknowledgements T h e a u t h o r s are i n d e b t e d to L.S. Vlasenko, E.B. S o n i n a n d K.B. T r a i t o for helpful discussions.

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