Thermal fluctuation in high-temperature superconductor HgBa2CaCu2O6+δ

PHYSICA ELSEVIER

Physica C 228 (1994) 211-215

Thermal fluctuation in high-temperature superconductor HgBazCaCuzO6 + Z.J. Huang a,1, y.y. Xue b, R.L. Meng b, X.D. Qiu b, Z.D. Hao b, C.W. Chub,. a Department of Physics, National Taiwan University, Taipei, 10764, Taiwan b Texas Center for Superconductivity and the Department of Physics, University of Houston, Houston, TX 77204-5932, USA Received 12 April 1994; revised manuscript received 23 May 1994

Abstract The reversible magnetization M has been carefully measured on a polycrystalline HgBa2CaCu206+~sample ( Hg- 1212), with a superconducting transition temperature Tc~ 119 K and a transition width AT~ 2 K. The magnetization is field independent at 116 K, suggesting a significant role of thermal fluctuations. The value of this magnetization leads to an estimated superconducting volume fraction of 65% based on a quasi-2D thermal fluctuation model. After corrections for fluctuation and random grain orientation, the superconducting parameters of K~ 60, He2(0) ~ 53 T, ~.b(0) ~ 25 .~, and hob(0) ~ 1500 .~ are obtained.

1. Introduction Recently, superconductivity above 130 K has been discovered in the Hg based HTS's [ 1]. The phase with superconducting transition temperature Tc = 110 to 126 K has been identified as HgBazCaCu206 +d (Hg- 1212) [2], and the phase with T c = l l 0 to 135 K [3] as HgBa2Ca2Cu308+d (Hg-1223). In addition to their potential in applications [3], these compounds also serve as a new testing ground for various proposed models. The magnetic properties are of particular interest because they are related to the mechanism of superconductivity and many fundamental superconducting parameters [5]. Many unusual phenomena have been observed in the magnetization of various high-temperature superconductors (HTS's). Among them are the field-independent magnetization (FIM) at a temperature T* near Tc [5 ], and the scaling behavior, * Corresponding author. On leave from Texas Center of Superconductivity and the Department of Physics, University of Houston, Houston, TX 77204, USA. 0921-4534/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSD1092 1 - 4 5 3 4 ( 9 4 ) 0 0 3 4 6 - H

in which the magnetization can be factorized as M(H, T) = @ ( T ) F ( H ) over nearly the whole reversible region [6]. Theoretically, FIM is attributed to both the vortexdeformation entropy at low field [7] and the orderparameter fluctuation at high field [8]. These effects are more prominent for the quasi-2D Bi and T! compounds than the less anisotropic YBa2Cu307 ~ (Y123). The scaling behavior, observed for Bi2SrzCaCu208 + ~ (Bi-2212) and Bi2Sr2Ca2Cu3Olo + (Bi-2223) [6], has not been observed for Y-123. This suggests that the observations are related to the anisotropy and the coupling strength between layers. It has been noticed that the spacing s between two adjacent CuOz blocks of Hg-12t2 is about 12.7 A, which is between those of Y-123 and Bi-2212. Many observations, such as the irreversibility line, suggest that the anisotropy of Hg-1212 is also between those of Bi-2212 and Y-123. Therefore, the Hg-1212 system may be an excellent candidate to bridge the 3D Y- 123 and the quasi-2D Bi family.

212

Z.J. Huang et al. / Physica (7228 (1994) 211 215

Ideally, a single-crystalline sample is desired for the study of magnetic properties, although the small size of the sample often makes the experiment very delicate. However, there is no Hg-1212 single crystal available at this moment. Fortunately, it is proved that the polycrystalline samples keep the fundamental signature of the magnetic properties of the cuprate 191. In this paper, we report a careful measurement of M as a function of T and H for a high-quality Hg- 1212 polycrystalline sample with a T~.~ 119 K and a transition width ATe. ~ 2 K. A field-independent M * is observed at 116 K. In addition, a scaling law M ~ [ I - ( T/7"j ) e I F(H) with T~ ~ 118 K is observed over almost the entire reversible region. All these appear to be a manifestation of a strong vortex fluctuation. Following the theoretical model proposed by Balaevskii et al. 171, where the thermal fluctuation effect due to the quasi-2D nature of the vortex pancakes is considered, the superconducting volume fraction in our sample is estimated to about 65%, which is consistent with X-ray and low-field magnetization measurements. After corrections related to the random orientation of the grains, some of the superconducting parameters were deduced. Among them are: K~6(), H c 2 ( 0 ) ~ 5 3 T, ~,;,(0)=25 A, and A(O) ~ 1500 ,~.

2. Experiments The Hg-1212 sample is prepared by the controlled vapor/solid reaction process given details of in Ref. [ 10]. The structure characterization was carried out by X-ray powder diffraction using a Rigaku D-MAX III powder diffractometer. Bar samples with dimensions of 3 × 2 × 6 mm 3 were cut from the obtained pellets for the electrical and magnetic measurements. The resistance was determined using the standard four-lead technique with a LR-400 AC bridge operating at 16 Hz and current from 0.1 >A to 1 mA. A Quantum Design SQUID magnetometer was used to measure the magnetization.

3. Results and discussion Fig. 1 shows the low-field DC magnetization at both the zero-field cooled mode (ZFC) during warming and the tield-cooled (FC) modes. The M at 10 K in the

t"•

•

t

eeQo~lNIl~

.(

Fig. 1 I)C n m g n e t i z a l i o n a s a l u n c l i o n of temperature lor Hg {212 at 5 0 e , Insert: an expanded vie,,,., of lhc Iransition. Solid s', mbol,~ FC, open symbols: Z F C

ZFC mode corresponds Io 80¢/, of the sample volume based on a density of/) = 6.4 g / c m ~without the demag netization correction. This value is an overestimation of the true superconducting volume fraction, bul seen> to be roughly the same as the weight fraction of Hg 1212 deduced from the neutron powder diffraction (NPD) data on similar samples 111 I. The M in F(" mode corresponds to a superconducting w~lume frac tion of 20%. However. it has been suggested [ 121 lhat the M at the FC mode severely underestimates lhc superconducting volume for ceramic HTS samples duc to pinning as well as the large penetration depth in the c direction. We believe that the superconducting frac. tion of the sample is more likely to be wilhin 60% to 80%. The superconducting onset temperature is about 119 K (Fig. 1 ) with a narrow transition width - 2 K. between 10% to 90% of the FC transition. At high field, the paramagnetic contribution of the impurity phases becomes signilicant. In this cxpcri ment, the magnetization between 175 and 250 K at 5.5 T was titled to the Curie law X=xo+C/T. wilt1 X o = 1 . 6 × 1 0 7 e m u / g and C = 3 . 3 3 4 × 1 ( ) -~ e m u / (both included the contributions from the sample holder). The magnetization at 0.1 T was also measured and was the same within experimental resolution, suggesting negligible ferromagnetic contributions. Thc obtained parameters were then used for the background subtraction. A set of typical ZFC data at high field is displayed in Fig. 2. One interesting feature is the FIM near T~. This phenomenon was first observed 151 in many HTS and organic single crystals with H perpen

213

Z.J. H u a n g et al. / P h y s i c a C 2 2 8 (1994) 2 1 1 - 2 1 5

0.0

TcSUH

Hg1212

0.2 "~ -0.4

/%..'- o~oo / / /

-0.6

'A#

f,g'' u=,

-0.8

t

/

* 05

~,~

a 02

¢

• 01

-1.0 20

¢

,',

dl

, ,

t j

40

J

60

80 T(K)

I

100

120

140

Fig. 2. ZFC magnetization of the sample at high fields. 0.00 TcSUH

T* F

-0,01 H(T) -0.02 ~ 0.5 -0.03

/j~/~

Hgl212

/

-0.04

z~

l

*

2

-0.05

/2//1

-0.06 / I I I 110

It

115

,

~

120 T(K)

. ,,,........ ,

~

125

130

Fig. 3. Expanded view of ZFC data near T *. 0.1 C2.Z ~0

0.0 -0.1 -0.2 -0.3 -0.4 -0.5

o o ,

~ 5

1 10 T 2( 103K 2 )

TcSUH 15

Fluctuations, either associated with the vortex position entropy [7] or related to the superconducting order parameter [9], have been invoked to interpret FIM in single-crystalline samples. Cho et al. [9] have further argued that the FIM of a ceramic sample should happen in the same temperature T* with a two times smaller magnetization M * -=M( T* ) comparing with the corresponding single-crystalline samples. Using the CuO2 block distance s = 12.7 A. and the observed T* = 119 K in Hg-1212, M* is calculated to be - 0 . 3 G for a polycrystalline sample based on the proposed model [7,9]. The value is in line with the observed M ( T *) ~ - 0.2 G (Fig. 3). The discrepancy has been observed before [ 7 ], and was attributed to the possible non-superconducting phases in the sample [7,9,15]. Thompson et al. [ 15 ] further used that to calculate the superconducting volume fraction. Following the same procedure, the superconducting volume fraction will be ~ 65% for the Hg-1212 sample, which is consistent with our NPD data and ZFC magnetization at low field. We will use this value in the following calculations. The observed lower field boundary BI, of the FIM region is about 1 T (Fig. 3), which is much higher than those of Bi-2212 or Bi-2223 (about 0.1 T or lower). According to Ref. [ 8],

20

Fig. 4. M vs. T 2 for the sample at 1 T ( t h e behavior is similar at other fields).

dicular to the conducting layers. Later, a similar FIM was also observed in ceramic Bi-2223 samples [9].

=

B't

Ilb.......~ 0

-rrA~In

[

(/~ J / / ~ a b )

]

4¢~nTA----~,.,b)J

mainly depends on the value of Aj, with Gb the coherence length in the ab plane, As = ys, and y the anisotropy ratio. Since the s of Hg-1212 is only slightly smaller than that of Bi-2212, the y has to be rather small to match the observed Bit. In other words, the Hg1212 is less anisotropic than Bi-2212. This is consistent with the result from the irreversibility line [4J and can be understood as a result of stronger inter-layer coupling. Another interesting result is that the Tand H dependences of the M can be factorized into M ( T ) ~ Mo[ 1 - (T/TI) 2] F(H) with T~ "-, 118 K over the entire reversible region except very close to Tc (Fig. 4). This separation of H and T dependences has been observed in Bi-2212 and Bi-2223 single crystals [5], but not in Y-123. In the case of Bi-2212 and Bi-2223, this factorization of the T and H dependences leads to a temperature-independent H¢2, therefore an unphysical divergence of K near T *. This anomalous behavior was

Z.J. Huang et al. / Physica C 228 (1994) 211-215

214

suggested as a manifestation of the quasi-2D nature in Bi-2122 [5,7]. In this sense, the Hg-1212 is similar to Bi based HTS and is more anisotropic than Y123. To extract the superconducting parameters, the obtained M(T, H) has to be corrected for the random grain orientation. To do that, we extended the argument of Ref. [ 10] for the field-independent M * to lower T. If the anisotropy ratio is large, the magnetization M, of a polycrystalline sample will only come from the HII c components, as demonstrated in Ref. [ 13], and should be directly related to

Fit to

['~,~- 125 K

.<

b

,<

0" O -~'

(a)

I~SL;II i -,~

5(I

32~r2A~h

In

eH

,i

,Ji,

I0t~

IRK',

a~/eHA

of a single crystal with Hllc. The constants r/and a are parameters of order unity. Following Cho et al. [9], the M,(H, T) in a field H~j << H << H~2 is given by Ms = (cos

clean Iirmt

/ . a l ¢ 0 i = 1500 \

I!11)(I

Mo-

12!2

}t(; 2q{!(~

t

60

O)Mo '+ 4 0

+ (cos 01n cos 0)

,ho

2 ~ (l-g), 32"rr h;h

Hei212

(1) 2O

where ( P ) denotes the angular average, A.b is the penetration depth, and

(b)

I~S[H

0 7(}

32'rr 2h~bkB T

g=

s,/,~

(2)

80

9(i)

]00

F i g . 5. ( a ) E x t r a c t e d A as a f u n c t i o n o f T. a n d ( b ) e x t r a c t e d

For a random distribution, ( c o s 0 ) = ~ , and (cos 01ncos 0) = - ~ [ 15]. As a result, M~can be written as ,

M,.-

1 40 /I-In rlH~2 2 32rr2A 2 L eH/¢e

gin

gH~2 ] a~J' -

-

(3) or

Ms(H, T) =(1/2)Mo (~ee, T) •

(4)

Therefore, Mo(H, T) can be calculated directly with Mo = 2M~ and H=Ha/V/e, here Ha is the applied field. This relation allows us to convert the measured Ms( Ha, T) to the magnetization Mo(H, T) of a single crystal of the same compound with nllc. Here, M~(Ha, T) = M/0.65 with M being the observed raw magnetization and 0.65 the estimated superconducting volume fraction. The extracted A as a function of T is displayed

? ]<~

I~K, u

in Fig. 5(a). The dashed line is a fit to the BCS clean limit with T~o~ 125 K and A(0) ~ 1500 ~,. The BCS clean limit fits our data slightly better than the dirty limit and the obtained T~o is higher than the T~ determined from the low-field magnetization measurement. This discrepancy of T~ is typical tbr HTS and has been attributed to thermal fluctuations [15]. The obtained parameter K is almost a constant, ~ 60, below 100 K (Fig. 5 ( b ) ) . From the simple relations, K=A/~ and H¢2 = q~o/2'rrsC2, H e 2 ( 0 ) ~ 53 T and ~,,t,(O)= 25 +~ follow. In conclusion, the reversible magnetization M has been measured in a high-quality Hg-1212 polycrystalline sample. A T 2 dependence of M and a field-independent magnetization at 116 K are observed. All these can be attributed to the significant thermal fluctuations as in the case of Bi-2212. We show that the magnetization of a single crystal with HIIc can be directly calculated from the magnetization of a ceramic sample through a simple scaling. The superconducting para-

z.J. Huang et al. / Physica C 228 (1994) 211-215

meters, i.e. K ~ 6 0 , He2 ( 0 ) ~ 5 3 T, ~ab(0) = 2 5 ,~, a n d A ( 0 ) ~ 1 5 0 0 / ~ , are o b t a i n e d .

Acknowledgements This w o r k is s u p p o r t e d in part b y U S A F O S R F 4 9 6 2 0 - 9 3 - 1 - 0 3 1 0 , N S F G r a n t No. N M R 9 1 - 2 2 0 4 3 , A R P A G r a n t No. M D A 9 7 2 - 9 0 - J - 1 0 0 1 . T e x a s C e n t e r for S u p e r c o n d u c t i v i t y at the U n i v e r s i t y o f H o u s t o n , and the T.L.L. T e m p l e F o u n d a t i o n .

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