Measurement and understanding of the temperature dependence of the lower critical field in YNi2B2C

IlllUlll ELSEVIER

Physica B 223&224 (19961 86 89

Measurement and understanding of the temperature dependence of the lower critical field in YNizBzC T.V. Chandrasekhar Rao ~'*, P.K. Mishra a, G. Ravikumar a, V.C. Sahni a, K. Ghosh b,

Gautam I. Menon b, S. Rarnakrishnan b, A.K. Grover b, Girish Chandra b ~'Solid State Physics Division. Bhabha Atomic' Research Centre, Bombay 400085, India b Tata Institute ~?fFundamental Research, Bombay 400005, India

Abstract The lower critical field (Her(T)) values in YNi2B2C (To = 15.45 K) are found to fit the quadratic form H c l ( T ) = 220 [1 - ( T / T o ) 2] Oe from 5 to 14 K. These values are consistent with an analysis which uses a thermodynarnical critical field He(0) of 1.7 kOe (deduced from experiments). However, measured values of H~I(T) above 14.4 K deviate from the quadratic relation. Taking cue from the presence of intergranularity effects above 14.4 K in our YNi2BzC sample, the He1 data are quantitatively described in terms of a two-component magnetic response.

The accurate determination of lower critical field He1 is complicated by various factors such as flux pinning effects, sample shape and morphology [1, 2]. Recently, some of us elucidated a reliable method [3] for the evaluation of He1 in a sample ofa borocarbide superconductor YNi2B2C (YNBC) [4, 5]. A striking feature of the measured H c l ( T ) versus T (see Fig. 1) is a concave upward feature in the interval from 14.4K to Tc ( ~ 15.45 K), although the shape of the Hcl(T) curve below 14.4 K is well described by the familiar quadratic form: H~I(T) = Hcx(0)(1 - t2), where t ( = T / T ~ ) is the reduced temperature. It was conjectured by Ghosh et al. [3] that the observed behaviour of H¢I(T) near To(0) is caused by intergranularity effects. Fig. 2 shows a typical electron micrograph of our brittle YNBC sample where grains are separated by intergranular regions. The carbon and/or boron stoichiometries in the intergranular regions need not be the same as those in the intragrain regions. This can

* Corresponding author.

influence the measurement of parameters of superconductivity, especially, close to T~. In particular, the Tc's of the intra-grain and inter-grain regions could be different and so also their magnetic responses [6, 7]. The existence of two (quasi) critical temperatures, namely, an intrinsic temperature and the coupling temperature, is well documented in the literature. It is believed [8] that the intrinsic transition temperature corresponds to the onset of superconductivity within the grains (in high T~ cuprates) or in an alloy of which the filaments are made (in multi-strand wires). The coupling T~ is associated with the weak links, which could exhibit superconductivity either due to Josephson tunnelling (in an insulating/ semiconducting matrix) or the proximity effect (in a metallic matrix). The intra-grain and inter-grain electromagnetic response could thus be of a two-component type. Fig. 3 summarizes the temperature dependence of different measured quantities between 12 and 16 K. The onset temperature of the negative peak in DC magnetization data (in field cooled warm-up measurements) is seen to coincide (cf. Figs. 3(a) and (b)) with the temperature

0921-4526/96/$15.00 ,~i 1996 Elsevier Science B.V. All rights reserved PII S092 1 - 4 5 2 6 ( 9 6 ) 0 0 0 4 6 - 4

T.V. ChandrasekharRao et al. /Physica B 223&224 H996) 86 89 above which the experimental values of H¢~ drop below the H¢a(0) (1 -- t 2) fit to the data at lower temperatures. This suggests that the measured values of Hc~ above 14.4 K correspond to a preferential penetration of the

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FIT Ho~(O) [t-(T/T~)

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T =15.45 I( ]

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TEivIPERATURR(I,[) Fig. I. Variation of lower critical field He1 with in YNi2B2C. The solid line corresponds to the fit 22011 -(T/15.45) 2] Oe. The inset shows the behaviour near Tc on an expanded scale. The dashed line is a fit to the model based on proximity effect.

87

applied field in the intergranular regions and the solid line in Fig. 3(a) corresponds to the field values at which the applied field would penetrate the intra-grain regions. This picture is also in tune with the claim [3] that the onset of negative peak, the change in dM/dH with T (see Fig. 3(c)) and the faster drop in H¢I(T) above 14.4 K are direct signatures of the two component response in YNBC. The above behaviour of Hcl(T) in YNBC is reminiscent of the temperature dependence of the first penetration field for superconductor-normal metalsuperconductor junction (S-N-S), as studied theoretically by Dobrosavljevic and de Gennes [9] and Cowen et al. [10]. An S - N - S junction exhibits perfect diamagnetic behaviour up to a field value which is less than the He1 value of the pure superconductor (S). We assume first that the intra-grain regions have a To(0) value ( ~. 15.45 K), consistent with the fit of Hcl(T) values of quadratic behaviour at low temperatures, and that the inter-grain region in its bulk form has a lower To. We propose that over the temperature interval 14.4-15.45 K, the observed H,I behaviour is a manifestation of the superconductivity induced in the inter-grain region due to the proximity effect. Following the analysis of Cowen et al. [10], the reduced lower critical field h~(a,) ( = Hcl/x/2Hc) of the S - N - S junction system can be written as he1 (a,) = he1 (0)exp( - 7 a,/~,),

(1)

Fig. 2. A typical electron micrograph showing the brittleness of our YNi2B2C sample. The white spots are the residues of the powder used for polishing the specimen.

T V. ChandrasekharRao et al. / Physica B 223&224 (1996) 86-89

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The variation of temperature primarily affects the ~ n , since the other parameters are nearly temperature-independent. For a, ,~ ~,, the Hcl(T) will have quadratic temperature dependence (i.e. H¢a(T) oc [1 - t2]). However, for a. > ~.n, HcI(T) will get modulated by an exponential dependence ( ~ exp( - 7a,/~,) so that Hca(T) would fall rapidly close to T¢. As suggested by an earlier study [10], one can map the thickness dependence to the temperature dependence of the lower critical field. Since our interest is in the temperature dependence (rather than the thickness dependence), we rewrite Eq. (1) as

Ho~(T) = H¢~(0)[1 - (T/TcA)2]exp( - 7'/~.), '

'

'

'

I

,

0.0

,

6.6

where 7' is another constant. However, we know that the Hc1(T) follows a quadratic relation below 14.4 K. In order to account for this observation, we assume that ~n is given [11, 12] by

0

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O -0.1

(b)

o

{ hvFl~U2[l + 2 ]~/2 ~.(T) = \6~kBT/ In(TTTcDJ '

-0.2 0

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(4)

0 0

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(3)

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where TcB is the transition temperature of the inter-grain region in YNBC in its stand alone state. In principle, a distribution TcB's cannot be ruled out. We assume a single value for the sake of simplicity. Note the weak divergence of the coherence length ¢,(T) as T ~ TCB. Combining (3) and (4), we obtain

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H¢1 = H~(0)[1 - (T/TcA)2]exp( - o:/~.(T)),

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TEMPERATURE (K) Fig. 3. The temperature variation of ( a ) H ~ , (b)4rcMvcw, (c) Z,~ and AM/AH. where hel(0 ) is the reduced critical field of the pure superconductor, 2a, is the thickness of the normal layer and 7 is a constant of the order 1. ~ is the coherence length in the normal region and it can be written as

( hvFl ~ 1/2 ~" = \67tk, TJ

'

(2)

where vv is the Fermi velocity and I is the mean free path of the normal metal.

(5)

where 7 is a constant which is proportional to, among other terms, the characteristic size of the normal region and TCA is the transition temperature of the intra-grain region. From the electron micrograph, we note that the thickness of the normal region (in the interval Tca < T < TCA) is much greater than ~. which supports the use of Eq. (5). We treat the c~as a free parameter in our fit of the measured He1 data in YNBC between 14.4 and 15.45 K and the first field penetration is believed to occur at the "weakest link". A priori, given a polycrystalline sample, the factor ~ can only be estimated. O n fitting our data to the expression (5), the values of TcB and ~ are found to be 14.38 K and 2.84, respectively. In this fit we have assumed TCA to be 15.45 K. Below 14.4 K, the intergranular regions themselves become bulk superconductors resulting in a single component response. From the inset of Fig. 1 (dashed line), it is clear that the functional form given by Eq. (5) provides a remarkably good fit to the experimental data within error bars. To conclude, we have shown that the faster decline of Hc 1(T) near Tc in a brittle YNBC sample can be accounted for using a proximity effect model.

T.V. Chandrasekhar Rao et al. /Physica B 223& 224 (1996) 86 89

References [1] A.K. Grover, in: Studies of High Temperature Superconductors, Vol. 14, ed. A.V. Narlikar (Nova Science Publishers Inc., NY, 1994). [2] L. Burlachkov et al., Phys. Rev. B 45 (1992) 8193. [3] K. Ghosh et al., Phys. Rev. B 52 (1995) 68. [4] R. Nagarajan et al., Phys. Rev. Lett. 72 (1994) 274. 1-53 R.J. Cava et al., Nature 367 (1994) 252. [6] J. Jung et al., Phys. Rev. B 49 (1994) 12188. [7] O.B. Huyn, Phys. Rev. B 48 (1993) 1244.

89

[8] R.B. Goldfarb et al., in: Magnetic Susceptibility of Superconductors and Other Spin Systems, eds. R.A. Hein et al. (Plenum Press, NY, 1991), pp. 49-80 and references cited therein. [9] L. Dobrosavljevic and P.G. de Gennes, Solid State Commun. 5 (1967) 177. [10] D.F. Cowen et al., Phys. Rev. B 30 (1984) 1194. I-11] J. Clarke, J. de Physique Colloque C 2, Supplement No. 2--3 (1968) 3 16. [12] T.Y. Hsiang and D.K. Finnemore, Solid State Commun. 33 (1980) 847.