Magnetostriction in High-Tc cuprate single crystals

Physica C 235-240 (1994)237-240 North-Holland

PUYSlCA

Magnetostriction in High-To Cuprate Single Crystals H. Ikuta, N. Hirota, K. Kishio and K. Kitazawa Department of Applied Chemistry, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan Magnetostriction, the length change of a sample under application of a magnetic field, was measured on high-T~ cuprate single crystals. The magnetic field was applied along the c-axis direction and the resulting length change was recorded along the ab-plane. The magnetostriction displayed a large irreversibility between field ascending and descending process, and fast relaxation of the magnetostriction was observed. A model based on the force internally exerted on the specimen due to the flux pinning quantitatively accounts well for the experimental results.

I. I N T R O D U C T I O N The physical properties of high temperature superconductors (HTSC's) under magnetic fields have been of interest from both fundamental and technological points of view. We have previously reported a large superconducting state magnetostriction in Bi2Sr2CaCu2Os single crystal [1]. The relative sample length change (AL/L) was of the order of 10-4 , which is two to three orders larger than the values normally reported for conventional superconductors [2]. The deformation of a superconductor under a magnetic field is usually attributed to the change in the free energy [2,3], but this thermodynamieal effect cannot account for the experimental observations made on Bi2Sr~CaCu2Os. The observations were, however, in a good agreement with a model based on a pinning induced mechanism. Here we report our further investigation of magnetostriction in HTSC single crystals. 2. E X P E R I M E N T A L The sample length change was measured by a capacitive method using a Andeen-Hagerling Inc. Model 2500A capacitance bridge. The data described below are for transverse magnetostriction, i.e., length changes along a direction perpendicular to the magnetic field. Following zero field cooling (ZFC) of the sample, the magnetic field was applied along the crystallographic c-axis and was cycled with a constant sweep rate of 10 mT/s up to q-6 T. Magnetization data were measured by

a vibrating sample magnetometer (VSM), EG&G PAR4500. Experimental results for two (Lal-xSrx)2CuO4 single crystals are reported here. They were grown by the travelling solvent floating zone (TSFZ) technique, of which the details have been described elsewhere [4]. The sizes of the crystals were 1.05 x 3.30 x 2.90 (mm3) and 0.5 x 2.45 x 1.35 (mm3) with Sr contents of x=0.07 and 0.05, respectively. For both samples, length changes were measured along the first dimension listed above, with the magnetic field applied in the direction of the last dimension, being along the crystalline c-axis.

3. R E S U L T S

Figure l(a) shows the relative sample length change (AL/L) of the x=0.05 single crystal as a function of the external field (Be) measured at 5.2 K. In the field ascending branch, the sample decreased in length until near Be=l T, increased for further increase in Be, and finally was expanded compared to the ZFC length. By reversing the field sweep direction at 6 T, the magnetostriction curve displayed a large hysteresis and AL was positive at 0 T. The magnetostriction curve was symmetrical for both signs of Be, except for the initial stage. Figure l(b) shows the magnetostriction curve of the x=0.07 sample at 5.1 K. We see that the decrease in sample length during the field ascending branch is monotonic for this crystal, but

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a large hysteresis in the magnetostriction loop and A L > 0 at 0 T during the field sweep were again observed. In this sample, the shape of the magnetostrietion curve is rather similar to the Bi2Sr2CaCu2Os case reported previously [1], except that the curvature of the magnetostriction curve decreased by approaching 0 T in the descending branch. Figure 2 shows the relaxation curves measured on the x=0.07 sample. To ensure full field penetration into the sample, the magnetic field was first swept up to 6 T and was held at the fields noted in the figure. The magnetostriction decreased monotonically with time at most fields, at least within the observed time window. However, at 2 T in the ascending branch, the magnetostriction first increased until t ~ 200 s, and then began to decrease.

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Figure 1. Magnetostriction loops of single crystalline ( L a l - x S r x ) 2 C u 0 4 ; (a) x=O.05 at 5.2 K (two continuous field loops), (b) x=O.07 at 5.1 K

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Figure 2. Relaxation of magnetostriction of ihe ( L a l - , S r : ) 2 C u O 4 (x=0.07) single crystal at 5 K: (a) field descending branch, (b) field ascending branch.

4. D I S C U S S I O N The sample length change (AL) due to the pillning induced mechanism for a specimen having a slab geometry can be expressed as follows ill: AL L

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[|ere Cll is the elastic constant of the material. H0 the permeability of vacuum, L = 2 H the sample. length, Be the applied field, and B(x) is th(, local magnetic flux density. The gradient of the local field distribution Js proportional to the critical current density (J,:) in the critical state model. Therefore, if the field dependence of Jc is deduced from an alternative experiment, the magnetostriction curve can

239

H. Ikuta et al./Physica C 235-240 (1994) 237-240

be theoretically predicted using Eq. (1), allowing a quantitative comparison with the experiment. Figure 3(a) shows the magnetization data of the x=0.05 sample by open circles. The solid line is the result of the least squares fitting to the magnetization loop where we have assumed that Jc is described with the following exponential model [5,6]: Jc(B) = =FJcoexp ( - I B I / B o ) .

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Figure 3(b) shows the theoretical magnetostriction curve calculated with the parameters determined from the magnetization curve. The elastic constant used in this calculation was the cll value reported by Nohara et al. for a x=0.07 single crystal at 50 K, 2.634x 1011 N/m 2 [7]. Comparing Figs. l(a) and 3(b), we see that the general shape of the hysteresis curve is well reproduced with the calculation. The quantitative agreement is also good, differing only by a factor of about two. Therefore, it should be concluded that the major contribution to the observed magnetostriction had indeed its origin in the pinning induced mechanism. Obviously, however, the pinning induced mechanism alone is not enough to account for all the behavior of the experimental result shown in Fig. l(a). We expect AL<0 for the whole ascending branch in our model except near Be=0, because the flux lines exert compressive forces on the crystal by being restricted to penetrate inward the sample due to the pinning effect. The experimental result, on the other hand, shows that the sample is expanded compared to the ZFC length at high fields where the pinning effect becomes weak. When the pinning force is rather weak, the total magnetostriction should be affected substantially by the thermodynamical effect. Positive contribution to the magnetostriction can then be expected, if the pressure dependence of the critical field H¢, OHc/Op, is positive [2,3]. In this context it is worthwhile to point out that OHc/Op>O is consistent with the enhancement of the critical temperature by pressure in (Lal_,Sr,)2CuO4 [8]. Figure 4 shows the magnetization curve of the z=0.07 sample. The characteristic feature of this data is the appearance of a second peak at higher

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fields, showing a rather complex field dependence of Je. Therefore, a fitting to this data and the calculation of the theoretical magnetostriction curve were not made for this sample. However, the observed magnetostriction curve is qualitatively in a good agreement with the result of the simulations made using Eq. (1) [9], except for the behavior pointed out above for the descending branch near Be=O. The structure near Be=O has probably the same origin with the second peak in the magnetization curve. The magnitude of the observed magnetostriction is also well within the upper limit of the model, A L / L = - 5 . 4 4 × 10-5 at 6 T, which is evaluated by inserting B(x)=O into Eq. (1).

240

H. lkuta et al./Physica C 235 240 (1994) 237 240

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5. C O N C L U S I O N S

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Magnetostriction and its relaxation were mea-sured on single crystalline HTSC's. The observed magnetostriction loop was quantitatively in good agreement with the model based on the pinning induced mechanism. When the pinning effect becomes weak at high fields in the x=0.05 sample, a positive magnetostriction was observed which can be interpreted as the manifestation of a positive pressure coefficient of He. The results of the relaxation measurement on the x=0.07 sample were also in a good agreement with the model, including the peculiar behavior observed at 2 T of the ascending branch.

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Finally, we discuss the relaxation data. Because the inhomogeneous flux line distribution relaxes to the thermally equilibrium when the field sweep is held, a relaxation of magnetostriction toward A L = 0 is naturally expected. The results shown in Fig. 2 indeed indicate a monotonic relaxation at most fields, but the 2 T curve of the ascending branch displayed an unexpected behavior in this sense. Nevertheless, our model can also account for this observation. We assume that the local supercurrent density can be approximated by its average over the sampie (J(t)), causing a Bean model like flux density distribution. AL in the field ascending branch is then expressed as follows [9]: AL(t) -

J(t)d2c~l (B~- ~#oJ(t)d) .

(3)

This equation shows that the absolute value of AL has a maximum at Jm=3B~/2pod. Suppose that the supercurrent is larger than Jm at the beginning of relaxation (but smaller than 2Jm so that AL(0) < 0). The ratio AL(t)/AL(O) then increases first until J(t)=Jm and decreases only thereafter by decreasing J(t). Hence, we see that the behavior of the relaxation curve taken at 2 T is consistent with the model.

ACKNOWLEDGMENTS

This research has been partially supported by the NEDO (The New Energy Development Organization of Japan) International Joint Research Grant. REFERENCES

1. H. ikuta, N. Hirota, Y. Nakayama, K. Kishio and K. Kitazawa, Phys. Rev. Lett. 70 (1993) 2166. 2. G. Br//ndli, Phys. kondens. Materie 11. 93 (1970); ibid., 111 (1970). 3. D. Shoenberg, Superconductivity, (Cambridge University Press, London, 1960). 4. T. Kimura, K. Kishio, T. Kobayashi. Y. Nakayama, N. Motohira, K. Kitazawa and K. Yamafuji, Physica C 1 9 2 , 2 4 7 (1992). 5. S. Senoussi, M. Oussdna, G. Collin and I. A. Campbell, Phys. Rev. B 37, 9792 (1988). 6. P. Chaddah, K. V. Bhagwat and G. Ravikumar, Physica C 1 5 9 , 5 7 0 (1989). 7. M. Nohara, T. Suzuki, Y. Maeno, T. Fujita, 1. Tanaka and H. Kojima, Physica C 1 8 5 - 1 8 9 . 1397 (1991). 8. N. Tanahashi, Y. Iye, T. Tamegai, (L Murayama, N. M&ri, S. Yomo, N. Okazaki and K. Kitazawa, Jpn. J. Appl. Phys. 28, L762 (1989). 9. H. Ikuta, K. Kishio and K. Kitazawa,

preprint.