Magnetic-field-induced enhancement of the vortex pinning in the overdoped regime of La 2−x Sr x CuO 4 : Relation to the microscopic phase separation
Yoichi Tanabe, Tadashi Adachi, Keisuke Omori, Hidetaka Sato, Takashi Noji, Yoji Koike
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Magnetic-field-induced enhancement of the vortex pinning in theoverdoped regime of La − x Sr x CuO : Relation to the microscopic phaseseparation Yoichi Tanabe ∗ , Tadashi Adachi , Keisuke Omori , Hidetaka Sato , Takashi Noji and
Yoji Koike
Department of Applied Physics, Graduate School of Engineering, Tohoku University,6-6-05 Aoba, Aramaki, Aoba-ku, Sendai 980-8579
In order to investigate the inhomogeneity of the superconducting (SC) state in the over-doped high- T c cuprates, we have measured the magnetic susceptibility, χ , of La − x Sr x CuO (LSCO) single crystals in the overdoped regime in magnetic fields parallel to the c-axis upto 7 T on warming after zero-field cooling. It has been found for x = 0.198 and 0.219 thatthe temperature dependence of χ in 1 T shows a plateau, that is, χ is almost independent oftemperature in a moderate temperature-range in the SC state. Moreover, a so-called secondpeak in the magnetization curve has markedly appeared in these crystals. These results indi-cate an anomalous enhancement of the vortex pinning and strongly suggest the occurrence ofa microscopic phase separation into SC and normal-state regions in the overdoped high- T c cuprates. KEYWORDS: phase separation, La − x Sr x CuO , magnetic susceptibility, second-peak effect
1. Introduction
Recently, the electronic inhomogeneity in the overdoped high- T c cuprates has attractedinterest in relation to the mechanism of the high- T c superconductivity. Early studies of thespecific heat of La − x Sr x CuO (LSCO) and Tl Ba CuO δ (TBCO) have revealed that theelectronic specific-heat coefficient in the superconducting (SC) state extrapolated to zero tem-perature increases with an increase of the hole concentration, p , in the overdoped regime.
1, 2
These results indicate that the number of quasiparticles increases with increasing p even in theSC ground state, suggesting the occurrence of a phase separation into SC and normal-stateregions in the overdoped high- T c cuprates. The phase separation in the overdoped regimehas also been suggested by transverse-field muon-spin-relaxation measurements of TBCO
3, 4 and Y . Ca . Ba Cu − z Zn z O − δ revealing that the muon-spin depolarization rate propor-tional to the SC carrier density decreases with increasing p and by nuclear-magnetic-resonancemeasurements of LSCO revealing that the residual spin Knight shift in the SC ground stateincreases with increasing p . Very recently, we have investigated the possible phase separation ∗ E-mail address: [email protected] 1/7 . Phys. Soc. Jpn.
Letter in the overdoped regime through the estimation of the SC volume fraction of LSCO frommeasurements of the magnetic susceptibility, χ , on field cooling. As a result, it has beenfound that the absolute value of χ at 2 K on field cooling decreases with an increase of x .Therefore, it has been concluded that the SC volume fraction decreases with increasing x ,supporting the occurrence of the phase separation into SC and normal-state regions in theoverdoped regime of LSCO.The next issue is whether the phase separation is as microscopic as suggested from thescanning-tunneling-microscopy measurements or as macroscopic as being comparable to thepenetration depth of a few thousand angstrom. In a microscopically phase-separated state,weak SC regions may appear around the boundary between intrinsic SC and normal-stateregions due to the proximity effect. In this case, the application of a moderate magnetic fieldmay bring about the destruction of the weak superconductivity, producing pinning centers forvortices in the CuO plane. Therefore, an enhancement of the vortex pinning by the applicationof a moderate magnetic field may be detected by measuring χ or the magnetization, M . Onthe other hand, in a macroscopically phase-separated state, weak SC regions between intrinsicSC and normal-state regions do not become dominant. In this case, no marked enhancementof the vortex pinning due to the destruction of the weak SC regions is expected. In this paper,we have measured the temperature dependence of χ in various magnetic fields on warmingafter zero-field cooling and also measured the magnetization curve, M vs. H , up to 7 T atvarious temperatures in the overdoped regime of LSCO, in order to clarify whether the scaleof the phase separation is microscopic or macroscopic.
2. Experimental details
Single crystals of LSCO were grown by the traveling-solvent floating-zone (TSFZ) methodunder flowing O gas of 4 or 9 bar. The details of the preparation of powders for the feedand solvent rods and the single-crystal growth have been reported elsewhere.
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As-grownsingle-crystal rods were annealed in flowing O gas of 1 bar at 900 o C for 50 h, cooled down to500 o C at a rate of 8 o C/h, kept at 500 o C for 50 h and then cooled down to room temperatureat a rate of 8 o C/h. The quality of the single crystals was checked by the x-ray back-Lauephotography to be good. The crystals were also checked by the powder x-ray diffraction to bea single phase. The chemical composition of the single crystals was analyzed by the inductivelycoupled plasma optical emission spectrometry (ICP-OES). The distribution of the Sr contentwas also checked using an electron probe microanalyzer (EPMA) to be homogeneous in acrystal within the experimental accuracy. The oxygen deficiency δ in La − x Sr x CuO − δ wasestimated from the iodometric titration to be 0.014 ± x = 0.178 - 0.261. For the χ vs. T and M vs. H measurements, bulk singlecrystals were formed into the same rectangular shape of 1.82 mm and 0.68 mm in the ab-plane and 0.98 mm along the c-axis with the error of ± . Phys. Soc. Jpn. Letter effect identical to each other. Both χ vs. T and M vs. H measurements were carried out inmagnetic fields up to 7 T at low temperatures down to 2 K, using a superconducting quantuminterference device (SQUID) magnetometer (Quantum Design, MPMS-XL7).
3. Results
Figure 1 shows the temperature dependence of χ in magnetic fields of 0.001 T ≤ H ≤ x = 0.198. The SC transition in afield of 0.001 T below the lower critical field, H c1 , is sharp suggesting the good quality ofthe crystal. With increasing field, the SC transition becomes broad, but a clear two-steptransition is observed in 1 T. In high magnetic fields above 1 T, the two-step transition tendsto be smeared out with increasing field and changes to a single broad one in 7 T. In thecase of χ vs. T on field cooling, on the other hand, the SC transition tends to become broadmonotonically with increasing field and no two-step transition is observed.Figure 2 shows the temperature dependence of χ in magnetic fields of 0.001 T ≤ H ≤
7T on warming after zero-field cooling for LSCO with x = 0.178 - 0.261. The SC transitionshows a weak two-step feature for x = 0.178 and shows a clear two-step transition for x = 0.198 and 0.219. On the other hand, the two-step transition tends to be smeared outfor x ≥ χ vs. T measurements for a bulk single crystal of NbSe which is regarded as a conventionalhomogeneous superconductor. Therefore, the two-step SC transition observed in LSCO isprobably a characteristic feature of the overdoped high- T c cuprates.Figures 3(a) and (b) show M vs. H for LSCO with x = 0.198 at temperatures of 2 K ≤ T ≤
26 K and that with 0.178 ≤ x ≤ x = 0.198, a so-called secondpeak due to a large hysteresis of M vs. H in magnetic fields between H c and the upper criticalfield, H c , is observed at all measured temperatures. The second peak indicates an increaseof the vortex pinning, as typically observed in commercial bulk materials of REBa Cu O − δ including a small amount of the second phase of RE BaCuO .
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In Fig. 3(a), it is foundthat M vs. H curves at 10 K and 15 K overlap each other in magnetic fields around 1 - 2 T,which is consistent with the result that χ vs. T in 1 T is almost independent of temperaturebetween 10 K and 20 K as shown in Figs. 3(a) and (b). Moreover, H = 1 T at 10 K in M vs. H is the onset field above which the vortex-pinning effect becomes marked, and T = 10 K in1 T in χ vs. T is the onset temperature above which χ is almost independent of temperature.In Fig. 3(b), it is found that the second peak is also observed for 0.178 ≤ x ≤ χ vs. T as shown in Fig. 2.These results indicate that the two-step SC transition in χ vs. T is well correlated with thesecond peak in M vs. H . . Phys. Soc. Jpn. Letter
4. Discussion
The clear two-step SC transition in χ vs. T on warming after zero-field cooling observedfor LSCO with x = 0.198 and 0.219 indicates that the penetration of vortices into the crystalis blocked in spite of warming in a moderate temperature-range. Considering the correlationwith the second peak in M vs. H , these results are understood as follows. That is, strongvortex-pinning takes place near the surface of the crystal in a moderate temperature-rangeon warming for x = 0.198 and 0.219 so that the magnetic field can not penetrate into theinside of the crystal, leading to the appearance of a plateau in χ vs. T . It is noted that,although the second peak in M vs. H has been observed in some high- T c cuprates, suchalmost temperature-independent χ vs. T in a wide temperature-range as in the present casehas never been observed to date, to our knowledge, suggesting an unusual mechanism of thevortex pinning in the overdoped LSCO.
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Formerly, it has been pointed out that a second peak appears in M vs. H in the overdopedLSCO and that it originates from the existence of oxygen defects.
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That is, it has beensupposed that oxygen defects bring about local destruction of the superconductivity, producingweak SC regions around themselves due to the proximity effect. With increasing field, theweak SC regions change into normal-state ones earlier than intrinsic SC regions to operate aspinning centers for vortices, resulting in an enhancement of the vortex pinning. In the presentcase, however, the oxygen deficiency δ is as small as 0.014 ± x = 0.178 - 0.261. Moreover, the strong vortex-pinning is realized ina moderate temperature-range for x = 0.198 and 0.219 and the vortex pinning becomes weakfor x ≥ x = 0.198 and 0.219 can not explain the present results also, because neither marked increasein the width of the x-ray diffraction peaks nor marked increase in the normal-state in-planeelectrical resistivity at low temperatures were observed around x = 0.198 - 0.219.Here, we propose a possible scenario based upon a microscopic phase separation into SCand normal-state regions to explain the present results. Figures 4(a) and (b) schematicallyshow the H - T phase diagram and the temperature dependence of χ on warming afterzero-field cooling in a microscopically phase-separated state, respectively. In a microscopicallyphase-separated state, weak SC regions appear around the boundary between intrinsic SC andnormal-state regions due to the proximity effect. Supposed that microscopic weak SC regionsare ubiquitously distributed in a crystal, the superconductivity in weak SC regions tends tobe destroyed earlier than that in intrinsic SC regions with increasing temperature or field,so that the weak SC regions change to normal-state regions regarded as pinning centers forvortices. In the case of Fig. 4(i), the applied magnetic field, H , is between H c1 in the intrinsicSC regions and the upper critical field in the weak SC regions, H wc2 , at the lowest temperature, . Phys. Soc. Jpn. Letter T . In this case, the number of vortices penetrating into the crystal increases with increasingtemperature, resulting in the decrease of the shielding effect of superconducting currents.When the temperature reaches T in Fig. 4, a number of microscopic normal-state regionsappear in the crystal due to the destruction of the superconductivity in the weak SC regions,as shown in Fig. 4(ii). In this case, the magnetic flux coming from the outside of the crystalis pinned in the normal-state regions near the surface of the crystal. With further increasingtemperature, the magnetic flux coming from the outside of the crystal is still pinned in thenormal-state regions near the surface of the crystal, as shown in Fig. 4(iii), due to the largeSC condensation energy of the intrinsic SC regions, leading to the appearance of a plateau in χ vs. T . When the temperature reaches T in Fig. 4, vortices enter the inside of the crystal,because the SC condensation energy in the intrinsic SC regions decreases at temperaturesnear the SC transition temperature, T c . This results in the decrease and disappearance of theshielding effect, as shown in Figs. 4(iv) and (v). This kind of behavior of χ vs. T is clearlyobserved for x = 0.198 and 0.219.According to this scenario, the x dependence of the distribution of vortices in the CuO plane is also understood as shown in insets of Fig. 2. There, the penetration of vortices into theinside of the crystal is schematically shown for x = 0.178 - 0.261, supposing that normal-stateregions appear due to the destruction of weak SC regions on warming in a microscopicallyphase-separated state. For x = 0.178, the SC volume fraction is much larger than those of x = 0.198 and 0.219. In this case, vortices can penetrate into the inside of the crystal due to asmall number of pinning centers for vortices, resulting in the weak two-step feature in χ vs. T . Once normal-state regions become dominant with increasing x for x ≥ χ vs T for x ≥ x = 0.219.It has already been reported from the magnetization measurements that the vortex-pinningeffect is weak on account of the small SC volume fraction in the overdoped regime of LSCO,TBCO, Bi Sr CuO δ , Y − x Ca x Ba Cu O − δ , Bi Sr CaCu O δ . Therefore, the new im-portant information from the present results is that a microscopic phase separation into SCand normal-state regions takes place in the overdoped regime of LSCO, because the presentresults can hardly be explained if the phase separation is macroscopic. Finally, it is notedthat the strong pinning effect is not directly related to the crystal structure, because thestructures of x = 0.198 and 0.219 in the SC state are different from each other; the former isorthorhombic, while the latter is tetragonal.
5. Summary
In summary, it has been found from χ vs. T measurements in magnetic fields parallel to thec-axis up to 7 T on warming after zero-field cooling in the overdoped regime of LSCO single . Phys. Soc. Jpn. Letter crystals that χ is independent of temperature in a moderate temperature-range in the SC statein 1 T for x = 0.198 and 0.219, while the almost temperature-independent χ disappears for x ≥ M vs. H measurements in theoverdoped regime of LSCO. These results indicate an anomalous enhancement of the vortexpinning and are understood assuming the occurrence of a microscopic phase separation intoSC and normal-state regions in the overdoped regime. That is, microscopic weak SC regionsappear around the boundary between intrinsic SC regions and normal-state regions due tothe proximity effect, and the superconductivity of the weak SC regions is destroyed earlierthan that of the intrinsic SC regions with increasing temperature or field so that the weakSC regions operate as strong pinning centers for vortices, resulting in strong vortex pinningin a moderate range of temperature or field in a microscopically phase-separated SC state.Accordingly, these results strongly suggest that a microscopic phase separation into SC andnormal-state regions takes place in the overdoped high- T c cuprates. Acknowledgments
We are indebted to K. Takada and M. Ishikuro for their help in the ICP-OES analysis.The EPMA analysis was supported by Y. Murakami in the Advanced Research Center ofMetallic Glasses, Institute for Materials Research (IMR), Tohoku University and K. Kudo inIMR, Tohoku University. Fruitful discussions with T. Nishizaki and S. Awaji are gratefullyacknowledged. The χ measurements were carried out at the Center for Low TemperatureScience, Tohoku University. This work was supported by the Iketani Science and TechnologyFoundation and also by a Grant-in-Aid for Scientific Research from the Ministry of Education,Culture, Sports, Science and Technology, Japan. . Phys. Soc. Jpn. Letter
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Fig. 1. (a) Temperature dependence of the magnetic susceptibility, χ , for La − x Sr x CuO with x =0 .
198 in magnetic fields of 0.001 T ≤ H ≤ χ in (a). . Phys. Soc. Jpn. Letter
Fig. 2. (Color online) Temperature dependence of the magnetic susceptibility, χ , for La − x Sr x CuO with x = 0 . − .
261 in magnetic fields of 0.001 T ≤ H ≤ plane at moderate temperatures shown by arrows. . Phys. Soc. Jpn. Letter
Fig. 3. Magnetization curves, M vs. H , parallel to the c-axis up to 7 T for La − x Sr x CuO (a) with x = 0.198 at temperatures of 2 K ≤ T ≤
26 K and (b) with 0.178 ≤ x ≤ M vs. H for x = 0.238 and 0.261. Arrows indicate so-called secondpeaks. . Phys. Soc. Jpn. Letter
Fig. 4. (Color online) Schematic figures of (a) the H - T phase diagram and (b) the temperaturedependence of χ on warming after zero-field cooling in a microscopically phase-separated statein H = H , H , H . H c1 and H c2 are the lower and upper critical fields in intrinsic SC regions,respectively. H wc1 and H wc2 are the lower and upper critical fields in weak SC regions, respectively.Right figures (i) - (v) show the expected spatial distribution of vortices in the CuO plane at (i)- (v) in (b), respectively.plane at (i)- (v) in (b), respectively.