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Pinning, thermally activated depinning and their importance for tuning the nanoprecipitate size and density in high Jc YBa2Cu3O7−x films
Physica C 469 (2009) 2021–2028
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Pinning, thermally activated depinning and their importance for tuning the nanoprecipitate size and density in high Jc YBa2Cu3O7x films Zhijun Chen *, Fumitake Kametani, Alex Gurevich, David Larbalestier National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310, USA
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Article history: Accepted 20 August 2009 Available online 26 August 2009 PACS: 74.25.Fy 74.25.Qt 74.25.Sv 74.62.Dh 74.72.Bk 74.78.Bz Keywords: YBCO Coated conductor Pinning Nanoprecipitate Thermally activated depinning Critical current density
a b s t r a c t YBa2Cu3O7x (Y123) films with quantitatively controlled artificial nanoprecipitate pinning centers were grown by pulsed laser deposition (PLD) and characterized by transport over wide temperature (T) and magnetic field (H) ranges and by transmission electron microscopy (TEM). The critical current density Jc was found to be determined by the interplay of strong vortex pinning and thermally activated depinning (TAD), which together produced a non-monotonic dependence of Jc on c-axis pin spacing dc. At low T and H, Jc increased with decreasing dc, reaching the very high Jc 48 MA/cm2 20% of the depairing current density Jd at 10 K, self-field and dc 10 nm, but at higher T and H when TAD effects become significant, Jc was optimized at larger dc because longer vortex segments confined between nanoprecipitates are less prone to thermal fluctuations. We conclude that precipitates should extend at least several coherence lengths along vortices in order to produce irreversibility fields Hirr(77 K) greater than 7 T and maximum bulk pinning forces Fp,max(77 K) greater than 7–8 GN/m3 (values appropriate for H parallel to the caxis). Our results show that there is no universal pin array that optimizes Jc at all T and H. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction It is well accepted that the critical current density Jc in YBCO can be significantly enhanced by incorporating a high density of strong, nanoprecipitate vortex pinning centers. Very high self-field values of Jc(77 K) > 5 MA/cm2 15% of the depairing current density Jd(77 K) 40 MA/cm2, have been demonstrated by almost all major YBCO fabrication techniques [1–4]. In addition, exceptional maximum pinning force Fp,max values in the range of 20–28 GN/ m3 at 77 K have been achieved by several groups [5–7]. Such Fp,max(77 K) values exceed the 18 GN/m3 found in fully optimized Nb–Ti superconductor at 4.2 K [8], hitherto thought to be the most highly optimized low-Tc superconductor (LTS). On the other hand, the majority of reported Fp,max(77 K) lie between 5 and 12 GN/m3 [9–13], well below the very best values, even for films with selffield Jc(77 K) 0.15Jd. This lack of correlation between self-field and in-field Jc values makes it clear that there are important subtleties to the in-field vortex pinning that are not yet fully understood. * Corresponding author. Present address: Materials Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, USA. E-mail address: [email protected] (Z. Chen). 0921-4534/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2009.08.013
One of the most active areas of present YBCO study is thus to understand how samples with excellent self-field Jc(77 K) can have their in-field Jc improved. More specifically there is broad interest to understand whether there is some universal pin array which optimizes Jc(T, H) under all conditions or whether specific types of pin must be engineered to maximize Jc(T, H) in specific domains of field and temperature. We are motivated to ask this question not just from the general viewpoint of optimizing pinning in the important 65–77 K range, but also in view of growing interest of using YBCO to build very high field magnets [14] in the field domain of H > 25 T where no Nb-based superconductor can be used. As has been emphasized recently [5,15], pinning optimization at 77 K has to be done in the domain of T and H where thermally activated depinning (TAD) effects are strong, and weak point pinning is ineffective [2,16]. But at low temperatures where TAD effects are reduced, weak point pinning can significantly contribute to Jc [5,15], even at H > 30 T, which is only 0.3Hirr(4 K) [17]. How to optimize pinning in such a broad T–H domain is still unclear, given that BaZrO3 (BZO) [18,19] or BaSnO3 (BSO) [6,13] nanorods, the presently favorite strong correlated pin when H is parallel to the c-axis, although very effective in fields of a few tesla, do not grow in sufficient density to optimize Jc in fields of 5 T and above. It is the
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complicated interactions between Jc in the high and low T and H limits, strong nanoprecipitate pinning and thermally activated depinning effects that this work seeks to clarify. Our systematic study of Jc in terms of pin density and spacing finds that Jc at 77 K and low fields (0–1 T) increases monotonically with decreasing c-axis pin spacing dc [20]. By extending our measurements over wide temperature (10–77 K) and field (0–9 T) ranges, we show that the dependence of Jc on dc can change significantly as T and H are varied. We find that the interplay of thermal fluctuations of vortices and vortex pinning by nanoprecipitates makes Jc increase with decreasing dc at low temperatures and fields, while reversing the trend at higher T and H as thermally activated depinning becomes stronger. In this higher TAD domain, elongating the pinning nanoparticles along the field direction produces an enhancement of the elementary pinning force fp which inhibits thermally activated depinning effects, consistent with many previous studies of the effectiveness of nanorods [6,13,18,19,21]. On the other hand, the low temperature and high field Jc does not benefit as much from increasing the strength of the single-particle elementary pinning force as from increasing the density of pinning centers (thus favoring smaller dc) because thermally activated depinning effects are small. Thus, our results show that quantitative optimization of Jc over wide field and temperature ranges requires much greater attention to the details of pin size and pin density.
and t123 = 10 nm. Note that t211 only quantifies the nominal thickness of the insulating Y211 pin layers which actually decompose into a dense array of discrete disk-shaped nanoprecipitates dispersed within the Y123 during the multilayer deposition. The actual thickness dt of the precipitates was determined by TEM, which showed that the nanoprecipitates are not Y211 but Y2O3. Although both phases are insulating and thus similar in their pinning effects, actually there are likely to be second order differences, e.g. strain fields, in their pinning effects that we do not address here but have been recently noted to be rather significant by Harrington et al. [23]. Four-point transport measurements were carried out in a 9 T PPMS system on bridges 100 lm wide and 500 lm long patterned with a Nd-doped yttrium aluminum garnet laser. Broad range measurements were performed with H perpendicular to the film plane and thus parallel to the c-axis. Some measurements of the angular dependence of Jc(h), where h is the angle between H and the abplanes of Y123, were made in fields of 1 and 4 T. To measure Jc at lower temperatures down to 10 K, narrower links 10 lm wide by 200 lm long were prepared with a focused ion beam (FIB) tool to restrict Ic to <4 A. In all cases, Jc was determined with a 1 lV/cm criterion. High resolution scanning electron microscopy (SEM) images were taken in a Zeiss 1540, while TEM imaging was performed in a JEOL JEM-2011.
3. Results 2. Experimental details YBCO films were deposited on (100) oriented single crystal SrTiO3 (STO) substrates by PLD using a conventional excimer laser (Lambda Physik model LPX 201i) operating at 248 nm wavelength. Pinning centers were introduced artificially by ablation of separate Y123 and Y2BaCuO5 (Y211) targets to form multilayer films [11,22]. All films were grown at a substrate temperature Tg 810 °C with a laser fluence El 2 J/cm2 at a repetition rate of 5 Hz and a target-to-substrate distance dts of 5.7 cm. This higher than usual Tg was used to achieve a smoother film surface, so that nanoprecipitate densities could be better quantified. The films had a final thickness 550 nm with only small variations. Depositions were performed in 250 mtorr of flowing oxygen and the films were annealed after deposition in situ at 500 °C under 800 torr O2 for 45 min. Eight films were studied in this work, two being nominally identical single layer (SL) films, and six being multilayer (ML) films in two sequences. One sequence kept the nominal Y123 sub-layer thickness t123 constant at 10 nm, varying the Y211 sub-layer thickness t211 from 1.1 to 1.5 to 1.9 nm, while the second kept t211 constant and varied t123 from 10 to 20 to 30 nm. Detailed architectures and basic superconducting properties of all samples are listed in Table 1. The Y123 and Y211 thicknesses provide the sample ID of the ML films; for example ML-1.9-10 means that t211 = 1.9 nm
Table 1 provides a summary of several key features of the films. The transition temperatures Tc were all close, varying from 89.3 to 90.3 K as defined by the zero-resistance point in small current transport measurements. These values and their concave resistance R(T) curves are all consistent with the films being oxygen overdoped, as was intended from the post deposition annealing step. The transport current densities J sfc (77 K) varied from 3.0 to 4.2 MA/cm2 and Fp,max from 3.7 to 4.6 GN/m3. Fig. 1 presents a high resolution SEM image of the top surface of ML-1.5-10 in which the nanoprecipitates are clearly visible, though some are only seen at tilted angles due to their small size. The precipitates cover the Y123 uniformly with an average surface ab-plane spacing 20 nm, equivalent to an areal density of Ni 2.5 1015 m2 and an effective vortex density of 5 T. SEM images taken on ML-1.1-10 and ML-1.9-10 (not shown here) suggest Ni < 1 1015 and 3.1 1015 m2, respectively, the latter density being equivalent to the rather high matching field BU of 6 T. Most nanoprecipitates are 10–15 nm in size, except for a few which have coalesced to 30–50 nm. Also noticeable in all films were pin holes 100–300 nm in diameter. Since pin holes of similar size and areal density were found in all the films studied in this work, their presence should not affect our quantitative comparisons. Fig. 2a–c present TEM images of ML-1.5-10 at three different magnifications so as to allow the uniformity of precipitation to
Table 1 Detailed architectures and key superconducting properties for all PLD samples studied in this work. SL and ML denote single layer and multilayer, respectively. The two numbers after ML represent the Y211 sub-layer thickness t211 and the Y123 sub-layer thickness t123 (in nm), respectively. Tc is the critical temperature measured by transport method at the zero-resistance point. Note
Sample ID
Architecture
Tc (°C)
2 Jsf c (77 K) (MA/cm )
Jc(4 T,77 K) (MA/cm2)
Fp,max(77 K) (GN/m3)
Single layer Y123 films
SL-regular-1 SL-regular-2 ML-1.1-10 ML-1.5-10 ML-1.9-10 ML2-1.5-10 ML-1.5-20 ML-1.5-30
Pure Y123 (t = 520 nm) Pure Y123 (t = 500 nm) (Y12310 nm + Y2111.1 nm) 50 (Y12310 nm + Y2111.5 nm) 50 (Y12310 nm + Y2111.9 nm) 50 (Y12310 nm + Y2111.5 nm) 50 (Y12320 nm + Y2111.5 nm) 50 (Y12330 nm + Y2111.5 nm) 50
89.9 89.3 89.5 90.3 90 89.8 89.4 89.4
3.3 3.6 3.5 3.9 3.0 4.2 3.9 3.6
0.052 0.041 0.040 0.047 0.039 0.031 0.037 0.039
4.1 3.7 4.5 4.8 4.1 4.2 4.6 4.3
Multilayer (Y123 + Y211/Y2O3) N films
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Fig. 1. High resolution SEM image taken on the top surface of ML-1.5-10 to show the nanoprecipitate formation.
be assessed. As shown in the diffraction contrast image of Fig. 2a, we successfully made a uniform, nanoprecipitate-containing microstructure throughout the entire film by multilayer deposition. Fig. 2b shows that nanoprecipitates were indeed found in planes separated by 10 nm along the film thickness, making t123 a well defined parameter. Stacking faults, very common in many Y123 films, were barely seen. However, a higher concentration of defects and precipitates was observed within 20 nm of the Y123/STO interface, similar to our earlier observation on a (Y123 + Y211) N multilayer film reported by Kim et al. [10] and in the study of Wang et al. [24]. This segregation of precipitates at the interface may release the misfit strain caused by heteroepitaxial growth of Y123 on STO. Because of this segregation, there is a precipitate-free area 20 nm thick on top of the segregation zone. Multiple high resolution TEM (HRTEM) observations revealed that a typical precipitate has a thin disk-shape 3 nm thick and 10– 15 nm in diameter, as shown in the HRTEM image of Fig. 2c. TEM images also showed that as t211 and t123 vary for the various ML films the precipitate thickness dt remains rather thin and constant at 3 nm, leaving the nanoprecipitate areal density Ni and c-axis pin spacing dc as the prime variables between films. Since the precipitates are discrete and arranged in well defined planes separated by Y123 layers, dc is indeed the Y123 sub-layer thickness t123. To avoid further confusion of the two concepts, we here distinguish between the use of t123 to define the growth parameter and dc to describe the experimentally observed pin spacing along the c-axis, although the TEM indeed shows them to be the same. The diffraction pattern derived from the fast Fourier transform (FFT) of Fig. 2c indicates that the lattice structure of the precipitate is actually Y2O3 rather than Y211, suggesting reactions between Y123 and Y211 during film growth. It is also noticeable that little strain contrast is seen on the top and bottom of precipitates, indicating that the effective pinning size is probably very close to the physical size without significant strain-enhanced zone, as is often seen, for example in (Y123 + Y211) N multilayers [10]. Although the reason for Y2O3 rather than Y211 as the precipitate phase is presently unclear, it is clear that such reactions do not prevent a rather uniform precipitate arrangement. On the other hand, even though both Y2O3 and Y211 are insulating, their pinning efficiency is expected to be different, since our earlier study found strong strain fields associated with Y211 nanoprecipitates embedded in Y123 [10], possibly extending their pinning dimension [23]. Consistent with this observation, the mismatch for Y211 precipitates is large and positive (7%) compared to 2.7% for Y2O3 [25]. Fig. 3 shows the self-field Jc (J sfc ) and Fp,max measured at 77 K on the varying t211 set of films compared against a pure Y123 film (SLregular-1, t211 = 0). t123 10 nm was chosen to compare to films grown earlier by Haugan et al. [11,26]. Both J sfc and Fp,max follow the same dependence on t211, increasing as t211 grows from 0 to
Fig. 2. (a) Low magnification cross-sectional TEM image shows a uniform distribution of the precipitates through thickness. (b) At a higher magnification, it is observed that the precipitates are formed in planes separated by 10 nm, as was originally designed. The Y123/STO interface area has a higher precipitate concentration than the matrix. (c) HRTEM image shows a typical precipitate of 10–15 nm wide and 3 nm thick. The diffraction pattern derived from FFT indicates that the lattice structure of precipitate is Y2O3 rather than Y211.
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Fig. 3. Jsfc and Fp,max as functions of t211 measured at 77 K. At a constant t123 10 nm, both J sfc and Fp,max increase with increasing t211 from 0 to 1.5 nm, but then decrease at t211 1.9 nm. The corresponding nanoprecipitate areal densities Ni at different t211 values are: Ni < 1 1015 m2 for t211 = 1.1 nm, Ni 2.5 1015 m2 for t211 = 1.5 nm, and Ni 3.1 1015 m2 for t211 = 1.9 nm, respectively.
1.5 nm, but then decreasing as t211 grows to 1.9 nm. Clearly, on varying the nanoprecipitate concentration from 10 vol.% (ML-1.110) to 13 vol.% (ML-1.5-10) to 16 vol.% (ML-1.9-10), the maximum Jsfc and Fp,max of 3.9 MA/cm2 and 4.8 GN/m3 are both reached in the same ML-1.5-10 film. The nanoprecipitates add only 17% to J sfc at the optimum thickness t211 1.5 nm as compared to J sfc ¼ 3:25 MA=cm2 for t211 = 0, indicating the significant effect of other pinning centers existing in our PLD films. Fig. 4 plots Jc as a function of pin separation along the c-axis (t123 or dc) measured at self-field and 4 T at 77 K on the second set of ML films: ML2-1.5-10, ML-1.5-20, and ML-1.5-30, for which the Y123 sub-layer thickness t123 varies from 10 to 20 to 30 nm at a constant nominal t211 of 1.5 nm. The results at first sight look counter intuitive, since although J sfc (77 K) increases from 3.5 to 3.6 to 3.9 and to 4.2 MA/cm2 as t123 or dc decreases from 500 nm (single layer pure Y123 film) to 10 nm, the dependence of Jc(77 K, 4 T) on t123 is completely reversed. Indeed the highest Jc(4 T) occurs for the film with no added nanoprecipitates. For all three varying t123 ML films, Fp,max(77 K) does not exceed 5 GN/ m3. Both the Jc fall-off at 4 T and the sub-optimum Fp,max of the
Fig. 4. Jc as a function of the c-axis pin spacing dc (or t123) measured at self-field and H = 4 T at 77 K. At a constant t211 1.5 nm, Jsfc increases monotonically with decreasing dc, while Jc(4 T) decreases with decreasing dc. Here t123 500 nm represents the pure Y123 film SL-regular-2.
ML films suggest that these ML films are suffering from strong thermally activated depinning at 77 K [2,16], in spite of them containing more than 10 vol.% of insulating precipitates with diameters close to the vortex core diameter 2nab = 8 nm at 77 K [27], where nab is the coherence length along the ab-planes. The implications that TAD effects are producing a strong degradation of the 77 K properties can be tested explicitly by measuring Jc over a wide range of T and H. Fig. 5a–c present Jc as a function of temperature measured respectively at 0.5 T, 4 T, and 8 T for the four films of Fig. 4. At 0.5 T, although all Jc(T) curves seem to cluster near 77 K, they start to diverge below 70 K, as shown in Fig. 5a. In fact, at all temperatures, the magnitude of Jc(0.5 T) shows a consistent order: Jc(ML2-1.5-10) > Jc(ML-1.5-20) > Jc(ML-1.5-30) > Jc(SLregular-2), showing that denser precipitates with smaller dc favor higher Jc. At 4 T, Fig. 5b shows that even though Jc(4 T) starts with a reversed order at 77 K as shown in Fig. 4, as T decreases Jc(ML21.5-10) quickly surpasses Jc(SL-regular-2) at 70 K. Following that, Jc(ML-1.5-30) and Jc(ML-1.5-20) are exceeded by Jc(ML2-1.5-10) successively at 65 K and 55 K. To better reveal the cross-over, the inset of Fig. 5b plots DJc(T, 4 T) for T = 50–70 K for the three ML films, where DJc = Jc Jc(SL-regular-2). Below 55 K, a consistent Jc(4 T) order is found: Jc(ML2-1.5-10) > Jc(ML-1.5-20) > Jc(ML-1.530) > Jc(SL-regular-2), which is the same as the H = 0.5 T situation shown in Fig. 5a. At even higher field H = 8 T, Jc(T) curves cross in a similar way as at 4 T, as shown in Fig. 5c. The cross-over temperature, however, shifts down to 50 K between ML2-1.5-10 and ML-1.5-30, and to 36 K between ML2-1.5-10 and ML-1.5-20, as shown in the inset of Fig. 5c, which presents DJc(T, 8 T) for T = 30–60 K. When T < 36 K, Jc once again reaches a consistent order: Jc(ML2-1.5-10) > Jc(ML-1.5-20) > Jc(ML-1.5-30) > Jc(SL-regular2), thus again reverting to the expected result that Jc is enhanced by denser precipitates and lower dc.
4. Discussion 4.1. General considerations A particular goal of our work was to perform a systematic, quantitative pinning study. In this respect, the current (Y123 + Y211/Y2O3) N multilayer films indeed have a well defined nanostructure, as revealed by the SEM and TEM images in Figs. 1 and 2. In addition, our controlled nanoprecipitate additions do yield systematic influences on the superconducting properties, as demonstrated by the variation of superconducting properties shown in Figs. 3 and 4, which show that both Jc and Fp,max are improved by varying t123 and t211. In fact, high J sfc (77 K) 4.2 MA/cm2 on a 610 nm thick multilayer film ML2-1.5-10 was achieved, a value fully consistent with the maximum envelope of the generally accepted Jc vs. film thickness curve [28]. On the other hand, the improvement of Fp,max only to 4.8 GN/m3 seems rather unremarkable, given the very high density (2.5 1015 m2) of nanoprecipitate pinning centers and the fact that a much higher Fp,max of 10 GN/m3 was found in nominally rather similar (Y123 + Y211) N multilayer films [10]. The potential explanation that we want to explore here, as pointed out by Figs. 4 and 5, is that strong thermally activated depinning effects greatly reduce Jc and Fp,max at 77 K. We believe that such TAD effects can easily be underestimated when dealing with a high density of non-superconducting precipitates with size very close to the vortex core diameter. These considerations have motivated us to clarify the Jc behavior of our films over a wide range of temperature and field, so as to assess the precipitate size and operating temperature domain where thermally activated depinning dominates the behavior. One important message of this study is that special attention has to be paid to the pin size along the magnetic field direction when pins with diame-
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Fig. 5. Jc as a function of temperature for SL-regular-2, ML2-1.5-10, ML-1.5-20, and ML-1.5-30 at (a) 0.5 T, (b) 4 T, and (c) 8 T. For (a), the four curves are well separated in the whole temperature range. For (b) and (c), cross-over of the Jc(T) curves happens at various temperatures depending on H and dc. The inset of (b) and (c) shows DJc(T) = Jc Jc(SL-regular-2) for H = 4 T and 8 T, respectively, to better reveal the cross-over.
ters close to the vortex core diameter are introduced into Y123. It is a remarkable fact of pinning engineering in present Y123 films that too high a density of too small nanoprecipitates can be grown and that small enhancements of pin size can be highly effective in enhancing Jc(H) in the high temperature domain around 77 K.
data (black curve, 77 K and self-field) shown in Fig. 4. On the other hand, Eq. (1) considers only vortex pinning, disregarding thermal fluctuation depinning effects. The strength of thermally activated depinning can be quantified by a dimensionless parameter s, which is the ratio of the thermal energy and the pinning energy [20].
4.2. Vortex pinning and depinning effects
s¼ From the SEM and TEM observations in Figs. 1 and 2, we know that our ML films contain 5–16 vol.% of 10–15 nm sized (the vortex core diameter 2nab = 8 nm at 77 K and 4 nm at 4 K) insulating precipitate with a high matching field BU 5–6 T, making them, in principle, almost ideal for strong single-vortex, core pinning. Given the fact that strong pinning precipitates will decouple vortex lines into independently pinned short segments equal to the c-axis pin spacing dc (when Hkc) [29,30], the maximum self-field J sfc in the absence of TAD effects can then be estimated by considering depinning of elliptical vortex segments whose ends are fixed by neighboring precipitates [10,20,31]:
J sfc ffi
U0 2pl0 ka kc dc
ln
dc nc
ð1Þ
where U0 is the flux quantum, l0 the vacuum permeability, ka and kc the penetration depth along the ab-plane and the c-axis respectively, and nc the coherence length along the c-axis. Eq. (1) suggests a monotonic increase of Jc(dc) with decreasing dc for dc > 3nc, which is indeed consistent with the experimental J sfc (dc)
pkB T J c0 U0 dc l
ð2Þ
where kB is the Boltzmann constant, Jc0(T, H) is the critical current density produced by pins other than the nanoprecipitates, l is of the order of the pin spacing in the ab-plane, 17–20 nm for most films (except for ML-1.1-10 which only has a sparse nanoprecipitate coverage) in this study. Eq. (2) indicates that thermally activated depinning increases as dc decreases, because shorter vortex segments fluctuate more strongly than longer vortex segments, thus making thermal smearing of the pinning potential and reduction of Jc more pronounced at smaller dc. For s 1 (which corresponds to low T and H), the effect of thermally activated depinning is weak, and Jc(d) increases as the pin spacing dc decreases in accordance with Eq. (1). However, at higher T and H, Jc(T, H) in Eq. (2) decreases, so the magnitude of vortex fluctuations and the strength of TAD increases. As a result, the reversed Jc(dc) dependence at 77 K and 4 T seen in the red curve of Fig. 4 develops. The Jc of more densely spaced precipitate arrays is then lower because shorter vortex segments with smaller dc are more easily thermally depinned than longer segments.
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Jc as a function of dc for different s can be calculated for a sineGordon pinning model, as was discussed in detail in Ref. [20]. These calculations are summarized in Fig. 6. At small s values (low T and H), Jc first increases as dc decreases before it reaches a maximum at some intermediate value of dc then quickly drops to zero. As s increases, the Jc(dc) peak diminishes and shifts to higher dc. Further increase of the TAD parameter s results in the disappearance of the peak so that Jc decreases monotonically as dc decreases. Fig. 6 suggests two opposite Jc(dc) dependencies (labeled here as A and B), which we find to correspond to the self-field and 4 T behavior of Jc(dc) in Fig. 4, respectively. Type A behavior represents the domain where Jc is enhanced by increasing the density of precipitates and reducing t123 or dc because TAD effects are still weak at low fields where pinning potentials are strong, while behavior B corresponds to the opposite behavior as TAD effects dominate near the irreversibility field Hirr, which occurs at 6.7 T at 77 K for these films. The key result of Fig. 4 is that this transition occurs between self-field and 4 T at 77 K, thus showing very explicitly that selffield optimization is not the same as in-field optimization. Considering behavior over a wider range of T and H, Eq. (2) shows that s at a fixed dc can be changed by varying T and H, as was done in Fig. 5: increasing T and/or H raises s, and decreasing T and/or H reduces s. The calculations shown in Fig. 6 are qualitatively consistent with the experimental results shown in Fig. 5: except at H = 0.5 T, for which type A behavior was observed at all temperatures, an A to B cross-over of Jc(H, T) behavior change as a function of dc was found. Consistent with Fig. 6, the cross-over takes place at higher fields at lower temperatures, because higher H produces a more pronounced TAD effect, requiring lower temperatures to prevent enhanced TAD effects. The behavior of Jc(dc) shown in Fig. 6 clarifies the complicated relationship between Jc, dc and s, suggesting that an assessment of s (determined by operational T and H) should be performed before pinning optimization at and near 77 K, where most applications of Y123 are foreseen. This applies not only to pinning studies with controlled, anisotropic nanoparticle additions (like the present work) but also to the more usual pinning engineering by random nanoparticles, because the incorporation of strong pinning nanoparticles into Y123 always reduces dc and thus risks increasing s. The key is thus to find the right balance between strengthening the elementary pinning force and reducing thermally activated depinning effects. By comparison, the strategy for improving Jc(H) in the low T limit is much more straightforward
Fig. 6. Evolution of the dependence Jc(dc) for different values of the parameter s: (1) 0.0065, (2) 0.01, (3) 0.015, and (4) 0.025. Here s is the ratio of the thermal energy and the pinning energy and is used to quantify the strength of thermally activated depinning, and Jc0 is the critical current density for the vortex segment of length dc0 collectively pinned by point defects between the nanoprecipitates [20].
because Jc tends to increase monotonically with increasing pin density and decreasing dc, so long as the insulating pin volume fraction does not exceed too much the optimum value of 11% [20]. In support of this conclusion, our ML2-1.5-10 film with 16 vol.% of pin and the smallest dc 10 nm, attained a J sfc of 48 MA/ cm2 at 10 K, which is 20% of Jd (250 MA/cm2 at 10 K, assuming a thermodynamic critical field Hc(10 K) 0.92 T and the London penetration depth k(10 K) 160 nm). Extensive evaluation of Jc at 4 K is still rare but a study of the exceptionally strong pinning film of Gutierrez et al. [5] made with 15–30 nm sized dense, random BZO nanoprecipitates with Fp,max(77 K) of 20 GN/m3 at 77 K is instructive. Although the BZO film had a four times greater Fp,max(77 K) than our film ML2-1.5-10, Jc of ML2-1.5-10 outperformed the BZO film by 20% at 4 T and 4.2 K. Our conclusion is thus that pinning centers must be specifically optimized to take account of strong thermally activated depinning conditions found in fields greater than 1–2 T at 77 K. 4.3. The importance of pin length in raising fp As follows from the TEM images shown in Fig. 2, the precipitates in the present ML films are mostly only 3 nm thick along the c-axis, significantly thinner than most strong pinning precipitates, whose dimensions are reported to lie in the range of a few to ten times this size in the literature [5,10,32], some of which are highly c-axis correlated nanorods that may be hundreds of nanometers long [6,18]. For the present ML films, the oblate Y2O3 precipitates have a much higher degree of correlation in shape and alignment along ab-planes, suggesting that they should be much more effective pinning centers at high T for Hkab than for Hkc. This conclusion is indeed consistent with our angular dependent Jc(h, 77 K) measurements. As shown in Fig. 7, Jc(h) is enhanced progressively and more strongly in the Hkab direction than in the Hkc direction as t211 is increased. When the field H = 1 T is inclined by 45° with respect to the c-axis, both ML-1.1-10 and ML-1.5-10 shows 40% Jc improvement compared to the non-ML film (SL-regular-1). The difference between the two ML films is negligible despite their largely different precipitate areal densities (Ni < 1 1015 m2 vs. Ni 2.5 1015 m2). However, when H is parallel to the ab-planes, a strong monotonic dependence of Jc on t211 is evident: Jc is improved by 70% from SL-regular-1 to ML1.1-10, and by 157% from SL-regular-1 to ML-1.5-10, as the precipitates become better ab-plane correlated with increasing areal density. At H = 4 T, Jc shows no improvement as t211 increases when H is applied in the vicinity of Hkc, as neither dt nor the c-axis
Fig. 7. Jc(h) curves for SL-regular-1, ML-1.1-10, and ML-1.5-10 measured at 77 K and 1 T (solid symbol) and 4 T (cross-filled symbol).
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correlation increases. Yet a pronounced, monotonic increasing dependence of Jc on t211 is still observed when H is applied within 20° of the ab-planes. To understand why oblate Y2O3 precipitates with diameter D = 10–15 nm > 2nab(77 K) = 8 nm and a thickness dt = 3 nm < 2nab(77 K) are not very effective pinning centers at 77 K for Hkc, we first estimate the elementary core pinning force fp for the vortex semi-loop resulting from subdividing a vortex line by the oblate nanoprecipitates as shown in Fig. 8. The transport current pushes the vortex segments toward the edges of parallel diskshaped precipitates where it bows out at the edges under the Lorentz force, as illustrated in Fig. 8. The maximum pinning force fp Ep/nab results from the gain in the condensation energy Ep l0 H2c pdt n2ab =2 [33] in the volume of the dielectric precipitate, pdt n2ab , which crosses the vortex core. Substituting here the thermodynamic critical field, Hc = U0/23/2l0pkabnab, we obtain:
fp
U0 dt 16pl0 k2ab nab
ð3Þ
For thin precipitates, fp is therefore reduced by the small ratio dt/2nab. This reduction does occur for our films since fp is reduced by the ratio dt/2nab 0.4 at 77 K and 0.5 at 4 K. This small thickness reduction in fp facilitates further decrease of Jc(77 K) by thermal
Fig. 8. Illustration of a bowing vortex segment confined by parallel, dt-thick diskshaped precipitates with a c-axis spacing dc.
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fluctuations of a vortex segment confined between parallel diskshape precipitates where it is also affected by other point pinning defects existing in our PLD films and responsible for the significant J sfc values at t211 = 0 shown in Fig. 2. To further test this argument, we compare the ML-1.5-30 film to a recently studied Y123 coated conductor (CC) grown by metal-organic chemical vapor deposition (MOCVD) whose pinning nanostructure of RE2O3 is very similar to the present ML films. Details of the nanostructure and pinning properties of this MOCVD CC have been given elsewhere [17,30]. Briefly, we found that (Y,Sm)2O3 precipitates 10–15 nm in diameter were separated horizontally by 20 nm and formed in planes almost parallel to the ab-planes of Y123 with an average vertical interval of 30 nm. However, a critical parameter of this MOCVD film in the context of the present discussion is that dt is 8–10 nm for the MOCVD CC and 3 nm for ML-1.5-30, even as the diameter, areal density and ab-plane spacing of the precipitates in the MOCVD CC are very similar to those in ML-1.5-30. According to Eq. (2), fp would thus be 3 times higher for the MOCVD CC than for ML1.5-30 under similar measurement conditions. Fig. 9 plots Jc(H, 77 K) and Fp,max(77 K) for ML2-1.5-30 and the MOCVD CC. Indeed the difference in Jc is dramatic for fields H > 3 T, a point that is especially clear in the enhancement of the irreversibility field Hirr (defined at Jc = 100 A/cm2) from 6.7 to 8.9 T, as shown in Fig. 9a. This enhancement is entirely consistent with our argument that elongated pinning centers with larger fp can more effectively suppress TAD, thus increasing the in-field Jc and the irreversibility field Hirr. The comparison clearly shows that thermally activated depinning can powerfully degrade Jc in the T–H domain most relevant to power applications of the Y123 coated conductors. Elongating pins along the desired principal field direction of the application significantly increases Jc. We can also note that both YBCO films reach their maximum pinning force Fp,max at fields well below the vortex matching field BU (5 T) of the precipitate density, as shown in Fig. 9b, suggesting that many precipitates are ineffective due to TAD effects. Indeed, the field at which Fp,max(77 K) occurs and the enhancement of Hirr(77 K) can be very good guides to the degree to which more effective pinning centers can suppress TAD effects. In the present ML films Fp,max(77 K) occurs at 1.5 T and Hirr(77 K) is 6.7 T, whereas the corresponding values for the coated conductor with precipitates 3 times longer along the c-axis are 2 T and 8.9 T. Both films have similar Tc values of 90 K. The BSO-containing nanorod samples of Mele et al. with average nanorod lengths of 140 nm which achieved the
Fig. 9. (a) A comparison of Jc(H, 77 K) between an MOCVD CC [17] and ML-1.5-30, both of which have dc 30 nm. Starting at almost the same point, a big deviation starts to develop when H > 2 T. The inset shows Jc(T, 8 T) curves for the two samples in comparison. (b) A comparison of Fp(H, 77 K) between the MOCVD CC and ML-1.5-30. Because of the longer nanoprecipitates along the c-axis, both the field at which Fp,max occurs and Hirr are increased for the MOCVD CC comparing against ML-1.5-30. On the other hand, both films reach Fp,max at fields well below the matching field BU due to the strong TAD effects at the high temperature of 77 K.
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spectacular Fp,max(77 K) values of 28 GN/m3 have Hirr(77 K) of >9 T [6], even though Tc (88.6 K) was depressed by 1.4 K. Therefore, we conclude that the size of nanoprecipitates along the preferred field direction is of crucial importance to the magnitude of the pinning force at or near 77 K. Since this requires extensive TEM study to define, we also note that the field at which Fp,max and Hirr occur can be very good guides to whether TAD effects are important. The connection to Hirr and Fp,max may be particularly valuable for coated conductor evaluations, where there are in general always some operating current-blocking effects produced by higher angle grain boundaries, sub-micron second phases, cracks, substrate scratches, etc. that render the absolute magnitude of Jc uncertain. This is certainly true for the present MOCVD conductor as noted earlier by Chen et al. [30], where considerable blocking phases were present. But whatever their role in depressing the real magnitude of Fp,max, they play no role in depressing Hirr or the position of Fp,max. The inset of Fig. 9a presents Jc as a function of T measured at H = 8 T for our ML and the MOCVD CC samples. The nearly constant gap between the two Jc(T) curves indicates a diminishing relative difference of the two Jc(T) as T decreases, the difference being only 2% at 10 K and 8 T. This strongly diminishing gap between the two samples as T is lowered suggests that the extra pinning strength from the elongated precipitates is beneficial to Jc only under strong TAD conditions. For low T applications, a denser pinning structure (below the current-blocking threshold) leads to the highest Jc at low temperatures where TAD effects are weak. On the other hand, increasing pin density may play the opposite role at high temperatures, because TAD effects become more effective as the length of thermally fluctuating vortex segments dc decreases (see Fig. 6). This again indicates that there is no universal pinning nanostructure, which is equally effective at low and high temperatures and in different field regions. 5. Summary A series of PLD grown single layer Y123 and multilayer (Y123 + Y211/Y2O3) N films were studied over a broad range of multiple variables, including temperature, field, pinning center areal density, c-axis spacing, and their extension along the c-axis, aiming at a thorough understanding of the optimum pinning structures in Y123. Pinning defects formed in the ML films are a high density of thin-disk-shaped Y2O3 nanoprecipitates. Even though our results do not lead directly to champion Jc or Fp,max values for Y123 at 77 K, we have clarified the important relationship between two important and opposite effects that control Jc and Fp: vortex core pinning and thermally activated vortex depinning, which are both strongly affected by T, H, and dc. Our results indicate that a direct solution for improving Jc at low temperatures is to reduce dc, while at high temperatures, increasing the pinning precipitate extension along the field direction is the effective way to Jc(H) enhancement. Acknowledgements We would like to thank Aixia Xu for assistance with some of the transport measurements, as well as Aixia Xu and Jan Jaroszynski for many discussions of pinning in the low temperature limit. The work was supported by the US Department of Energy, Office of Electricity Transmission and Distribution.
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Physica C journal homepage: www.elsevier.com/locate/physc
Pinning, thermally activated depinning and their importance for tuning the nanoprecipitate size and density in high Jc YBa2Cu3O7x films Zhijun Chen *, Fumitake Kametani, Alex Gurevich, David Larbalestier National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310, USA
a r t i c l e
i n f o
Article history: Accepted 20 August 2009 Available online 26 August 2009 PACS: 74.25.Fy 74.25.Qt 74.25.Sv 74.62.Dh 74.72.Bk 74.78.Bz Keywords: YBCO Coated conductor Pinning Nanoprecipitate Thermally activated depinning Critical current density
a b s t r a c t YBa2Cu3O7x (Y123) films with quantitatively controlled artificial nanoprecipitate pinning centers were grown by pulsed laser deposition (PLD) and characterized by transport over wide temperature (T) and magnetic field (H) ranges and by transmission electron microscopy (TEM). The critical current density Jc was found to be determined by the interplay of strong vortex pinning and thermally activated depinning (TAD), which together produced a non-monotonic dependence of Jc on c-axis pin spacing dc. At low T and H, Jc increased with decreasing dc, reaching the very high Jc 48 MA/cm2 20% of the depairing current density Jd at 10 K, self-field and dc 10 nm, but at higher T and H when TAD effects become significant, Jc was optimized at larger dc because longer vortex segments confined between nanoprecipitates are less prone to thermal fluctuations. We conclude that precipitates should extend at least several coherence lengths along vortices in order to produce irreversibility fields Hirr(77 K) greater than 7 T and maximum bulk pinning forces Fp,max(77 K) greater than 7–8 GN/m3 (values appropriate for H parallel to the caxis). Our results show that there is no universal pin array that optimizes Jc at all T and H. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction It is well accepted that the critical current density Jc in YBCO can be significantly enhanced by incorporating a high density of strong, nanoprecipitate vortex pinning centers. Very high self-field values of Jc(77 K) > 5 MA/cm2 15% of the depairing current density Jd(77 K) 40 MA/cm2, have been demonstrated by almost all major YBCO fabrication techniques [1–4]. In addition, exceptional maximum pinning force Fp,max values in the range of 20–28 GN/ m3 at 77 K have been achieved by several groups [5–7]. Such Fp,max(77 K) values exceed the 18 GN/m3 found in fully optimized Nb–Ti superconductor at 4.2 K [8], hitherto thought to be the most highly optimized low-Tc superconductor (LTS). On the other hand, the majority of reported Fp,max(77 K) lie between 5 and 12 GN/m3 [9–13], well below the very best values, even for films with selffield Jc(77 K) 0.15Jd. This lack of correlation between self-field and in-field Jc values makes it clear that there are important subtleties to the in-field vortex pinning that are not yet fully understood. * Corresponding author. Present address: Materials Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, USA. E-mail address: [email protected] (Z. Chen). 0921-4534/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2009.08.013
One of the most active areas of present YBCO study is thus to understand how samples with excellent self-field Jc(77 K) can have their in-field Jc improved. More specifically there is broad interest to understand whether there is some universal pin array which optimizes Jc(T, H) under all conditions or whether specific types of pin must be engineered to maximize Jc(T, H) in specific domains of field and temperature. We are motivated to ask this question not just from the general viewpoint of optimizing pinning in the important 65–77 K range, but also in view of growing interest of using YBCO to build very high field magnets [14] in the field domain of H > 25 T where no Nb-based superconductor can be used. As has been emphasized recently [5,15], pinning optimization at 77 K has to be done in the domain of T and H where thermally activated depinning (TAD) effects are strong, and weak point pinning is ineffective [2,16]. But at low temperatures where TAD effects are reduced, weak point pinning can significantly contribute to Jc [5,15], even at H > 30 T, which is only 0.3Hirr(4 K) [17]. How to optimize pinning in such a broad T–H domain is still unclear, given that BaZrO3 (BZO) [18,19] or BaSnO3 (BSO) [6,13] nanorods, the presently favorite strong correlated pin when H is parallel to the c-axis, although very effective in fields of a few tesla, do not grow in sufficient density to optimize Jc in fields of 5 T and above. It is the
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complicated interactions between Jc in the high and low T and H limits, strong nanoprecipitate pinning and thermally activated depinning effects that this work seeks to clarify. Our systematic study of Jc in terms of pin density and spacing finds that Jc at 77 K and low fields (0–1 T) increases monotonically with decreasing c-axis pin spacing dc [20]. By extending our measurements over wide temperature (10–77 K) and field (0–9 T) ranges, we show that the dependence of Jc on dc can change significantly as T and H are varied. We find that the interplay of thermal fluctuations of vortices and vortex pinning by nanoprecipitates makes Jc increase with decreasing dc at low temperatures and fields, while reversing the trend at higher T and H as thermally activated depinning becomes stronger. In this higher TAD domain, elongating the pinning nanoparticles along the field direction produces an enhancement of the elementary pinning force fp which inhibits thermally activated depinning effects, consistent with many previous studies of the effectiveness of nanorods [6,13,18,19,21]. On the other hand, the low temperature and high field Jc does not benefit as much from increasing the strength of the single-particle elementary pinning force as from increasing the density of pinning centers (thus favoring smaller dc) because thermally activated depinning effects are small. Thus, our results show that quantitative optimization of Jc over wide field and temperature ranges requires much greater attention to the details of pin size and pin density.
and t123 = 10 nm. Note that t211 only quantifies the nominal thickness of the insulating Y211 pin layers which actually decompose into a dense array of discrete disk-shaped nanoprecipitates dispersed within the Y123 during the multilayer deposition. The actual thickness dt of the precipitates was determined by TEM, which showed that the nanoprecipitates are not Y211 but Y2O3. Although both phases are insulating and thus similar in their pinning effects, actually there are likely to be second order differences, e.g. strain fields, in their pinning effects that we do not address here but have been recently noted to be rather significant by Harrington et al. [23]. Four-point transport measurements were carried out in a 9 T PPMS system on bridges 100 lm wide and 500 lm long patterned with a Nd-doped yttrium aluminum garnet laser. Broad range measurements were performed with H perpendicular to the film plane and thus parallel to the c-axis. Some measurements of the angular dependence of Jc(h), where h is the angle between H and the abplanes of Y123, were made in fields of 1 and 4 T. To measure Jc at lower temperatures down to 10 K, narrower links 10 lm wide by 200 lm long were prepared with a focused ion beam (FIB) tool to restrict Ic to <4 A. In all cases, Jc was determined with a 1 lV/cm criterion. High resolution scanning electron microscopy (SEM) images were taken in a Zeiss 1540, while TEM imaging was performed in a JEOL JEM-2011.
3. Results 2. Experimental details YBCO films were deposited on (100) oriented single crystal SrTiO3 (STO) substrates by PLD using a conventional excimer laser (Lambda Physik model LPX 201i) operating at 248 nm wavelength. Pinning centers were introduced artificially by ablation of separate Y123 and Y2BaCuO5 (Y211) targets to form multilayer films [11,22]. All films were grown at a substrate temperature Tg 810 °C with a laser fluence El 2 J/cm2 at a repetition rate of 5 Hz and a target-to-substrate distance dts of 5.7 cm. This higher than usual Tg was used to achieve a smoother film surface, so that nanoprecipitate densities could be better quantified. The films had a final thickness 550 nm with only small variations. Depositions were performed in 250 mtorr of flowing oxygen and the films were annealed after deposition in situ at 500 °C under 800 torr O2 for 45 min. Eight films were studied in this work, two being nominally identical single layer (SL) films, and six being multilayer (ML) films in two sequences. One sequence kept the nominal Y123 sub-layer thickness t123 constant at 10 nm, varying the Y211 sub-layer thickness t211 from 1.1 to 1.5 to 1.9 nm, while the second kept t211 constant and varied t123 from 10 to 20 to 30 nm. Detailed architectures and basic superconducting properties of all samples are listed in Table 1. The Y123 and Y211 thicknesses provide the sample ID of the ML films; for example ML-1.9-10 means that t211 = 1.9 nm
Table 1 provides a summary of several key features of the films. The transition temperatures Tc were all close, varying from 89.3 to 90.3 K as defined by the zero-resistance point in small current transport measurements. These values and their concave resistance R(T) curves are all consistent with the films being oxygen overdoped, as was intended from the post deposition annealing step. The transport current densities J sfc (77 K) varied from 3.0 to 4.2 MA/cm2 and Fp,max from 3.7 to 4.6 GN/m3. Fig. 1 presents a high resolution SEM image of the top surface of ML-1.5-10 in which the nanoprecipitates are clearly visible, though some are only seen at tilted angles due to their small size. The precipitates cover the Y123 uniformly with an average surface ab-plane spacing 20 nm, equivalent to an areal density of Ni 2.5 1015 m2 and an effective vortex density of 5 T. SEM images taken on ML-1.1-10 and ML-1.9-10 (not shown here) suggest Ni < 1 1015 and 3.1 1015 m2, respectively, the latter density being equivalent to the rather high matching field BU of 6 T. Most nanoprecipitates are 10–15 nm in size, except for a few which have coalesced to 30–50 nm. Also noticeable in all films were pin holes 100–300 nm in diameter. Since pin holes of similar size and areal density were found in all the films studied in this work, their presence should not affect our quantitative comparisons. Fig. 2a–c present TEM images of ML-1.5-10 at three different magnifications so as to allow the uniformity of precipitation to
Table 1 Detailed architectures and key superconducting properties for all PLD samples studied in this work. SL and ML denote single layer and multilayer, respectively. The two numbers after ML represent the Y211 sub-layer thickness t211 and the Y123 sub-layer thickness t123 (in nm), respectively. Tc is the critical temperature measured by transport method at the zero-resistance point. Note
Sample ID
Architecture
Tc (°C)
2 Jsf c (77 K) (MA/cm )
Jc(4 T,77 K) (MA/cm2)
Fp,max(77 K) (GN/m3)
Single layer Y123 films
SL-regular-1 SL-regular-2 ML-1.1-10 ML-1.5-10 ML-1.9-10 ML2-1.5-10 ML-1.5-20 ML-1.5-30
Pure Y123 (t = 520 nm) Pure Y123 (t = 500 nm) (Y12310 nm + Y2111.1 nm) 50 (Y12310 nm + Y2111.5 nm) 50 (Y12310 nm + Y2111.9 nm) 50 (Y12310 nm + Y2111.5 nm) 50 (Y12320 nm + Y2111.5 nm) 50 (Y12330 nm + Y2111.5 nm) 50
89.9 89.3 89.5 90.3 90 89.8 89.4 89.4
3.3 3.6 3.5 3.9 3.0 4.2 3.9 3.6
0.052 0.041 0.040 0.047 0.039 0.031 0.037 0.039
4.1 3.7 4.5 4.8 4.1 4.2 4.6 4.3
Multilayer (Y123 + Y211/Y2O3) N films
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Fig. 1. High resolution SEM image taken on the top surface of ML-1.5-10 to show the nanoprecipitate formation.
be assessed. As shown in the diffraction contrast image of Fig. 2a, we successfully made a uniform, nanoprecipitate-containing microstructure throughout the entire film by multilayer deposition. Fig. 2b shows that nanoprecipitates were indeed found in planes separated by 10 nm along the film thickness, making t123 a well defined parameter. Stacking faults, very common in many Y123 films, were barely seen. However, a higher concentration of defects and precipitates was observed within 20 nm of the Y123/STO interface, similar to our earlier observation on a (Y123 + Y211) N multilayer film reported by Kim et al. [10] and in the study of Wang et al. [24]. This segregation of precipitates at the interface may release the misfit strain caused by heteroepitaxial growth of Y123 on STO. Because of this segregation, there is a precipitate-free area 20 nm thick on top of the segregation zone. Multiple high resolution TEM (HRTEM) observations revealed that a typical precipitate has a thin disk-shape 3 nm thick and 10– 15 nm in diameter, as shown in the HRTEM image of Fig. 2c. TEM images also showed that as t211 and t123 vary for the various ML films the precipitate thickness dt remains rather thin and constant at 3 nm, leaving the nanoprecipitate areal density Ni and c-axis pin spacing dc as the prime variables between films. Since the precipitates are discrete and arranged in well defined planes separated by Y123 layers, dc is indeed the Y123 sub-layer thickness t123. To avoid further confusion of the two concepts, we here distinguish between the use of t123 to define the growth parameter and dc to describe the experimentally observed pin spacing along the c-axis, although the TEM indeed shows them to be the same. The diffraction pattern derived from the fast Fourier transform (FFT) of Fig. 2c indicates that the lattice structure of the precipitate is actually Y2O3 rather than Y211, suggesting reactions between Y123 and Y211 during film growth. It is also noticeable that little strain contrast is seen on the top and bottom of precipitates, indicating that the effective pinning size is probably very close to the physical size without significant strain-enhanced zone, as is often seen, for example in (Y123 + Y211) N multilayers [10]. Although the reason for Y2O3 rather than Y211 as the precipitate phase is presently unclear, it is clear that such reactions do not prevent a rather uniform precipitate arrangement. On the other hand, even though both Y2O3 and Y211 are insulating, their pinning efficiency is expected to be different, since our earlier study found strong strain fields associated with Y211 nanoprecipitates embedded in Y123 [10], possibly extending their pinning dimension [23]. Consistent with this observation, the mismatch for Y211 precipitates is large and positive (7%) compared to 2.7% for Y2O3 [25]. Fig. 3 shows the self-field Jc (J sfc ) and Fp,max measured at 77 K on the varying t211 set of films compared against a pure Y123 film (SLregular-1, t211 = 0). t123 10 nm was chosen to compare to films grown earlier by Haugan et al. [11,26]. Both J sfc and Fp,max follow the same dependence on t211, increasing as t211 grows from 0 to
Fig. 2. (a) Low magnification cross-sectional TEM image shows a uniform distribution of the precipitates through thickness. (b) At a higher magnification, it is observed that the precipitates are formed in planes separated by 10 nm, as was originally designed. The Y123/STO interface area has a higher precipitate concentration than the matrix. (c) HRTEM image shows a typical precipitate of 10–15 nm wide and 3 nm thick. The diffraction pattern derived from FFT indicates that the lattice structure of precipitate is Y2O3 rather than Y211.
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Fig. 3. Jsfc and Fp,max as functions of t211 measured at 77 K. At a constant t123 10 nm, both J sfc and Fp,max increase with increasing t211 from 0 to 1.5 nm, but then decrease at t211 1.9 nm. The corresponding nanoprecipitate areal densities Ni at different t211 values are: Ni < 1 1015 m2 for t211 = 1.1 nm, Ni 2.5 1015 m2 for t211 = 1.5 nm, and Ni 3.1 1015 m2 for t211 = 1.9 nm, respectively.
1.5 nm, but then decreasing as t211 grows to 1.9 nm. Clearly, on varying the nanoprecipitate concentration from 10 vol.% (ML-1.110) to 13 vol.% (ML-1.5-10) to 16 vol.% (ML-1.9-10), the maximum Jsfc and Fp,max of 3.9 MA/cm2 and 4.8 GN/m3 are both reached in the same ML-1.5-10 film. The nanoprecipitates add only 17% to J sfc at the optimum thickness t211 1.5 nm as compared to J sfc ¼ 3:25 MA=cm2 for t211 = 0, indicating the significant effect of other pinning centers existing in our PLD films. Fig. 4 plots Jc as a function of pin separation along the c-axis (t123 or dc) measured at self-field and 4 T at 77 K on the second set of ML films: ML2-1.5-10, ML-1.5-20, and ML-1.5-30, for which the Y123 sub-layer thickness t123 varies from 10 to 20 to 30 nm at a constant nominal t211 of 1.5 nm. The results at first sight look counter intuitive, since although J sfc (77 K) increases from 3.5 to 3.6 to 3.9 and to 4.2 MA/cm2 as t123 or dc decreases from 500 nm (single layer pure Y123 film) to 10 nm, the dependence of Jc(77 K, 4 T) on t123 is completely reversed. Indeed the highest Jc(4 T) occurs for the film with no added nanoprecipitates. For all three varying t123 ML films, Fp,max(77 K) does not exceed 5 GN/ m3. Both the Jc fall-off at 4 T and the sub-optimum Fp,max of the
Fig. 4. Jc as a function of the c-axis pin spacing dc (or t123) measured at self-field and H = 4 T at 77 K. At a constant t211 1.5 nm, Jsfc increases monotonically with decreasing dc, while Jc(4 T) decreases with decreasing dc. Here t123 500 nm represents the pure Y123 film SL-regular-2.
ML films suggest that these ML films are suffering from strong thermally activated depinning at 77 K [2,16], in spite of them containing more than 10 vol.% of insulating precipitates with diameters close to the vortex core diameter 2nab = 8 nm at 77 K [27], where nab is the coherence length along the ab-planes. The implications that TAD effects are producing a strong degradation of the 77 K properties can be tested explicitly by measuring Jc over a wide range of T and H. Fig. 5a–c present Jc as a function of temperature measured respectively at 0.5 T, 4 T, and 8 T for the four films of Fig. 4. At 0.5 T, although all Jc(T) curves seem to cluster near 77 K, they start to diverge below 70 K, as shown in Fig. 5a. In fact, at all temperatures, the magnitude of Jc(0.5 T) shows a consistent order: Jc(ML2-1.5-10) > Jc(ML-1.5-20) > Jc(ML-1.5-30) > Jc(SLregular-2), showing that denser precipitates with smaller dc favor higher Jc. At 4 T, Fig. 5b shows that even though Jc(4 T) starts with a reversed order at 77 K as shown in Fig. 4, as T decreases Jc(ML21.5-10) quickly surpasses Jc(SL-regular-2) at 70 K. Following that, Jc(ML-1.5-30) and Jc(ML-1.5-20) are exceeded by Jc(ML2-1.5-10) successively at 65 K and 55 K. To better reveal the cross-over, the inset of Fig. 5b plots DJc(T, 4 T) for T = 50–70 K for the three ML films, where DJc = Jc Jc(SL-regular-2). Below 55 K, a consistent Jc(4 T) order is found: Jc(ML2-1.5-10) > Jc(ML-1.5-20) > Jc(ML-1.530) > Jc(SL-regular-2), which is the same as the H = 0.5 T situation shown in Fig. 5a. At even higher field H = 8 T, Jc(T) curves cross in a similar way as at 4 T, as shown in Fig. 5c. The cross-over temperature, however, shifts down to 50 K between ML2-1.5-10 and ML-1.5-30, and to 36 K between ML2-1.5-10 and ML-1.5-20, as shown in the inset of Fig. 5c, which presents DJc(T, 8 T) for T = 30–60 K. When T < 36 K, Jc once again reaches a consistent order: Jc(ML2-1.5-10) > Jc(ML-1.5-20) > Jc(ML-1.5-30) > Jc(SL-regular2), thus again reverting to the expected result that Jc is enhanced by denser precipitates and lower dc.
4. Discussion 4.1. General considerations A particular goal of our work was to perform a systematic, quantitative pinning study. In this respect, the current (Y123 + Y211/Y2O3) N multilayer films indeed have a well defined nanostructure, as revealed by the SEM and TEM images in Figs. 1 and 2. In addition, our controlled nanoprecipitate additions do yield systematic influences on the superconducting properties, as demonstrated by the variation of superconducting properties shown in Figs. 3 and 4, which show that both Jc and Fp,max are improved by varying t123 and t211. In fact, high J sfc (77 K) 4.2 MA/cm2 on a 610 nm thick multilayer film ML2-1.5-10 was achieved, a value fully consistent with the maximum envelope of the generally accepted Jc vs. film thickness curve [28]. On the other hand, the improvement of Fp,max only to 4.8 GN/m3 seems rather unremarkable, given the very high density (2.5 1015 m2) of nanoprecipitate pinning centers and the fact that a much higher Fp,max of 10 GN/m3 was found in nominally rather similar (Y123 + Y211) N multilayer films [10]. The potential explanation that we want to explore here, as pointed out by Figs. 4 and 5, is that strong thermally activated depinning effects greatly reduce Jc and Fp,max at 77 K. We believe that such TAD effects can easily be underestimated when dealing with a high density of non-superconducting precipitates with size very close to the vortex core diameter. These considerations have motivated us to clarify the Jc behavior of our films over a wide range of temperature and field, so as to assess the precipitate size and operating temperature domain where thermally activated depinning dominates the behavior. One important message of this study is that special attention has to be paid to the pin size along the magnetic field direction when pins with diame-
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Fig. 5. Jc as a function of temperature for SL-regular-2, ML2-1.5-10, ML-1.5-20, and ML-1.5-30 at (a) 0.5 T, (b) 4 T, and (c) 8 T. For (a), the four curves are well separated in the whole temperature range. For (b) and (c), cross-over of the Jc(T) curves happens at various temperatures depending on H and dc. The inset of (b) and (c) shows DJc(T) = Jc Jc(SL-regular-2) for H = 4 T and 8 T, respectively, to better reveal the cross-over.
ters close to the vortex core diameter are introduced into Y123. It is a remarkable fact of pinning engineering in present Y123 films that too high a density of too small nanoprecipitates can be grown and that small enhancements of pin size can be highly effective in enhancing Jc(H) in the high temperature domain around 77 K.
data (black curve, 77 K and self-field) shown in Fig. 4. On the other hand, Eq. (1) considers only vortex pinning, disregarding thermal fluctuation depinning effects. The strength of thermally activated depinning can be quantified by a dimensionless parameter s, which is the ratio of the thermal energy and the pinning energy [20].
4.2. Vortex pinning and depinning effects
s¼ From the SEM and TEM observations in Figs. 1 and 2, we know that our ML films contain 5–16 vol.% of 10–15 nm sized (the vortex core diameter 2nab = 8 nm at 77 K and 4 nm at 4 K) insulating precipitate with a high matching field BU 5–6 T, making them, in principle, almost ideal for strong single-vortex, core pinning. Given the fact that strong pinning precipitates will decouple vortex lines into independently pinned short segments equal to the c-axis pin spacing dc (when Hkc) [29,30], the maximum self-field J sfc in the absence of TAD effects can then be estimated by considering depinning of elliptical vortex segments whose ends are fixed by neighboring precipitates [10,20,31]:
J sfc ffi
U0 2pl0 ka kc dc
ln
dc nc
ð1Þ
where U0 is the flux quantum, l0 the vacuum permeability, ka and kc the penetration depth along the ab-plane and the c-axis respectively, and nc the coherence length along the c-axis. Eq. (1) suggests a monotonic increase of Jc(dc) with decreasing dc for dc > 3nc, which is indeed consistent with the experimental J sfc (dc)
pkB T J c0 U0 dc l
ð2Þ
where kB is the Boltzmann constant, Jc0(T, H) is the critical current density produced by pins other than the nanoprecipitates, l is of the order of the pin spacing in the ab-plane, 17–20 nm for most films (except for ML-1.1-10 which only has a sparse nanoprecipitate coverage) in this study. Eq. (2) indicates that thermally activated depinning increases as dc decreases, because shorter vortex segments fluctuate more strongly than longer vortex segments, thus making thermal smearing of the pinning potential and reduction of Jc more pronounced at smaller dc. For s 1 (which corresponds to low T and H), the effect of thermally activated depinning is weak, and Jc(d) increases as the pin spacing dc decreases in accordance with Eq. (1). However, at higher T and H, Jc(T, H) in Eq. (2) decreases, so the magnitude of vortex fluctuations and the strength of TAD increases. As a result, the reversed Jc(dc) dependence at 77 K and 4 T seen in the red curve of Fig. 4 develops. The Jc of more densely spaced precipitate arrays is then lower because shorter vortex segments with smaller dc are more easily thermally depinned than longer segments.
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Jc as a function of dc for different s can be calculated for a sineGordon pinning model, as was discussed in detail in Ref. [20]. These calculations are summarized in Fig. 6. At small s values (low T and H), Jc first increases as dc decreases before it reaches a maximum at some intermediate value of dc then quickly drops to zero. As s increases, the Jc(dc) peak diminishes and shifts to higher dc. Further increase of the TAD parameter s results in the disappearance of the peak so that Jc decreases monotonically as dc decreases. Fig. 6 suggests two opposite Jc(dc) dependencies (labeled here as A and B), which we find to correspond to the self-field and 4 T behavior of Jc(dc) in Fig. 4, respectively. Type A behavior represents the domain where Jc is enhanced by increasing the density of precipitates and reducing t123 or dc because TAD effects are still weak at low fields where pinning potentials are strong, while behavior B corresponds to the opposite behavior as TAD effects dominate near the irreversibility field Hirr, which occurs at 6.7 T at 77 K for these films. The key result of Fig. 4 is that this transition occurs between self-field and 4 T at 77 K, thus showing very explicitly that selffield optimization is not the same as in-field optimization. Considering behavior over a wider range of T and H, Eq. (2) shows that s at a fixed dc can be changed by varying T and H, as was done in Fig. 5: increasing T and/or H raises s, and decreasing T and/or H reduces s. The calculations shown in Fig. 6 are qualitatively consistent with the experimental results shown in Fig. 5: except at H = 0.5 T, for which type A behavior was observed at all temperatures, an A to B cross-over of Jc(H, T) behavior change as a function of dc was found. Consistent with Fig. 6, the cross-over takes place at higher fields at lower temperatures, because higher H produces a more pronounced TAD effect, requiring lower temperatures to prevent enhanced TAD effects. The behavior of Jc(dc) shown in Fig. 6 clarifies the complicated relationship between Jc, dc and s, suggesting that an assessment of s (determined by operational T and H) should be performed before pinning optimization at and near 77 K, where most applications of Y123 are foreseen. This applies not only to pinning studies with controlled, anisotropic nanoparticle additions (like the present work) but also to the more usual pinning engineering by random nanoparticles, because the incorporation of strong pinning nanoparticles into Y123 always reduces dc and thus risks increasing s. The key is thus to find the right balance between strengthening the elementary pinning force and reducing thermally activated depinning effects. By comparison, the strategy for improving Jc(H) in the low T limit is much more straightforward
Fig. 6. Evolution of the dependence Jc(dc) for different values of the parameter s: (1) 0.0065, (2) 0.01, (3) 0.015, and (4) 0.025. Here s is the ratio of the thermal energy and the pinning energy and is used to quantify the strength of thermally activated depinning, and Jc0 is the critical current density for the vortex segment of length dc0 collectively pinned by point defects between the nanoprecipitates [20].
because Jc tends to increase monotonically with increasing pin density and decreasing dc, so long as the insulating pin volume fraction does not exceed too much the optimum value of 11% [20]. In support of this conclusion, our ML2-1.5-10 film with 16 vol.% of pin and the smallest dc 10 nm, attained a J sfc of 48 MA/ cm2 at 10 K, which is 20% of Jd (250 MA/cm2 at 10 K, assuming a thermodynamic critical field Hc(10 K) 0.92 T and the London penetration depth k(10 K) 160 nm). Extensive evaluation of Jc at 4 K is still rare but a study of the exceptionally strong pinning film of Gutierrez et al. [5] made with 15–30 nm sized dense, random BZO nanoprecipitates with Fp,max(77 K) of 20 GN/m3 at 77 K is instructive. Although the BZO film had a four times greater Fp,max(77 K) than our film ML2-1.5-10, Jc of ML2-1.5-10 outperformed the BZO film by 20% at 4 T and 4.2 K. Our conclusion is thus that pinning centers must be specifically optimized to take account of strong thermally activated depinning conditions found in fields greater than 1–2 T at 77 K. 4.3. The importance of pin length in raising fp As follows from the TEM images shown in Fig. 2, the precipitates in the present ML films are mostly only 3 nm thick along the c-axis, significantly thinner than most strong pinning precipitates, whose dimensions are reported to lie in the range of a few to ten times this size in the literature [5,10,32], some of which are highly c-axis correlated nanorods that may be hundreds of nanometers long [6,18]. For the present ML films, the oblate Y2O3 precipitates have a much higher degree of correlation in shape and alignment along ab-planes, suggesting that they should be much more effective pinning centers at high T for Hkab than for Hkc. This conclusion is indeed consistent with our angular dependent Jc(h, 77 K) measurements. As shown in Fig. 7, Jc(h) is enhanced progressively and more strongly in the Hkab direction than in the Hkc direction as t211 is increased. When the field H = 1 T is inclined by 45° with respect to the c-axis, both ML-1.1-10 and ML-1.5-10 shows 40% Jc improvement compared to the non-ML film (SL-regular-1). The difference between the two ML films is negligible despite their largely different precipitate areal densities (Ni < 1 1015 m2 vs. Ni 2.5 1015 m2). However, when H is parallel to the ab-planes, a strong monotonic dependence of Jc on t211 is evident: Jc is improved by 70% from SL-regular-1 to ML1.1-10, and by 157% from SL-regular-1 to ML-1.5-10, as the precipitates become better ab-plane correlated with increasing areal density. At H = 4 T, Jc shows no improvement as t211 increases when H is applied in the vicinity of Hkc, as neither dt nor the c-axis
Fig. 7. Jc(h) curves for SL-regular-1, ML-1.1-10, and ML-1.5-10 measured at 77 K and 1 T (solid symbol) and 4 T (cross-filled symbol).
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correlation increases. Yet a pronounced, monotonic increasing dependence of Jc on t211 is still observed when H is applied within 20° of the ab-planes. To understand why oblate Y2O3 precipitates with diameter D = 10–15 nm > 2nab(77 K) = 8 nm and a thickness dt = 3 nm < 2nab(77 K) are not very effective pinning centers at 77 K for Hkc, we first estimate the elementary core pinning force fp for the vortex semi-loop resulting from subdividing a vortex line by the oblate nanoprecipitates as shown in Fig. 8. The transport current pushes the vortex segments toward the edges of parallel diskshaped precipitates where it bows out at the edges under the Lorentz force, as illustrated in Fig. 8. The maximum pinning force fp Ep/nab results from the gain in the condensation energy Ep l0 H2c pdt n2ab =2 [33] in the volume of the dielectric precipitate, pdt n2ab , which crosses the vortex core. Substituting here the thermodynamic critical field, Hc = U0/23/2l0pkabnab, we obtain:
fp
U0 dt 16pl0 k2ab nab
ð3Þ
For thin precipitates, fp is therefore reduced by the small ratio dt/2nab. This reduction does occur for our films since fp is reduced by the ratio dt/2nab 0.4 at 77 K and 0.5 at 4 K. This small thickness reduction in fp facilitates further decrease of Jc(77 K) by thermal
Fig. 8. Illustration of a bowing vortex segment confined by parallel, dt-thick diskshaped precipitates with a c-axis spacing dc.
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fluctuations of a vortex segment confined between parallel diskshape precipitates where it is also affected by other point pinning defects existing in our PLD films and responsible for the significant J sfc values at t211 = 0 shown in Fig. 2. To further test this argument, we compare the ML-1.5-30 film to a recently studied Y123 coated conductor (CC) grown by metal-organic chemical vapor deposition (MOCVD) whose pinning nanostructure of RE2O3 is very similar to the present ML films. Details of the nanostructure and pinning properties of this MOCVD CC have been given elsewhere [17,30]. Briefly, we found that (Y,Sm)2O3 precipitates 10–15 nm in diameter were separated horizontally by 20 nm and formed in planes almost parallel to the ab-planes of Y123 with an average vertical interval of 30 nm. However, a critical parameter of this MOCVD film in the context of the present discussion is that dt is 8–10 nm for the MOCVD CC and 3 nm for ML-1.5-30, even as the diameter, areal density and ab-plane spacing of the precipitates in the MOCVD CC are very similar to those in ML-1.5-30. According to Eq. (2), fp would thus be 3 times higher for the MOCVD CC than for ML1.5-30 under similar measurement conditions. Fig. 9 plots Jc(H, 77 K) and Fp,max(77 K) for ML2-1.5-30 and the MOCVD CC. Indeed the difference in Jc is dramatic for fields H > 3 T, a point that is especially clear in the enhancement of the irreversibility field Hirr (defined at Jc = 100 A/cm2) from 6.7 to 8.9 T, as shown in Fig. 9a. This enhancement is entirely consistent with our argument that elongated pinning centers with larger fp can more effectively suppress TAD, thus increasing the in-field Jc and the irreversibility field Hirr. The comparison clearly shows that thermally activated depinning can powerfully degrade Jc in the T–H domain most relevant to power applications of the Y123 coated conductors. Elongating pins along the desired principal field direction of the application significantly increases Jc. We can also note that both YBCO films reach their maximum pinning force Fp,max at fields well below the vortex matching field BU (5 T) of the precipitate density, as shown in Fig. 9b, suggesting that many precipitates are ineffective due to TAD effects. Indeed, the field at which Fp,max(77 K) occurs and the enhancement of Hirr(77 K) can be very good guides to the degree to which more effective pinning centers can suppress TAD effects. In the present ML films Fp,max(77 K) occurs at 1.5 T and Hirr(77 K) is 6.7 T, whereas the corresponding values for the coated conductor with precipitates 3 times longer along the c-axis are 2 T and 8.9 T. Both films have similar Tc values of 90 K. The BSO-containing nanorod samples of Mele et al. with average nanorod lengths of 140 nm which achieved the
Fig. 9. (a) A comparison of Jc(H, 77 K) between an MOCVD CC [17] and ML-1.5-30, both of which have dc 30 nm. Starting at almost the same point, a big deviation starts to develop when H > 2 T. The inset shows Jc(T, 8 T) curves for the two samples in comparison. (b) A comparison of Fp(H, 77 K) between the MOCVD CC and ML-1.5-30. Because of the longer nanoprecipitates along the c-axis, both the field at which Fp,max occurs and Hirr are increased for the MOCVD CC comparing against ML-1.5-30. On the other hand, both films reach Fp,max at fields well below the matching field BU due to the strong TAD effects at the high temperature of 77 K.
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spectacular Fp,max(77 K) values of 28 GN/m3 have Hirr(77 K) of >9 T [6], even though Tc (88.6 K) was depressed by 1.4 K. Therefore, we conclude that the size of nanoprecipitates along the preferred field direction is of crucial importance to the magnitude of the pinning force at or near 77 K. Since this requires extensive TEM study to define, we also note that the field at which Fp,max and Hirr occur can be very good guides to whether TAD effects are important. The connection to Hirr and Fp,max may be particularly valuable for coated conductor evaluations, where there are in general always some operating current-blocking effects produced by higher angle grain boundaries, sub-micron second phases, cracks, substrate scratches, etc. that render the absolute magnitude of Jc uncertain. This is certainly true for the present MOCVD conductor as noted earlier by Chen et al. [30], where considerable blocking phases were present. But whatever their role in depressing the real magnitude of Fp,max, they play no role in depressing Hirr or the position of Fp,max. The inset of Fig. 9a presents Jc as a function of T measured at H = 8 T for our ML and the MOCVD CC samples. The nearly constant gap between the two Jc(T) curves indicates a diminishing relative difference of the two Jc(T) as T decreases, the difference being only 2% at 10 K and 8 T. This strongly diminishing gap between the two samples as T is lowered suggests that the extra pinning strength from the elongated precipitates is beneficial to Jc only under strong TAD conditions. For low T applications, a denser pinning structure (below the current-blocking threshold) leads to the highest Jc at low temperatures where TAD effects are weak. On the other hand, increasing pin density may play the opposite role at high temperatures, because TAD effects become more effective as the length of thermally fluctuating vortex segments dc decreases (see Fig. 6). This again indicates that there is no universal pinning nanostructure, which is equally effective at low and high temperatures and in different field regions. 5. Summary A series of PLD grown single layer Y123 and multilayer (Y123 + Y211/Y2O3) N films were studied over a broad range of multiple variables, including temperature, field, pinning center areal density, c-axis spacing, and their extension along the c-axis, aiming at a thorough understanding of the optimum pinning structures in Y123. Pinning defects formed in the ML films are a high density of thin-disk-shaped Y2O3 nanoprecipitates. Even though our results do not lead directly to champion Jc or Fp,max values for Y123 at 77 K, we have clarified the important relationship between two important and opposite effects that control Jc and Fp: vortex core pinning and thermally activated vortex depinning, which are both strongly affected by T, H, and dc. Our results indicate that a direct solution for improving Jc at low temperatures is to reduce dc, while at high temperatures, increasing the pinning precipitate extension along the field direction is the effective way to Jc(H) enhancement. Acknowledgements We would like to thank Aixia Xu for assistance with some of the transport measurements, as well as Aixia Xu and Jan Jaroszynski for many discussions of pinning in the low temperature limit. The work was supported by the US Department of Energy, Office of Electricity Transmission and Distribution.
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