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Nb hybrids
Physica C: Superconductivity and its applications 544 (2018) 33–39
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Superconducting thermomagnetic instabilities tuned through electric-field-controlled strain in Nb/PMN-PT/Nb hybrids M. Zeibekis a, S.J. Zhang b, D. Stamopoulos a,c,∗ a
Institute of Nanoscience and Nanotechnology, National Center for Scientific Research ‘Demokritos’, 153 10, Aghia Paraskevi, Athens, Greece Institute for Superconducting and Electronic Materials, Australian Institute of Innovative Materials, University of Wollongong, NSW 2500, Wollongong, Australia c Department of Solid State Physics, National and Kapodistrian University of Athens, Zografou Panepistimioupolis, 157 84, Zografou, Athens, Greece b
a r t i c l e
i n f o
Article history: Received 5 September 2017 Accepted 28 October 2017 Available online 31 October 2017 Keywords: Piezoelectric/superconducting hybrids Critical current Thermomagnetic instabilities Converse piezoelectric effect
a b s t r a c t Electric-field-controlled piezoelectric strain has been used, recently, to modify the superconducting properties in a new class of piezoelectric/superconducting (PE/SC) hybrids. Here, we investigate the appearance of thermomagnetic instabilities (TMIs) and the respective modification of the critical current density (JC ) through the application of electric field (Eex ) in PE/SC hybrids. Specifically, the SC nanolayers are Nb (thickness, dSC = 20 nm) deposited on both surfaces of PE macroscopic crystals of (1-x)Pb(Mg1/3 Nb2/3 )O3 xPbTiO3 (PMN-PT) with optimum composition x = 0.31 (thickness, dPE = 0.5–0.8 mm). The appearance of TMIs and the modification of JC by Eex is studied for two PMN-PT crystals of drastically different surface roughness (Sa). In the case of the PMN-PT crystal with low Sa (on the order of a few tenths of nm) TMIs are absent so that JC does not change under the variation of Eex . On the contrary, in the case of the PMN-PT crystal with high Sa (on the order of a few hundreds of nm) Eex induces TMIs in the Nb nanolayers. Specifically, the number of TMIs exhibits a non-monotonic increase on Eex , thus causing a non-monotonic degradation of JC . These experimental data are interpreted in terms of the variation of both volume strain and surface roughness on Eex . This work highlights practical means to control the current-carrying capability of SC nanolayers through strain provided by PE substrates. © 2017 Elsevier B.V. All rights reserved.
1. Introduction A new class of hybrids consisting of a superconducting (SC) nanolayer deposited on a bulk piezoelectric (PE) substrate offers the unique opportunity to investigate dynamically the influence of volume strain on the properties of the SC nanolayer by simply changing the electric field (Eex ) that is applied to the PE substrate. Experimental studies in these hybrids have been focused on the influence of volume strain on the transition temperature (TC ) in high-TC SC nanolayers such are YBa2 Cu3 O7-δ [1,2], La2-x Srx CuO4 [3], BaFe1.8 Co0.2 As2 [3] and FeSe0.3 Te0.7 [4]. Since these hybrids operate at cryogenic conditions (around the TC of the SC) where the piezoelectric properties of the PE substrate are degraded, it is appropriate to use PE materials that belong to the compound family (1x)Pb(Mg1/3 Nb2/3 )O3 -xPbTiO3 and especially the ones with x = 0.31 (PMN-PT) due to their outstanding piezoelectric activity [5–7]. Another critical parameter of superconductivity is the critical current density (JC ), which characterizes the maximum lossless ∗
Corresponding author. E-mail addresses: [email protected], [email protected] (D. Stamopoulos). https://doi.org/10.1016/j.physc.2017.10.015 0921-4534/© 2017 Elsevier B.V. All rights reserved.
current density that the SC is able to maintain without dissipation. Although JC is an important characteristic of SCs from the viewpoint of technological applications, the piezoelectric modification of JC has not been explored so far in PE/SC hybrids. For this reason, we have focused our study on the variation of JC in respect to the applied Eex in PE/SC hybrids that are consisting of two Nb nanolayers with the same thickness (dSC ) deposited on both surfaces of PMN-PT crystals (Nb/PMN-PT/Nb). Moreover, we have included another experimental parameter in our study; we examine how the surface roughness (Sa) of the PMN-PT crystal contributes additionally to the piezoelectric modification of JC in Nb nanolayers. To do so, two Nb/PMN-PT/Nb hybrids with dSC = 20 nm have been prepared. The first is consisting of a PMN-PT crystal with polished surfaces (PMN-PTp ) of low surface roughness ( is on the order of few tenths of nm), while the second of a PMN-PT crystal with non-polished surfaces (PMN-PTnp ) of high surface roughness ( is on the order of a few hundreds of nm). The parameter of Sa that can be considered as a measure of the surface conditions of a SC nanolayer, acts as a structural defect and thus it affects the JC of the SC. In particular, in thin SC nanolayers the distribution of the supercurrent differs drastically for the case of perfectly planar [8–12] and relatively rough
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[13–17] ones. Earlier studies in planar SC nanolayers have shown that the Sa may affect JC in several ways, such are through the spatial variation of flux lines around the surface [13], due to the thickness dSC modulation [15,16] and by the enhanced contribution of the surface pinning against the volume pinning [14,17]. It should be noted that in these studies [13–17] the Sa is referred to SC nanolayers deposited on atomically flat substrates, meaning that their Sa values are lower than their thickness dSC . In our case and in particular for Nb nanolayers deposited on top of the PMNPTnp substrate the extremely high values of Sa causes a considerable modification in two fundamental parameters of the surface geometry of Nb nanolayers. Firstly, due to the Sa the thickness of Nb nanolayer at the lateral side of morphological peaks of the surface has an effective thickness value (deff ) which is lower than the nominal thickness dSC . Secondly, although the external magnetic field (H) is applied parallel to the surfaces of the hybrid, the parts of Nb nanolayers with deff experience a local magnetic field with a non-zero normal component and thus the strength of the parallel component of the magnetic field (Hpar ) is lower than the applied H. These two fundamental parameters affect considerably the current-carrying capability of Nb nanolayers, even when no Eex is applied to the hybrid. In the present study, the parameter of Sa is not examined as a stationary parameter, but as a parameter that can be dynamically varied upon the application of Eex in Nb/PMN-PT/Nb hybrids. In particular, the application of Eex causes the macroscopic deformation of the PMN-PT crystals which induces changes in the morphological landscape of their surfaces. Both the induced volume strain and the morphological landscape modification are experienced by the deposited Nb nanolayers of the hybrids and their combined variation leads to the variation of JC . Specifically, in the case of the Nb/PMN-PT/Nb hybrid consisting of the PMN-PTp crystal the JC remains unaffected upon the application of Eex , while in the case of the Nb/PMN-PT/Nb hybrid with the PMN-PTnp crystal the JC is degraded significantly by the increase of Eex . This degradation of JC in the latter hybrid, is manifested by the appearance of magnetization jumps, known as thermomagnetic instabilities (TMIs) [18– 24] in the m(H) loops obtained at different Eex . The variation of TMIs and thus of JC upon increasing Eex is interpreted in terms of the variation of both volume strain and surface roughness that are experienced by Nb nanolayers in Nb/ PMN-PTnp /Nb hybrid. 2. Experimental 2.1. Samples preparation High quality (1-x)Pb(Mg1/3 Nb2/3 )03 -xPbTiO3 crystals with x = 0.31 were grown as presented in [25], were cut into rectangular shape substrates with dimensions of 6 × 5 x(0.5–0.8) mm3 (the large face perpendicular to [011] direction) and were left unpoled. Here, we studied (a) as prepared crystals with non-polished surfaces (PMN-PTnp ) and (b) polished crystals (PMN-PTp ) that exhibit relatively smooth surfaces. The Nb nanolayers (thickness; dSC = 20 nm) were deposited on either PMN-PTnp or PMN-PTp crystals by dc magnetron sputtering [Edwards 306A unit, Edwards, Sanborn, NY, USA] as presented in [26] and also act as electrodes for the application of the external voltage to the PMN-PT crystal. The depositions of Nb films have been performed at the same deposition run in both substrates (PMN-PTnp and PMN-PTp crystals), in order to maintain the same growth conditions. 2.2. Techniques Atomic Force Microscopy (AFM) data were acquired by means of a scanning probe microscope NT-MDT Solver PRO [NT-MDT Co, Moscow, Russia] by using NCHR cantilevers [Nano and More
GmbH, Wetzlar, Germany], as presented in [27]. The surface roughness (mean surface roughness:=<|z–|>) was calculated by means of the instrument software from images of dimensions 20 × 20 μm2 . Apart from the surface characterization of PMN-PT crystals, AFM images of dimensions 10 × 10 μm2 have been also used to study the evolution of in respect to the applied Eex . To do so, a special protocol has been employed for these measurements. In particular, starting at a safe distance (≈1 mm) between the sample surface and the AFM tip we applied a dc voltage constantly for 1 minute, after zeroing the applied voltage we followed the landing procedure where the sample surface approaches the AFM tip and finally we obtain an AFM image. After scanning the same area upon the consecutive increase of Eex with the step of 0.25 kV/cm, we estimate the evolution of in respect to Eex . It should be stressed that we were not able to conduct the AFM measurements with a biased Eex , due to the strong electrostatic interaction between the AFM tip and the accumulated charges on the surface of the sample. Regarding to the superconducting properties of the Nb/PMNPT/Nb hybrids, magnetization m(H) loops under the application of an Eex were obtained with a homemade probe by using a SQUID magnetometer MPMS 5.5 T [Quantum Design, San Diego, CA, USA] as a host cryostat. Importantly, the applied electric field was normal to the surface of the hybrids (Eex = Eex,z ), while the magnetic field was parallel to the surface of the hybrids. Finally, the strainelectric field curve, S(Eex ), was obtained by using the technique already presented in [27,28] that utilizes a conventional optical microscope for the local observation of deformation upon application of Eex to the PMN-PT crystal. To be consistent with the electric-field configuration employed in the magnetization measurements, the strain-electric field curve, S(Eex ), was recorded while the electric field was applied normal to the surface of the hybrids (Eex = Eex,z ), as well. In the rest of the paper we simply use the notation Eex for the electric field, meaning that it is normal to the surface of the hybrids. 3. Results and discussion Fig. 1 presents representative experimental results in a vertical arrangement for two Nb(20 nm)/PMN-PT/Nb(20 nm) hybrids with different surface morphology, owing to the use of two different PMN-PT crystals that are the PMN-PTp and the PMN-PTnp . Each column of Fig. 1 combines an AFM image (of a scanning area 20 × 10 μm2 ) with the respective m(H) loops obtained at Eex = 0.0 0, 1.0 0, 2.0 0 and 3.50 (or 3.30) kV/cm for each hybrid. Specifically, the left column of Fig. 1 (Fig. 1(a.i)−(a.iv)) refers to the hybrid Nb(20 nm)/PMNPTp /Nb(20 nm) with ≈44 nm (Sa = 25 nm in Fig. 1(a)) and TC = 7 K, while the right one (Fig. 1(b.i)−(b.iv)) refers to the hybrid Nb(20 nm)/PMN-PTnp /Nb(20 nm) with ≈218 nm (Sa = 216 nm in Fig. 1(b)) and TC = 6.6 K. We should stress that due to the different TC of these hybrids, the m(H) loops were obtained at different temperatures (T
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Fig. 3. Number of TMIs counted in the ascending and the descending branches of H (1st and 2nd quadrants) based on three different procedures: spheres refer to micro TMIs, triangles refer to macro TMIs and squares refer to TMIs recorded by using the mathematical criterion δ m = |mi+1 -mi | > 0.5mi . Lines serve as guide to the eye. Triangles data and squares data are multiplied by a factor of 8 and 4, respectively, for the sake of presentation in the same vertical scale.
Fig. 1. (a)-(b) Representative AFM images (20 × 10 μm2 ) of (a) the crystal PMN-PTp and (b) the crystal PMN-PTnp (the mean surface roughness, Sa, of the particular areas is (a) Sa = 25 nm and (b) Sa = 216 nm). Notice the different scale in the z values that is shown in the height color bar that accompanies each image. (a.i)–(a.iv), (b.i)– (b.iv) Representative magnetic hysteresis loops obtained at various Eex for the hybrids Nb(20 nm)/PMN-PTp /Nb(20 nm) and Nb(20 nm)/PMN-PTnp /Nb(20 nm), respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. A representative example of the three different criteria employed here to ascribe the occurrence of a TMI in the m(H) loop obtained at 3.30 kV/cm. The green filled squares refer to the raw data of m(H) obtained at Eex = 3.30 kV/cm, while the grey open squares refer to the smoothed m(H) curve. The black vertical arrow show a micro TMI that is placed outside the error zone of ± 5·10−7 emu of the smoothed m(H) curve (marked by the black-dotted circle), the red vertical arrow show a macro TMI that exist in the smoothed m(H) curve (marked by the red-dotted circle) and the incline blue dashed arrows show a TMIs that occurs in successive data points (blue vertical arrow-heads) of the raw m(H) curves based on the mathematical criterion δ m = |mi+1 -mi | > 0.5mi . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Eex = 0.00 kV/cm (that corresponds to the strain-free state of the hybrid in respect to the Eex ) turns into noisy m(H) loops where irregular jumps in magnetization are induced by the increase of Eex (that corresponds to the strain states of the hybrid in respect to Eex ). These magnetization jumps are flux jumps resulting from the development of TMIs in Nb nanolayers. Aiming to examine the evolution of TMI occurrences as Eex increases, we have used three different criteria for recording the number of TMIs in the m(H) loop at each applied Eex . A representative example of each criterion is presented in Fig. 2, which shows the m(H) loop obtained at the maximum applied field Eex = 3.30 kV/cm. Apart from the raw data of the particular m(H)
loop (green filled squares in Fig. 2) we have also included the respective smooth m(H) curve (gray open squares in Fig. 2) that was calculated by using the adjacent-averaging method of 5 data points from raw data, offered from the Origin software package [OriginPro 8.5, OriginLab Corporation, Northampton, MA, USA]. Furthermore, by taking into consideration that the accuracy level of our SQUID magnetometer to record a magnetic moment is on the order of 10−7 emu, we have placed an error zone of ± 5·10−7 emu (grey lines) around the smoothed m(H) curve. According to the first criterion, a TMI event is ascribed at each distinct point of raw data that is placed outside this error zone, as depicted by the black vertical arrow in Fig. 2. These TMIs are termed here as microscopic TMIs (micro TMIs). Now, exclusively from the smoothed m(H) curves, the second criterion ascribes a TMI event at the part of m(H) smoothed curves where the magnetic moment of consecutive points is decreased progressively by approaching lower magnetization value, as depicted by the red vertical arrow in Fig. 2. These TMIs are termed here as macroscopic TMIs (macro TMIs). Finally, without taking into account the smoothed m(H) curves, we have used a strict mathematical criterion that ascribes a TMI event directly from the raw data. This is the third criterion and it counts a TMI event whenever the variation of magnetization during a flux jump (δ m = |mi+1 -mi |) meets the condition δ m > 0.5mi (where mi is the initial value of magnetization when a TMI is triggered and mi+1 is the final value of magnetization when a TMI is completed). A representative example of a TMI according to the third criterion is depicted by the blue-dashed inclined arrows in Fig. 2. All three criteria have been used to count the TMI occurrences in both the ascending (1st quadrant) and the descending (2nd quadrant) branches of the magnetic field in the m(H) loop obtained at each Eex . Fig. 3 shows the evolution of the number of TMIs that were recorded from each employed criterion in respect to Eex . For the sake of presentation, we have scaled up the number of macro TMIs by a factor of 8 and the number of TMIs according to third criterion (δ m > 0.5mi ) by a factor of 4, since each criterion results to a different number of the counted TMIs. From Fig. 3 it becomes apparent that for every employed criterion, the number of TMIs follows the same non-monotonic variation with the increase of Eex . From this non-monotonic variation of TMIs one can recognize two characteristic Eex . The first characteristic Eex (Ech,1 ) is located around 1.30 kV/cm and corresponds to a local maximum in the number of TMIs, while the second one (Ech,2 ) is located around 2.00 kV/cm where all criteria have recorded a local minimum in the number of TMIs that signifies the partial cessation of TMI occurrences. Finally, at Eex = 2.70 kV/cm all criteria show the maximization of TMIs that are saturated in this maximum value for Eex ≥ 2.70 kV/cm.
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Fig. 5. Sx (Eex ) curves measured along the x direction of a PMN-PT crystal, obtained from a local technique that is described in [27,28].
Fig. 4. Variation of the normalized JC (in respect to the JC0 ) as a function of Eex for H = 0 Oe (open symbols), 150 Oe (semi-filled symbols) and 400 Oe (filled symbols) for (a) Nb(20 nm)/PMN-PTp /Nb(20 nm) and (b) Nb(20 nm)/PMN-PTnp /Nb(20 nm). The results shown in (c) refer to the latter hybrid and is obtained from the smoothed m(H) curves. In all panels, the lines serve as guides to the eye. Horizontal dashed lines in panels (b) and (c) show the initial normalized value for Eex = 0.00 kV/cm.
It is worth noting that the TMIs are observed and recorded in the regime of relatively high magnetic fields in m(H) loops, unlike to their expected appearance in the lower part of m(H) loops where JC obtains high values. This suggests that the appearance of TMIs is stimulated by an external cause with finite influence against the pinning forces in Nb nanolayers. In particular, this external cause is able to overcome only the weak pinning forces that are manifested by the low values of JC and not the strength of stronger pinning forces in Nb nanolayers. Before examining the origins of this external cause, it is appropriate to study the variation of JC in respect to Eex . In the present study, the values of JC is considered to be proportional to the absolute difference of the magnetic moments (m) obtained along the ascending branch and the descending branch of m(H) loops for constant magnetic field (JC ∝ m≡|masc (H)-mdesc (H)|). Fig. 4(a)−(c) show the modification of the normalized values of JC (defined as JC /JC0 , where JC0 is the value JC at Eex = 0.00 kV/cm) obtained at H = 0 Oe (black open symbols), 150 Oe (blue semifilled symbols) and 400 Oe (red filled symbols) as a function of Eex for the raw data of both Nb(20 nm)/PMN-PTp /Nb(20 nm), Nb(20 nm)/PMN-PTnp /Nb(20 nm) and for the smoothed data of Nb(20 nm)/PMN-PTnp /Nb(20 nm), respectively. As it is shown in Fig. 4(a), the fact that the m(H) loops of the hybrid Nb(20 nm)/PMN-PTp /Nb(20 nm) remained unaffected upon the application of Eex (Fig. 1(a.i)−(a.iv)) is reflected to the negligible modification of the normalized JC . On the contrary, the appearance of TMIs in the m(H) loops of the hybrid Nb(20 nm)/PMNPTnp /Nb(20 nm) and their variation upon increasing Eex results to a respective modification in the normalized values of JC . Fig. 4(b) shows that the non-monotonic variation of the normalized JC obtained at H = 150 Oe and 400 Oe is in perfect accordance with the respective variation of TMIs shown in Fig. 3. Specifically, at the Ech,1 ≈1.30 kV/cm where TMIs are maximized locally the JC obtains a local minimum value and at the Ech,2 ≈2.00 kV/cm where TMIs are minimized the JC obtains a maximum value that is equal to JC0 . Moreover, the increased number of TMIs at Eex > Ech,2 results to a progressive degradation in the normalized JC . The same non-
monotonic variation of JC , but with lower degree of degradation in the normalized values of JC is also shown in Fig. 4(c) that refers to the data coming from the smoothed m(H) curves. We continue our study by investigating the physical quantities related to the PMN-PT substrate of these hybrids that could motivate the variation of TMIs and therefore the consistent degradation of JC upon increasing Eex in Nb nanolayers. As it is expected the application of Eex in these hybrids causes primarily the macroscopic deformation of PMN-PT crystals, which is delivered to the deposited Nb nanolayers causing the respective deformation of them. In order to estimate the induced deformation that is experienced from Nb nanolayers we measured the strainelectric field curve (S(Eex )) of the PMN-PT crystal. Fig. 5 presents the Sx (Eex ) curve that was obtained along the x macroscopic axis of a PMN-PT crystal upon the progressive increase of Eex from 0 up to 3.50 kV/cm. As it is shown in Fig. 5, at Eex = Ech,1 (≈1.3 kV/cm) the Sx exhibits a small peak of positive strain corresponding to a tensile strain (upward arrow), at Eex = Ech,2 (= 2.0 kV/cm) the strain returns to zero value (downward arrow), while for Eex > 2.0 kV/cm the magnitude of the compressive strain is increased progressively. Using these data one could interpret the appearance of TMIs in terms of strain, since the non-monotonic variation of the number of TMIs (and thus of JC ) upon increasing Eex seems to coincide with the behavior of the Sx (Eex ) curve. In particular, the peak of tensile strain (Sx > 0) at Eex = Ech,1 coincides with the local maximization of TMIs (local minimization of JC ), the return of Sx to zero value at Eex = Ech,2 coincides with the partial cessation of TMIs occurrences (local maximization of JC ) and eventually the increased magnitude of compressive strain (Sx <0) at Eex > Ech,2 coincides with the respective increase in the number of TMIs (progressive degradation of JC ). Although it seems that the strain motivates the nonmonotonic variation of TMIs and JC , it can explain only partially our data, since the hybrid that consists of a polished PMN-PT does not exhibit any changes in the m(H) loops upon applying Eex . This significant difference between the two hybrids suggests that the appearance of TMIs and therefore the degradation of JC are also related to the surface morphological landscape of the PMN-PTnp . To understand the influence of the morphological landscape of PMN-PT on the appearance of TMIs we examine how the surface morphology (given by) is modified by the increase of Eex . Fig. 6 shows the evolution of in respect to the applied Eex for both the Nb(20 nm)/PMN-PTp /Nb(20 nm) (blue open squares) and the Nb(20 nm)/PMN-PTnp /Nb(20 nm) (red spheres). In each hybrid and at every applied Eex , the refers to the mean value of Sa among three neighboring scanning areas of 10 × 10 μm2 . As it is evident in Fig. 6 the remain almost constant upon the application of Eex in the hybrid Nb(20 nm)/PMN-PTp /Nb(20 nm), while on the contrary significant changes of are recorded in the hybrid Nb(20 nm)/PMN-PTnp /Nb(20 nm). Particularly in the latter case, starting from Eex = 0.00 kV/cm the increase of Eex causes
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Fig. 6. The evolution of in respect to the applied Eex for both the Nb(20 nm)/PMN-PTp /Nb(20 nm) (blue open squares) and the Nb(20 nm)/PMNPTnp /Nb(20 nm) (red spheres). The is obtained as the mean value of Sa among three neighboring scanning areas of 10 × 10 μm2 . For comparison reasons, equal value ranges are set before and after the break in the vertical axis. The black dotted lines are guide to the eye to highlight the weak step of at Ech,1 . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the progressive reduction of passing through a weak step at Eex = 1.30 kV/cm (as shown between the two black dotted lines in Fig. 6) and reaches a minimum value at Eex = 2.00 kV/cm, while the further increase of Eex results to the progressive increase of that becomes equal to the initial value at Eex = 3.00 kV/cm. Interestingly, the evolution of (obtained from local AFM measurements) in respect to Eex follows closely the behavior of Sx (Eex ) curve obtained from the local technique of piezoelectric characterization. In particular, the fact that both Ech,1 and Ech,2 in the Sx (Eex ) curve (Fig. 5) coincide with the respective characteristic values of Eex in the variation of (red solid spheres in Fig. 6) confirms that the modification of surface morphology is totally driven by the induced strain. Moreover, it should be noted that these AFM measurements have been performed after removing the applied Eex (see paragraph 2.2). This means that these measurements provide only qualitative proofs regarding the tendency of the modification of and it is reasonable to consider that the magnitude of the respective changes of when the Eex is biased to the hybrid are greater than these shown in Fig. 6. To visualize how changes upon the variation of Eex on the hybrid Nb(20 nm)/PMN-PTnp /Nb(20 nm), Fig. 7 presents both quantitative (Fig. 7(a.i)−(a.ii)) and qualitative (Fig. 7(b.i)−(b.iii)) results coming from AFM measurements. Fig. 7(a.i) shows an AFM image of an area 10 × 10 μm2 that was obtained at Eex = 0.00 kV/cm. To quantify the surface modification, we have placed a straight horizontal line along a specific value, yo = 4.3 μm, of the y-axis in Fig. 7(a.i) (white thick line) and the height profile (z-axis) obtained across this line is presented in Fig. 7(a.ii) for three representative values of Eex , that are Eex = 0.00 (solid black line), 1.25 (dashed blue line) and 2.00 (short-dashed red line) kV/cm. The data of Fig. 7(a.ii) prove that the application of Eex motivates the development of strain in the entire volume of the PE material that, as expected, is accompanied by changes on the surface. Accordingly, upon application of Eex , change of surface roughness is expected, as well. The surface modification upon the application of Eex is presented qualitatively in Fig. 7(b.i)−(b.iii), where the AFM images refer to the 6 × 6 μm2 subarea of Fig. 7(a.i) (white dotted square) and they have been obtained at Eex = 0.00, 1.25 and 2.00 kV/cm, respectively. All Fig. 7(b.i)−(b.iii) exhibit the same height scale along the measured z-axis (see the colorbar that accompanies each figure; zmax ∼1.6 μm). From these data becomes apparent that the increase of Eex causes a clear surface modification. For instance, focusing on the upper right side of Fig. 7(b.i) we see that upon increasing Eex the area of low height (area with blue color) is progressively shifted at higher levels, Fig. 7(b.ii)−(b.iii), thus it gradu-
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ally shrinks. This behavior justifies the observed reduction of of the PMN-PTnp in Fig. 6. Given the fact that the morphological landscape of the PMN-PTnp is fully transferred to the deposited nanolayers of Nb with thickness 20 nm, it is reasonable to assume that the induced changes of Sa upon increasing Eex are also experienced by the nanolayers of Nb. Before proceeding to discuss the mechanism that motivates/promotes the appearance of TMIs and their non-monotonic variation upon increasing Eex , let us first consider more closely the initial strain-free state, in respect to the application of Eex , (Eex = 0.00 kV/cm) of the hybrid Nb(20 nm)/PMN-PTnp /Nb(20 nm) and especially the influence of Sa on the current-carrying capability of Nb nanolayers. To illustrate schematically the influence of Sa on Nb nanolayers Fig. 8(a) shows a representative AFM image of a scanning area ∼900 × 900 nm2 obtained at Eex = 0.00 kV/cm and Fig. 8(b) shows the height profile along the vertical black line of Fig. 8(a), accompanied with a grey zone that represents the deposited Nb nanolayer of expected thickness 20 nm. As it becomes apparent from Fig. 8(b), the high Sa has two significant results on the Nb nanolayer. The first is the modulation of the Nb nanolayers thickness from its nominal value (dnom ), that is preserved only on top of horizontal areas of the substrate surface, to an effective value (deff ) at the inclined areas of the substrate surface (lateral sides). It is easy to show that the relation between dnom and deff is given from the simple expression deff = dnom ·cosθ . The second is that the Nb nanolayer experiences a local redirection of the applied magnetic field (H) that has a nonzero perpendicular component (Hnorm ) at the parts of Nb deposited on the lateral sides of peaks, which weakens the strength of the parallel magnetic field (Hpar ) into a values given by the expression Hpar = H·cosθ . Accordingly, the required surface conditions that promote either the nucleation or the pinning of flux lines can be satisfied at different areas across the surface of Nb nanolayers. This leads to the heterogeneous nucleation of superconductivity and accompanied distribution of flux lines that accumulate at locations of the surface where the minimization of their free energy is ensured, creating flux spots (bundle of flux lines) [13]. It is well known that in thin SC nanolayers the distribution of the supercurrent differs drastically for the case of perfectly planar [8–12] and relatively rough [13–17] ones. In the case of a SC nanolayer with extremely high the flow of supercurrent across its surface is more difficult to be estimated and even in some cases there is not a continuous network to support the supercurrent flow all over its surface. Consequently, one can easily conclude that the extremely high suppresses the current-carrying capability of Nb nanolayers. Apart from the low current-carrying capability of Nb nanolayer in the hybrid Nb(20 nm)/PMN-PTnp /Nb(20 nm) no TMIs have been recorded at Eex = 0.00 kV/cm, irrespectively of the value of the magnetic field, H. This means that the TMIs are triggered exclusively upon the application of Eex . As we have shown experimentally in Fig. 6 the increase of Eex changes the , which reflects respective changes in the morphological landscape of Nb nanolayers as shown in Fig. 7(b.i)−(b.iii). This means that both the effective thickness (deff = dnom ·cosθ ) and the strength of the local magnetic field Hpar = H·cosθ are modified upon application of Eex and thus the pinning conditions are also changed around the surface of Nb nanolayers. So, in terms of flux spots the application of Eex motivates/promotes their motion to alternative surface sites that are more favorable due to the newly developed minimization of the free energy. The energy dissipation from the motion of flux spots releases a noticeable amount of thermal energy, which is absorbed by the Nb nanolayers and locally increases their temperature. This initiates a sequence that motivates and/or promotes TMIs [18–24]. Studies on the development of TMIs in Nb nanolayers that are based on magneto-optical measurements [29,30], have shown that TMIs are triggered and/or promoted at different sites across
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Fig. 7. AFM data of the hybrid Nb(20 nm)/PMN-PTnp /Nb(20 nm). (a.i) Representative AFM image 10 × 10 μm2 obtained at Eex = 0.00 kV/cm. (a.ii) The height profile along the white horizontal line in (a.i) for three representative values of the electric field, Eex = 0.00 (solid black line), 1.25 (dashed blue line) and 2.00 (short-dashed red line) kV/cm. (b.i)–(b.iii) Three AFM images 6 × 6 μm2 that refer to the subarea of (a.i) marked by the white dotted square and they have been obtained at Eex = 0.00, 1.25 and 2.00 kV/cm, respectively. The rectangular shapes (solid white line) that have been placed at the right side of panels (b.i)–(b.iii), serve as guides to the eye showing the modification of the morphological landscape upon the application of Eex . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. (a) A representative AFM image of a scanning area ∼ 900 × 900 nm2 for a substrate PMN-PTnp . In the AFM image the black line denotes a specific scan and its height profile is presented in (b). The grey zone in (b) represents a Nb nanolayer with nominal thickness dnom = 20 nm deposited on top of the PMN-PTnp . The black double-arrows indicate the thickness of Nb nanolayer that is either equal to deff at the lateral side of morphological peaks or to dnom on top of surface peaks. The solid black arrows mark the direction of H and its respective components, Hnorm and Hpar .
the surface of the SC and for different values of H. Hence, it is reasonable to consider that TMIs exhibit a local character and so their appearance can be justified consistently by experimental data originated from local techniques of characterization, such as in our
case the measurements of strain and surface roughness upon varying Eex . Although the modification of the surface morphology upon applying Eex may justify qualitatively the appearance of TMIs, it cannot fully explain quantitatively their non-monotonic variation as Eex increases progressively: the pronounced maximum of TMIs that is clearly evident in Fig. 3 at Ech,1 is accompanied by an only weak step in as presented in Fig. 6 at the same value Ech,1 . For the interpretation of the non-monotonic variation of TMIs (and thus of the non-monotonic degradation of JC ) we have to take into account the two-fold action of Eex in Nb(20 nm)/PMN-PTnp /Nb(20 nm) hybrid, since the application of Eex induces changes in both the volume strain and surface roughness that are ultimately delivered to the deposited Nb nanolayers. In this context, we distinguish three successive intervals in the entire range of Eex , the first is for Eex ≤ Ech, 1 , the second is for Ech,1 Ech,2 . In the first interval, as Eex increases the magnitude of the induced volume strain is almost zero while progressively decreases (Fig. 6). Thus the appearance of TMIs is caused by the modification of the surface morphology of Nb nanolayers. At Eex = Ech,1 the appearance of a weak tensile strain (Sx > 0 in Fig. 5) leads to the local maximization of the number of TMIs at this field. Continuing with the increase of Eex in the second interval, the induced volume strain returns to zero at Ech, 2 , while the surface modification becomes more pronounced. Thus, the variation of the TMIs depends exclusively on the variation of . Under this light, the minimization of at Ech,2 ≈2.00 kV/cm diminishes the influence of surface morphology on both deff and Hpar and this is accompanied with the minimization of the recorded TMIs (maximization of JC ), but not with the complete cessation of them. As Eex increases above the Ech,2 the magnitude of the induced compressive volume strain obtains progressively higher values as also the increase. So, in the third interval of Eex the influence of strain dominates the impact of , leading to the gradual increase of TMIs (decrease of JC ) that seems to be saturated at a maximum value above Eex = 2.70 kV/cm (JC becomes zero at Eex = 3.30 kV/cm).
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4. Conclusions
References
In the present study we investigated the appearence of TMIs and the respective modification of JC upon application of Eex on two Nb(20 nm)/PMN-PT/Nb(20 nm) hybrids with significant differences in the surface roughness of PMN-PT crystals. The hybrid consisting of a PMN-PT crystal with low≈44 nm (polished surfaces) shows no indications of TMIs and JC modification upon variation of Eex . On the contrary, in the hybrid consisting of a PMNPT crystal with high ≈290 nm (non-polished surfaces) the variation of Eex induces TMIs in the Nb nanolayers. The variation of TMIs exhibits a non-monotonic increase on Eex , thus causing the respective non-monotonic degradation of JC . In order to explain this non-monotonic behavior we studied the evolution of the physical quantities related to the PMN-PT crystals with Eex . These quantities are the volume strain and the surface roughness (imposed from the PMN-PT crystals to the Nb nanolayers) that both are tuned through the application of Eex . The extremely high affects the thickness of Nb nanolayers and the magnitude of the parallel component of the magnetic field, leading to the heterogeneous distribution of flux lines and this lays the foundation for understanding the appearance of TMIs in the corresponding hybrid. Finally, the non-monotonic variation of TMIs and thus of JC in respect to Eex , is interpreted by the different contribution of volume strain and surface roughness on the mechanism that triggers and/or promotes TMIs, within well-defined intervals of Eex . This work provides sufficient experimental evidences on the control of the current-carrying capability of SC nanolayers through the simple application of an external voltage to PE/SC hybrids. Thus, it may be a useful guide for the realization of similar hybrids in possible future applications.
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Acknowledgements One of the authors (M.Z.) acknowledges the A.G. Leventis Foundation for support through a scholarship. The authors acknowledge Dr. Jun Luo at TRS Technologies for offering part of the PMN-PT crystals.
Contents lists available at ScienceDirect
Physica C: Superconductivity and its applications journal homepage: www.elsevier.com/locate/physc
Superconducting thermomagnetic instabilities tuned through electric-field-controlled strain in Nb/PMN-PT/Nb hybrids M. Zeibekis a, S.J. Zhang b, D. Stamopoulos a,c,∗ a
Institute of Nanoscience and Nanotechnology, National Center for Scientific Research ‘Demokritos’, 153 10, Aghia Paraskevi, Athens, Greece Institute for Superconducting and Electronic Materials, Australian Institute of Innovative Materials, University of Wollongong, NSW 2500, Wollongong, Australia c Department of Solid State Physics, National and Kapodistrian University of Athens, Zografou Panepistimioupolis, 157 84, Zografou, Athens, Greece b
a r t i c l e
i n f o
Article history: Received 5 September 2017 Accepted 28 October 2017 Available online 31 October 2017 Keywords: Piezoelectric/superconducting hybrids Critical current Thermomagnetic instabilities Converse piezoelectric effect
a b s t r a c t Electric-field-controlled piezoelectric strain has been used, recently, to modify the superconducting properties in a new class of piezoelectric/superconducting (PE/SC) hybrids. Here, we investigate the appearance of thermomagnetic instabilities (TMIs) and the respective modification of the critical current density (JC ) through the application of electric field (Eex ) in PE/SC hybrids. Specifically, the SC nanolayers are Nb (thickness, dSC = 20 nm) deposited on both surfaces of PE macroscopic crystals of (1-x)Pb(Mg1/3 Nb2/3 )O3 xPbTiO3 (PMN-PT) with optimum composition x = 0.31 (thickness, dPE = 0.5–0.8 mm). The appearance of TMIs and the modification of JC by Eex is studied for two PMN-PT crystals of drastically different surface roughness (Sa). In the case of the PMN-PT crystal with low Sa (on the order of a few tenths of nm) TMIs are absent so that JC does not change under the variation of Eex . On the contrary, in the case of the PMN-PT crystal with high Sa (on the order of a few hundreds of nm) Eex induces TMIs in the Nb nanolayers. Specifically, the number of TMIs exhibits a non-monotonic increase on Eex , thus causing a non-monotonic degradation of JC . These experimental data are interpreted in terms of the variation of both volume strain and surface roughness on Eex . This work highlights practical means to control the current-carrying capability of SC nanolayers through strain provided by PE substrates. © 2017 Elsevier B.V. All rights reserved.
1. Introduction A new class of hybrids consisting of a superconducting (SC) nanolayer deposited on a bulk piezoelectric (PE) substrate offers the unique opportunity to investigate dynamically the influence of volume strain on the properties of the SC nanolayer by simply changing the electric field (Eex ) that is applied to the PE substrate. Experimental studies in these hybrids have been focused on the influence of volume strain on the transition temperature (TC ) in high-TC SC nanolayers such are YBa2 Cu3 O7-δ [1,2], La2-x Srx CuO4 [3], BaFe1.8 Co0.2 As2 [3] and FeSe0.3 Te0.7 [4]. Since these hybrids operate at cryogenic conditions (around the TC of the SC) where the piezoelectric properties of the PE substrate are degraded, it is appropriate to use PE materials that belong to the compound family (1x)Pb(Mg1/3 Nb2/3 )O3 -xPbTiO3 and especially the ones with x = 0.31 (PMN-PT) due to their outstanding piezoelectric activity [5–7]. Another critical parameter of superconductivity is the critical current density (JC ), which characterizes the maximum lossless ∗
Corresponding author. E-mail addresses: [email protected], [email protected] (D. Stamopoulos). https://doi.org/10.1016/j.physc.2017.10.015 0921-4534/© 2017 Elsevier B.V. All rights reserved.
current density that the SC is able to maintain without dissipation. Although JC is an important characteristic of SCs from the viewpoint of technological applications, the piezoelectric modification of JC has not been explored so far in PE/SC hybrids. For this reason, we have focused our study on the variation of JC in respect to the applied Eex in PE/SC hybrids that are consisting of two Nb nanolayers with the same thickness (dSC ) deposited on both surfaces of PMN-PT crystals (Nb/PMN-PT/Nb). Moreover, we have included another experimental parameter in our study; we examine how the surface roughness (Sa) of the PMN-PT crystal contributes additionally to the piezoelectric modification of JC in Nb nanolayers. To do so, two Nb/PMN-PT/Nb hybrids with dSC = 20 nm have been prepared. The first is consisting of a PMN-PT crystal with polished surfaces (PMN-PTp ) of low surface roughness (
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[13–17] ones. Earlier studies in planar SC nanolayers have shown that the Sa may affect JC in several ways, such are through the spatial variation of flux lines around the surface [13], due to the thickness dSC modulation [15,16] and by the enhanced contribution of the surface pinning against the volume pinning [14,17]. It should be noted that in these studies [13–17] the Sa is referred to SC nanolayers deposited on atomically flat substrates, meaning that their Sa values are lower than their thickness dSC . In our case and in particular for Nb nanolayers deposited on top of the PMNPTnp substrate the extremely high values of Sa causes a considerable modification in two fundamental parameters of the surface geometry of Nb nanolayers. Firstly, due to the Sa the thickness of Nb nanolayer at the lateral side of morphological peaks of the surface has an effective thickness value (deff ) which is lower than the nominal thickness dSC . Secondly, although the external magnetic field (H) is applied parallel to the surfaces of the hybrid, the parts of Nb nanolayers with deff experience a local magnetic field with a non-zero normal component and thus the strength of the parallel component of the magnetic field (Hpar ) is lower than the applied H. These two fundamental parameters affect considerably the current-carrying capability of Nb nanolayers, even when no Eex is applied to the hybrid. In the present study, the parameter of Sa is not examined as a stationary parameter, but as a parameter that can be dynamically varied upon the application of Eex in Nb/PMN-PT/Nb hybrids. In particular, the application of Eex causes the macroscopic deformation of the PMN-PT crystals which induces changes in the morphological landscape of their surfaces. Both the induced volume strain and the morphological landscape modification are experienced by the deposited Nb nanolayers of the hybrids and their combined variation leads to the variation of JC . Specifically, in the case of the Nb/PMN-PT/Nb hybrid consisting of the PMN-PTp crystal the JC remains unaffected upon the application of Eex , while in the case of the Nb/PMN-PT/Nb hybrid with the PMN-PTnp crystal the JC is degraded significantly by the increase of Eex . This degradation of JC in the latter hybrid, is manifested by the appearance of magnetization jumps, known as thermomagnetic instabilities (TMIs) [18– 24] in the m(H) loops obtained at different Eex . The variation of TMIs and thus of JC upon increasing Eex is interpreted in terms of the variation of both volume strain and surface roughness that are experienced by Nb nanolayers in Nb/ PMN-PTnp /Nb hybrid. 2. Experimental 2.1. Samples preparation High quality (1-x)Pb(Mg1/3 Nb2/3 )03 -xPbTiO3 crystals with x = 0.31 were grown as presented in [25], were cut into rectangular shape substrates with dimensions of 6 × 5 x(0.5–0.8) mm3 (the large face perpendicular to [011] direction) and were left unpoled. Here, we studied (a) as prepared crystals with non-polished surfaces (PMN-PTnp ) and (b) polished crystals (PMN-PTp ) that exhibit relatively smooth surfaces. The Nb nanolayers (thickness; dSC = 20 nm) were deposited on either PMN-PTnp or PMN-PTp crystals by dc magnetron sputtering [Edwards 306A unit, Edwards, Sanborn, NY, USA] as presented in [26] and also act as electrodes for the application of the external voltage to the PMN-PT crystal. The depositions of Nb films have been performed at the same deposition run in both substrates (PMN-PTnp and PMN-PTp crystals), in order to maintain the same growth conditions. 2.2. Techniques Atomic Force Microscopy (AFM) data were acquired by means of a scanning probe microscope NT-MDT Solver PRO [NT-MDT Co, Moscow, Russia] by using NCHR cantilevers [Nano and More
GmbH, Wetzlar, Germany], as presented in [27]. The surface roughness (mean surface roughness:
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Fig. 3. Number of TMIs counted in the ascending and the descending branches of H (1st and 2nd quadrants) based on three different procedures: spheres refer to micro TMIs, triangles refer to macro TMIs and squares refer to TMIs recorded by using the mathematical criterion δ m = |mi+1 -mi | > 0.5mi . Lines serve as guide to the eye. Triangles data and squares data are multiplied by a factor of 8 and 4, respectively, for the sake of presentation in the same vertical scale.
Fig. 1. (a)-(b) Representative AFM images (20 × 10 μm2 ) of (a) the crystal PMN-PTp and (b) the crystal PMN-PTnp (the mean surface roughness, Sa, of the particular areas is (a) Sa = 25 nm and (b) Sa = 216 nm). Notice the different scale in the z values that is shown in the height color bar that accompanies each image. (a.i)–(a.iv), (b.i)– (b.iv) Representative magnetic hysteresis loops obtained at various Eex for the hybrids Nb(20 nm)/PMN-PTp /Nb(20 nm) and Nb(20 nm)/PMN-PTnp /Nb(20 nm), respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. A representative example of the three different criteria employed here to ascribe the occurrence of a TMI in the m(H) loop obtained at 3.30 kV/cm. The green filled squares refer to the raw data of m(H) obtained at Eex = 3.30 kV/cm, while the grey open squares refer to the smoothed m(H) curve. The black vertical arrow show a micro TMI that is placed outside the error zone of ± 5·10−7 emu of the smoothed m(H) curve (marked by the black-dotted circle), the red vertical arrow show a macro TMI that exist in the smoothed m(H) curve (marked by the red-dotted circle) and the incline blue dashed arrows show a TMIs that occurs in successive data points (blue vertical arrow-heads) of the raw m(H) curves based on the mathematical criterion δ m = |mi+1 -mi | > 0.5mi . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Eex = 0.00 kV/cm (that corresponds to the strain-free state of the hybrid in respect to the Eex ) turns into noisy m(H) loops where irregular jumps in magnetization are induced by the increase of Eex (that corresponds to the strain states of the hybrid in respect to Eex ). These magnetization jumps are flux jumps resulting from the development of TMIs in Nb nanolayers. Aiming to examine the evolution of TMI occurrences as Eex increases, we have used three different criteria for recording the number of TMIs in the m(H) loop at each applied Eex . A representative example of each criterion is presented in Fig. 2, which shows the m(H) loop obtained at the maximum applied field Eex = 3.30 kV/cm. Apart from the raw data of the particular m(H)
loop (green filled squares in Fig. 2) we have also included the respective smooth m(H) curve (gray open squares in Fig. 2) that was calculated by using the adjacent-averaging method of 5 data points from raw data, offered from the Origin software package [OriginPro 8.5, OriginLab Corporation, Northampton, MA, USA]. Furthermore, by taking into consideration that the accuracy level of our SQUID magnetometer to record a magnetic moment is on the order of 10−7 emu, we have placed an error zone of ± 5·10−7 emu (grey lines) around the smoothed m(H) curve. According to the first criterion, a TMI event is ascribed at each distinct point of raw data that is placed outside this error zone, as depicted by the black vertical arrow in Fig. 2. These TMIs are termed here as microscopic TMIs (micro TMIs). Now, exclusively from the smoothed m(H) curves, the second criterion ascribes a TMI event at the part of m(H) smoothed curves where the magnetic moment of consecutive points is decreased progressively by approaching lower magnetization value, as depicted by the red vertical arrow in Fig. 2. These TMIs are termed here as macroscopic TMIs (macro TMIs). Finally, without taking into account the smoothed m(H) curves, we have used a strict mathematical criterion that ascribes a TMI event directly from the raw data. This is the third criterion and it counts a TMI event whenever the variation of magnetization during a flux jump (δ m = |mi+1 -mi |) meets the condition δ m > 0.5mi (where mi is the initial value of magnetization when a TMI is triggered and mi+1 is the final value of magnetization when a TMI is completed). A representative example of a TMI according to the third criterion is depicted by the blue-dashed inclined arrows in Fig. 2. All three criteria have been used to count the TMI occurrences in both the ascending (1st quadrant) and the descending (2nd quadrant) branches of the magnetic field in the m(H) loop obtained at each Eex . Fig. 3 shows the evolution of the number of TMIs that were recorded from each employed criterion in respect to Eex . For the sake of presentation, we have scaled up the number of macro TMIs by a factor of 8 and the number of TMIs according to third criterion (δ m > 0.5mi ) by a factor of 4, since each criterion results to a different number of the counted TMIs. From Fig. 3 it becomes apparent that for every employed criterion, the number of TMIs follows the same non-monotonic variation with the increase of Eex . From this non-monotonic variation of TMIs one can recognize two characteristic Eex . The first characteristic Eex (Ech,1 ) is located around 1.30 kV/cm and corresponds to a local maximum in the number of TMIs, while the second one (Ech,2 ) is located around 2.00 kV/cm where all criteria have recorded a local minimum in the number of TMIs that signifies the partial cessation of TMI occurrences. Finally, at Eex = 2.70 kV/cm all criteria show the maximization of TMIs that are saturated in this maximum value for Eex ≥ 2.70 kV/cm.
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Fig. 5. Sx (Eex ) curves measured along the x direction of a PMN-PT crystal, obtained from a local technique that is described in [27,28].
Fig. 4. Variation of the normalized JC (in respect to the JC0 ) as a function of Eex for H = 0 Oe (open symbols), 150 Oe (semi-filled symbols) and 400 Oe (filled symbols) for (a) Nb(20 nm)/PMN-PTp /Nb(20 nm) and (b) Nb(20 nm)/PMN-PTnp /Nb(20 nm). The results shown in (c) refer to the latter hybrid and is obtained from the smoothed m(H) curves. In all panels, the lines serve as guides to the eye. Horizontal dashed lines in panels (b) and (c) show the initial normalized value for Eex = 0.00 kV/cm.
It is worth noting that the TMIs are observed and recorded in the regime of relatively high magnetic fields in m(H) loops, unlike to their expected appearance in the lower part of m(H) loops where JC obtains high values. This suggests that the appearance of TMIs is stimulated by an external cause with finite influence against the pinning forces in Nb nanolayers. In particular, this external cause is able to overcome only the weak pinning forces that are manifested by the low values of JC and not the strength of stronger pinning forces in Nb nanolayers. Before examining the origins of this external cause, it is appropriate to study the variation of JC in respect to Eex . In the present study, the values of JC is considered to be proportional to the absolute difference of the magnetic moments (m) obtained along the ascending branch and the descending branch of m(H) loops for constant magnetic field (JC ∝ m≡|masc (H)-mdesc (H)|). Fig. 4(a)−(c) show the modification of the normalized values of JC (defined as JC /JC0 , where JC0 is the value JC at Eex = 0.00 kV/cm) obtained at H = 0 Oe (black open symbols), 150 Oe (blue semifilled symbols) and 400 Oe (red filled symbols) as a function of Eex for the raw data of both Nb(20 nm)/PMN-PTp /Nb(20 nm), Nb(20 nm)/PMN-PTnp /Nb(20 nm) and for the smoothed data of Nb(20 nm)/PMN-PTnp /Nb(20 nm), respectively. As it is shown in Fig. 4(a), the fact that the m(H) loops of the hybrid Nb(20 nm)/PMN-PTp /Nb(20 nm) remained unaffected upon the application of Eex (Fig. 1(a.i)−(a.iv)) is reflected to the negligible modification of the normalized JC . On the contrary, the appearance of TMIs in the m(H) loops of the hybrid Nb(20 nm)/PMNPTnp /Nb(20 nm) and their variation upon increasing Eex results to a respective modification in the normalized values of JC . Fig. 4(b) shows that the non-monotonic variation of the normalized JC obtained at H = 150 Oe and 400 Oe is in perfect accordance with the respective variation of TMIs shown in Fig. 3. Specifically, at the Ech,1 ≈1.30 kV/cm where TMIs are maximized locally the JC obtains a local minimum value and at the Ech,2 ≈2.00 kV/cm where TMIs are minimized the JC obtains a maximum value that is equal to JC0 . Moreover, the increased number of TMIs at Eex > Ech,2 results to a progressive degradation in the normalized JC . The same non-
monotonic variation of JC , but with lower degree of degradation in the normalized values of JC is also shown in Fig. 4(c) that refers to the data coming from the smoothed m(H) curves. We continue our study by investigating the physical quantities related to the PMN-PT substrate of these hybrids that could motivate the variation of TMIs and therefore the consistent degradation of JC upon increasing Eex in Nb nanolayers. As it is expected the application of Eex in these hybrids causes primarily the macroscopic deformation of PMN-PT crystals, which is delivered to the deposited Nb nanolayers causing the respective deformation of them. In order to estimate the induced deformation that is experienced from Nb nanolayers we measured the strainelectric field curve (S(Eex )) of the PMN-PT crystal. Fig. 5 presents the Sx (Eex ) curve that was obtained along the x macroscopic axis of a PMN-PT crystal upon the progressive increase of Eex from 0 up to 3.50 kV/cm. As it is shown in Fig. 5, at Eex = Ech,1 (≈1.3 kV/cm) the Sx exhibits a small peak of positive strain corresponding to a tensile strain (upward arrow), at Eex = Ech,2 (= 2.0 kV/cm) the strain returns to zero value (downward arrow), while for Eex > 2.0 kV/cm the magnitude of the compressive strain is increased progressively. Using these data one could interpret the appearance of TMIs in terms of strain, since the non-monotonic variation of the number of TMIs (and thus of JC ) upon increasing Eex seems to coincide with the behavior of the Sx (Eex ) curve. In particular, the peak of tensile strain (Sx > 0) at Eex = Ech,1 coincides with the local maximization of TMIs (local minimization of JC ), the return of Sx to zero value at Eex = Ech,2 coincides with the partial cessation of TMIs occurrences (local maximization of JC ) and eventually the increased magnitude of compressive strain (Sx <0) at Eex > Ech,2 coincides with the respective increase in the number of TMIs (progressive degradation of JC ). Although it seems that the strain motivates the nonmonotonic variation of TMIs and JC , it can explain only partially our data, since the hybrid that consists of a polished PMN-PT does not exhibit any changes in the m(H) loops upon applying Eex . This significant difference between the two hybrids suggests that the appearance of TMIs and therefore the degradation of JC are also related to the surface morphological landscape of the PMN-PTnp . To understand the influence of the morphological landscape of PMN-PT on the appearance of TMIs we examine how the surface morphology (given by
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Fig. 6. The evolution of
the progressive reduction of
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ally shrinks. This behavior justifies the observed reduction of
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Fig. 7. AFM data of the hybrid Nb(20 nm)/PMN-PTnp /Nb(20 nm). (a.i) Representative AFM image 10 × 10 μm2 obtained at Eex = 0.00 kV/cm. (a.ii) The height profile along the white horizontal line in (a.i) for three representative values of the electric field, Eex = 0.00 (solid black line), 1.25 (dashed blue line) and 2.00 (short-dashed red line) kV/cm. (b.i)–(b.iii) Three AFM images 6 × 6 μm2 that refer to the subarea of (a.i) marked by the white dotted square and they have been obtained at Eex = 0.00, 1.25 and 2.00 kV/cm, respectively. The rectangular shapes (solid white line) that have been placed at the right side of panels (b.i)–(b.iii), serve as guides to the eye showing the modification of the morphological landscape upon the application of Eex . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. (a) A representative AFM image of a scanning area ∼ 900 × 900 nm2 for a substrate PMN-PTnp . In the AFM image the black line denotes a specific scan and its height profile is presented in (b). The grey zone in (b) represents a Nb nanolayer with nominal thickness dnom = 20 nm deposited on top of the PMN-PTnp . The black double-arrows indicate the thickness of Nb nanolayer that is either equal to deff at the lateral side of morphological peaks or to dnom on top of surface peaks. The solid black arrows mark the direction of H and its respective components, Hnorm and Hpar .
the surface of the SC and for different values of H. Hence, it is reasonable to consider that TMIs exhibit a local character and so their appearance can be justified consistently by experimental data originated from local techniques of characterization, such as in our
case the measurements of strain and surface roughness upon varying Eex . Although the modification of the surface morphology upon applying Eex may justify qualitatively the appearance of TMIs, it cannot fully explain quantitatively their non-monotonic variation as Eex increases progressively: the pronounced maximum of TMIs that is clearly evident in Fig. 3 at Ech,1 is accompanied by an only weak step in
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4. Conclusions
References
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Acknowledgements One of the authors (M.Z.) acknowledges the A.G. Leventis Foundation for support through a scholarship. The authors acknowledge Dr. Jun Luo at TRS Technologies for offering part of the PMN-PT crystals.