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Effect of DC current injection on AC supercurrent carrying ability of ring shaped HTS thin films
Physica C 471 (2011) 577–581
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Physica C journal homepage: www.elsevier.com/locate/physc
Effect of DC current injection on AC supercurrent carrying ability of ring shaped HTS thin films T. Nurgaliev a,⇑, E. Mateev a, B. Blagoev a, L. Neshkov a, I. Nedkov a, L.S. Uspenskaya b a b
Institute of Electronics, Bulgarian Academy of Sciences, 72 Tsarigradsko Chausse, 1784 Sofia, Bulgaria Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow, Russia
a r t i c l e
i n f o
Article history: Received 10 June 2011 Accepted 13 July 2011 Available online 23 July 2011 Keywords: HTS thin film LSMO electrode Critical current DC current injection
a b s t r a c t The effect of DC current injection on the AC current carrying characteristics of superconducting thin film rings was analyzed because of the possibility for using similar ferromagnetic/high temperature superconducting (FM/HTS) structures for contactless investigation of the spin-injection process. It was shown, that the injection leads to decreasing of the critical current IC1, determined by using AC magnetic field. A superposition of AC and DC currents in the HTS ring and a breaking of Cooper pairs may cause this effect. The effect was investigated experimentally at 77 K in HTS Y1Ba2Cu3O7x (YBCO) thin film samples with YBCO or La0.7Sr0.3MnO3 (LSMO) current injecting electrodes: IC1 of the last sample was found to be more sensitive to the injection process. The results allow concluding, that a change of the IC1 caused by both mechanisms can be evaluated separately and the contactless method can be successfully used for the investigation of the spin-injection effect. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction The spin-dependent properties of superconductors in superconductor/ferromagnet heterostructures [1–4] have raised huge interest in recent years for both understanding the physical processes in such structures and for the potential application in spintronics devices which exploit the spins of charge carriers rather than their charge. The injection of spin-polarized charge carriers from materials with colossal magnetoresistance into high temperature superconductors (HTS) causes strong nonequilibrium effects and affects the electronic transport properties of the superconducting films [4–6]. The half-metal manganite compound La0.7Sr0.3MnO3 (LSMO), that exhibits a ferromagnetic (FM) state below TCurie 350 K and the spin polarization of the eg – electrons of which is close to 100%, and a high temperature superconductor Y1Ba2Cu3O7x (YBCO) with the critical temperature TC 92 K can be used as components of such structures [7–9]. The similar lattice constants and growth conditions of these materials make it possible to epitaxially grow superlattices and heterostructures using various technologies. It was shown experimentally, that the spin injection process in LSMO/YBCO/LSMO and LCMO/YBCO/LCMO thin film structures can reduce the critical temperature of the structures by up to 15% [4]. It was demonstrated also that the suppression of the critical current density caused by the injection of spin polarized quasiparticles into YBCO thin film through thin insulating SrTiO3 or metallic Au barriers exceeds the ⇑ Corresponding author. Fax: +359 2 9753201. E-mail addresses: [email protected], [email protected] (T. Nurgaliev). 0921-4534/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2011.07.003
suppression caused by the unpolarized quasiparticles by several times [6,10]. Conventionally the information about the spin injection or diffusion effects on the characteristics of FM/HTS structures is obtained from the measurements of the resistance (using the four probe method) or of the quasi static magnetic parameters of these structures [4–8,11]. On the other hand, the methods, based on the analysis of the sample response to variable magnetic fields and used for contactless measurements of the critical parameters of HTS materials [12–16], after their appropriate modification could serve as supplementary tools for the investigation of the spin – transfer effects in FM/HTS structures. For this reason in this paper we investigate the effect of DC current injection on the AC current carrying characteristics of a superconducting thin film sample with a ring shape and present experimental results obtained in such HTS YBCO samples containing the current injecting HTS YBCO or FM LSMO electrodes.
2. Experimental set-up and sample configuration The sketch of the YBCO/LSMO structure and the measurement equipment are shown in Fig. 1. The sample consists of a thin film HTS YBCO ring 1, placed on a dielectric (LaAlO3) substrate, and two electrodes 2, 3 which are used for injection of DC current into the ring. Electrode 2, electrically contacting with the narrow part of the ring, was either an HTS YBCO (sample 1) or a FM LSMO thin film strip (sample 2), while the second electrode 3 was an HTS YBCO strip for both samples. For preparing structure 2 first the
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Fig. 1. The sample geometry and the measurement set-up: 1 – HTS YBCO ring; 2 – LSMO or YBCO electrode; 3 – HTS YBCO electrode; 4 and 5 – drive and receive coils, respectively.
FM LSMO thin film electrode (with a thickness of tF 30 nm) was deposited by RF magnetron sputtering on 10 5 mm LAO substrate. A stainless steel mask was used to form a necessary configuration of the electrode during the deposition process. Afterwards the HTS YBCO thin film with the thickness of tSC 60 nm was grown on the top of this structure using a DC magnetron sputtering equipments. The growing procedure and conditions of the HTS YBCO and FM LSMO films and sandwiches were described elsewhere [17]. Conventional photolithography and chemical etching were used for patterning of the HTS part of the structure and forming sample 2. Sample 1 consisted of HTS thin film components only. Experiments were performed at 77 K (the sample was immersed into liquid nitrogen bath). The AC current in the HTS ring was excited by magnetic field of small coil 4, placed near the ring (Fig. 1). Another small coil 5 was used to register the third harmonics of the response signal Ures, which arises when the current in the HTS ring reaches its critical value IC. The measurements were performed at different magnitudes of the injected DC current I0.
the basis of an equivalent circuit, presented in Fig. 2. For sake of simplicity we assume, that the width w of the HTS superconducting ring is the same all along the ring and the induced current density is constant across the ring. These assumptions are justified for our HTS thin film sample (tSC k, w < r, where k is the magnetic penetration depth, r is the radius of the ring) and can not affect significantly the results of the analysis. The equivalent scheme of the superconducting ring includes the inductances LC ¼ 0:5ðL þ Lk Þ (where L Lk, L and Lk are the external inductance and the internal kinetic inductance of the HTS ring, respectively) and the active resistances Rx, Ry of the two ‘‘shoulders’’ of the ring. The mutual inductance between the two ‘‘shoulders’’ of the ring was not taken into account in this paper. Electrical current I0 is injected into HTS ring through resistance R0 from a DC voltage source E0. The magnetic field of the AC current I1cos(xt) flowing through drive coil 4 induces the electromotive force (EMF) MðdI1 =dtÞ ¼ xMI1 sinðxtÞ (where M is the mutual inductance of the ring and the drive coil 4, x is the angular frequency of the AC current) in the ring. The 3d harmonics of the response signal in the receive coil is induced by the magnetic field of AC current Ix, Iy flowing in HTS ring 1, when the current in the ring reaches its critical value IC and a nonlinearity of the electric characteristics appears. In the framework of the above equivalent circuit, the currents Ix, Iy, flowing in the ‘‘shoulders’’ of the HTS ring satisfy the following system of equations:
ðL þ Lin Þ
1 dIx xMI1 þ I x Rx þ R0 I 0 ¼ E 0 þ sinðxtÞ; 2 dt 2
ð1Þ
ðL þ Lin Þ
1 dIy xMI1 þ I y Ry þ R0 I 0 ¼ E 0 sinðxtÞ; 2 dt 2
ð2Þ
Ix þ I y ¼ I 0 :
The amplitude of the AC current in the ring is I ¼ MI1 =ðL þ Lin Þ if Rx = Ry = 0 and there is no injected DC current (I0 = 0). The resistances Rx and Ry of the two ‘‘shoulders’’ of the HTS ring arise due to the magnetic flux movement process and can be described as functions of the dimensionless current strengths ix, iy:
Rx ¼ 0:5qFðix Þ; 3. Functioning peculiarities of the structure To elucidate how the DC current passing through the HTS ring affects the generation of the third harmonics of the circulating AC current (which induces the 3-d harmonics of the response signal in the receive coil and is used for determination of IC) the functioning peculiarities of the measuring system (Fig. 1) were analyzed on
ð3Þ
Ry ¼ 0:5qFðiy Þ;
ð4Þ
where ix;y ¼ Ix;y =IC , q is a parameter, IC is the critical current of the superconducting ring. Eqs. (1)–(3) can be transformed to a dimensionless form:
xðL þ Lin Þ dix 1 di0 1 þ ½ix Fðix Þ ði0 ix ÞFði0 ix Þ 2 q ds 2 ds ¼ iF sinðsÞ; xðL þ Lin Þ 1 di0 1 þ ½ix Fðix Þ þ ði0 ix ÞFði0 ix Þ þ 2r0 i0 ¼ 2e0 ; 2 ds 2 q
ð5Þ ð6Þ
where s ¼ xt, i0 ¼ I0 =IC , iF ¼ xMI1 =ðqIC Þ – dimensionless voltage, induced in the ring, r0 ¼ R0 =q, r 0 11. At low frequencies (x/ 2p 6 100 Hz) the following situation may be realistic: xðLex þ Lin Þ=q 1. In this case ix can be determined as a solution of the following nonlinear algebraic equation:
Fig. 2. The equivalent circuit of the sample interacting with the drive coil 4: 2Ld, 2LC – the inductances of the drive coil and the HTS YBCO ring, respectively; Rx + Ry is the YBCO ring resistance.
ix Fðix Þ ði0 ix ÞFði0 ix Þ ¼ iF sinðsÞ;
ð7Þ
iy ¼ i0 ix ;
ð8Þ
where i0 ¼ e0 =r0 . The current–voltage characteristics of HTS materials for different activation regimes of the fluxons can be described by the power law EðJÞ ¼ EC ðJ=J C Þm [18–22], where m is a parameter known as the creep exponent [23,24]. This parameter depends on the activation energy of the fluxons and on the temperature and is valid for the interval 1 6 m < 1. The case m = 1 corresponds to the
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resistive (ohmic) or flux flow regime and m ! 1 – to the Bean model [25]. For this reason the current-dependent part of the resistance of the superconducting film in (1)–(4) can be described by the following expression
Fðix;y Þ ¼ ðix;y Þm ;
ð9Þ
which leads to a zero resistance of the film at ix,y ? 0. In our calculations we used a following slightly modified expression as well
Fðix;y Þ ¼ coshðix;y Þm ;
ð10Þ
which assumes a presence of a small finite value of the resistance of the superconducting film at ix,y ? 0. It can be noted, that the AC magnetic field of the drive coil, affecting the superconducting ring, leads to the arising of a small AC component of the injected current if i0 – 0:
i0 ðsÞ i0 þ di0 ðsÞ; di0 ðsÞ ¼
1 ½ix Fðix Þ þ ði0 ix ÞFði0 ix Þ: 2r 0
ð11Þ
Fig. 4. The current profiles ix(s) (curves 1a–3a) and iy(s) (curves 1b–3b) in the two shoulders of the HTS ring: iF = 0.8; xL/q = 1.2; i0 = 0, 1, 2 (curves 1a and b–3a and b, respectively). Expression (10) with m = 4 was used for the calculations of the current profiles.
ð12Þ
Fig. 3 and 4 illustrate the evolution of the induced AC current profiles ix(s), iy(s) in the superconducting ring with the increasing of the injected DC current intensity i0, obtained as a numerical solution of nonlinear differential equations (5) and (6). It is seen, that the phase, the intensity and the profile of the AC current ix,y induced in the ring by the harmonic external magnetic field, depend strongly on the injected DC current intensity i0 as the DC current affects the resistance and the ratio between the active and inductive components of the complex resistance of the sample. In general, the DC current i0 leads to a decreasing of the variable current intensity in the ring and to a worsening of the screening properties of the superconducting sample with respect to the AC magnetic field. The dependences of the module of the 3-d harmonics of the current ji3 j which circulates in the superconducting ring (Z 2 Z sþ2p 2 )1=2 sþ2p 1 ji3 j ¼ ðix iy Þsinð3sÞds þ ðix iy Þcosð3sÞds 2p s s ð13Þ
Fig. 5. Dependences of the 3-d harmonics of the induced current in the HTS ring on the AC voltage iF, induced in the HTS ring. Calculations were made for xL/q = 1.2, i0 = 0 (curve 1), 0.2 (curve 2), 0.4 (curves 3 and 4), 1 (curve 5), 2 (curve 6). Curve 4 was calculated for a smaller value of the critical current IC1 = 0.95IC. Current dependent part of the resistance was described by expression (9) with m = 6.
on the dimensionless induced voltage iF ¼ xMI1 =ðqIC Þ, calculated numerically from (5) and (6) for different intensities of the injected DC current i0, are shown in Fig. 4. When alternating currents ix, iy flowing across the ring reach their critical value (Figs. 5 and 6, curve 1, calculated for the case i0 = 0, ix = iy), the nonlinearity of the electric characteristics of the ring strongly increases and an intensive
Fig. 6. Dependences of the 3-d harmonics of the induced current in the HTS ring on the AC voltage iF, induced in the HTS ring. Calculations were made for xL/q = 1.2, i0 = 0 (curve 1), 0.2 (curve 2), 0.4 (curves 3 and 4), 1 (curve 5), 2 (curve 6). Curve 4 was calculated for a smaller value of the critical current IC1 = 0.95IC. Current dependent part of the resistance was described by expression (10) with m = 4. Fig. 3. The current profiles ix(s) (curves 1a–3a) and iy(s) (curves 1b–3b) in the two shoulders of the HTS ring: iF = 0.8; xL/q = 1.2; i0 = 0, 1, 2 (curves 1a and b–3a and b, respectively). Expression (9) with m = 6 was used for the calculations of the current profiles.
generation of the third harmonics of the current is started. This leads to a drastic change of the behavior of the response signal
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Ures |i3| induced in the receive coil. The value of iF (Figs. 5 and 6, curve 1), where a maximum nonlinearity of |i3| vs iF dependence is observed, can be used for the determination of the critical current IC of HTS ring when i0 = 0. The injection of a DC current i0 into the superconducting ring causes a shifting of |i3| vs iF dependence towards the left hand side (Figs. 5 and 6, curves 2–6), i.e. to a decreasing of the critical current value IC1, determined by using an AC magnetic field. This decrease is not caused by a change of the spin state of the superconducting charge carriers – the nonlinearity of the electrical characteristics in this case arises at smaller values of iF due to the superposition of the AC current, induced in the ring, and the DC current, injected into the ring. The magnitude of the shift also depends on the current–voltage characteristics of the HTS film (compare Figs. 5 and 6) and it is small when i0 is small. On the other hand, an injection of DC current from a ferromagnetic material (which is characterized with spin polarized charge carriers) into the superconducting ring can provoke a breaking of Cooper pairs and forming a local nonequilibrium state (with a lower critical temperature TC and a critical current density JC) in the superconductor close to the surface of the current injecting electrode. This will cause an additional shifting of |i3| vs iF dependences towards the smaller values of iF. Curves 4 in Figs. 5 and 6 were calculated assuming that the DC current i0 = 0.4 causes a decreasing of IC by 5%. These curves demonstrate summary effects, which are caused by the conventional DC and AC currents superposition effect (see also Fig. 5 and 6, curves 3) and the effect, related to the real change of IC (due, for example, to the pair breaking mechanism). The obtained results allow concluding, that the changes of IC1 caused by both mechanisms can be registered by contactless way and be evaluated easily especially in the case when the sample together with a FM current injecting electrode contains a reference electrode made from the same material as the sample.
4. Experimental results and discussion The dependence of the amplitude of the 3-d harmonics Ures of the response signal on the amplitude I = (M/L)I1 of the screening AC current induced in YBCO samples 1 and 2 by the magnetic field of the driving coil (see the set-up and the sample configurations in Fig. 1) are presented in Figs. 7 and 8, respectively. It can be seen that the amplitude of the third harmonics of the response signal is negligible at small amplitudes of the driving current and it increases drastically when the current in the HTS ring reaches its critical value. The critical currents IC of these samples, were
Fig. 7. Dependence of the 3-d harmonics of the response signal on the amplitude of the screening AC current (M/L)I1 induced in the YBCO ring 1 (completely HTS YBCO structure) by the magnetic field of the driving coil. The injected current intensity I0 is 0 mA (squares), 12 mA (circles) and 20 mA (triangles).
Fig. 8. Dependence of the 3-d harmonics of the response signal on the amplitude of the screening AC current (M/L)I1 induced in the YBCO ring 2 (HTS YBCO structure with LSMO electrode) by the magnetic field of the driving coil. The injected current intensity I0 is 0 mA (squares), 20 mA (circles) and 40 mA (triangles).
0.024 A and 0.23 A, respectively, at the absence of the injected current I0. The DC current injection leads to a shifting of experimental dependences towards the left hand side which is equivalent to a decreasing of the critical current density IC1 (Figs. 7 and 8), determined using alternative current. The change of the DC current polarity did not cause a noticeable change of IC1 in both samples. For the sake of comparison of the experimental results the injected current I0 and the change of such critical current DIC1 = IC IC1 in each sample were expressed in dimensionless forms as I0/IC and DIC1/IC, respectively. The dependence of the dimensionless critical current density on the dimensionless injected current strength for both samples 1 and 2 are presented in Fig. 9. The same figure illustrates the changes of IC1 caused by the DC and AC currents superposition effect, which were calculated on the basis of the model of Bean and the formulas (4)–(13) as well. In theoretical plane, a maximum change of JC1 due to the DC and AC currents superposition effect may be observed in the samples described by the critical state model of Bean (Fig. 9, curve 3), and the changes are smaller for the samples with not very steep current – voltage characteristics (Fig. 9, curves 4 and 5). It can be seen that the effect of a DC current injection on the critical current IC1 is weak for sample 1 (Fig. 9, curve 2) with HTS electrodes. This
Fig. 9. Dependences of the changes in the dimensionless critical current on the dimensionless injected current intensities in samples 1 (closed squares) and 2 (closed circles). The dependences 3–5 – were determined on the basis of the calculation using the model of Bean (curve 3) and formulas (9) (curve 5) and (10) (curve 4) for the current – dependent part of the resistance of the sample. Dependence 6 demonstrates the change of the critical current DIC1/IC in sample 2 caused by the second mechanism (see the text).
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means, that the steepness of the current–voltage characteristics of this sample is low and the injected DC current practically does not cause a change in the spin state of the superconducting charge carriers in this sample. The change of the critical current IC1 of sample 2 with an LSMO electrode, exposed to the DC current injection process, is significantly stronger (Fig. 9, curve 1) than the changes, determined on the basis of the above calculations (Fig. 9, curves 3–5) made by taking into account only the DC and AC current superposition processes. It is reasonable to conclude, that both the conventional DC and AC currents superposition effect (see also Figs. 5 and 6, curves 3) and the modification of the spin state of the charge carriers in the HTS YBCO sample under the action of the DC current, injected from a LSMO electrode, cause the modification of IC1 in this case. The change of the critical current DIC1/IC caused by this second mechanism can be evaluated to be 0.009, 0.016, 0.035 and 0.13 at I0/IC = 0.043, 0.087, 0.13 and 0.174, respectively (Fig. 9, dependence 6), if we assume, that the characteristics of this sample are described by the Bean model. There are several microscopic mechanisms of the coupling at the interface of the HTS/LSMO structure [2,4,5,8,9] which affect the critical parameters of the HTS component. The proximity effect related to the tunneling of Cooper-pairs into the non-superconducting FM side can lead to both, a reduction and an oscillation of the critical temperature of the superconducting part of the heterostructure. On the other hand, the large exchange energy of the magnetic layer prevents Cooper-pairs from tunneling into the LSMO film and this mechanism is less effective [5] for the reduction of the critical parameters of HTS in the structure. There is also an inverse proximity effect, when the spin polarized quasiparticles penetrate into the HTS layer on a certain length scale [1,5] of order 10 nm [5]. According to the results of [5] in the HTS/manganite structure an existence of a long-range inverse magnetic proximity effect which affects the properties of YBCO films up to thicknesses of more than 100 nm is possible as well. The effect is due to the anisotropy of the d-wave parameter, because of which the coherence length tends to approach infinity in the (110) nodal direction of the YBCO Fermi surface. The injected current intensity and polarity affect the effectiveness of the above processes and leads to a modification of the critical parameters of the FM/HTS structure. In the last case changes of the electrical properties of the HTS component are possible if the main part of the quasiparticles in the injected current crosses the interface without ‘‘losing’’ their spin-orientations. The spin-diffusion length in cuprate superconductors is of order 10–20 nm [4] or more in some directions. So, a reduction of TC and JC occur in the same length scale in the HTS component of the structure. The above mechanisms, together with the effect of the superposition of DC and AC currents, provide sensitivity of the critical parameters of the HTS film to the current injection process in FM/HTS structures, as it was observed by contactless way in our experiments. The results allow concluding, that a change of the IC1 caused by both mechanisms can be evaluated separately (especially in the case when the sample together with a FM current injecting electrode contains a reference electrode made from the same material as the sample) and the contactless method can be successfully used for the investigation of the spin-injection effect.
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5. Conclusion The effect of DC current injection on the AC current carrying characteristics of superconducting thin film samples of ring shape were analyzed because of the possibility for using similar ferromagnetic/high temperature superconducting structures for contactless investigation of the spin-injection process. It was shown, that an injection of the DC current leads to decreasing of the critical current value IC1, determined from the response of the HTS ring to the AC magnetic field, due to the superposition effect of AC and DC currents in the sample. If the DC current provokes a breaking of Cooper pairs in the superconductor, this causes an additional decreasing of IC1. The effect was investigated experimentally at 77 K in HTS YBCO and YBCO–LSMO thin film configurations, prepared using magnetron sputtering, conventional photolithography and wet etching procedures. The DC current was injected (from HTS YBCO or ferromagnetic LSMO electrodes) into an HTS YBCO ring and the critical current IC1 was determined from the third harmonics response of the HTS ring to AC magnetic field. The experiments demonstrated a sensitivity of IC1 to the current injection process (especially, in the case of a FM LSMO current-injecting electrode). The results allow concluding, that a change of the IC1 caused by the superposition process of AC and DC currents and by possible Cooper pairs breaking process can be evaluated separately by contactless method and used for investigation of the spin-injection effect.
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Physica C journal homepage: www.elsevier.com/locate/physc
Effect of DC current injection on AC supercurrent carrying ability of ring shaped HTS thin films T. Nurgaliev a,⇑, E. Mateev a, B. Blagoev a, L. Neshkov a, I. Nedkov a, L.S. Uspenskaya b a b
Institute of Electronics, Bulgarian Academy of Sciences, 72 Tsarigradsko Chausse, 1784 Sofia, Bulgaria Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow, Russia
a r t i c l e
i n f o
Article history: Received 10 June 2011 Accepted 13 July 2011 Available online 23 July 2011 Keywords: HTS thin film LSMO electrode Critical current DC current injection
a b s t r a c t The effect of DC current injection on the AC current carrying characteristics of superconducting thin film rings was analyzed because of the possibility for using similar ferromagnetic/high temperature superconducting (FM/HTS) structures for contactless investigation of the spin-injection process. It was shown, that the injection leads to decreasing of the critical current IC1, determined by using AC magnetic field. A superposition of AC and DC currents in the HTS ring and a breaking of Cooper pairs may cause this effect. The effect was investigated experimentally at 77 K in HTS Y1Ba2Cu3O7x (YBCO) thin film samples with YBCO or La0.7Sr0.3MnO3 (LSMO) current injecting electrodes: IC1 of the last sample was found to be more sensitive to the injection process. The results allow concluding, that a change of the IC1 caused by both mechanisms can be evaluated separately and the contactless method can be successfully used for the investigation of the spin-injection effect. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction The spin-dependent properties of superconductors in superconductor/ferromagnet heterostructures [1–4] have raised huge interest in recent years for both understanding the physical processes in such structures and for the potential application in spintronics devices which exploit the spins of charge carriers rather than their charge. The injection of spin-polarized charge carriers from materials with colossal magnetoresistance into high temperature superconductors (HTS) causes strong nonequilibrium effects and affects the electronic transport properties of the superconducting films [4–6]. The half-metal manganite compound La0.7Sr0.3MnO3 (LSMO), that exhibits a ferromagnetic (FM) state below TCurie 350 K and the spin polarization of the eg – electrons of which is close to 100%, and a high temperature superconductor Y1Ba2Cu3O7x (YBCO) with the critical temperature TC 92 K can be used as components of such structures [7–9]. The similar lattice constants and growth conditions of these materials make it possible to epitaxially grow superlattices and heterostructures using various technologies. It was shown experimentally, that the spin injection process in LSMO/YBCO/LSMO and LCMO/YBCO/LCMO thin film structures can reduce the critical temperature of the structures by up to 15% [4]. It was demonstrated also that the suppression of the critical current density caused by the injection of spin polarized quasiparticles into YBCO thin film through thin insulating SrTiO3 or metallic Au barriers exceeds the ⇑ Corresponding author. Fax: +359 2 9753201. E-mail addresses: [email protected], [email protected] (T. Nurgaliev). 0921-4534/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2011.07.003
suppression caused by the unpolarized quasiparticles by several times [6,10]. Conventionally the information about the spin injection or diffusion effects on the characteristics of FM/HTS structures is obtained from the measurements of the resistance (using the four probe method) or of the quasi static magnetic parameters of these structures [4–8,11]. On the other hand, the methods, based on the analysis of the sample response to variable magnetic fields and used for contactless measurements of the critical parameters of HTS materials [12–16], after their appropriate modification could serve as supplementary tools for the investigation of the spin – transfer effects in FM/HTS structures. For this reason in this paper we investigate the effect of DC current injection on the AC current carrying characteristics of a superconducting thin film sample with a ring shape and present experimental results obtained in such HTS YBCO samples containing the current injecting HTS YBCO or FM LSMO electrodes.
2. Experimental set-up and sample configuration The sketch of the YBCO/LSMO structure and the measurement equipment are shown in Fig. 1. The sample consists of a thin film HTS YBCO ring 1, placed on a dielectric (LaAlO3) substrate, and two electrodes 2, 3 which are used for injection of DC current into the ring. Electrode 2, electrically contacting with the narrow part of the ring, was either an HTS YBCO (sample 1) or a FM LSMO thin film strip (sample 2), while the second electrode 3 was an HTS YBCO strip for both samples. For preparing structure 2 first the
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Fig. 1. The sample geometry and the measurement set-up: 1 – HTS YBCO ring; 2 – LSMO or YBCO electrode; 3 – HTS YBCO electrode; 4 and 5 – drive and receive coils, respectively.
FM LSMO thin film electrode (with a thickness of tF 30 nm) was deposited by RF magnetron sputtering on 10 5 mm LAO substrate. A stainless steel mask was used to form a necessary configuration of the electrode during the deposition process. Afterwards the HTS YBCO thin film with the thickness of tSC 60 nm was grown on the top of this structure using a DC magnetron sputtering equipments. The growing procedure and conditions of the HTS YBCO and FM LSMO films and sandwiches were described elsewhere [17]. Conventional photolithography and chemical etching were used for patterning of the HTS part of the structure and forming sample 2. Sample 1 consisted of HTS thin film components only. Experiments were performed at 77 K (the sample was immersed into liquid nitrogen bath). The AC current in the HTS ring was excited by magnetic field of small coil 4, placed near the ring (Fig. 1). Another small coil 5 was used to register the third harmonics of the response signal Ures, which arises when the current in the HTS ring reaches its critical value IC. The measurements were performed at different magnitudes of the injected DC current I0.
the basis of an equivalent circuit, presented in Fig. 2. For sake of simplicity we assume, that the width w of the HTS superconducting ring is the same all along the ring and the induced current density is constant across the ring. These assumptions are justified for our HTS thin film sample (tSC k, w < r, where k is the magnetic penetration depth, r is the radius of the ring) and can not affect significantly the results of the analysis. The equivalent scheme of the superconducting ring includes the inductances LC ¼ 0:5ðL þ Lk Þ (where L Lk, L and Lk are the external inductance and the internal kinetic inductance of the HTS ring, respectively) and the active resistances Rx, Ry of the two ‘‘shoulders’’ of the ring. The mutual inductance between the two ‘‘shoulders’’ of the ring was not taken into account in this paper. Electrical current I0 is injected into HTS ring through resistance R0 from a DC voltage source E0. The magnetic field of the AC current I1cos(xt) flowing through drive coil 4 induces the electromotive force (EMF) MðdI1 =dtÞ ¼ xMI1 sinðxtÞ (where M is the mutual inductance of the ring and the drive coil 4, x is the angular frequency of the AC current) in the ring. The 3d harmonics of the response signal in the receive coil is induced by the magnetic field of AC current Ix, Iy flowing in HTS ring 1, when the current in the ring reaches its critical value IC and a nonlinearity of the electric characteristics appears. In the framework of the above equivalent circuit, the currents Ix, Iy, flowing in the ‘‘shoulders’’ of the HTS ring satisfy the following system of equations:
ðL þ Lin Þ
1 dIx xMI1 þ I x Rx þ R0 I 0 ¼ E 0 þ sinðxtÞ; 2 dt 2
ð1Þ
ðL þ Lin Þ
1 dIy xMI1 þ I y Ry þ R0 I 0 ¼ E 0 sinðxtÞ; 2 dt 2
ð2Þ
Ix þ I y ¼ I 0 :
The amplitude of the AC current in the ring is I ¼ MI1 =ðL þ Lin Þ if Rx = Ry = 0 and there is no injected DC current (I0 = 0). The resistances Rx and Ry of the two ‘‘shoulders’’ of the HTS ring arise due to the magnetic flux movement process and can be described as functions of the dimensionless current strengths ix, iy:
Rx ¼ 0:5qFðix Þ; 3. Functioning peculiarities of the structure To elucidate how the DC current passing through the HTS ring affects the generation of the third harmonics of the circulating AC current (which induces the 3-d harmonics of the response signal in the receive coil and is used for determination of IC) the functioning peculiarities of the measuring system (Fig. 1) were analyzed on
ð3Þ
Ry ¼ 0:5qFðiy Þ;
ð4Þ
where ix;y ¼ Ix;y =IC , q is a parameter, IC is the critical current of the superconducting ring. Eqs. (1)–(3) can be transformed to a dimensionless form:
xðL þ Lin Þ dix 1 di0 1 þ ½ix Fðix Þ ði0 ix ÞFði0 ix Þ 2 q ds 2 ds ¼ iF sinðsÞ; xðL þ Lin Þ 1 di0 1 þ ½ix Fðix Þ þ ði0 ix ÞFði0 ix Þ þ 2r0 i0 ¼ 2e0 ; 2 ds 2 q
ð5Þ ð6Þ
where s ¼ xt, i0 ¼ I0 =IC , iF ¼ xMI1 =ðqIC Þ – dimensionless voltage, induced in the ring, r0 ¼ R0 =q, r 0 11. At low frequencies (x/ 2p 6 100 Hz) the following situation may be realistic: xðLex þ Lin Þ=q 1. In this case ix can be determined as a solution of the following nonlinear algebraic equation:
Fig. 2. The equivalent circuit of the sample interacting with the drive coil 4: 2Ld, 2LC – the inductances of the drive coil and the HTS YBCO ring, respectively; Rx + Ry is the YBCO ring resistance.
ix Fðix Þ ði0 ix ÞFði0 ix Þ ¼ iF sinðsÞ;
ð7Þ
iy ¼ i0 ix ;
ð8Þ
where i0 ¼ e0 =r0 . The current–voltage characteristics of HTS materials for different activation regimes of the fluxons can be described by the power law EðJÞ ¼ EC ðJ=J C Þm [18–22], where m is a parameter known as the creep exponent [23,24]. This parameter depends on the activation energy of the fluxons and on the temperature and is valid for the interval 1 6 m < 1. The case m = 1 corresponds to the
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resistive (ohmic) or flux flow regime and m ! 1 – to the Bean model [25]. For this reason the current-dependent part of the resistance of the superconducting film in (1)–(4) can be described by the following expression
Fðix;y Þ ¼ ðix;y Þm ;
ð9Þ
which leads to a zero resistance of the film at ix,y ? 0. In our calculations we used a following slightly modified expression as well
Fðix;y Þ ¼ coshðix;y Þm ;
ð10Þ
which assumes a presence of a small finite value of the resistance of the superconducting film at ix,y ? 0. It can be noted, that the AC magnetic field of the drive coil, affecting the superconducting ring, leads to the arising of a small AC component of the injected current if i0 – 0:
i0 ðsÞ i0 þ di0 ðsÞ; di0 ðsÞ ¼
1 ½ix Fðix Þ þ ði0 ix ÞFði0 ix Þ: 2r 0
ð11Þ
Fig. 4. The current profiles ix(s) (curves 1a–3a) and iy(s) (curves 1b–3b) in the two shoulders of the HTS ring: iF = 0.8; xL/q = 1.2; i0 = 0, 1, 2 (curves 1a and b–3a and b, respectively). Expression (10) with m = 4 was used for the calculations of the current profiles.
ð12Þ
Fig. 3 and 4 illustrate the evolution of the induced AC current profiles ix(s), iy(s) in the superconducting ring with the increasing of the injected DC current intensity i0, obtained as a numerical solution of nonlinear differential equations (5) and (6). It is seen, that the phase, the intensity and the profile of the AC current ix,y induced in the ring by the harmonic external magnetic field, depend strongly on the injected DC current intensity i0 as the DC current affects the resistance and the ratio between the active and inductive components of the complex resistance of the sample. In general, the DC current i0 leads to a decreasing of the variable current intensity in the ring and to a worsening of the screening properties of the superconducting sample with respect to the AC magnetic field. The dependences of the module of the 3-d harmonics of the current ji3 j which circulates in the superconducting ring (Z 2 Z sþ2p 2 )1=2 sþ2p 1 ji3 j ¼ ðix iy Þsinð3sÞds þ ðix iy Þcosð3sÞds 2p s s ð13Þ
Fig. 5. Dependences of the 3-d harmonics of the induced current in the HTS ring on the AC voltage iF, induced in the HTS ring. Calculations were made for xL/q = 1.2, i0 = 0 (curve 1), 0.2 (curve 2), 0.4 (curves 3 and 4), 1 (curve 5), 2 (curve 6). Curve 4 was calculated for a smaller value of the critical current IC1 = 0.95IC. Current dependent part of the resistance was described by expression (9) with m = 6.
on the dimensionless induced voltage iF ¼ xMI1 =ðqIC Þ, calculated numerically from (5) and (6) for different intensities of the injected DC current i0, are shown in Fig. 4. When alternating currents ix, iy flowing across the ring reach their critical value (Figs. 5 and 6, curve 1, calculated for the case i0 = 0, ix = iy), the nonlinearity of the electric characteristics of the ring strongly increases and an intensive
Fig. 6. Dependences of the 3-d harmonics of the induced current in the HTS ring on the AC voltage iF, induced in the HTS ring. Calculations were made for xL/q = 1.2, i0 = 0 (curve 1), 0.2 (curve 2), 0.4 (curves 3 and 4), 1 (curve 5), 2 (curve 6). Curve 4 was calculated for a smaller value of the critical current IC1 = 0.95IC. Current dependent part of the resistance was described by expression (10) with m = 4. Fig. 3. The current profiles ix(s) (curves 1a–3a) and iy(s) (curves 1b–3b) in the two shoulders of the HTS ring: iF = 0.8; xL/q = 1.2; i0 = 0, 1, 2 (curves 1a and b–3a and b, respectively). Expression (9) with m = 6 was used for the calculations of the current profiles.
generation of the third harmonics of the current is started. This leads to a drastic change of the behavior of the response signal
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Ures |i3| induced in the receive coil. The value of iF (Figs. 5 and 6, curve 1), where a maximum nonlinearity of |i3| vs iF dependence is observed, can be used for the determination of the critical current IC of HTS ring when i0 = 0. The injection of a DC current i0 into the superconducting ring causes a shifting of |i3| vs iF dependence towards the left hand side (Figs. 5 and 6, curves 2–6), i.e. to a decreasing of the critical current value IC1, determined by using an AC magnetic field. This decrease is not caused by a change of the spin state of the superconducting charge carriers – the nonlinearity of the electrical characteristics in this case arises at smaller values of iF due to the superposition of the AC current, induced in the ring, and the DC current, injected into the ring. The magnitude of the shift also depends on the current–voltage characteristics of the HTS film (compare Figs. 5 and 6) and it is small when i0 is small. On the other hand, an injection of DC current from a ferromagnetic material (which is characterized with spin polarized charge carriers) into the superconducting ring can provoke a breaking of Cooper pairs and forming a local nonequilibrium state (with a lower critical temperature TC and a critical current density JC) in the superconductor close to the surface of the current injecting electrode. This will cause an additional shifting of |i3| vs iF dependences towards the smaller values of iF. Curves 4 in Figs. 5 and 6 were calculated assuming that the DC current i0 = 0.4 causes a decreasing of IC by 5%. These curves demonstrate summary effects, which are caused by the conventional DC and AC currents superposition effect (see also Fig. 5 and 6, curves 3) and the effect, related to the real change of IC (due, for example, to the pair breaking mechanism). The obtained results allow concluding, that the changes of IC1 caused by both mechanisms can be registered by contactless way and be evaluated easily especially in the case when the sample together with a FM current injecting electrode contains a reference electrode made from the same material as the sample.
4. Experimental results and discussion The dependence of the amplitude of the 3-d harmonics Ures of the response signal on the amplitude I = (M/L)I1 of the screening AC current induced in YBCO samples 1 and 2 by the magnetic field of the driving coil (see the set-up and the sample configurations in Fig. 1) are presented in Figs. 7 and 8, respectively. It can be seen that the amplitude of the third harmonics of the response signal is negligible at small amplitudes of the driving current and it increases drastically when the current in the HTS ring reaches its critical value. The critical currents IC of these samples, were
Fig. 7. Dependence of the 3-d harmonics of the response signal on the amplitude of the screening AC current (M/L)I1 induced in the YBCO ring 1 (completely HTS YBCO structure) by the magnetic field of the driving coil. The injected current intensity I0 is 0 mA (squares), 12 mA (circles) and 20 mA (triangles).
Fig. 8. Dependence of the 3-d harmonics of the response signal on the amplitude of the screening AC current (M/L)I1 induced in the YBCO ring 2 (HTS YBCO structure with LSMO electrode) by the magnetic field of the driving coil. The injected current intensity I0 is 0 mA (squares), 20 mA (circles) and 40 mA (triangles).
0.024 A and 0.23 A, respectively, at the absence of the injected current I0. The DC current injection leads to a shifting of experimental dependences towards the left hand side which is equivalent to a decreasing of the critical current density IC1 (Figs. 7 and 8), determined using alternative current. The change of the DC current polarity did not cause a noticeable change of IC1 in both samples. For the sake of comparison of the experimental results the injected current I0 and the change of such critical current DIC1 = IC IC1 in each sample were expressed in dimensionless forms as I0/IC and DIC1/IC, respectively. The dependence of the dimensionless critical current density on the dimensionless injected current strength for both samples 1 and 2 are presented in Fig. 9. The same figure illustrates the changes of IC1 caused by the DC and AC currents superposition effect, which were calculated on the basis of the model of Bean and the formulas (4)–(13) as well. In theoretical plane, a maximum change of JC1 due to the DC and AC currents superposition effect may be observed in the samples described by the critical state model of Bean (Fig. 9, curve 3), and the changes are smaller for the samples with not very steep current – voltage characteristics (Fig. 9, curves 4 and 5). It can be seen that the effect of a DC current injection on the critical current IC1 is weak for sample 1 (Fig. 9, curve 2) with HTS electrodes. This
Fig. 9. Dependences of the changes in the dimensionless critical current on the dimensionless injected current intensities in samples 1 (closed squares) and 2 (closed circles). The dependences 3–5 – were determined on the basis of the calculation using the model of Bean (curve 3) and formulas (9) (curve 5) and (10) (curve 4) for the current – dependent part of the resistance of the sample. Dependence 6 demonstrates the change of the critical current DIC1/IC in sample 2 caused by the second mechanism (see the text).
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means, that the steepness of the current–voltage characteristics of this sample is low and the injected DC current practically does not cause a change in the spin state of the superconducting charge carriers in this sample. The change of the critical current IC1 of sample 2 with an LSMO electrode, exposed to the DC current injection process, is significantly stronger (Fig. 9, curve 1) than the changes, determined on the basis of the above calculations (Fig. 9, curves 3–5) made by taking into account only the DC and AC current superposition processes. It is reasonable to conclude, that both the conventional DC and AC currents superposition effect (see also Figs. 5 and 6, curves 3) and the modification of the spin state of the charge carriers in the HTS YBCO sample under the action of the DC current, injected from a LSMO electrode, cause the modification of IC1 in this case. The change of the critical current DIC1/IC caused by this second mechanism can be evaluated to be 0.009, 0.016, 0.035 and 0.13 at I0/IC = 0.043, 0.087, 0.13 and 0.174, respectively (Fig. 9, dependence 6), if we assume, that the characteristics of this sample are described by the Bean model. There are several microscopic mechanisms of the coupling at the interface of the HTS/LSMO structure [2,4,5,8,9] which affect the critical parameters of the HTS component. The proximity effect related to the tunneling of Cooper-pairs into the non-superconducting FM side can lead to both, a reduction and an oscillation of the critical temperature of the superconducting part of the heterostructure. On the other hand, the large exchange energy of the magnetic layer prevents Cooper-pairs from tunneling into the LSMO film and this mechanism is less effective [5] for the reduction of the critical parameters of HTS in the structure. There is also an inverse proximity effect, when the spin polarized quasiparticles penetrate into the HTS layer on a certain length scale [1,5] of order 10 nm [5]. According to the results of [5] in the HTS/manganite structure an existence of a long-range inverse magnetic proximity effect which affects the properties of YBCO films up to thicknesses of more than 100 nm is possible as well. The effect is due to the anisotropy of the d-wave parameter, because of which the coherence length tends to approach infinity in the (110) nodal direction of the YBCO Fermi surface. The injected current intensity and polarity affect the effectiveness of the above processes and leads to a modification of the critical parameters of the FM/HTS structure. In the last case changes of the electrical properties of the HTS component are possible if the main part of the quasiparticles in the injected current crosses the interface without ‘‘losing’’ their spin-orientations. The spin-diffusion length in cuprate superconductors is of order 10–20 nm [4] or more in some directions. So, a reduction of TC and JC occur in the same length scale in the HTS component of the structure. The above mechanisms, together with the effect of the superposition of DC and AC currents, provide sensitivity of the critical parameters of the HTS film to the current injection process in FM/HTS structures, as it was observed by contactless way in our experiments. The results allow concluding, that a change of the IC1 caused by both mechanisms can be evaluated separately (especially in the case when the sample together with a FM current injecting electrode contains a reference electrode made from the same material as the sample) and the contactless method can be successfully used for the investigation of the spin-injection effect.
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5. Conclusion The effect of DC current injection on the AC current carrying characteristics of superconducting thin film samples of ring shape were analyzed because of the possibility for using similar ferromagnetic/high temperature superconducting structures for contactless investigation of the spin-injection process. It was shown, that an injection of the DC current leads to decreasing of the critical current value IC1, determined from the response of the HTS ring to the AC magnetic field, due to the superposition effect of AC and DC currents in the sample. If the DC current provokes a breaking of Cooper pairs in the superconductor, this causes an additional decreasing of IC1. The effect was investigated experimentally at 77 K in HTS YBCO and YBCO–LSMO thin film configurations, prepared using magnetron sputtering, conventional photolithography and wet etching procedures. The DC current was injected (from HTS YBCO or ferromagnetic LSMO electrodes) into an HTS YBCO ring and the critical current IC1 was determined from the third harmonics response of the HTS ring to AC magnetic field. The experiments demonstrated a sensitivity of IC1 to the current injection process (especially, in the case of a FM LSMO current-injecting electrode). The results allow concluding, that a change of the IC1 caused by the superposition process of AC and DC currents and by possible Cooper pairs breaking process can be evaluated separately by contactless method and used for investigation of the spin-injection effect.
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