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Penetration and de-pinning of vortices in sub-micrometer Ba(Fe,Co)2As2 thin film bridges
Physica C 479 (2012) 164–166
Contents lists available at SciVerse ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Penetration and de-pinning of vortices in sub-micrometer Ba(Fe,Co)2As2 thin film bridges Dagmar Rall a,⇑, Laura Rehm a, Konstantin Il’in a, Michael Siegel a, Kazumasa Iida b, Silvia Haindl b, Fritz Kurth b, Bernhard Holzapfel b, Ludwig Schultz b, Jie Yong c, Thomas Lemberger c a b c
Institut für Mikro- und Nanoelektronische Systeme (IMS), KIT, Hertzstrasse 16, 76187 Karlsruhe, Germany Institute for Metallic Materials (IMW), IFW Dresden, P.O. Box 270116, 01171 Dresden, Germany Dept. of Physics, The Ohio State University, Columbus, OH 43210, USA
a r t i c l e
i n f o
Article history: Accepted 27 December 2011 Available online 5 January 2012 Keywords: Ferroarsenide Thin film devices Vortex penetration Superconducting transport current
a b s t r a c t For the development of superconducting electronic devices made from iron-arsenide superconductors, thin films have to be patterned into sub-micrometer sized structures while retaining high superconducting transition temperature (TC) and critical current (IC) values. To investigate current transport properties, we structure Ba(Fe,Co)2As2 thin films with and without Fe buffer layers into lm- and sub-lm-bridges and measure the temperature- and field-dependent IC. The process of penetration and de-pinning of selfgenerated and externally excited magnetic vortices in such bridges is discussed. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction The deposition of the novel Fe-based superconductors as very thin but still epitaxial films has principally enabled their application in microfabricated electronic devices like superconducting radiation detectors, cryogenic electronics, quantum interference devices, etc. The properties of the thin films have been studied extensively [1,2]. However, from the application point of view, it is important to consider the effects of transport currents and vortex dynamics that appear in structured samples of a defined width w. For typical electronic devices, the film thickness d is much smaller than the effective thin-film penetration depth k\ = k2/d (k being the London penetration depth), leaving the description essentially two-dimensional. The structure size w, however, is in many cases comparable to k\. In this regime, the sample edges act as Bean–Livingston barriers [3] to the intrusion of vortices. The quality of patterning defines the roughness and defect density at the edges and has direct influence on the current carrying capability of the superconductor. Additionally, the bias current operating the device will exert a force on the vortices, as well as generate a self-field that can cause vortex entry across the barrier. The achievable critical current of the device can in this case be reduced significantly below the depairing critical ⇑ Corresponding author. Address: Institut für Mikro- und Nanoelektronische Systeme, Karlsruher Institut fuer Technologie (KIT), Hertzstrasse 16, Bldg. 06.41, Room 107, 76187 Karlsruhe, Germany. Tel.: +49 (0)721 608 44994; fax: +49 (0)721 757 925. E-mail address: [email protected] (D. Rall). 0921-4534/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2011.12.035
current. To study these influences, we consider simple bridge structures of defined width w and length l that are patterned from a suitably thin pnictide film. One of the iron-based superconductor families that are successfully grown as films with thicknesses below d = 100 nm is the AEFe2As2 (AE alkali earth elements). It shows solid temporal and chemical stability as well as high critical temperature TC (up to 38 K in a hole-doped bulk sample [4], 22 K for electron-doping [5]) and critical current densities jC (up to 4 MA/cm2 for a 250 nm film [6]), making it attractive for device applications. 2. Experiment In this paper, two different sample architectures have been studied: A 50 nm thick Ba(Fe0.9,Co0.1)2As2 film was deposited on an (La,Sr)(Al,Ta)O3 (LSAT) (1 0 0) substrate at 650 °C by pulsed laser deposition from a stoichiometric sintered target. The other film with 100 nm thickness of Ba(Fe0.9,Co0.1)2As2 was deposited on Febuffered (20 nm) MgO (1 0 0) at 700 °C. Application of an Fe buffer has been shown to improve the texture quality of the Ba-122 and thus the superconducting properties of the film [7,8]. In case of the Fe/Ba-122 bilayer, single bridges were fabricated by patterning the Ba(Fe0.9,Co0.1)2As2 film and also the underlying iron buffer layer with standard photolithography and ion-milling techniques. After surface cleaning with acetone and isopropanol, the film was coated with a photoresist layer (320 nm). Afterwards single bridges with designed widths w between 1 and 10 lm and 4 mm2-sized contact pads were patterned using standard contact photolithography. The developed resist is functioning
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3
jc [MA/cm2]
as mask for the following etching process, in which Ar ions accelerated by an applied electric field at U = 250 V removed the non-coated film regions. The resist remained on the Ba-122 surface to protect the bridges from further chemical influences. The Ba-122 film without Fe buffer layer was processed in a similar manner, but with electron-beam lithography using negative ebeam resist. The bridges were in this case structured with widths down to 0.5 lm. The patterned contact pads were bonded with aluminum wires to a four-point measurement setup. The samples are cooled down in a pulse tube cooler fitted with a superconducting magnet coil.
2
3.05 µm 1.68 µm 1.22 µm 0.90 µm
1
3. Results
3 T 2 jC ðTÞ ¼ jC ð0Þ 1 TC
ð1Þ
well for T close to TC (solid line). For T < Tdev, the jC values deviate from this dependency, indicating that the critical current is no longer limited by the depairing of Cooper pairs. Instead it is defined by the penetration and movement of vortices inside the superconducting bridge. Even for the largest bridges, this range of coincidence is relatively wide [9]. As w reduces, the experimental data follow Eq. (1) even further, down to Tdev/TC = 0.37 for the 0.90 lm wide bridge, similar to what has been observed in Nb sub-lm bridges [11]. Thus, at a given temperature T TC, the critical current density is effectively increased by reduction of the sample width. The same reduction can be achieved by application of an external magnetic field normal to the sample surface, indicating that the effect is caused by the self-generated magnetic field of the applied
0 0.0
0.2
0.4
0.6
(1-T/Tc)1.5 Fig. 1. Temperature dependence of the critical current density for several Ba-122 bridges of different width w. The black line is the GL-depairing current from Eq. (1). It coincides well with the data before deviating at T < Tdev, where Tdev is lower for smaller w.
1.5
1.2 µm 3.4 µm 8.4 µm 1.0
2
jc [MA/cm ]
The samples showed a resistive transition that was in both material cases for the bridges with large w only slightly shifted to lower temperatures in respect to the unstructured films. For the wide Ba-122 structures, the half-resistance critical temperature was TC = 21.35 K and the resistive transition width from 10% to 90% of Rn was DT = 2.4–2.8 K (for single crystals: DT = 0.6 K [5]). TC is reduced gradually for narrower bridges as we approach the sub-lm regime, down to 20.2 K for the smallest width, which is due to the proximity effect of the sample edges. The normal state resistivity, taken at T = 25 K, was qn = 301 lX cm. The bridges made from the Fe/Ba-122 bilayer showed a similar behavior, with TC = 20.3 K for the widest bridges and reduced for the narrower ones, and DT = 3.7–4.2 K. The resistivity qn = 98.1 lX cm is much lower due to the current shunting, since the resistivity of Fe is lower than that of Ba(Fe0.9,Co0.1)2As2 in the normal state. The current–voltage characteristics show strong differences between the films with and without Fe buffer layer. In case of the Fe/Ba-122 samples, the superconducting film is in its resistive state short-cut by the iron layer. The transition from the superconducting to the resistive state is in this case not abrupt, but a smooth and non-hysteretic change where each point is in a quasi-equilibrium. This self-stabilizing property may have considerable advantages in applications where the device is operated close to or at the transition. The critical current of the samples was in both cases determined by a voltage threshold slightly above the system noise. At 4.2 K, critical current densities up to 3.22 MA/cm2 were achieved for the films deposited directly on LSAT (similar to the ones presented in [9]). For Fe/Ba-122, 1.71 MA/cm2 are reached, which is comparable to what has been reported for a Fe/Ba-122 bilayer with a relatively wide bridge width of 500 lm [7] and higher than what is reported for bulk single crystals: 0.4 MA/cm2 at 4.2 K [10]. The temperature dependencies of the critical current density jC(T) of Ba(Fe0.9,Co0.1)2As2 on LSAT are shown in Fig. 1 for bridges of several different widths. They follow the Ginzburg–Landau depairing critical current density
0.5
0.0 0.0
0.5
1.0
1.5
2.0
2.5
B [T] Fig. 2. Field-dependent critical current density for B normal to the sample surface, measured at 7.4 K. Three selected Fe/Ba-122 bridges are shown. The data is fit by Eq. (2) for B < B⁄ (solid lines) and Eq. (3) for B > B⁄ (dashed lines).
transport current, which is higher for wider bridges. The fielddependent critical current density jC(B) shows no hysteresis and is symmetric to the magnetic field polarity. At a given temperature, increase of the external magnetic field leads to a weaker initial reduction than observed in single crystals (compare eg Ref. [12]). Similar dependencies on magnetic field have been found for both films, but generally the films without buffer layer show a steeper jC(B) dependence. Fig. 2 shows the jC(B) measurements for the Fe/ Ba-122 bilayers at 7.4 K of three selected bridges. Here, also, the effective critical current density that can be achieved is increased by reduction of the sample width. The reduction of jC by the magnetic field changes in slope, indicating a different vortex entry barrier for the various bridges. 4. Discussion The magnetic penetration depth k has been inductively measured on the Ba-122 film before structuring both with and without iron buffer layer [16]. This results in k(0) 408 nm without Fe buffer layer and 790 nm with the buffer layer. The reason for this big difference is unknown but the 2-D film penetration depth (k = k2/d)
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in both cases are much larger than the film thickness d. The temperature of k in both cases can be well fitted by a small BCS-like gap with D 1.1kBTC [16], which is close to the previous optical studies on these films, and close to values measured on similar films [13]. From the measured temperature dependence of the upper critical field dBC2(T)/dT = 2.06 T/K, similar to the bulk value 2.5 T/K from Ref. [10], we estimate the diffusion coefficient D = 4kB/pe (dBC2/dT)1 = 0.533 cm2/s. With this, BC2(0) in the WHH limit is BC2(0) = 0.69TC dBC2/dT = 31T and the coherence length is determined to be n(0) = 3.3 nm. The corresponding values for the Fe/Ba-122 films are dBC2(T)/dT = 2.64 T/K, BC2(0) = 36.9 T and n(0) = 2.95 nm. For discussion of the field-dependent critical current density of the Fe/Ba-122 films, we follow the theoretical model given in Ref. [14] for thin film strips with dimensions d w 6 k\, typical for superconducting devices. For low magnetic fields 0 6 B 6 B⁄, the current density exceeds the de-pinning current density in the whole bridge and the film is in the Meissner state. The critical current density, for which the bridge undergoes transition to the resistive state, is given by
pffiffiffi 3 2 jC ðBÞ ¼ jC ð0Þð1 þ 6h þ 3 3h Þ;
ð2Þ
where h = pnwB/U0l0. In the case of the Fe/Ba-122 samples, this dependence describes the measurements well up to B⁄ 0.4 T for the 1.2 lm wide bridge, but the deviation from this dependence occurs at different magnetic fields for the different bridges (solid lines in Fig. 2). B⁄ denotes the field at which the mixed state starts to emerge. For a pin-free film, the critical current in the Meissner regime is only defined by the vortex entry at the sample edges, which is when the Ginzburg–Landau depairing current density is reached at the edges of the bridge. However, defects and roughness of the bridge edges can reduce this barrier and allow vortex entry for lower currents. In the absence of pinning, jC(B) has a linear dependence on B [15]. We observe this linear dependence in the magnetic field measurements for temperatures close to TC, i.e. in the regime where the critical current without external magnetic field reaches the depairing value. For B > B⁄, the critical current density is then defined as the current for which the vortices are de-pinned and start to move:
jC ðBÞ ¼ jp þ aðjpb jp Þ2 =2wB
ð3Þ
where a = 2pk\l0/c, jpb is the pair-breaking current density and jp the de-pinning current density. In the limit of a pin-free film or for large enough magnetic fields, the general jC B1 behavior should be observed. However, this regime was not reached in our measurements, indicating a rather strong pinning present in the film. If jp(B) = const is assumed, the data fits well with de-pinning currents jp = 0.18 MA/cm2 for the 8.4 lm wide bridges, rising up to jp = 0.53 MA/cm2 for the narrowest bridge of 1.2 lm (dashed lines in Fig. 2). The field-dependent critical current of the Ba-122 samples without the buffer layer show a similar behavior, with generally stronger reduction of jC with the external magnetic field. This indicates a weaker pinning of the vortices in the material.
5. Conclusion Microbridges and sub-lm bridges of Ba(Fe0.9,Co0.1)2As2 thin films with and without Fe buffer layer have been structured and investigated. In such devices, the depairing limit defines the critical current density in a wide temperature range. For temperatures T TC, the critical current is reduced by vortex penetration and vortex dynamics caused by the transport current generated self field. For both materials, this suppression is reduced if the bridge width w is smaller. For low external magnetic fields, the current is limited by the entry of self-field generated vortices into the bridge. The bridge edges act as barriers for the vortices entering into the strip. As the magnetic field is further increased, the de-pinning and movement of the vortices defines the critical current, with a stronger pinning effect in the iron buffered material. Acknowledgements The work at IMS Karlsruhe is supported in part by the DFG Center for Functional Nanostructures under sub-project A4.3. The work at IFW Dresden was financially supported by the German Research Foundation under Project HA 5934/3-1. The work at Ohio State University is supported by the US Department of Energy, under Grant No. FG02-08ER46533. References [1] S. Mohan, T. Taen, H. Yagyuda, Y. Nakajima, T. Tamegai, T. Katase, H. Hiramatsu, H. Hosono, Supercond. Sci. Technol. 23 (2010) 105016. [2] K. Iida, J. Hänisch, T. Thersleff, F. Kurth, M. Kidszun, S. Haindl, R. Hühne, L. Schultz, B. Holzapfel, Phys. Rev. B 81 (2010) 100507. [3] C.P. Bean, J.D. Livingston, Phys. Rev. Lett. 12 (1964) 14. [4] M. Rotter, M. Tegel, D. Johrendt, Phys. Rev. Lett. 101 (2008) 107006. [5] A.S. Sefat, R. Jin, M.A. McGuire, B.C. Sales, D.J. Singh, D. Mandrus, Phys. Rev. Lett. 101 (2008) 117004. [6] T. Katase, Y. Ishimaru, A. Tsukamoto, H. Hiramatsu, T. Kamiya, K. Tanabe, H. Hosono, Appl. Phys. Lett. 96 (2010) 142507. [7] K. Iida, S. Haindl, T. Thersleff, J. Hänisch, F. Kurth, M. Kidszun, R. Hühne, I. Mönch, L. Schultz, B. Holzapfel, R. Heller, Appl. Phys. Lett. 97 (17) (2010) 172507. [8] T. Thersleff, K. Iida, S. Haindl, M. Kidszun, D. Pohl, A. Hartmann, F. Kurth, J. Hänisch, R. Hühne, B. Rellinghaus, L. Schultz, B. Holzapfel, Appl. Phys. Lett. 97 (2) (2010) 022506. [9] D. Rall, K. Il’in, K. Iida, S. Haindl, F. Kurth, T. Thersleff, L. Schultz, B. Holzapfel, M. Siegel, Phys. Rev. B 83 (13) (2011). [10] A. Yamamoto, J. Jaroszynski, C. Tarantini, L. Balicas, J. Jiang, A. Gurevich, D.C. Larbalestier, R. Jin, A.S. Sefat, M.A. McGuire, B.C. Sales, D.K. Christen, D. Mandrus, Appl. Phys. Lett. 94 (2009) 062511. [11] K. Ilin, D. Rall, M. Siegel, A. Engel, A. Schilling, A. Semenov, H.-W. Hübers, Physica C 470 (2010) 953. [12] S. Lee, J. Jiang, Y. Zhang, C.W. Bark, J.D. Weiss, C. Tarantini, C.T. Nelson, H.W. Jang, C.M. Folkman, S.H. Baek, A. Polyanskii, D. Abraimov, A. Yamamoto, J.W. Park, X.Q. Pan, E.E. Hellstrom, D.C. Larbalestier, C.B. Eom, Nat. Mater. 9 (2010) 397. [13] B. Gorshunov, D. Wu, A.A. Voronkov, P. Kallina, K. Iida, S. Haindl, F. Kurth, L. Schultz, B. Holzapfel, M. Dressel, Phys. Rev. B 81 (2010) 060509. [14] G.M. Maksimova, N.V. Zhelezina, I.L. Maksimov, Europhys. Lett. 53 (5) (2001) 639. [15] B.L.T. Plourde, D.J. Van Harlingen, D.Yu Vodolazov, R. Besseling, M.B.S. Hesselberth, P.H. Kes, Phys. Rev. B 64 (2001) 014503. [16] J. Yong, S. Lee, J. Jiang, C.W. Bark, J.D. Weiss, E.E. Hellstrom, D.C. Larbalestier, C.B. Eom, T.R. Lemberger, Phys. Rev. B 83 (2001) 104510.
Contents lists available at SciVerse ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Penetration and de-pinning of vortices in sub-micrometer Ba(Fe,Co)2As2 thin film bridges Dagmar Rall a,⇑, Laura Rehm a, Konstantin Il’in a, Michael Siegel a, Kazumasa Iida b, Silvia Haindl b, Fritz Kurth b, Bernhard Holzapfel b, Ludwig Schultz b, Jie Yong c, Thomas Lemberger c a b c
Institut für Mikro- und Nanoelektronische Systeme (IMS), KIT, Hertzstrasse 16, 76187 Karlsruhe, Germany Institute for Metallic Materials (IMW), IFW Dresden, P.O. Box 270116, 01171 Dresden, Germany Dept. of Physics, The Ohio State University, Columbus, OH 43210, USA
a r t i c l e
i n f o
Article history: Accepted 27 December 2011 Available online 5 January 2012 Keywords: Ferroarsenide Thin film devices Vortex penetration Superconducting transport current
a b s t r a c t For the development of superconducting electronic devices made from iron-arsenide superconductors, thin films have to be patterned into sub-micrometer sized structures while retaining high superconducting transition temperature (TC) and critical current (IC) values. To investigate current transport properties, we structure Ba(Fe,Co)2As2 thin films with and without Fe buffer layers into lm- and sub-lm-bridges and measure the temperature- and field-dependent IC. The process of penetration and de-pinning of selfgenerated and externally excited magnetic vortices in such bridges is discussed. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction The deposition of the novel Fe-based superconductors as very thin but still epitaxial films has principally enabled their application in microfabricated electronic devices like superconducting radiation detectors, cryogenic electronics, quantum interference devices, etc. The properties of the thin films have been studied extensively [1,2]. However, from the application point of view, it is important to consider the effects of transport currents and vortex dynamics that appear in structured samples of a defined width w. For typical electronic devices, the film thickness d is much smaller than the effective thin-film penetration depth k\ = k2/d (k being the London penetration depth), leaving the description essentially two-dimensional. The structure size w, however, is in many cases comparable to k\. In this regime, the sample edges act as Bean–Livingston barriers [3] to the intrusion of vortices. The quality of patterning defines the roughness and defect density at the edges and has direct influence on the current carrying capability of the superconductor. Additionally, the bias current operating the device will exert a force on the vortices, as well as generate a self-field that can cause vortex entry across the barrier. The achievable critical current of the device can in this case be reduced significantly below the depairing critical ⇑ Corresponding author. Address: Institut für Mikro- und Nanoelektronische Systeme, Karlsruher Institut fuer Technologie (KIT), Hertzstrasse 16, Bldg. 06.41, Room 107, 76187 Karlsruhe, Germany. Tel.: +49 (0)721 608 44994; fax: +49 (0)721 757 925. E-mail address: [email protected] (D. Rall). 0921-4534/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2011.12.035
current. To study these influences, we consider simple bridge structures of defined width w and length l that are patterned from a suitably thin pnictide film. One of the iron-based superconductor families that are successfully grown as films with thicknesses below d = 100 nm is the AEFe2As2 (AE alkali earth elements). It shows solid temporal and chemical stability as well as high critical temperature TC (up to 38 K in a hole-doped bulk sample [4], 22 K for electron-doping [5]) and critical current densities jC (up to 4 MA/cm2 for a 250 nm film [6]), making it attractive for device applications. 2. Experiment In this paper, two different sample architectures have been studied: A 50 nm thick Ba(Fe0.9,Co0.1)2As2 film was deposited on an (La,Sr)(Al,Ta)O3 (LSAT) (1 0 0) substrate at 650 °C by pulsed laser deposition from a stoichiometric sintered target. The other film with 100 nm thickness of Ba(Fe0.9,Co0.1)2As2 was deposited on Febuffered (20 nm) MgO (1 0 0) at 700 °C. Application of an Fe buffer has been shown to improve the texture quality of the Ba-122 and thus the superconducting properties of the film [7,8]. In case of the Fe/Ba-122 bilayer, single bridges were fabricated by patterning the Ba(Fe0.9,Co0.1)2As2 film and also the underlying iron buffer layer with standard photolithography and ion-milling techniques. After surface cleaning with acetone and isopropanol, the film was coated with a photoresist layer (320 nm). Afterwards single bridges with designed widths w between 1 and 10 lm and 4 mm2-sized contact pads were patterned using standard contact photolithography. The developed resist is functioning
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3
jc [MA/cm2]
as mask for the following etching process, in which Ar ions accelerated by an applied electric field at U = 250 V removed the non-coated film regions. The resist remained on the Ba-122 surface to protect the bridges from further chemical influences. The Ba-122 film without Fe buffer layer was processed in a similar manner, but with electron-beam lithography using negative ebeam resist. The bridges were in this case structured with widths down to 0.5 lm. The patterned contact pads were bonded with aluminum wires to a four-point measurement setup. The samples are cooled down in a pulse tube cooler fitted with a superconducting magnet coil.
2
3.05 µm 1.68 µm 1.22 µm 0.90 µm
1
3. Results
3 T 2 jC ðTÞ ¼ jC ð0Þ 1 TC
ð1Þ
well for T close to TC (solid line). For T < Tdev, the jC values deviate from this dependency, indicating that the critical current is no longer limited by the depairing of Cooper pairs. Instead it is defined by the penetration and movement of vortices inside the superconducting bridge. Even for the largest bridges, this range of coincidence is relatively wide [9]. As w reduces, the experimental data follow Eq. (1) even further, down to Tdev/TC = 0.37 for the 0.90 lm wide bridge, similar to what has been observed in Nb sub-lm bridges [11]. Thus, at a given temperature T TC, the critical current density is effectively increased by reduction of the sample width. The same reduction can be achieved by application of an external magnetic field normal to the sample surface, indicating that the effect is caused by the self-generated magnetic field of the applied
0 0.0
0.2
0.4
0.6
(1-T/Tc)1.5 Fig. 1. Temperature dependence of the critical current density for several Ba-122 bridges of different width w. The black line is the GL-depairing current from Eq. (1). It coincides well with the data before deviating at T < Tdev, where Tdev is lower for smaller w.
1.5
1.2 µm 3.4 µm 8.4 µm 1.0
2
jc [MA/cm ]
The samples showed a resistive transition that was in both material cases for the bridges with large w only slightly shifted to lower temperatures in respect to the unstructured films. For the wide Ba-122 structures, the half-resistance critical temperature was TC = 21.35 K and the resistive transition width from 10% to 90% of Rn was DT = 2.4–2.8 K (for single crystals: DT = 0.6 K [5]). TC is reduced gradually for narrower bridges as we approach the sub-lm regime, down to 20.2 K for the smallest width, which is due to the proximity effect of the sample edges. The normal state resistivity, taken at T = 25 K, was qn = 301 lX cm. The bridges made from the Fe/Ba-122 bilayer showed a similar behavior, with TC = 20.3 K for the widest bridges and reduced for the narrower ones, and DT = 3.7–4.2 K. The resistivity qn = 98.1 lX cm is much lower due to the current shunting, since the resistivity of Fe is lower than that of Ba(Fe0.9,Co0.1)2As2 in the normal state. The current–voltage characteristics show strong differences between the films with and without Fe buffer layer. In case of the Fe/Ba-122 samples, the superconducting film is in its resistive state short-cut by the iron layer. The transition from the superconducting to the resistive state is in this case not abrupt, but a smooth and non-hysteretic change where each point is in a quasi-equilibrium. This self-stabilizing property may have considerable advantages in applications where the device is operated close to or at the transition. The critical current of the samples was in both cases determined by a voltage threshold slightly above the system noise. At 4.2 K, critical current densities up to 3.22 MA/cm2 were achieved for the films deposited directly on LSAT (similar to the ones presented in [9]). For Fe/Ba-122, 1.71 MA/cm2 are reached, which is comparable to what has been reported for a Fe/Ba-122 bilayer with a relatively wide bridge width of 500 lm [7] and higher than what is reported for bulk single crystals: 0.4 MA/cm2 at 4.2 K [10]. The temperature dependencies of the critical current density jC(T) of Ba(Fe0.9,Co0.1)2As2 on LSAT are shown in Fig. 1 for bridges of several different widths. They follow the Ginzburg–Landau depairing critical current density
0.5
0.0 0.0
0.5
1.0
1.5
2.0
2.5
B [T] Fig. 2. Field-dependent critical current density for B normal to the sample surface, measured at 7.4 K. Three selected Fe/Ba-122 bridges are shown. The data is fit by Eq. (2) for B < B⁄ (solid lines) and Eq. (3) for B > B⁄ (dashed lines).
transport current, which is higher for wider bridges. The fielddependent critical current density jC(B) shows no hysteresis and is symmetric to the magnetic field polarity. At a given temperature, increase of the external magnetic field leads to a weaker initial reduction than observed in single crystals (compare eg Ref. [12]). Similar dependencies on magnetic field have been found for both films, but generally the films without buffer layer show a steeper jC(B) dependence. Fig. 2 shows the jC(B) measurements for the Fe/ Ba-122 bilayers at 7.4 K of three selected bridges. Here, also, the effective critical current density that can be achieved is increased by reduction of the sample width. The reduction of jC by the magnetic field changes in slope, indicating a different vortex entry barrier for the various bridges. 4. Discussion The magnetic penetration depth k has been inductively measured on the Ba-122 film before structuring both with and without iron buffer layer [16]. This results in k(0) 408 nm without Fe buffer layer and 790 nm with the buffer layer. The reason for this big difference is unknown but the 2-D film penetration depth (k = k2/d)
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in both cases are much larger than the film thickness d. The temperature of k in both cases can be well fitted by a small BCS-like gap with D 1.1kBTC [16], which is close to the previous optical studies on these films, and close to values measured on similar films [13]. From the measured temperature dependence of the upper critical field dBC2(T)/dT = 2.06 T/K, similar to the bulk value 2.5 T/K from Ref. [10], we estimate the diffusion coefficient D = 4kB/pe (dBC2/dT)1 = 0.533 cm2/s. With this, BC2(0) in the WHH limit is BC2(0) = 0.69TC dBC2/dT = 31T and the coherence length is determined to be n(0) = 3.3 nm. The corresponding values for the Fe/Ba-122 films are dBC2(T)/dT = 2.64 T/K, BC2(0) = 36.9 T and n(0) = 2.95 nm. For discussion of the field-dependent critical current density of the Fe/Ba-122 films, we follow the theoretical model given in Ref. [14] for thin film strips with dimensions d w 6 k\, typical for superconducting devices. For low magnetic fields 0 6 B 6 B⁄, the current density exceeds the de-pinning current density in the whole bridge and the film is in the Meissner state. The critical current density, for which the bridge undergoes transition to the resistive state, is given by
pffiffiffi 3 2 jC ðBÞ ¼ jC ð0Þð1 þ 6h þ 3 3h Þ;
ð2Þ
where h = pnwB/U0l0. In the case of the Fe/Ba-122 samples, this dependence describes the measurements well up to B⁄ 0.4 T for the 1.2 lm wide bridge, but the deviation from this dependence occurs at different magnetic fields for the different bridges (solid lines in Fig. 2). B⁄ denotes the field at which the mixed state starts to emerge. For a pin-free film, the critical current in the Meissner regime is only defined by the vortex entry at the sample edges, which is when the Ginzburg–Landau depairing current density is reached at the edges of the bridge. However, defects and roughness of the bridge edges can reduce this barrier and allow vortex entry for lower currents. In the absence of pinning, jC(B) has a linear dependence on B [15]. We observe this linear dependence in the magnetic field measurements for temperatures close to TC, i.e. in the regime where the critical current without external magnetic field reaches the depairing value. For B > B⁄, the critical current density is then defined as the current for which the vortices are de-pinned and start to move:
jC ðBÞ ¼ jp þ aðjpb jp Þ2 =2wB
ð3Þ
where a = 2pk\l0/c, jpb is the pair-breaking current density and jp the de-pinning current density. In the limit of a pin-free film or for large enough magnetic fields, the general jC B1 behavior should be observed. However, this regime was not reached in our measurements, indicating a rather strong pinning present in the film. If jp(B) = const is assumed, the data fits well with de-pinning currents jp = 0.18 MA/cm2 for the 8.4 lm wide bridges, rising up to jp = 0.53 MA/cm2 for the narrowest bridge of 1.2 lm (dashed lines in Fig. 2). The field-dependent critical current of the Ba-122 samples without the buffer layer show a similar behavior, with generally stronger reduction of jC with the external magnetic field. This indicates a weaker pinning of the vortices in the material.
5. Conclusion Microbridges and sub-lm bridges of Ba(Fe0.9,Co0.1)2As2 thin films with and without Fe buffer layer have been structured and investigated. In such devices, the depairing limit defines the critical current density in a wide temperature range. For temperatures T TC, the critical current is reduced by vortex penetration and vortex dynamics caused by the transport current generated self field. For both materials, this suppression is reduced if the bridge width w is smaller. For low external magnetic fields, the current is limited by the entry of self-field generated vortices into the bridge. The bridge edges act as barriers for the vortices entering into the strip. As the magnetic field is further increased, the de-pinning and movement of the vortices defines the critical current, with a stronger pinning effect in the iron buffered material. Acknowledgements The work at IMS Karlsruhe is supported in part by the DFG Center for Functional Nanostructures under sub-project A4.3. The work at IFW Dresden was financially supported by the German Research Foundation under Project HA 5934/3-1. The work at Ohio State University is supported by the US Department of Energy, under Grant No. FG02-08ER46533. References [1] S. Mohan, T. Taen, H. Yagyuda, Y. Nakajima, T. Tamegai, T. Katase, H. Hiramatsu, H. Hosono, Supercond. Sci. Technol. 23 (2010) 105016. [2] K. Iida, J. Hänisch, T. Thersleff, F. Kurth, M. Kidszun, S. Haindl, R. Hühne, L. Schultz, B. Holzapfel, Phys. Rev. B 81 (2010) 100507. [3] C.P. Bean, J.D. Livingston, Phys. Rev. Lett. 12 (1964) 14. [4] M. Rotter, M. Tegel, D. Johrendt, Phys. Rev. Lett. 101 (2008) 107006. [5] A.S. Sefat, R. Jin, M.A. McGuire, B.C. Sales, D.J. Singh, D. Mandrus, Phys. Rev. Lett. 101 (2008) 117004. [6] T. Katase, Y. Ishimaru, A. Tsukamoto, H. Hiramatsu, T. Kamiya, K. Tanabe, H. Hosono, Appl. Phys. Lett. 96 (2010) 142507. [7] K. Iida, S. Haindl, T. Thersleff, J. Hänisch, F. Kurth, M. Kidszun, R. Hühne, I. Mönch, L. Schultz, B. Holzapfel, R. Heller, Appl. Phys. Lett. 97 (17) (2010) 172507. [8] T. Thersleff, K. Iida, S. Haindl, M. Kidszun, D. Pohl, A. Hartmann, F. Kurth, J. Hänisch, R. Hühne, B. Rellinghaus, L. Schultz, B. Holzapfel, Appl. Phys. Lett. 97 (2) (2010) 022506. [9] D. Rall, K. Il’in, K. Iida, S. Haindl, F. Kurth, T. Thersleff, L. Schultz, B. Holzapfel, M. Siegel, Phys. Rev. B 83 (13) (2011). [10] A. Yamamoto, J. Jaroszynski, C. Tarantini, L. Balicas, J. Jiang, A. Gurevich, D.C. Larbalestier, R. Jin, A.S. Sefat, M.A. McGuire, B.C. Sales, D.K. Christen, D. Mandrus, Appl. Phys. Lett. 94 (2009) 062511. [11] K. Ilin, D. Rall, M. Siegel, A. Engel, A. Schilling, A. Semenov, H.-W. Hübers, Physica C 470 (2010) 953. [12] S. Lee, J. Jiang, Y. Zhang, C.W. Bark, J.D. Weiss, C. Tarantini, C.T. Nelson, H.W. Jang, C.M. Folkman, S.H. Baek, A. Polyanskii, D. Abraimov, A. Yamamoto, J.W. Park, X.Q. Pan, E.E. Hellstrom, D.C. Larbalestier, C.B. Eom, Nat. Mater. 9 (2010) 397. [13] B. Gorshunov, D. Wu, A.A. Voronkov, P. Kallina, K. Iida, S. Haindl, F. Kurth, L. Schultz, B. Holzapfel, M. Dressel, Phys. Rev. B 81 (2010) 060509. [14] G.M. Maksimova, N.V. Zhelezina, I.L. Maksimov, Europhys. Lett. 53 (5) (2001) 639. [15] B.L.T. Plourde, D.J. Van Harlingen, D.Yu Vodolazov, R. Besseling, M.B.S. Hesselberth, P.H. Kes, Phys. Rev. B 64 (2001) 014503. [16] J. Yong, S. Lee, J. Jiang, C.W. Bark, J.D. Weiss, E.E. Hellstrom, D.C. Larbalestier, C.B. Eom, T.R. Lemberger, Phys. Rev. B 83 (2001) 104510.