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Upper critical fields in as-grown MgB2 films prepared by ultra-high-vacuum MBE
Physica C 463–465 (2007) 216–219 www.elsevier.com/locate/physc
Upper critical fields in as-grown MgB2 films prepared by ultra-high-vacuum MBE S. Noguchi
a,b,c,*
, A. Kuribayashi a,c, T. Oba d, H. Iriuda d, Y. Harada e, M. Yoshizawa d,e, T. Ishida a,b,c
a
b
Department of Physics and Electronics, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan Institute for Nanofabrication Research, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan c CREST, Japan Science and Technology Agency, 4-1-8, Honcho, Kawaguchi, Saitama 332-0012, Japan d Graduate School of Engineering, Iwate University, 4-3-5 Ueda, Morioka, Iwate 020-8551, Japan e JST Satellite Iwate, 3-35-2 Iioka-shinden, Morioka, Iwate 020-0852, Japan Accepted 6 March 2007 Available online 24 May 2007
Abstract We report on the upper critical fields (Hc2’s) of as-grown MgB2 thin films deposited on the epitaxial Ti buffer layer on c-plane ZnO substrates by using a molecular beam epitaxy (MBE) apparatus. The Hc2 was estimated from the magnetoresistance measurements under the pulsed magnetic field up to 37 T. Hc2(T) for both H k ab-plane and H k c-axis were measured to obtain the anisotropic superconducting properties. The results are successfully analyzed with the Gurevich theory of dirty two-gap superconductivity with a cleaner p band case. Ó 2007 Published by Elsevier B.V. PACS: 74.25.Dw; 74.70.Ad; 74.78.w Keywords: MgB2 thin films; Upper critical field; Anisotropy; Gurevich theory
1. Introduction MgB2 has attracted much attention not only to the highest superconducting transition temperature Tc among intermetallic superconductors but also to the physics of two-gap superconductivity [1]. There are two weakly coupled superconducting gaps in a two-dimensional r band and a three-dimensional p band of boron orbitals. So, there are multiple impurity scattering for each of the r and p intraband and the interband scattering. On the upper critical field Hc2, a significant enhancement and anomalous *
Corresponding author. Address: Department of Physics and Electronics, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan. Tel.: +81 72 254 9262; fax: +81 72 254 9908. E-mail address: [email protected] (S. Noguchi). 0921-4534/$ - see front matter Ó 2007 Published by Elsevier B.V. doi:10.1016/j.physc.2007.03.446
temperature dependence have been reported in thin films or disordered bulk samples so far [2–7]. Recently, the temperature dependence of Hc2(T) and the orientational dependence of Hc2(h) have been calculated for two-band superconductors in the dirty limit on the basis of the two-gap Usadel equations in which the intraband electron diffusivities Dr and Dp and intra- and interband coupling constants kmm0 ðm; m0 ¼ r; pÞ are introduced [8,9]. We have measured the magnetoresistance of the MgB2 thin films prepared by sputtering method [5] and molecular beam epitaxy (MBE) [6] under the high magnetic fields up to 37 T and obtained the whole region of the Hc2(T) phase diagram. In this report, we present the experimental and calculated results of the Hc2(T) for H k ab-plane and H k c-axis of the MgB2 thin films deposited on Ti buffered c-plane ZnO substrates by using the ultra-high-vacuum MBE apparatus.
S. Noguchi et al. / Physica C 463–465 (2007) 216–219
2. Experimental MgB2 films were deposited on Ti buffer layers on ZnO(0 0 0 1) substrates at 200 °C without post annealing process by using an MBE method with the co-evaporation conditions of low deposition rate in ultra-high-vacuum [10]. The film thickness is 200 nm. The structure and crystallinity were characterized by X-ray diffraction. It reveals that the MgB2 films have well oriented to the c-axis. Magnetoresistance measurements were performed with dc fourterminal method for two MgB2 films whose difference is the thickness of the Ti buffer layers denoted to #Ti(10 nm) and #Ti(50 nm). Magnetic fields are applied up to 37 T using a home-made pulsed-magnet system for the H k ab-plane and H k c-axis at several temperatures below Tc down to 1.8 K. 3. Results Fig. 1 shows the magnetoresistance curves of the MgB2 film #Ti(10 nm) at several temperatures from 1.5 to 31 K for the H k ab-plane and H k c-axis. No hysteresis is
217
observed. The normal-state resistivity for the #Ti(10 nm) and #Ti(50 nm) films are 40 and 4 lX cm, respectively. The Hc2’s were defined as the midpoint of the resistive transition and the transition widths were defined as the fields between 10% and 90% of the normal resistance. Thus obtained Hc2(T) phase diagrams for two samples are shown in Fig. 2. Tc is 32 K for the #Ti(10 nm) film and 38 K for the #Ti(50 nm) film. As for #Ti(10 nm), relatively large slopes of the Hc2(T) curves are recognized at around 30 K for both the field directions H k ab and H k c. The value of the H ab c2 ð0Þ attains to 39 T. On the other hand, the #Ti(50 nm) film has relative low Hc2 values with small slope of the Hc2(T) curves for both direction H k ab and H k c. For comparison the Hc2 data for single crystal [11] are drawn by dashed lines in the figure. The Hc2 for #Ti(50 nm) takes a middle position between that for #Ti(10 nm) and the single crystal. Namely, the #Ti(50 nm) film is much cleaner than the #Ti(10 nm) film as discussed later. Superconducting anisotropy parameter c defined as c H ab c2 =H c2 was obtained as a function of temperature as 40 #Ti(10nm) #Ti(50nm) single crystal
μ0Hc2ab (T)
30
20
10
0
0
10
20
30
40
T (K) 20
μ 0 Hc2c (T)
#Ti(10nm) #Ti(50nm) single crystal
10
0 0
10
20
30
40
T (K) Fig. 1. Magnetoresistance curves of the MgB2 film #Ti(10 nm) at several temperatures for (a) H k ab-plane and (b) H k c-axis. The Hc2 is defined as the midpoint of the resistive transition.
Fig. 2. Hc2(T) curves of two MgB2 films #Ti(10 nm) and #Ti(50 nm) for (a) H k ab-plane and (b) H k c-axis. Solid lines are calculation curves by the Gurevich theory. Dashed lines are the data for MgB2 single crystal [11] for comparison.
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2.5
1
Hc2 / Hc2(0)
ab
c
γ (=Hc2 /Hc2 )
2
1.5
1
0.5
0
Dπ/Dσ = 100 Dπ/Dσ = 1 Dπ/Dσ = 0.2 Dπ/Dσ = 0.1 experiment
0.8
#Ti(10 nm) #Ti(50 nm)
0.6
0.4
0.2
10
20
0 0
30
0.2
0.4
T (K) Fig. 3. Superconducting anisotropy parameter c for MgB2 films #Ti(10 nm) and #Ti(50 nm). Solid lines are calculation curves.
1
1 Dπ/Dσ = 10 Dπ/Dσ = 100 experiment
Hc2 / Hc2(0)
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
T / Tc 1 Dπ/Dσ = 0.1 Dπ/Dσ = 0.2 experiment
0.8
Hc2 / Hc2(0)
Experimentally obtained data of the Hc2(T) and c were analyzed by fitting the Gurevich theory [8] based on twogap Usadel equations in which impurity scattering is introduced as the intraband electron diffusivities Dr and Dp for the r and p bands, respectively. Although the #Ti(50 nm) film is located at the boundary between the dirty and the clean limit judging from the normal-state resistivity, this calculation is still effective because the significant enhancement of the Hc2(T) compared to the data of a single crystal is observed as shown in Fig. 2. In the calculation, four superconducting coupling constants krr, krp, kpr and kpp are also the parameters, which are fixed to be 0.81, 0.119, 0.09 and 0.285, respectively in the Gurevich paper [8]. We calculated the Hc2 curve for different values of Dp/Dr as shown in Fig. 4 with the experimental data normalized by Tc and the Hc2(0). Fitting between the experimental data and calculation is not so good in the whole H T region. Then, we varied the coupling constants krp and kpr simultaneously, by multiplying a factor with keeping the ratio of krp/kpr = 1.3 as described in Ref. [8]. The results are shown in Fig. 5, where the simulation with three times larger krp and kpr with Dp/Dr = 10 gave the best fitting to the experimental data. Therefore, we used four superconducting coupling constants krr = 0.81, krp = 0.357, kpr = 0.27 and kpp = 0.285 in contrast to the Gurevich paper. Golubov et al. have also deduced the coupling constants krr = 1.017, krp = 0.448, kpr = 0.213 and kpp = 0.155 from first-principles calculations for two-band model [12]. Therefore, the values used in this fitting are acceptable. In this way, the best fits to the experimental data of the
0.8
Fig. 4. Calculated curves for Hc2(T) with different values of Dp/Dr. Experimental data of the #Ti(10 nm) film for H k ab-plane are plotted by open circles.
shown in Fig. 3. c(T = 0) for the #Ti(10 nm) film is 2, while that for the #Ti(50 nm) film is higher value of 2.25. With increasing temperature the c values decrease for both films. This is a basis for determining the ratio of the diffusion constant for r and p band. 4. Analysis
0.6
T / Tc
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
T / Tc Fig. 5. Calculated curves for Hc2(T) with fixed values of (a) Dp/Dr = 10 (solid lines) and 100 (dashed lines) and (b) Dp/Dr = 0.1 (solid lines) and 0.2 (dashed lines). Varying parameters are krp and kpr by multiplying factors of 1, 2, 3 and 4 corresponding to the curves from upper-right to lower-left. Experimental data of the #Ti(10 nm) film for H k ab-plane are plotted by open circles.
S. Noguchi et al. / Physica C 463–465 (2007) 216–219
Hc2(T) and c(T) were obtained as shown in Figs. 2 and 3, respectively drawn by solid lines. Fitting parameters are Dp/Dr = 4 for #Ti(10 nm) and 5 for #Ti(50 nm). The results for the MgB2 films deposited on the Ti buffered ZnO substrates show the case of Dp/Dr > 1, which means the films have the cleaner p band than the r band. Since the absolute values of diffusion constants are in inverse proportion to Hc2(0), the #Ti(50 nm) film has much larger Dr and Dp values, namely it is much cleaner than the #Ti(10 nm) film although the ratio Dp/Dr is not so different. The #Ti(50 nm) film shows excellent orientation in ab-plane as well as c-axis orientation from the X-ray / scan measurements of the (1 1 2) peak [13]. This is consistently confirmed from the Hc2 measurements. 5. Conclusion We report on the Hc2’s of the as-grown MgB2 thin films prepared by using an MBE apparatus on ZnO substrates with different Ti buffer layer thicknesses. Hc2(T) for both H k ab-plane and H k c-axis were measured to obtain the anisotropic superconducting properties. The results are well described by the Gurevich theory of dirty two-gap superconductivity with a cleaner p band. References [1] A.Y. Liu, I.I. Mazin, J. Kortus, Phys. Rev. Lett. 87 (2001) 087005.
219
[2] M.H. Jung, M. Jaime, A.H. Lacerda, G.S. Boebinger, W.N. Kang, H.J. Kim, E.M. Choi, S.I. Lee, Chem. Phys. Lett. 343 (2001) 447. [3] V. Ferrando, P. Manfrinetti, D. Marre, M. Putti, I. Sheikin, C. Tarantini, C. Ferdeghini, Phys. Rev. B 68 (2003) 094517. [4] A. Gurevich, S. Patnaik, V. Braccini, K.H. Kim, C. Mielke, X. Song, L.D. Cooley, S.D. Bu, D.M. Kim, J.H. Choi, L.J. Belenky, J. Giencke, M.K. Lee, W. Tian, X.Q. Pan, A. Siri, E.E. Hellstrom, C.B. Eom, D.C. Larbalestier, Supercond. Sci. Technol. 17 (2004) 278. [5] S. Noguchi, S. Miki, H. Shimakage, Z. Wang, K. Satoh, T. Yotsuya, T. Ishida, Physica C 426–431 (2005) 1449. [6] T. Oba, P. Sun, Y. Harada, T. Takahashi, H. Iriuda, M. Seki, Y. Nakanishi, S. Noguchi, T. Ishida, M. Yoshizawa, J. Magn. Magn. Mater. 310 (2007) e107. [7] V. Braccini, A. Gurevich, J.E. Giencke, M.C. Jewell, C.B. Eom, D.C. Larbalestier, A. Pogrebnyakov, Y. Cui, B.T. Liu, Y.F. Hu, J.M. Redwing, Qi Li, X.X. Xi, R.K. Singh, R. Gandikota, J. Kim, B. Wilkens, N. Newman, J. Rowell, R. Moeckly, V. Ferrando, C. Tarantini, D. Marre, M. Putti, C. Ferdeghini, R. Vaglio, E. Haanappel, Phys. Rev. B 71 (2005) 012504. [8] A. Gurevich, Phys. Rev. B 67 (2003) 184515. [9] A.A. Golubov, A.E. Koshelev, Phys. Rev. B 68 (2003) 104503. [10] Y. Harada, M. Uduka, Y. Nakanishi, N. Yoshimoto, M. Yoshizawa, Physica C 412–414 (2004) 1383. [11] L. Lyard, P. Samuely, P. Szabo, T. Klein, C. Marcenat, L. Paulius, K.H.P. Kim, C.U. Jung, H.-S. Lee, Phys. Rev. B 66 (2002) 180502. [12] A.A. Golubov, J. Kortus, O.V. Dolgov, O. Jepsen, Y. Kong, O.K. Andersen, B.J. Gibson, K. Ahn, R.K. Kremer, J. Phys.: Conden. Matter 14 (2002) 1353. [13] Y. Harada, H. Iriuda, T. Oba, H. Endo, S. Goto, M. Yoshizawa, private communication.
Upper critical fields in as-grown MgB2 films prepared by ultra-high-vacuum MBE S. Noguchi
a,b,c,*
, A. Kuribayashi a,c, T. Oba d, H. Iriuda d, Y. Harada e, M. Yoshizawa d,e, T. Ishida a,b,c
a
b
Department of Physics and Electronics, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan Institute for Nanofabrication Research, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan c CREST, Japan Science and Technology Agency, 4-1-8, Honcho, Kawaguchi, Saitama 332-0012, Japan d Graduate School of Engineering, Iwate University, 4-3-5 Ueda, Morioka, Iwate 020-8551, Japan e JST Satellite Iwate, 3-35-2 Iioka-shinden, Morioka, Iwate 020-0852, Japan Accepted 6 March 2007 Available online 24 May 2007
Abstract We report on the upper critical fields (Hc2’s) of as-grown MgB2 thin films deposited on the epitaxial Ti buffer layer on c-plane ZnO substrates by using a molecular beam epitaxy (MBE) apparatus. The Hc2 was estimated from the magnetoresistance measurements under the pulsed magnetic field up to 37 T. Hc2(T) for both H k ab-plane and H k c-axis were measured to obtain the anisotropic superconducting properties. The results are successfully analyzed with the Gurevich theory of dirty two-gap superconductivity with a cleaner p band case. Ó 2007 Published by Elsevier B.V. PACS: 74.25.Dw; 74.70.Ad; 74.78.w Keywords: MgB2 thin films; Upper critical field; Anisotropy; Gurevich theory
1. Introduction MgB2 has attracted much attention not only to the highest superconducting transition temperature Tc among intermetallic superconductors but also to the physics of two-gap superconductivity [1]. There are two weakly coupled superconducting gaps in a two-dimensional r band and a three-dimensional p band of boron orbitals. So, there are multiple impurity scattering for each of the r and p intraband and the interband scattering. On the upper critical field Hc2, a significant enhancement and anomalous *
Corresponding author. Address: Department of Physics and Electronics, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan. Tel.: +81 72 254 9262; fax: +81 72 254 9908. E-mail address: [email protected] (S. Noguchi). 0921-4534/$ - see front matter Ó 2007 Published by Elsevier B.V. doi:10.1016/j.physc.2007.03.446
temperature dependence have been reported in thin films or disordered bulk samples so far [2–7]. Recently, the temperature dependence of Hc2(T) and the orientational dependence of Hc2(h) have been calculated for two-band superconductors in the dirty limit on the basis of the two-gap Usadel equations in which the intraband electron diffusivities Dr and Dp and intra- and interband coupling constants kmm0 ðm; m0 ¼ r; pÞ are introduced [8,9]. We have measured the magnetoresistance of the MgB2 thin films prepared by sputtering method [5] and molecular beam epitaxy (MBE) [6] under the high magnetic fields up to 37 T and obtained the whole region of the Hc2(T) phase diagram. In this report, we present the experimental and calculated results of the Hc2(T) for H k ab-plane and H k c-axis of the MgB2 thin films deposited on Ti buffered c-plane ZnO substrates by using the ultra-high-vacuum MBE apparatus.
S. Noguchi et al. / Physica C 463–465 (2007) 216–219
2. Experimental MgB2 films were deposited on Ti buffer layers on ZnO(0 0 0 1) substrates at 200 °C without post annealing process by using an MBE method with the co-evaporation conditions of low deposition rate in ultra-high-vacuum [10]. The film thickness is 200 nm. The structure and crystallinity were characterized by X-ray diffraction. It reveals that the MgB2 films have well oriented to the c-axis. Magnetoresistance measurements were performed with dc fourterminal method for two MgB2 films whose difference is the thickness of the Ti buffer layers denoted to #Ti(10 nm) and #Ti(50 nm). Magnetic fields are applied up to 37 T using a home-made pulsed-magnet system for the H k ab-plane and H k c-axis at several temperatures below Tc down to 1.8 K. 3. Results Fig. 1 shows the magnetoresistance curves of the MgB2 film #Ti(10 nm) at several temperatures from 1.5 to 31 K for the H k ab-plane and H k c-axis. No hysteresis is
217
observed. The normal-state resistivity for the #Ti(10 nm) and #Ti(50 nm) films are 40 and 4 lX cm, respectively. The Hc2’s were defined as the midpoint of the resistive transition and the transition widths were defined as the fields between 10% and 90% of the normal resistance. Thus obtained Hc2(T) phase diagrams for two samples are shown in Fig. 2. Tc is 32 K for the #Ti(10 nm) film and 38 K for the #Ti(50 nm) film. As for #Ti(10 nm), relatively large slopes of the Hc2(T) curves are recognized at around 30 K for both the field directions H k ab and H k c. The value of the H ab c2 ð0Þ attains to 39 T. On the other hand, the #Ti(50 nm) film has relative low Hc2 values with small slope of the Hc2(T) curves for both direction H k ab and H k c. For comparison the Hc2 data for single crystal [11] are drawn by dashed lines in the figure. The Hc2 for #Ti(50 nm) takes a middle position between that for #Ti(10 nm) and the single crystal. Namely, the #Ti(50 nm) film is much cleaner than the #Ti(10 nm) film as discussed later. Superconducting anisotropy parameter c defined as c H ab c2 =H c2 was obtained as a function of temperature as 40 #Ti(10nm) #Ti(50nm) single crystal
μ0Hc2ab (T)
30
20
10
0
0
10
20
30
40
T (K) 20
μ 0 Hc2c (T)
#Ti(10nm) #Ti(50nm) single crystal
10
0 0
10
20
30
40
T (K) Fig. 1. Magnetoresistance curves of the MgB2 film #Ti(10 nm) at several temperatures for (a) H k ab-plane and (b) H k c-axis. The Hc2 is defined as the midpoint of the resistive transition.
Fig. 2. Hc2(T) curves of two MgB2 films #Ti(10 nm) and #Ti(50 nm) for (a) H k ab-plane and (b) H k c-axis. Solid lines are calculation curves by the Gurevich theory. Dashed lines are the data for MgB2 single crystal [11] for comparison.
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S. Noguchi et al. / Physica C 463–465 (2007) 216–219
2.5
1
Hc2 / Hc2(0)
ab
c
γ (=Hc2 /Hc2 )
2
1.5
1
0.5
0
Dπ/Dσ = 100 Dπ/Dσ = 1 Dπ/Dσ = 0.2 Dπ/Dσ = 0.1 experiment
0.8
#Ti(10 nm) #Ti(50 nm)
0.6
0.4
0.2
10
20
0 0
30
0.2
0.4
T (K) Fig. 3. Superconducting anisotropy parameter c for MgB2 films #Ti(10 nm) and #Ti(50 nm). Solid lines are calculation curves.
1
1 Dπ/Dσ = 10 Dπ/Dσ = 100 experiment
Hc2 / Hc2(0)
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
T / Tc 1 Dπ/Dσ = 0.1 Dπ/Dσ = 0.2 experiment
0.8
Hc2 / Hc2(0)
Experimentally obtained data of the Hc2(T) and c were analyzed by fitting the Gurevich theory [8] based on twogap Usadel equations in which impurity scattering is introduced as the intraband electron diffusivities Dr and Dp for the r and p bands, respectively. Although the #Ti(50 nm) film is located at the boundary between the dirty and the clean limit judging from the normal-state resistivity, this calculation is still effective because the significant enhancement of the Hc2(T) compared to the data of a single crystal is observed as shown in Fig. 2. In the calculation, four superconducting coupling constants krr, krp, kpr and kpp are also the parameters, which are fixed to be 0.81, 0.119, 0.09 and 0.285, respectively in the Gurevich paper [8]. We calculated the Hc2 curve for different values of Dp/Dr as shown in Fig. 4 with the experimental data normalized by Tc and the Hc2(0). Fitting between the experimental data and calculation is not so good in the whole H T region. Then, we varied the coupling constants krp and kpr simultaneously, by multiplying a factor with keeping the ratio of krp/kpr = 1.3 as described in Ref. [8]. The results are shown in Fig. 5, where the simulation with three times larger krp and kpr with Dp/Dr = 10 gave the best fitting to the experimental data. Therefore, we used four superconducting coupling constants krr = 0.81, krp = 0.357, kpr = 0.27 and kpp = 0.285 in contrast to the Gurevich paper. Golubov et al. have also deduced the coupling constants krr = 1.017, krp = 0.448, kpr = 0.213 and kpp = 0.155 from first-principles calculations for two-band model [12]. Therefore, the values used in this fitting are acceptable. In this way, the best fits to the experimental data of the
0.8
Fig. 4. Calculated curves for Hc2(T) with different values of Dp/Dr. Experimental data of the #Ti(10 nm) film for H k ab-plane are plotted by open circles.
shown in Fig. 3. c(T = 0) for the #Ti(10 nm) film is 2, while that for the #Ti(50 nm) film is higher value of 2.25. With increasing temperature the c values decrease for both films. This is a basis for determining the ratio of the diffusion constant for r and p band. 4. Analysis
0.6
T / Tc
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
T / Tc Fig. 5. Calculated curves for Hc2(T) with fixed values of (a) Dp/Dr = 10 (solid lines) and 100 (dashed lines) and (b) Dp/Dr = 0.1 (solid lines) and 0.2 (dashed lines). Varying parameters are krp and kpr by multiplying factors of 1, 2, 3 and 4 corresponding to the curves from upper-right to lower-left. Experimental data of the #Ti(10 nm) film for H k ab-plane are plotted by open circles.
S. Noguchi et al. / Physica C 463–465 (2007) 216–219
Hc2(T) and c(T) were obtained as shown in Figs. 2 and 3, respectively drawn by solid lines. Fitting parameters are Dp/Dr = 4 for #Ti(10 nm) and 5 for #Ti(50 nm). The results for the MgB2 films deposited on the Ti buffered ZnO substrates show the case of Dp/Dr > 1, which means the films have the cleaner p band than the r band. Since the absolute values of diffusion constants are in inverse proportion to Hc2(0), the #Ti(50 nm) film has much larger Dr and Dp values, namely it is much cleaner than the #Ti(10 nm) film although the ratio Dp/Dr is not so different. The #Ti(50 nm) film shows excellent orientation in ab-plane as well as c-axis orientation from the X-ray / scan measurements of the (1 1 2) peak [13]. This is consistently confirmed from the Hc2 measurements. 5. Conclusion We report on the Hc2’s of the as-grown MgB2 thin films prepared by using an MBE apparatus on ZnO substrates with different Ti buffer layer thicknesses. Hc2(T) for both H k ab-plane and H k c-axis were measured to obtain the anisotropic superconducting properties. The results are well described by the Gurevich theory of dirty two-gap superconductivity with a cleaner p band. References [1] A.Y. Liu, I.I. Mazin, J. Kortus, Phys. Rev. Lett. 87 (2001) 087005.
219
[2] M.H. Jung, M. Jaime, A.H. Lacerda, G.S. Boebinger, W.N. Kang, H.J. Kim, E.M. Choi, S.I. Lee, Chem. Phys. Lett. 343 (2001) 447. [3] V. Ferrando, P. Manfrinetti, D. Marre, M. Putti, I. Sheikin, C. Tarantini, C. Ferdeghini, Phys. Rev. B 68 (2003) 094517. [4] A. Gurevich, S. Patnaik, V. Braccini, K.H. Kim, C. Mielke, X. Song, L.D. Cooley, S.D. Bu, D.M. Kim, J.H. Choi, L.J. Belenky, J. Giencke, M.K. Lee, W. Tian, X.Q. Pan, A. Siri, E.E. Hellstrom, C.B. Eom, D.C. Larbalestier, Supercond. Sci. Technol. 17 (2004) 278. [5] S. Noguchi, S. Miki, H. Shimakage, Z. Wang, K. Satoh, T. Yotsuya, T. Ishida, Physica C 426–431 (2005) 1449. [6] T. Oba, P. Sun, Y. Harada, T. Takahashi, H. Iriuda, M. Seki, Y. Nakanishi, S. Noguchi, T. Ishida, M. Yoshizawa, J. Magn. Magn. Mater. 310 (2007) e107. [7] V. Braccini, A. Gurevich, J.E. Giencke, M.C. Jewell, C.B. Eom, D.C. Larbalestier, A. Pogrebnyakov, Y. Cui, B.T. Liu, Y.F. Hu, J.M. Redwing, Qi Li, X.X. Xi, R.K. Singh, R. Gandikota, J. Kim, B. Wilkens, N. Newman, J. Rowell, R. Moeckly, V. Ferrando, C. Tarantini, D. Marre, M. Putti, C. Ferdeghini, R. Vaglio, E. Haanappel, Phys. Rev. B 71 (2005) 012504. [8] A. Gurevich, Phys. Rev. B 67 (2003) 184515. [9] A.A. Golubov, A.E. Koshelev, Phys. Rev. B 68 (2003) 104503. [10] Y. Harada, M. Uduka, Y. Nakanishi, N. Yoshimoto, M. Yoshizawa, Physica C 412–414 (2004) 1383. [11] L. Lyard, P. Samuely, P. Szabo, T. Klein, C. Marcenat, L. Paulius, K.H.P. Kim, C.U. Jung, H.-S. Lee, Phys. Rev. B 66 (2002) 180502. [12] A.A. Golubov, J. Kortus, O.V. Dolgov, O. Jepsen, Y. Kong, O.K. Andersen, B.J. Gibson, K. Ahn, R.K. Kremer, J. Phys.: Conden. Matter 14 (2002) 1353. [13] Y. Harada, H. Iriuda, T. Oba, H. Endo, S. Goto, M. Yoshizawa, private communication.