Anisotropy of critical current density in c-axis-oriented MgB 2 thin films Shashwati Sen, Ajay Singh, D. K. Aswal, S. K. Gupta,* J. V. Yakhmi, and V. C. Sahni Technical Physics & Prototype Engineering Division, Bhabha Atomic Research Center, Mumbai 400 085, India Eun-Mi Choi, Hyeong-Jin Kim, Kijoon H. P. Kim, Hyun-Sook Lee, W. N. Kang, and Sung-Ik Lee National Creative Research Initiative Center for Superconductivity, Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea Received 1 March 2002; published 6 June 2002 The critical current density ( J c ) has been measured in c-axis oriented MgB 2 thin films as a function of applied magnetic field Hand angle ( ) between H and the ab plane. The measurements have been carried out at various temperatures between 32 and 38 K. The field and angular dependence of J c indicates pinning by point pinning centers and is in a good agreement with the predictions of anisotropic Ginzburg-Landau model. Anisotropy parameter ( ) of 2.55 was determined from scaling behavior of J c . DOI: 10.1103/PhysRevB.65.214521 PACS numbers: 74.60.Ge, 74.76.-w, 74.70.Ad INTRODUCTION Following the recent discovery of superconductivity in MgB 2 with a critical temperature T c of 39 K, a large number of studies have been carried out to establish fundamental properties of this material so as to understand the mechanism of superconductivity. 1–5 MgB 2 is found to have a hexagonal crystal structure and band-structure calculations indicate that quasi-2D two-dimensionalboron planes are responsible for superconductivity. 1 The material shows anisotropic super- conducting properties and various measurements indicate an upper critical field H c 2 ab (0) between 12 and 40 T and an anisotropy ratio of 1.2–13. 2–4 Fluctuation conductivity measurements made in thin films of MgB 2 show two- dimensional nucleation of superconductivity. 1 Thin films of MgB 2 show very high values of critical current density J c and films with c-axis oriented normal to the substrate show magnetization J c of 1.610 7 A/cm 2 in zero field and 1 10 5 A/cm 2 in a field of 5 T at a temperature of 15 K. 5 While this shows the potential of MgB 2 for practical appli- cations, measurement of critical current anisotropy to under- stand flux-pinning mechanism has not been reported. Such a study is of considerable importance for various applications of the material and we report here results of such a study. The study of current voltage ( I -V ) characteristics and critical current I c of superconductors as a function of various parameters, such as magnetic field H, temperature and angle between field and crystal axis or current direction, has been carried out in many conventional and high-temperature su- perconductors. In many investigations made for conventional isotropic superconductors, field and temperature dependence of critical current density has been analyzed in terms of criti- cal state model. 6,7 In terms of this model, the critical current is determined by competition between Lorentz force due to applied current and pinning forces on the vortices. For mag- netic field H applied normal to the current direction, critical current density J c is related to pinning force per unit volume F p as F p =J c H . The dependence of J c on magnetic field and temperature is seen to have similar behavior over a wide range of microstructure, field, and temperatures and the scal- ing behavior of J c and F p is generally given by 7,8 F p =J c H =A H c 2 n H / H c 2 m 1 -H / H c 2 l . 1 High-temperature superconductors are highly anisotropic and show a rich variety of interesting behavior. The critical current has a strong dependence on the orientation of mag- netic field with respect to crystal axis. Highly anisotropic superconductor, Bi 2 Sr 2 CaCu 2 O x BSCCOdisplays a 2D su- perconducting behavior where superconducting CuO 2 planes are separated by non-superconducting or weakly supercon- ducting intermediate layers. The material shows very high J c for H ab plane compared to that for H c axis. Measurements as a function of angle show that J c is determined by the component of magnetic field along the c axis. This arises because the vortices parallel to the ab plane are strongly pinned by weakly superconducting layers between CuO 2 planes. This is called intrinsic pinning and has been used to explain angular dependence of J c . 9 Another high- temperature superconductor, YBa 2 Cu 3 O x YBCO, has lower anisotropy, and many of its physical properties can be understood in terms of anisotropic Ginzburg-Landau GL model. Blatter et al. 10 have shown that the anisotropic prop- erties of superconductors with anisotropy parameter ) scale with reduced magnetic field H , where =sin 2 + 2 cos 2 2 is angle between H and the ab plane and =1/ =H c 2c / H c 2ab . Gupta et al. 11 have shown that I -V characteristics in YBCO thin films scale with H except at small angles ( 10°) where the effect of intrinsic pinning has been ob- served. Similarly, Braithwaite et al. 12 have found that critical current scales with H indicating agreement with aniso- tropic GL model. Above scaling theory of Blatter et al. 10 does not give a functional dependence of J c with H and . Watanabe et al. 8 have obtained such a functional dependence using the conventional scaling law of Eq. 1, assuming that the anisotropy in J c depends on the anisotropy of upper criti- cal magnetic field H c 2 ( ). 8,13 This scaling behavior of J c is given by PHYSICAL REVIEW B, VOLUME 65, 214521 0163-1829/2002/6521/2145215/$20.00 ©2002 The American Physical Society 65 214521-1