Anisotropy in MgB 2 thin film studied by magnetic field dependent complex microwave conductivity A. Dul  ci  c a , M. Po zek a, * , D. Paar a , E.-M. Choi b , H.-J. Kim b , W.N. Kang b , S.-I. Lee b a Department of Physics, Faculty of Science, University of Zagreb, P.O.Box 331, HR-10002 Zagreb, Croatia b National Creative Research Initiative Center for Superconductivity and Department of Physics, Pohang University of Science and Technology, Pohang 790-784, South Korea Abstract Field and temperature dependent microwave measurements on high quality MgB 2 thin film have been performed. From the complex microwave conductivity one can identify the mean-field (MF) coherence length deeply in the mixed state, and the Ginzburg–Landau (GL) coherence length at the transition to the normal state. The analysis reveals the temperature independent anisotropy ratio n ab MF =n c MF  2, and n ab GL =n c GL  2:8. The analysis of depinning frequencies shows collective pinning behavior. Ó 2004 Elsevier B.V. All rights reserved. PACS: 74.25.Op; 74.25.Nf; 74.40.+k; 74.78.Db; 74.25.Qt Keywords: Microwave response; MgB 2 film; Mixed state; Depinning; Fluctuations There is a general agreement that coherence length in the recently discovered binary compound MgB 2 is anisotropic, but a controversy arised on the question whether this anisotropy is temperature dependent or not. Here, we study several aspects of anisotropy in MgB 2 superconductor by the magnetic field and tem- perature dependent microwave response in high quality MgB 2 thin film. The thin film of MgB 2 was grown on Al 2 O 3 substrate as described earlier [1,2]. The film thickness was 400 nm. Microwave measurements were carried out in an elliptical cavity resonating in e TE 111 mode at 9.3 GHz. The thin film was mounted on a sapphire sample holder and placed in the center of the cavity where the micro- wave electric field E x was maximum. The sample was oriented with ab-plane parallel to E x . The measured quantities were the Q-factor of the cavity loaded with the sample and the resonant frequency f . From the complex frequency shift D ~ x=x ¼ Df = f þ iDð1=2QÞ one can obtain by inversion the complex conductivity ~ r ¼ r 1  ir 2 of the film using the cavity perturbation expression [3]. Two approaches for the determination of the upper critical field are illustrated in Fig. 1. The response of the superconductor in the mixed state to an oscillating electric field E x is given by an effective complex con- ductivity [4]: 1 ~ r eff ¼ 1  B=B c2 1iðx 0 =xÞ 1  B B c2   ðr 1  ir 2 Þþ B B c2 r n þ 1 r n B=B c2 1  i x 0 x : From experimentally determined ~ r eff one can extract two quantities, B=B c2 and x 0 , for every measured point. B=B c2 is the volume fraction of the vortex cores in the sample volume, while x 0 is the depinning frequency. The linear part of the curves in Fig. 1(a) represents the MF behavior where vortices comprise many Landau levels [5]. The corresponding values of B MF c2 are shown by symbols in Fig. 2. As the transition to the normal state is approached, the higher Landau levels are lifted and the * Corresponding author. E-mail address: mpozek@phy.hr (M. Po zek). 0921-4534/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.03.101 www.elsevier.com/locate/physc Physica C 408–410 (2004) 662–663