DETERMINATION OF ENERGY GAP OF THE IRON-BASED OXYPNICTIDE AND LaOFeGe SUPERCONDUCTORS USING SPECIFIC HEAT CAPACITY TAREK MOHAMED FAYEZ AHMAD UNIVERSITI SAINS MALAYSIA 2013 DETERMINATION OF ENERGY GAP OF THE IRON-BASED OXYPNICTIDE AND LaOFeGe SUPERCONDUCTORS USING SPECIFIC HEAT CAPACITY By TAREK MOHAMED FAYEZ AHMAD Thesis submitted in fulfillment of the requirements for the degree of Doctor of Philosophy October 2013 DEDICATION To my father and mother To my brothers and sisters To my wife and my sons ii ACKNOWLEDGMENTS First and foremost, I give praise and thanks to the almighty Allah for giving me the strength to complete my research study. I would like to express my sincerest and deepest gratitude to my fatherly supervisor Professor Kamarulazizi Bin Ibrahim for his wisdom, guidance, and intellectual support. His encouraging attitude and self-less guidance throughout the years have enriched me with empirical insights and knowledge in my scientific and academic career. I would like to thank Universiti Sains Malaysia for their generous financial support. I also thank the staff members of the School of Physics for the co-operation, technical assistance, and support they extended during my studies. Finally, I thank my friends for encouraging and helping me throughout my journey in the academe. Tarek Mohamed Fayez Ahmad Penang, Malaysia. 2013 iii TABLE OF CONTENTS Page ACKNOWLEDGEMENTS iii TABLE OF CONTENTS iv LIST OF TABLES vii LIST OF FIGURES viii LIST OF SYMBOLS xii LIST OF MAJOR ABBREVIATIONS xiii ABSTRAK xiv ABSTRACT xvi CHAPTER 1: INTRODUCTION 1 1.1 Introduction to superconductivity 1 1.2 Problem statements 8 1.3 Research objectives 8 1.4 Scope of the research 9 1.5 Originality of the research 9 1.6 Outline of the thesis 10 CHAPTER 2: LITERATURE REVIEW OF SUPERCONDUCTING 12 FeAs-BASED 1111 OXYPNICTIDES 2.1 Introduction 12 2.2 Physical properties 12 2.2.1 Temperature dependence of specific heat capacity 12 2.2.2 Temperature dependence of resistivity 15 2.2.2.1 Doping effect 16 2.2.2.2 Effect of external pressure 19 2.2.2.3 Effect of concentration and lattice parameters 22 iv 2.2.2.4 Sintering temperature effect 23 2.2.2.5 Effect of magnetic field 24 2.2.3 Temperature dependence of magnetic susceptibility 25 2.2.4 Resistivity scaling 26 2.2.5 FTIR spectra probing of superconducting energy gap 28 2.2.6 Pseudogap 33 2.2.7 Summary 34 2.3 Methods of synthesis 36 2.3.1 Solid state method 36 2.3.2 Powder-in-tube method 38 2.3.3 Flux method 38 2.3.4 Low-temperature method 39 2.3.5 Two-step solid state method 40 2.3.6 Summary 40 CHAPTER 3: STRUCTURE AND THEORECAL MODELS OF 42 SUPERCONDUCTIVITY IN Fe-BASED 1111 OXYPNICTIDES 3.1 Introduction 42 3.2 Crystal structure 42 3.2.1 Summary 46 3.3 Theoretical studies 46 3.3.1 Summary 51 CHAPTER 4: METHODOLOGY 52 4.1 Introduction 52 4.2 Background of superconducting transition model 52 v 4.3 Synthesis of LaO1-xFxFeGe (x=0.0, 0.11, 0.13) compound 55 4.4 Instrumentations 58 4.4.1 High Resolution X-Ray Diffraction 58 4.4.2 Four probe measurement technique at low temperatures 60 4.4.3 Fourier Transform Infrared Spectrometer System 63 CHAPTER 5: RESULTS AND DISCUSSIONS 67 5.1 Introduction 67 5.2 Theoretical results 67 5.2.1 Superconducting transition model of specific heat 67 5.2.2 Transition point of LnO1-xFxFeAs (Ln=La, Sm) compounds 73 5.3 Experimental results 79 5.3.1 X-ray diffraction 79 5.3.2 Resistivity measurement at low temperatures 81 5.3.3 FTIR spectrum 83 5.3.4 Superconducting energy gap 85 CHAPTER 6: CONCLUSIONS 89 7.1 Introduction 89 7.2 Conclusions 89 7.3 Future prospects 91 REFERENCES 92 APPENDICES 113 Appendix 1: Iron-based oxypnictide phases 113 LIST OF PUBLICATIONS 118 vi LIST OF TABLES Page Table 4.1 Stoichiometric amounts for starting materials of nominal 56 compositions LaO1-xFxFeGe according to formulas 4.3 and 4.4. Table 5.1 Specific heat fitting parameters derived from Eq. (5.13c) with 75 temperature between 2 K and 200 K. Table 5.2 Specific heat fitting parameters derived from Eq. (5.13c) with 76 temperature between 8 K and 200 K. Table A1.1 Starting materials and superconducting transition temperature 113 of resistivity measurements for the LnOMPn oxypnictides phase. Impurities detected in these phases and lattice parameters are also presented. Method of synthesis are S=Solid state method, P=Powder-in-tube method, F=Flux method, L=Low-temperature method, and T=Two-step solid state method. vii LIST OF FIGURES Page Figure 1.1 Phase diagrams for type I and II superconductors showing 3 magnetic field versus temperature [1]. Figure 1.2 Resistivity versus temperature of a superconductor with 4 different definitions of transition temperature. Specific heat jump is observed at Tc in the temperature dependence of specific heat [2]. Figure 1.3 The structural and magnetic phase diagram of CeO1-xFxFeAs 6 (x = 0, 0.02, 0.04, 0.06, 0.16). The antiferromagnetic order (AFM) vanishes before the emergence of superconductivity (SC) for x ˃ 0.06. The red circles indicate the onset temperature of P4/nmm to Cmma phase transition. The black squares and green triangles designate the Neel temperatures of Fe (TN(Fe)) and Ce (TN(Ce)), respectively [37]. Figure 1.4 Phase diagram of the magnetic and superconducting 6 properties of SmO1-xFxFeAs. There is a clear region of coexistence between x=0.10 and x=0.15. Tc reaches its maximum value when the main static magnetism phase disappears. Evolution of the main magnetic transition temperature Tmag, the Sm ordering temperature TSm, the superconducting transition temperature Tc and the structural transition Ts, as a function of the F-doping concentration [38]. Figure 2.1 Temperature dependence of specific heat capacity of 13 BaNi2As2 compound. A jump at Tc was observed this curve [60]. Figure 2.2 Temperature dependence of specific heat capacity for 14 LaO0.9F0.1FeAs compound [64]. The jump was not visible in this curve. Figure 2.3 Temperature dependence of electrical resistivity for CeO1- 16 xFxFeAs, where the resistivity anomaly around 145 K at x=0 [17]. Figure 2.4 Schematic diagram of F-doping dependence of Tc and Tonset 17 on LaO1-xFxFeAs compound [31]. Figure 2.5 Dependence of the critical temperature of SmO1-xFxFeAs 21 (0.10 ≤ x ≤ 0.20) on the external pressure P. Tc increases monotonically as the F-doping level x increases to 0.20 [91]. Figure 2.6 Phase diagram showing the superconducting transition 23 temperatures as a function of the Ce doping level in La1- xCexO0.9F0.1FeAs compound [5]. viii Figure 2.7 Dependence of the lattice constant and onset transition 24 temperature on the sintering temperature for SmO0.8F0.2FeAs samples [43]. Figure 2.8 Temperature dependence of magnetic susceptibility for Gd1- 26 xThxOFeAs (x=0, 0.2) sample under zero-field cooled (ZFC) and field-cooled (FC) measurements [44]. Figure 2.9 Reflectivity ratio R(T)/R(45) for SmO0.8F0.2FeAs compound 29 at different temperatures [14]. Figure 2.10 The far-infrared reflectance spectra for LaO0.9F0.1FeAs 30 compound at different temperatures [15]. Figure 2.11 The reflectance spectra of infrared measurement for the pure 32 compound LaOFeAs at different temperatures [16]. Figure 2.12 The reflectance spectra of infrared measurement for the pure 32 compound CeOFeAs at different temperatures [17]. Figure 2.13 Schematic phase diagram of FeAs superconductors. Red, 35 green, and blue regions indicate the SDW, superconducting, and Fermi-liquid–like regions, respectively. In the strange metal region, unusual ρ(T) is observed. The black bar marks the doping level transition from the SDW state to superconductivity [104]. Figure 3.1 (a) Schematic crystal structure of LaO1-xFxFeAs. The 43 quaternary phase structure LaOFeAs contains eight atoms in the tetragonal unit cell [17]. (b) Schematic FeAs4 tetrahedrons with bond angles α and β (α ≠ β) [8]. Figure 3.2 (a) Fe3d-As4p band structure in eV of LaOFeAs along the 51 high-symmetry lines of the 2D Brillouin zone. Left: density functional theory DFT (dashed lines) and Gutzwiller variational theory GT (solid lines) in the paramagnetic phase PM for Hubbard interaction U and an average Hund’s-rule interaction J is (U, J) = (8, 0.6) eV. Right: GT bands in the PM (dashed lines) and spin density wave SDW (solid lines) phases in the Brillouin zone folded along the line ̅ ̅– ̅ ̅. (b) PM Fermi surface. Left: DFT. Right: GT for (U, J) = (8, 0.6) eV. High-symmetry points and the directions x, y and X, Y are shown [153]. Figure 4.1 Schematic chart of transition state model related to FTIR 55 spectrum, and specific heat of iron oxypnictides by fph and C(T), respectively. ix Figure 4.2 (a) Schematic diagram of system used for heating pellet. (b) 57 Boats used to hold sample. (c) Electrical poles at both ends of boats with sample between them. (d) Equipment with chamber and pumps. Figure 4.3 (a) Evacuated silica tube containing samples and (b) tube 57 furnace (Model Lenton VTF/12/60/700) used to anneal the pellets. Figure 4.4 (a) Schematic diagram of Bragg diffraction. Two diffracted 59 beams interfere constructively for certain angles when diffraction conditions are met. The angle of incidence equals the angle of reflection, and the path difference equals n wavelengths. (b) Image of high-resolution XRD diffractometer system (PANalytical X’Pert PRO MRD PW3040) with a Cu-K1 radiation source (=1.5406 Å) used to evaluate lattice parameters of samples.