ELECTRON TRANSPORT STUDIES OF THE FERROMAGNETIC SEMICONDUCTOR CALCIUM HEXABORIDE By STEPHANIE A. GETTY A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2001 I dedicate this dissertation to my parents for giving me the intellectual freedom to make my own way. ACKNOWLEDGMENTS I would like to express my thanks to those who have played a crucial part in my development as a physicist. I would especially like to express my sincerest gratitude toward the chair of my graduate committee, Professor Arthur Hebard, for his generous support when I needed it most, for the critical reading of this dissertation, and for kindly allowing me to participate as a member of his group. I would also like to thank the members of my supervisory committee for having given me indispensable guidance and support: Professor Andrew Rinzler, Professor Cammy Abernathy, and Professor Selman Hershfield. I would like to express my appreciation to the department staff, in particular Janet Germany for her infinite patience, and Darlene Latimer and Susan Rizzo for the lengths they have gone to in my best interest. Many thanks to the Machine Shop personnel for all their excellent work that has made my research possible: Mark Link, Bill Malphurs, Ed Storch, Ted Melton, John Van Leer, Stephen Griffin, and Bob Fowler. I extend my thanks to all my family and friends, who have given me encouragement and without whom I would not be the person I am. iii TABLE OF CONTENTS page ACKNOWLEDGMENTS..................................................................................................iii LIST OF FIGURES............................................................................................................ vi ABSTRACT ....................................................................................................................... ix CHAPTERS 1 INTRODUCTION ............................................................................................................ 1 1.1 Electronic and Magnetic Properties of the Hexaboride Family of Compounds ....... 2 1.1.1 The Divalent Hexaborides.................................................................................. 3 1.1.2 The Rare Earth Hexaborides .............................................................................. 5 1.1.3 Valence Fluctuating SmB6 and CeB6 .................................................................6 1.1.4 Ferromagnetic EuB6 ...........................................................................................8 1.2 Doping Studies of the Hexaborides......................................................................... 11 1.2.1 Carbon Doping of EuB6.................................................................................... 11 1.2.2 Lanthanum and Ytterbium Doping of SmB6 .................................................... 13 1.2.3 Cerium and Thorium Doping of CaB6 ............................................................. 14 2 PREVIOUS WORK IN CaB6 AND RELATED COMPOUNDS ................................. 17 2.1 Electron Tunneling Spectroscopy in EuB6 .............................................................. 17 2.2 Recent Experimental and Theoretical Results in CaB6 and SrB6............................. 20 2.2.1 Theoretical Studies ........................................................................................... 20 2.2.2 Experimental Studies........................................................................................ 25 3 PURPOSE OF EXPERIMENT ...................................................................................... 41 3.1 Technological Motivation........................................................................................ 42 3.2 Electrical Conductivity in Metals and Semiconductors .......................................... 44 3.2.1 Electrons in Applied Magnetic Field I: Magnetoresistance ............................. 45 3.2.2 Electrons in Applied Magnetic Field II: Hall Effect ........................................ 48 3.3 Electron Tunneling Spectroscopy............................................................................ 51 3.3.1 Theory of Tunneling......................................................................................... 51 iv 3.3.2 Zero Bias Anomalies ........................................................................................ 56 4 EXPERIMENTAL TECHNIQUES ............................................................................... 60 4.1 Crystal Growth and Doping..................................................................................... 60 4.2 Transport Measurement Techniques ....................................................................... 61 4.2.1 Resistivity, Hall Effect, and Magnetoresistance .............................................. 62 4.2.2 Tunneling Spectroscopy ................................................................................... 65 5 PRESENTATION OF RESULTS.................................................................................. 72 5.1 Resistivity Measurements........................................................................................ 73 5.2 Hall Effect Measurements ....................................................................................... 79 5.3 Magnetoresistance Measurements........................................................................... 84 5.4 Tunneling Measurements ........................................................................................ 86 6 INTERPRETATION AND MODELING OF THE DATA........................................... 91 6.1 Interpretation of the Data......................................................................................... 91 6.1.1 Ca1-δLaδB6......................................................................................................... 91 6.1.2 Stoichiometric CaB6 .......................................................................................102 6.1.3 Ca1-δB6 ............................................................................................................106 6.2 Band Structure Model............................................................................................111 7 SUMMARY..................................................................................................................115 7.1 Synopsis of Experimental Results.........................................................................115 7.2 Future Directions...................................................................................................116 LIST OF REFERENCES................................................................................................. 118 BIOGRAPHICAL SKETCH........................................................................................... 125 v LIST OF FIGURES Figure Page 1-1. CsCl crystal structure of the hexaborides....................................................................... 3 1-2. Tunneling conductance versus bias voltage in SmB6. ................................................... 6 1-3. Resistivity versus temperature in EuB6.......................................................................... 8 1-4. Resistivity versus temperature in EuB6 at various magnetic fields. .............................. 9 1-5. Resistivity and dρ/dT versus temperature in EuB6 ........................................................ 10 2-1. Tunneling conductance versus bias voltage in EuB6. .................................................... 19 2-2. The evolution of a semimetallic band structure with excitonic ordering....................... 21 2-3. The band structure of an excitonic system with electron doping................................... 22 2-4. Magnetization versus temperature in Ca0.995La0.005B6 showing a TC of approximately 600 K. .................................................................................................................. 26 2-5. Magnetization versus magnetic field at various La doping concentrations................... 27 2-6. Resistivity versus temperature in the electron doped Ca1-δLaδB6, Ca-deficient CaB6, and stoichiometric Ca1+δB6 (first report). ............................................................ 28 2-7. Resistivity versus temperature in Ca1+δB6 (first report)................................................. 29 2-8. Specific heat versus temperature in Ca1+δB6 and Ca0.995La0.005B6 (first report)............. 29 2-9. Spin relaxation rate versus temperature in SrB6 at various magnetic fields.................. 31 2-10. Optical reflectivity versus frequency in Ca0.995La0.005B6 Ca0.99La0.01B6, and CaB6..... 32 2-11. Angle resolved photoemission spectra in stoichiometric CaB6. .................................. 33 2-12. SXE and PFY intensities versus photon energy in various hexaborides. .................... 34 2-13. Electron spin resonance spectra in Ca0.995La0.005B6. .................................................... 35 vi 2-14. Magnetization versus magnetic field in Ca0.995La0.005B6 and CaB6 grown by FZ and Al-flux techniques. .............................................................................................. 36 2-15. Resistivity versus temperature in Ca0.995La0.005B6 and CaB6 grown by FZ and Al- flux techniques..................................................................................................... 38 2-16. Magnetization versus magnetic field in polycrystalline CaB6: growth conditions...... 39 2-17.