Dual Beam Detection Technique to Study Magneto-Optical Kerr
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DUAL BEAM DETECTION TECHNIQUE TO STUDY MAGNETO-OPTICAL KERR EFFECT By Shankar Chandra Acharya, Msc A thesis submitted to the Graduate Council of Texas State University in partial fulfillment of the requirements for the degree of Master of Science with a Major in Physics May 2019 Committee Members: Wilhelmus J Geerts, Chair Nikoleta Theodoropoulou Alexander Zakhidov COPYRIGHT By Shankar Chandra Acharya 2019 FAIR USE AND AUTHOR’S PERMISSION STATEMENT Fair Use This work is protected by the Copyright Laws of the United States (Public Law 94-553, section 107). Consistent with fair use as defined in the Copyright Laws, brief quotations from this material are allowed with proper acknowledgement. Use of this material for financial gain without the author’s express written permission is not allowed. Duplication Permission As the copyright holder of this work I, Shankar Chandra Acharya, authorize duplication of this work, in whole or in part, for educational or scholarly purposes only. ACKNOWLEDGEMENTS First of all, I would like to than my supervisor Dr. Wilhelmus J Geerts for his constant support and guidance. I feel grateful to have worked under such an inspiring researcher who has given me this opportunity to learn and explore scientific knowledge. I would also like to thank my committee members Dr. Nikoleta Theodoropoulou and Dr. Alexander Zakhidov for their constructive feedback which have contributed to my thesis project. I am grateful for my family and friends for their motivation and encouragement all these years of my studies. My mother and father have supported me during the difficult times and inspired me throughout my research. This material is based upon work supported by, or in part by, the U. S. Army Research Laboratory and the U. S. Army Research Office under contract/grant number W911NF1510394. Hinds Instruments and Thorlabs Inc. have to be thanked for lending us equipment. Nate England of Engineering and Collin Pane of Engineering Technology are thanked for helping with machine shop tasks. Furthermore, I would like to acknowledge travel support of the department of Physics, the College of Science, and the graduate college of Texas State University through the course of my thesis project. This allowed me to present part of the results presented in this thesis at the TSAPS spring-2018 meeting at Tarleton State University in Stephenville and at the 2018 International Conference on Magnetism in San Francisco. iv TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ............................................................................................... iv LIST OF TABLES ............................................................................................................ vii LIST OF FIGURES ......................................................................................................... viii LIST OF SYMBOLS ....................................................................................................... xiii CHAPTER 1. INTRODUCTION ...............................................................................................1 1.1 Motivation of the Study .........................................................................1 1.2 Magneto Optical Kerr Effect .................................................................4 1.3 Spin Orbit Interaction ............................................................................5 1.4 MOKE Geometries ................................................................................7 1.5 Overview on Single Beam Modulated MOKE and Dual Beam Modulated MOKE .......................................................................................9 1.6 Scope of the Thesis ..............................................................................10 2. MAGNETO OPTICAL KERR THEORY .........................................................12 2.1 Polarization of an Electromagnetic Waves ..........................................12 2.2 Jones Vectors of Polarized Light and Special Polarizations ................15 2.3 Jones Matrices ......................................................................................18 2.4 MOKE Setup Employing Polarizer and Analyzer ...............................30 2.5 MOKE Setup Employing a PEM .........................................................35 v 2.6 Apparatus for Dual MOKE Measurements..........................................44 2.6.1 Polarizer and Analyzer ..........................................................45 2.6.2 Light Source ..........................................................................47 2.6.3 Photo-Detectors.....................................................................48 3. DUAL BEAM DETECTOR TECHNIQUE ......................................................53 3.1 Optics Alignment of Dual Beam MOKE Setup ...................................56 3.2 Multiple Interference Effects in PEM ..................................................60 3.3 LabVIEW Programing .........................................................................71 3.4 Implementation of External Triggering ...............................................72 3.5 Noise of Laser on the Detectors ...........................................................73 3.6 Test Stability of PEM-100 ...................................................................74 4. EXPERIMENTAL RESULTS AND DISCUSSION ........................................80 4.1 Test as a Function of Analyzer Angle..................................................80 4.2 Test as a Function of PEM Tilt Angle .................................................84 4.3 Test as a Function of Retardation ........................................................96 5. TEST OF DBM SETUP WITH NICKEL OXIDE AND NICKEL IRON OXIDE SERIES ...................................................................................................102 6. DISCUSSION OF RESULTS AND FURTHER RESEARCH .......................109 APPENDIX SECTION ........................................................................................111 REFERENCES ....................................................................................................119 vi LIST OF TABLES Table Page 1 NEP, Transimpedance, Responsivity, noise, signal to noise ratio for active area for different detectors from Thorlabs Inc. under different noise setting of lock ins. ............. 52 2 S/N ratio for different combination of PEM and detector with field and sample as a function of PEM tilt angle................................................................................................. 94 3 Corresponding θk in degrees per Oe. for NiO (film and substrate). ........................... 116 4 Corresponding θk in degrees per Oe. for NiO (substrate). .......................................... 116 5 Corresponding θk in degrees per Oe. for NiFeO (film and substrate). ....................... 117 6 Corresponding θk in degrees per Oe. for NiFeO (substrate). ...................................... 117 vii LIST OF FIGURES Figure Page 1.1 Effect of exchange splitting and spin orbit interaction on the allowed optical transitions [11] .................................................................................................................... 6 1.2 Different MOKE geometries [45] ................................................................................. 8 2.1 Polarization of an ellipse……………………………………………………………..15 2.2 Jones vector of circularly and linearly polarized light ................................................ 18 2.3 Jones matrix mathematics operation ........................................................................... 19 2.4 Family of polarizing prisms [46] ................................................................................ 23 2.5 Photo elastic modulator [HINDS Instruments] ........................................................... 24 2.6 Simplest form of PEM-90 from HINDS ..................................................................... 25 2.7 Retardation of PEM [47] ............................................................................................. 26 2.8 Multiple interference effect in PEM [43].................................................................... 28 2.9 Phasor diagram for S and P component of light in the case of multiple interference effect ............................................................................................... 29 2.10 Experimental set-up used for Kerr Measurement ................................................. 30 2.11 Polarization Modulation Technique for Kerr Measurement [48] ............................. 36 2.12 Polarization Modulation for Kerr Measurement [33] ............................................... 37 2.13 The single beam detector setup using PEM and Glan-Taylor prism ........................ 38 2.14 Bessel functions 퐽0(푥), 퐽1(푥), 퐽2(푥) ....................................................................... 44 viii 2.15 Glan-Taylor Prism [49] ............................................................................................. 46 2.16 Wollaston prism [50] ................................................................................................ 47 2.17 Detector Responsivity (PDA-55) [Thorlabs] ............................................................ 49 3.1 Dual Beam Detector Magneto Optical Kerr Set-Up…………………………………55 Figure 3.2 Stages used and Schematic diagram on two detector MOKE analyzer detector unit ........................................................................................... 56 3.3 The DC signals on