STUDY OF FERROMAGNETISM IN DILUTED MAGNETIC SEMICONDUCTOR CaAs A thesis submitted to the School of Graduate Studies Addis Ababa University In partial Fulfilment of the Requirements for the Degree of Master of Science in Physics By Merhawi Abreha Addis Ababa, Ethiopia July 2007 ADDIS ABABA UNIVERSITY FACULTY OF SCIENCE DEPARTMENT OF PHYSICS The undersigned hereby certify that they have read and recommended to the Faculty of Science School of Graduate Studies for acceptance a thesis entitled “STUDY OF FERROMAGNETISM IN DILUTED MAGNETIC SEMICONDUCTOR CaAs” by Merhawi Abreha in partial fulfillment of the requirements for the degree of Master of Science in Physics. Name Signature Prof. P. Singh, Advisor −−−−−−−−−−−−−−−−− Dr. Tesgera B., Examiner −−−−−−−−−−−−−−−− Dr. Tewari H.S, Examiner −−−−−−−−−−−−−−−−− ii To My Departed Sister, Tsega. iii Acknowledgements It is a pleasure to express my warmest gratitude to Prof. P. Singh, my advisor, for all his advice, encouragement and critical comments. His friendly approach and constructive criticisms was appreciated during the period of my thesis work. It was a great privilege for me having him as my university advisor. I would like to thank all those who have contributed to the preparation of this work through their encouragement and motivation. In particular, I am indebted to Nebiat G/meskel who typed the lion’s share of the manuscript and to Mewael Giday (MU) and Abel W/mariam (Ethiopian Airlines-AA) who gave me the power of encourage- menttocompletemythesis. AlsoIwouldnotmovewithoutappreciatingthefollowing whose encouragement has been of great help for me: Haftom G/meskel, Mulugeta W/mariam, Getachew Yirga, Woini Araya, Berhan G/haweria and Aukubay Abreha. Finally I am unable to avoid mention of my unreserved acknowledgement to the Ministry of Education, Ethiopia, for sponsoring my School of Graduate Studies pro- gramme. Needless to say, I would appreciate any of your further suggestions and criticisms. Addis Ababa, Ethiopia Merhawi Abreha July ,2007 iv Abstract In the present study we study ferromagnetism of a transition free diluted magnetic semiconductor CaAs. Ferromagnetism in this curious material is due to the spin polarization of p-orbitals of the As atom. This mechanism is different from that of the CrAs in which Cr atoms possess magnetic moments [20, 23]. Ca atom does not have magnetic moments; its role is just to provide electrons with As atoms at the fcc site and to sustain crystal symmetry. The Curie temperature is estimated within an improvement over the mean-field approximation RKKY interaction for ho- mogeneous systems with randomly distributed localized spins and is obtained to be approximately proportional to the spin concentration. v Table of Contents Table of Contents vi Introduction 1 1 SEMICONDUCTORS 4 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Intrinsic Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Extrinsic Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Electrical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2 MAGNETIC PROPERTIES OF SEMICONDUCTORS 16 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Spontaneous Magnetization . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 Diamagnetism and Paramagnetism . . . . . . . . . . . . . . . . . . . 18 2.4 Ferromagnetism and Antiferromagnetism . . . . . . . . . . . . . . . . 19 2.5 Ferrimagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.6 Ferromagnetic Spin Waves . . . . . . . . . . . . . . . . . . . . . . . . 22 2.7 Role of Exchange Interaction in Ferromagnetism . . . . . . . . . . . . 22 3 DILUTED MAGNETIC SEMICONDUCTORS 26 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2 II-VI Ferromagnetic DMSs: . . . . . . . . . . . . . . . . . . . . . . . 27 3.3 III-V Ferromagnetic DMSs: . . . . . . . . . . . . . . . . . . . . . . . 28 3.4 Calcium Pnictides: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4 MECHANISM OF MAGNETISM IN CaAs 31 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2 The Ferromagnetic Interaction Hamiltonian . . . . . . . . . . . . . . 32 4.3 Ferromagnetic Transition Temperature . . . . . . . . . . . . . . . . . 34 vi 4.4 Magnetoresistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.5 The Origin of Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . 39 5 Conclusion 41 Bibliography 42 Declaration 45 vii Introduction The information technology we use today utilizes the mass, charge and spin of elec- trons in the solid state. Integrated circuits and high-frequency devices which are used for information processing and communications are made up of semiconductors such as silicon (Si), germanium (Ge) and gallium arsenide (GaAs). These devices have had great success using the charge of electrons. Mass storage of information is carried out by magnetic recording using spins of electrons in ferromagnetic materials. These include hard disks, magnetic tapes and magneto-optical disks. It is then quite natural to ask whether both the charge and spin of electrons can be used to further enhance the performance of devices so that we may be able to use the capability of mass storage and information processing at the same time [1]. Recently, the possibility of using electron’s spins in addition to their charge in in- formation technology has created much enthusiasm for a new branch of theoretical research on spin electronics (spintronics). Particular semiconducting materials which are considered to be ideal materials for spintronics are commonly known as diluted magnetic semiconductors (DMSs) or semimagnetic semiconductors (SMSCs). Almost complete search for possible magnetic materials has been performed utilizing 1 2 transition metal doping into II-VI compounds, like CdTe, CdSe, CdS, ZnSe, etc, or III-V crystals such as GaAs and InSb. For example, DMSs such as In Mn As and 1−x x Ga Mn As type were discovered by Munekata et al and Ohno et al where a small 1−x x concentration of Mn atoms, or in general of transition metal atoms, are randomly dis- tributed on the cation sites of the host material [2]. In this case the transition metal ions, used as the magnetic atoms, substitute the original cations of the host crystal. In fact, the strong magnetism is realized when the d-shell is partially occupied by electrons and is not half-filled. In a hypothetical zinc-blende structure compounds of II-V elements such as CaAs, CaP, CaC, SrAs, SrC, BaC and CaSb are found to be possible ferromagnetic mate- rials excluding transition metal atoms. In this case the d-orbitals on atoms of the G-II elements play essential roles for the magnetism [3, 13, 20, 21, 22]. Thus the half- metalicity and ferromagnetic properties appearing in the zinc-blende Ca compounds are new findings . In the first chapter of this thesis a brief review of semiconductors is given. We shall define semiconductors and discuss a few important concepts which distinguish them from other solids. We shall also consider carrier concentration and electrical conductivity in semiconductors. The discussion of magnetic properties of semiconductors comes under the second chapter. In this chapter we have included reviews of spontaneous magnetism, Curie- Weiss law of magnetization and different types of magnetization. In fact, the focus 3 of this chapter shall be on ferromagnetism. The third chapter of this paper concentrates on diluted magnetic semiconductors (DMSs). Some important examples of DMSs, including II-VI, III-V and Calcium compounds, are shortly discussed under this chapter. In chapter four, we focus on the electronic structure and magnetism of calcium ar- senide (CaAs). We shall show pd hybridization exchange interaction to produce magnetization in the curious material CaAs without transition metal atoms. Mag- netic properties of CaAs such as Curie-Weiss temperature, magnetic susceptibility, magnetization and magnetoresistance are discussed on the basis of mainly mean or molecular field theory. Finally, the fifth chapter summarizes the results obtained and gives concluding points of the thesis.