Magnetooptical Spectroscopy of the Rare-Earth Compounds: Development and Application
Uygun V. Valiev, John B. Gruber, and Gary W. Burdick
Magnetooptical Spectroscopy of the Rare-Earth Compounds: Development and Application Published by Scientific Research Publishing, Inc. ISBN: 978-1-935068-59-4 http://www.scirp.org
Copyright © 2012 by Scientific Research Publishing, Inc., USA. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Scientific Research Publishing, Inc., USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology new known or hereafter developed is forbidden. Requests to the Publisher for permission should be addressed to the SRP Copyrights Manager, Scientific Research Publishing, Inc., USA, E-mail:
[email protected].
Authors Uygun V. Valiev, Professor of Physics, Doctor of Sciences, Department of Optics and Laser Physics, Faculty of Physics, Mirzo Ulugbek National University of Uzbekistan (NUUz), Tashkent 100174, Uzbekistan John B. Gruber, Ph.D. Professor of Research, Department of Physics and Astronomy, The University of Texas at San Antonio, San Antonio, Texas 78249-0697 USA; former Director of the Institute of Modern Optics (1992-2005), Chair and Professor of Physics at San Jose State University, San Jose, CA 95192-0106 USA. Gary W. Burdick, Ph.D. Professor of Physics, Department of Physics, Andrews University, Berrien Springs, MI, 49104, USA; Associate Dean for Research and Creative Scholarship, School of Graduate Studies and Research, Andrews University, Berrien Springs, MI 49104, USA.
To the memory of our mentors, Profs. Rudolf Z. Levitin (Russia) and Glenn T. Seaborg (USA)
I
Contents Foreword……………………………………………………………………………………………1 Chapter 1 Magnetism of the rare-earth ions in crystals 1.1. Electronic structure and energy spectra of the “free” rare-earth ions.……………………………………………4 1.2. Paramagnetism of the “free” RE ions.……………………………………………………………………………6 1.3. Energy spectra and wavefunctions of Kramers and non-Kramers RE ions in the paramagnetic garnets and orthoaluminates.……………………………………………………………………………………………………7 1.4. Influence of the symmetry of the crystal field on the magnetic susceptibility of RE ions in crystals.…………14 1.5. Ising RE ions and behavior of their magnetic features.…………………………………………………………20 References ……………………………………………………………………………………………………………28
Chapter 2 Optics of the 4f → 4f and 4f → 5d transitions in crystals 2.1. Optical properties of RE ions in crystals.…………………………………………………………………………31 2.2. Selection rules for the magnetic-dipole and electric-dipole optical transitions in RE ions in crystals.…………34 2.3. Theory of intensities of “forbidden” RE3+ electric-dipole 4f → 4f transitions in crystalline hosts.………………35 2.4. Modern experimental methods of measuring the 4f → 4f optical spectra of RE compounds: site-selective polarized spectroscopy (SSPS) and “hot-band” spectroscopy.……………………………………45 2.5. Explanation regarding parity-allowed 4f → 5d optical transitions in RE ions within the framework of the “strong-weak” crystalline field approximation.…………………………………………………………………54 References ……………………………………………………………………………………………………………59
Chapter 3 Magnetooptics of 4f → 4f and 4f → 5d transitions in crystals 3.1. Phenomenological theory of linear magnetooptical effects.………………………………………………………63 3.2. Microscopic theory of the linear magnetooptical effects in paramagnetic RE garnets associated with allowed electric-dipole 4f → 5d transitions in the approximation of an “average” crystal field.………………66 3.3. The contribution of Van-Vleck mixing to the magnetooptics of the RE ions in crystals.………………………72 3.4. Faraday effect on the magnetic-dipole transitions in RE ions.……………………………………………………78 3.5. Features of the magnetic circular dichroism (MCD) and Faraday effect (FE) in RE compounds in the approximation of a “strong-weak” crystalline field within the ultraviolet spectral range.………………………82 3.6. Group-theory consideration of the Faraday effect in RE orthoaluminates.………………………………………91 3.7. “Anti-Zeeman” effect in absorption spectra of terbium-gallium garnet TbGG in a magnetic field.……………96 References …………………………………………………………………………………………………………105
II
Chapter 4 Magnetooptics of the 4f → 4f radiative transitions in crystals 4.1. Theory of the radiative 4f → 4f transitions in the magnetooptics of RE ions in crystals.………………………109 4.2. Spectra of the degree of magnetic circular polarization luminescence (MCPL) of non-Kramers RE ions in the garnet structure.…………………………………………………………………………………………………112 4.3. Spectra of the degree of magnetic circular polarization luminescence (MCPL) of Kramers RE ions in the garnet structure.…………………………………………………………………………………………………120 4.4. The role of Van-Vleck mixing in the magnetooptics of radiative transitions in RE ions.………………………127 References …………………………………………………………………………………………………………135
Conclusion……………………………………….………………………………………………..137 References …………………………………………………………………………………………………………139
III
Foreword Modern magnetooptics is a part of physics arising at the junction of two branches of knowledge—physical optics and physics of magnetic phenomena—and covering a wide range of problems regarding the anisotropy associated with optical features of materials placed in an external magnetic field. In fact, the disturbance of the medium by the magnetic field manifests itself as a difference in the optical characteristics of the medium (absorption, refraction, etc.) for clockwise and counterclockwise circularly polarized light radiation, and as the circular anisotropy of secondary radiation spectra (luminescence, combinational scattering, etc.). These effects, which differ greatly with respect to both the experimental methods used and the nature of the information extracted from the data, have continued to attract the attention of numerous investigators over many years. In the early stages of the intensive development of magnetooptical studies that began in the 1960’s and 1970’s, the focus of research was directed toward producing new magnetic rare-earth (RE) dielectrics characterized by large magnetooptical effects and high transparency within the visible and near infrared frequency range of the material. The astonishing results of these initial investigations quickly led to opportunities for the development of technical applications of these magnetooptical effects in the now well-recognized fields of photonics, optoelectronics, and microelectronics. In addition, there is considerable interest in the fundamental investigation of the magnetooptics of rare-earth magnetic dielectrics, as they provide an opportunity to solve fundamental problems in the physics of magnetic phenomena in solids. Namely, they provide the opportunity to gain deeper understanding and interpretation of the inter-relationship between the magnetooptical effects and magnetization, on the one hand, and the features of the energy spectrum formed by the crystalline electric environment of a RE ion in these magneto-dielectrics, on the other hand. Due to the high sensitivity of the magnetooptical effects (differential in essence) to external physical influences, these studies have allowed the investigator to obtain important and unique information not obtainable by other physical methods traditionally used to study the electronic structure, energy spectra, and wavefunctions of RE compounds. Obvious advantages to this approach, as described in this text, are the relatively simple modeling and calculation techniques that are available to interpret the magnetooptical spectra. Due to the highly selective nature and spin sensitivity of the magnetooptical effects, detailed results become available that cannot be observed in the analyses of optical spectra obtained from data produced by more traditional methods, including polarized absorption and fluorescence spectra. In the past 10 to 15 years, a large number of publications have appeared devoted to the magnetooptics and the optics of RE compounds. This book attempts to systematize the available experimental data on circular magnetooptical anisotropy of these compounds using recent developments in crystal field (CF) theory and in the theory of RE ion transition intensities of 4f → 4f and 4f → 5d transitions. The application of microscopic theory to magnetooptical phenomena has been developed by the investigations performed by the present authors and others found in the literature to date (2011). Representative of such a systemized approach of a comparison between theory and experiment is made in this text for the rare-earth garnets and orthoaluminates, whose optical, magnetic and magnetooptical features have been studied most thoroughly. Chapter 1 states the main physical ideas about the electronic structure and energy spectrum of the RE ions. Foundational to the detailed analyses we present in the forthcoming chapters, we include information on the crystalline structure of the materials and the magnetic features of the paramagnetic compounds containing the RE ions having either Kramers or non-Kramers energy sublevels (Stark levels). Systematics of RE garnets and orthoaluminates are presented, with special attention paid to the description of the strongly anisotropic (“Ising”) character found in the magnetic behavior of some RE ions. Chapter 2 discusses the current methods used to calculate RE3+ transition energies and intensities of forbidden (in the electric-dipole approximation) optical 4f → 4f transitions in RE compounds. Results obtained from recently developed experimental methods used to measure the optical features of RE compounds (such as hot-band spectroscopy and site-selective polarized spectroscopy) are interpreted in detail by applying group theory to the analyses of the optical spectra of several RE ions in crystal field environments of low symmetry, specifically Cs (orthoaluminate systems) and D2 (garnet systems). Also, a theoretical description of the optical spectra within the ultraviolet spectral range associated with the allowed 4f → 5d transitions in the Tb3+ and Ce3+ garnets is analyzed within the framework of a “strong-weak” crystalline field approximation. Chapter 3 presents the underlying principles of the phenomenological theory of magnetooptical phenomena that is general for all rare-earth dielectrics. A quantum-mechanical theory for the linear magnetooptical effects in paramagnetic RE garnets due to the allowed electric-dipole 4f → 5d transitions is considered in detail in the approximation of an “average” crystalline field. The theory of the Faraday effect is also applied to magnetic-dipole transitions in several RE ions. The role of the Van-Vleck contribution of mixing in the circular magnetooptics of the Eu3+, Sm3+ and Gd3+ RE 1
ions in the garnets is discussed in detail. The special features of the Faraday effect (FE) and magnetic circular dichroism (MCD) in YAG activated by the Tb3+ and Ce3+ RE ions are considered in the approximation of a “strong-weak” crystalline field within the ultraviolet spectral range. The nature of the magnetooptical activity (MOA) mechanism in the RE compounds with orthoaluminate structure is discussed using group theory as the tool for analysis. As a separate topic, the appearence of the so-called “Anti-Zeeman” effect is considered in the absorption spectra of terbium-gallium garnet TbGG in a magnetic field. Chapter 4 considers the basic physical ideas concerning the magnetooptics of radiative 4f → 4f transitions in RE compounds. Spectra are analyzed in depth that display the degree of magnetic circular polarization luminescence (MCPL) of the Tb3+ and Ho3+ non-Kramers RE ions in garnets. We discuss the special features regarding the behavior of the MCPL degree spectra of the paramagnetic garnet DyYAG which may be explained by the “quasi-Ising” behavior of the Dy3+ non-Kramers RE ion. At the same time, the large values of the MCPL degree observed in Er:YAG are explained by a Van-Vleck mixing of the excited states of the Er3+ RE ion by the external magnetic field. Even the rather general questions that arise regarding the theory that is required to explain the data are answered in this book with simple model approximations. It is our opinion that using these simple models makes it easier for a reader to understand the physical aspects of the questions that are involved, and at the same time allows us to perform direct mathematical calculations to obtain a final result without complicated mathematical methods of calculations. We should like to point out that the text does not represent a comprehensive monograph on the physics of the optical and magnetooptical phenomena found in all rare earth compounds, which covers a wide range of topics and material hosts not addressed by the authors. Some of these topics fall outside the present interest of the authors. However, research on other topics (both experimental and theoretical) in this field are presently underway by the authors, for which the space required here would have been prohibitive. Also, this text is not the first attempt to describe in detail the special features of the optical and magnetooptical phenomena in rare-earth compounds since a number of the interesting problems connected with the use of the magnetooptical methods of studying the 3d and 4f ions in crystals have already been considered in sufficient detail in the books published by the other authors: S.B. Piepho and P.N. Schatz, “Group Theory in Spectroscopy with Application to Magnetic Circular Dichroism” (Wiley, New York, 1983); A.K. Zvezdin and A.V. Kotov, “Modern Magneto-optics and Magnetooptical Materials” (Insitute of Physics Publishing, Philadelphia, 1997). Finally, we acknowledge that the experimental and theoretical results presented in this book could not have been realized without the active assistance and fruitful cooperation of our friends and colleagues, most notably, Profs. R.Z. Levitin, G.S. Krinchik, A.K. Zvezdin, A.I. Popov, A.S. Moskvin, I.S. Edelman (Russia), B.Yu. Sokolov (Uzbekistan), V. Nekvasil (Czech. Republic), and D.K. Sardar, and B. Zandi (USA). We thank them for their help and support.
2
https://books.google.com/books?id=SqbvBQAAQBAJ&pg=PA1&lpg=PA1&dq=magnetooptical +spectroscopy+of+the+rareearth+compounds:+development+and+application&source=bl&ots=EwvySSH7WS&sig=CLfrJhlj93QAFBRD6YeTL5lqI&hl=en&sa=X&ei=Tw7iVKe5J4WQyASysoGYCg&ved=0CD0Q6AEwBQ#v=onepage&q&f= false
