This book is designed to provide graduate students and research beginners with an introductory review of recent developments in the field of microscopic magneto-optics. The field contains the most important subjects in solid state physics, chemical physics, and electronic engineering. Microscopic studies of magneto-optics stem from those of ligand-field spectra of paramagnetic ions in solids and liquids, which are also well known to have brought developments in material research for solid-state lasers. As the introductory chapter of this monograph, Chap. 1 deals with the fundamental properties of ligand-field spectra in useful solids. Chapter 2 is on elementary excitations such as magnons and excitons in magnetically ordered crystals, a central aspect of recent developments in microscopic magneto optics. Chapter 3 concerns Raman spectroscopy accompanying magnetic ex citations of high energies in strongly correlated electron systems, which are related to high Tc superconductors. Chapter 4 is on recent developments in the studies of non-linear optical effects, citing experiments for Cr20 and de 3 scribing a microscopic theory for its second harmonic generation. In Chap. 5, after introducing a phenomenological theory of the Faraday and Kerr effects, we present a microscopic theory based on the ligand-field theory and discuss the future developments. Chapter 6 concerns diluted magnetic semiconduc tors, discussing formation, magnetic properties, and quantum confinement effects of magnetic polarons. Chapter 7 is also on diluted magnetic semi conductors, emphasizing the importance in growing new magnetic semicon ductors and in studying their remarkable magneto-optical properties.

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