Lectures on

Eugene Chudnovsky and Javier Tejada

224 pages, 9x6 inches
April 2006 Soft Cover
ISBN 1-58949-035-5


      Buy It


This is a textbook for graduate and upper-level undergraduate students, written by two prominent researchers (theorist and experimentalist) who have taught university-level magnetism for 30 years. It is designed as a self-contained one-semester course in modern and conventional magnetism that should prepare students for reading contemporary scientific literature.

The book is divided into three Chapters that discuss magnetic phenomena according to their spatial scale. The nanometer scale of individual atoms and molecules is considered in the first Chapter. The second Chapter studies microscopic models of the magnetic order in systems of many interacting atoms or itinerant electrons. Magnetism at the mesoscopic scale of magnetic domains is discussed in the third Chapter.

In selecting material for the book, the authors were giving preference to simple mathematically rigorous models that attempt to explain magnetic phenomena qualitatively. Such models form the language of condensed matter physics necessary for quantitative experimental or numerical study of solids. Throughout the book the agreement between theory and experiment is illustrated by data taken from real magnetic materials.

Each section is designed as a lecture. All derivations can be followed by the students step by step through independent reading or when presented on the blackboard by the instructor.  The derivations are self-contained or use results obtained in previous sections. Each section is accompanied by a few homework problems. Some require numerical work with common mathematical software.

Problem Solutions to Lectures on Magnetism is published in a separate book (ISBN 1-58949-56-8) 


1.      Magnetism at the Nanoscale
          1.1   Angular momentum and spin
          1.2   Magnetism of atoms
          1.3   Hydrogen molecule
          1.4   Exchange interaction and magnetic anisotropy
          1.5   Superparamagnetism
          1.6   Quantum mechanics of a large spin
          1.7   Quantum magnetization curve
          1.8   Spin-lattice relaxation of rigid atomic clusters

2.      Magnetism at the Microscopic Scale
          2.1   One-dimensional Heisenberg model
.2   Two-dimensional XY model

          2.3   Three-dimensional Heisenberg ferromagnet
          2.4   Three-dimensional antiferromagnet
          2.5   Magnetism of the electron gas
          2.6   Stoner model
          2.7   Spin excitations in Stoner model
          2.8   RKKY interaction

3.      Magnetism at the Mesoscopic Scale
          3.1   Field models of magnetization
          3.2   Exchange model in two dimensions
          3.3   Magnetic domains and domain walls
          3.4   Random anisotropy model of amorphous magnet
          3.5   Landau-Lifshitz equation
          3.6   Spin waves
          3.7   Magnetic resonance 
          3.8   Magnetic instantons


Magnetism of solids transcends many areas of condensed matter physics. It is one of the most important topics of material science. Until recently, fundamental theory and applications of magnetic materials have been rather far apart. Founding fathers of quantum physics focused their attention on explanation of magnetic order within quantum theory of interacting spins. This also has been the trend of modern theory of magnetism, especially in application to low-dimensional systems. On the contrary, most of practical applications of magnetic materials (such as, e.g., magnetic recording) are based upon classical theory. This is because the magnetic moment, formed by quantum interactions at the nanoscale, behaves as a macroscopic classical vector at the mesoscopic scale of, e.g., magnetic memory units. With the emergence of experimental nanoscience this situation has changed. Solid state experiment has approached the spatial scale where quantization of the magnetic moment becomes apparent. The field of molecular magnetism is one example of such a research. In this book we have attempted to show beautiful non-trivial connections between physics and mathematics of magnetic phenomena at different spatial scales. Magnetism at the nanometer scale of individual atoms and molecules is discussed in the first Chapter. Magnetic order at the mesoscopic scale of many interacting atoms and itinerant electrons is studied in the second Chapter. Magnetism at the macroscopic scale of magnetic domains is considered in the third Chapter.

The motivation for writing this book came in part from our observation that the basic knowledge of magnetism of solids among young physicists has been steadily declining. The reason is obvious. Due to the enormous progress of condensed matter physics during the last 50 years, the time allocated by university programs to each topic has reduced dramatically. Responding to that trend we have attempted to write a compact one-semester course on magnetism of solids for graduate and upper-level undergraduate students. In selecting the material we were guided by the principle that physics can only be understood through mathematics. The preference was given to simple mathematically rigorous models that explain magnetic phenomena qualitatively. Each of the 24 Sections of the book is designed as a lecture. All derivations are self-contained or use results obtained in previous sections. They can be followed by students step by step when presented on the blackboard or through independent reading. Each Section is accompanied by homework problems. Most of the problems are of analytical nature but some require simple numerical work with common mathematical software. Solutions of all problems are presented in an independent book co-authored by our students, Carlos Calero and Ferran Macia. Throughout the book we are using International System of units. The reader should keep this in mind when comparing our formulas with formulas of earlier books on magnetism of solids.

Finally, we would like to acknowledge contribution of our colleague and friend Professor Dmitry Garanin who provided us with invaluable comments at all stages of the work on this book.



Eugene Chudnovsky is a Distinguished Professor of Physics at the City University of New York. He was educated in Russia and spent one year at Tufts University before coming to New York in 1988. Dr. Chudnovsky is best known for his theory of amorphous magnets and his theory of quantum tunneling of the magnetic moment. He has published over 150 research papers and has given numerous invited and plenary talks at scientific meetings.

Dr. Javier Tejada is a Professor of Condensed Matter Physics and the head of the UBXLAB at the University of Barcelona where he directs experimental research in the field of nanomagnetism.  He has published over 250 research papers and holds 12 international patents. Dr. Tejada is best known for his experimental work on spin tunneling and molecular magnetism. He has co-authored a book with E. Chudnovsky on “Quantum Tunneling of the Magnetic Moment” (Cambridge University Press, 1998).

** As a promotional effort, before June 30 2007, the individual buyers will receive a 50% discount if they put order for this title directly to Rinton Sales (sales@rintonpress.com).