relation between physical phenomena and basic properties and how we can influence these. Think for example of magnetic anisotropy and spin-orbit coupling.
Throughout the book the text is interlarded with exercises, stimulating the students to not only read but also verify the assertions and perform (parts of) derivations by themselves. In addition, each chapter ends with a number of problems
that can be used to check whether the material has been understood.
The first chapter of this volume introduces a number of basic concepts and tools
necessary for the development of the theories and methods treated in the following
chapters. It explains various ways to generate many-electron spin-adapted functions, gives an introduction to perturbation theories and to effective Hamiltonian
theory. Chapter 2 treats atoms with and without an external magnetic field. This is
followed by a chapter on systems containing more than one magnetic center. In this
chapter the phenomenological Hamiltonians are introduced, beginning with the
Heisenberg and the Ising Hamiltonian and ending with Hamiltonians that include
biquadratic, cyclic or anisotropic exchange. Chapter 4 explains how quantum
chemical methods, reaching from simple mean field methods to accurate models,
can help to understand the magnetic properties. The simple models can give a
qualitative understanding of the phenomena. The more accurate models, such as
post Hartree-Fock models like DDCI, CASPT2 and NEVPT2 or broken symmetry
models based on density functional theory, are able to produce accurate predictions
of the energies and wave functions of the relevant states. Making accurate computations is one thing, mapping the results back onto the intuitive models yielding
parameters that can be compared with the ones deduced from experiments is
another. Effective Hamiltonian theory is a powerful tool to make these connections,
as shown in Chap. 5. The last chapter explains how the magnetic interactions in
solid-state compounds can be treated, with embedded cluster models and with
periodic approaches. It gives an account of the double exchange mechanism in
mixed valence systems, explaining the Goodenough-Kanamori rules. Finally, an
account is given of spin wave theory for (anti-)ferromagnets.
The book covers a full Master’s course, but a shorter course can be distilled from
it in many ways. One of them includes Chap. 2, the first two sections of Chap. 3 and
optionally one of the subsections of 3.4 to get acquainted with the spin Hamiltonian
formalism. After that, Sects. 4.1.1 and 4.1.2 combined with Sects. 4.3.1, 4.3.2 and
4.3.4 can be studied to connect the quantitative and qualitative computational
viewpoints of magnetic interactions. From Chap. 5, we recommend to include
Sects. 5.1.1 and 5.3, which provide us with the basic tools for analysis. If time
permits, one can close the short course with a brief account on some issues related
to the solid state: Sects. 6.3 and 6.5 provide some basic notions on this topic.
We end by noting that the outstanding book by the late Prof. Olivier Kahn,
O. Kahn, Molecular Magnetism, VCH Publishers, 1993, has been an inspiration for
the entire book.
Tarragona
Coen de Graaf
Groningen
Ria Broer
July 2015
viii
Preface
Throughout the book the text is interlarded with exercises, stimulating the students to not only read but also verify the assertions and perform (parts of) derivations by themselves. In addition, each chapter ends with a number of problems
that can be used to check whether the material has been understood.
The first chapter of this volume introduces a number of basic concepts and tools
necessary for the development of the theories and methods treated in the following
chapters. It explains various ways to generate many-electron spin-adapted functions, gives an introduction to perturbation theories and to effective Hamiltonian
theory. Chapter 2 treats atoms with and without an external magnetic field. This is
followed by a chapter on systems containing more than one magnetic center. In this
chapter the phenomenological Hamiltonians are introduced, beginning with the
Heisenberg and the Ising Hamiltonian and ending with Hamiltonians that include
biquadratic, cyclic or anisotropic exchange. Chapter 4 explains how quantum
chemical methods, reaching from simple mean field methods to accurate models,
can help to understand the magnetic properties. The simple models can give a
qualitative understanding of the phenomena. The more accurate models, such as
post Hartree-Fock models like DDCI, CASPT2 and NEVPT2 or broken symmetry
models based on density functional theory, are able to produce accurate predictions
of the energies and wave functions of the relevant states. Making accurate computations is one thing, mapping the results back onto the intuitive models yielding
parameters that can be compared with the ones deduced from experiments is
another. Effective Hamiltonian theory is a powerful tool to make these connections,
as shown in Chap. 5. The last chapter explains how the magnetic interactions in
solid-state compounds can be treated, with embedded cluster models and with
periodic approaches. It gives an account of the double exchange mechanism in
mixed valence systems, explaining the Goodenough-Kanamori rules. Finally, an
account is given of spin wave theory for (anti-)ferromagnets.
The book covers a full Master’s course, but a shorter course can be distilled from
it in many ways. One of them includes Chap. 2, the first two sections of Chap. 3 and
optionally one of the subsections of 3.4 to get acquainted with the spin Hamiltonian
formalism. After that, Sects. 4.1.1 and 4.1.2 combined with Sects. 4.3.1, 4.3.2 and
4.3.4 can be studied to connect the quantitative and qualitative computational
viewpoints of magnetic interactions. From Chap. 5, we recommend to include
Sects. 5.1.1 and 5.3, which provide us with the basic tools for analysis. If time
permits, one can close the short course with a brief account on some issues related
to the solid state: Sects. 6.3 and 6.5 provide some basic notions on this topic.
We end by noting that the outstanding book by the late Prof. Olivier Kahn,
O. Kahn, Molecular Magnetism, VCH Publishers, 1993, has been an inspiration for
the entire book.
Tarragona
Coen de Graaf
Groningen
Ria Broer
July 2015
viii
Preface