Chapter 2
Concepts in Magnetism
Stephen J. Blundell
Abstract I review some general concepts in magnetism including the nature of
magnetic exchange (direct, indirect and superexchange), and how exchange interactions play out in multiple spin systems. The nature of atomic orbitals and the way
in which they interact with the spin system is also considered. Several examples are
also treated, including the Jahn–Teller interaction and its role in the properties in
layered manganites.
2.1 Introduction
Magnetic properties are found in a wide variety of materials. In order to explain magnetism we need to consider a range of different behaviours in many different types
of magnetic system. Consider the following: Fe and Ni are both metallic elements
and exhibit ferromagnetism; MnO is an insulating oxide with a three-dimensional
antiferromagnetic structure; La 2 CuO 4 is a layered material which exhibits antiferromagnetism but, when doped, becomes superconducting; some compounds do not
order magnetically but show frustrated effects with an abundance of slow dynamics;
some molecules become single-molecule magnets in which the individual molecules
show quantum tunnelling of magnetization and a range of other interesting properties.
Theories of magnetism have to explain all these materials and more.
For a start, we must realize that a classical approach will not work. The Bohr–van
Leeuwen theorem [1] states that in a classical system there is no thermal equilibrium magnetization. We can prove this in outline as follows: in classical statistical
mechanics the partition function Z for N particles, each with charge q, is proportional to
· · ·
exp
−β E({r i , p i }
dr 1 · · · dr N d p 1 · · · d p N ,
(2.1)
S. J. Blundell (B)
Clarendon Laboratory, Oxford University, Department of Physics, Parks Road,
Oxford OX1 3PU, UK
e-mail: stephen.blundell@physics.ox.ac.uk
© The Author(s) 2021
H. Bulou et al. (eds.), Magnetism and Accelerator-Based Light Sources,
Springer Proceedings in Physics 262,
https://doi.org/10.1007/978-3-030-64623-3_2
39
Concepts in Magnetism
Stephen J. Blundell
Abstract I review some general concepts in magnetism including the nature of
magnetic exchange (direct, indirect and superexchange), and how exchange interactions play out in multiple spin systems. The nature of atomic orbitals and the way
in which they interact with the spin system is also considered. Several examples are
also treated, including the Jahn–Teller interaction and its role in the properties in
layered manganites.
2.1 Introduction
Magnetic properties are found in a wide variety of materials. In order to explain magnetism we need to consider a range of different behaviours in many different types
of magnetic system. Consider the following: Fe and Ni are both metallic elements
and exhibit ferromagnetism; MnO is an insulating oxide with a three-dimensional
antiferromagnetic structure; La 2 CuO 4 is a layered material which exhibits antiferromagnetism but, when doped, becomes superconducting; some compounds do not
order magnetically but show frustrated effects with an abundance of slow dynamics;
some molecules become single-molecule magnets in which the individual molecules
show quantum tunnelling of magnetization and a range of other interesting properties.
Theories of magnetism have to explain all these materials and more.
For a start, we must realize that a classical approach will not work. The Bohr–van
Leeuwen theorem [1] states that in a classical system there is no thermal equilibrium magnetization. We can prove this in outline as follows: in classical statistical
mechanics the partition function Z for N particles, each with charge q, is proportional to
· · ·
exp
−β E({r i , p i }
dr 1 · · · dr N d p 1 · · · d p N ,
(2.1)
S. J. Blundell (B)
Clarendon Laboratory, Oxford University, Department of Physics, Parks Road,
Oxford OX1 3PU, UK
e-mail: stephen.blundell@physics.ox.ac.uk
© The Author(s) 2021
H. Bulou et al. (eds.), Magnetism and Accelerator-Based Light Sources,
Springer Proceedings in Physics 262,
https://doi.org/10.1007/978-3-030-64623-3_2
39