CHARACTERIZATION OF MATERIALS 495
W22.32 Electron-Spin Resonance
Much of the inner workings of atoms has been elucidated by employing resonance
techniques in conjunction with the use of external magnetic fields. The physics of the
atom is described in terms of a succession of contributions to the Hamiltonian. These
describe the kinetic energy, the electrostatic interaction between the electrons and the
nucleus, the electron–electron electrostatic interactions, the spin–orbit coupling, the
spin–spin interaction, the interaction of the electron orbital angular momentum L and
spin S with external magnetic fields, the hyperfine interaction, the nuclear Zeeman and
quadrupole couplings, and various relativistic and quantum-electrodynamic corrections.
If the atom is not free but is embedded in a crystal, one must, in addition, consider the
effect of the crystal electric field imposed by the neighboring ions and electrons, the
interaction of the atomic spin with the spins on nearby atoms, and the possibility of
losing electrons to or gaining electrons from other atoms of the solid. These effects are
often by no means small and lead to major perturbations of the energy levels and the
corresponding spectroscopy. To the extent that they can be understood, however, they
provide a powerful analytical tool for probing the solid. The field is called electron-spin
resonance (ESR) or sometimes electron paramagnetic resonance (EPR). For simple
electron-spin systems, ESR may be described in terms of the Bloch equations, although
the quantum-mechanical approach is used in this section.
ESR is a very rich field and cannot be summarized adequately in a short amount of
space. It can provide information concerning donor or acceptor impurities in semicon-
ductors. It can be used to study transition metal ions. It is useful for analyzing color
centers in insulators. It is sensitive to electron and hole traps. There are two simple
uses for it: determining the symmetry of the site where the spin sits and determining
the valence of the magnetic ion.
In atomic physics one is concerned with the coupling of the nuclear spin, I,to
the electronic spin, J D L C S, to form a total angular momentum F D I C J.Inthe
presence of a magnetic induction B D
O
kB
0
, the Hamiltonian for a given electronic term
is written as
H D (L
· S C
B
B · L CgS C AS · I C
N
B · I,W22.208
where the first term is the spin–orbit coupling, the second term is the electronic Zeeman
effect, the third term represents the hyperfine coupling, and the last term is the nuclear
Zeeman effect (which is three orders of magnitude weaker). The parameter g is the
g factor of the electron and is approximately 2. One usually forms matrix elements
of this Hamiltonian in an appropriate basis, diagonalizes the matrix, and interprets the
eigenvalues as the energy levels. Resonance spectroscopy may then be used to drive
transitions between the energy levels and therefore to deduce the coupling constants,
( and A, as well as to determine L, S,andI.
The same basic idea is used in the solid, but the Hamiltonian becomes more compli-
cated. First, quenching of the orbital angular momentum may occur. This occurs in
the sp-bonded materials and transition metal ions (but not in the rare earths with f
electrons, which need to be considered separately). Since the crystal is not an isotropic
medium, the mean orbital angular momentum operator does not commute with the
potential energy function. On the other hand, to a first approximation, the electron and
nuclear spins are impervious to the presence of this anisotropy. In place of the full
rotational symmetry of the free atom, there is the point-group symmetry of the crystal.