9.2.1.2 Magnetic Hyperfine Field (Nuclear Zeeman Splitting)
The second important hyperfine interaction is the nuclear Zeeman splitting which
will occur if there is a magnetic field at the nucleus. A nucleus in a state with the
spin quantum number I > 0 will interact with a magnetic field by means of its
magnetic dipole moment. The nuclear Zeeman effect splits the nuclear state with the
spin quantum number I into 2I + 1 equally spaced nondegenerate states. For
57 Fe,
the excited state with I = 3/2 is split into four magnetic states and the ground state
with I = 1/2 into two states. Taking into account the selection rules for magnetic
dipole transitions, there are six allowed transitions. The effect is observed as a
resonance sextet. The relative line intensities exhibit a 3:2:1:1:2:3 pattern.
The magnetic hyperfine splitting can be used to determine the effective magnetic
field at the nucleus which is a superposition of an applied external field and an
internal field. The internal field (B int ) can be given as [10]:
B int ¼ B F þ B L þ B d
ð9:4Þ
where B F is the Fermi contact field and is a result of the interaction of the nucleus
with an imbalance in the s-electron spin density at the nucleus; B L is the contribution from the orbital motion of valence electrons with the quantum number L for
the total orbital moment and B d is spin-dipolar contribution arising from
non-spherical distribution of the electronic spin density.
The most important term is the Fermi contact field which is approximately 90%
of the total internal field. The term is a result of polarization effects on filled sorbitals. These can occur if the atom has unpaired electrons in d- or f-orbitals or if it
is chemically bonded to such an atom. The interaction of an unpaired d-electron
with the s-electrons of parallel spin will be different to that with the s-electrons of
opposed spin. The result is unbalanced of spin density at the nucleus [11].
Fig. 9.1 Transmission
57
Fe
Mössbauer effect spectrum of
Fe
2+ in MgO matrix
278
P. Stoch and A. Stoch
The second important hyperfine interaction is the nuclear Zeeman splitting which
will occur if there is a magnetic field at the nucleus. A nucleus in a state with the
spin quantum number I > 0 will interact with a magnetic field by means of its
magnetic dipole moment. The nuclear Zeeman effect splits the nuclear state with the
spin quantum number I into 2I + 1 equally spaced nondegenerate states. For
57 Fe,
the excited state with I = 3/2 is split into four magnetic states and the ground state
with I = 1/2 into two states. Taking into account the selection rules for magnetic
dipole transitions, there are six allowed transitions. The effect is observed as a
resonance sextet. The relative line intensities exhibit a 3:2:1:1:2:3 pattern.
The magnetic hyperfine splitting can be used to determine the effective magnetic
field at the nucleus which is a superposition of an applied external field and an
internal field. The internal field (B int ) can be given as [10]:
B int ¼ B F þ B L þ B d
ð9:4Þ
where B F is the Fermi contact field and is a result of the interaction of the nucleus
with an imbalance in the s-electron spin density at the nucleus; B L is the contribution from the orbital motion of valence electrons with the quantum number L for
the total orbital moment and B d is spin-dipolar contribution arising from
non-spherical distribution of the electronic spin density.
The most important term is the Fermi contact field which is approximately 90%
of the total internal field. The term is a result of polarization effects on filled sorbitals. These can occur if the atom has unpaired electrons in d- or f-orbitals or if it
is chemically bonded to such an atom. The interaction of an unpaired d-electron
with the s-electrons of parallel spin will be different to that with the s-electrons of
opposed spin. The result is unbalanced of spin density at the nucleus [11].
Fig. 9.1 Transmission
57
Fe
Mössbauer effect spectrum of
Fe
2+ in MgO matrix
278
P. Stoch and A. Stoch