magnetic storage of information, energy harvesters, antennas, transformers [1].
Unfortunately, the coupling and thus the effect is small what strongly reduce the
possibility of application of the materials. The magnetoelectricity is related to the
structure and its changes what additionally makes that they are really rare in nature.
In this chapter, we focus on an exemplary group of magnetoelectrics which are
oxides with a perovskite structure and especially on two examples like BiFeO 3 and
Pb(Fe 0.5 Nb 0.5 )O 3 in which coupling between magnetic and electric systems is
realized in a different way. However, in the beginning, we want to bring the reader
closer to
57 Fe Mössbauer spectrometry and the hyperfine interactions.
9.2 Mössbauer Spectroscopy
Mössbauer spectroscopy is one of the methods which gives the possibility to look at
the structure of the tested material from inside, from the point of view of the tested
nuclei. The fundamental of the method is an observation of recoilless emission and
resonant absorption of c-radiation by atomic nuclei. The resonant nuclear absorption is possible to be observed only if the given system is provided the amount of
energy equal the difference between lower and higher energy nuclear levels. This
can be possible between two the same atomic nuclei of which the first one is in the
excited state and the second in the ground state. The nucleus during the transition
from the excited to the ground state emits c quantum of energy precisely equal to
the difference in energy between those two states. The emitted quantum of energy
can be absorbed by the second nucleus which is in the ground state. The nucleus
absorbs the energy and is transferred to the excited state. This is the nuclear resonance transition between excited and ground states in the two nuclei. The process
is possible only if the energy difference between the excited and ground state is the
same for emitting and absorbing nuclei, and in this way a resonance condition is
achieved. Unfortunately, during the c quantum emission, the nucleus undergoes a
recoil process. Based on simple energy conservation rule, the emitting energy is less
by the recoil energy. The similar but opposite process is observed during the
absorption. The absorbing nucleus undergoes the recoil process, and the transferred
energy must be increased by the recoil energy. Thus, taking into account these two
processes, the energy of the c quantum should be higher by exactly twice the recoil
energy. The most well-known and frequently used Mössbauer isotope is
57 Fe for
which the c emission energy is 14.4 keV and the recoil energy is below
2 Â 10
−2 eV. Thus, to fulfill the resonance conditions in this case, the c quantum
energy should be increased by 4 Â 10
−2 eV. Although comparing these energies,
the difference is several orders, and the resonant condition cannot be observed. The
recoil energy is in inverse proportion to the mass of the system. If we were able to
somehow increase this mass, the recoil energy would be much smaller. Fortunately,
if we place the emitting and absorbing nuclei in a crystal lattice, there is a finite
probability that the momentum of the recoil accompanying the emission or
absorption of a photon is taken over by the crystal lattice. Thus, the mass in recoil
274
P. Stoch and A. Stoch
Unfortunately, the coupling and thus the effect is small what strongly reduce the
possibility of application of the materials. The magnetoelectricity is related to the
structure and its changes what additionally makes that they are really rare in nature.
In this chapter, we focus on an exemplary group of magnetoelectrics which are
oxides with a perovskite structure and especially on two examples like BiFeO 3 and
Pb(Fe 0.5 Nb 0.5 )O 3 in which coupling between magnetic and electric systems is
realized in a different way. However, in the beginning, we want to bring the reader
closer to
57 Fe Mössbauer spectrometry and the hyperfine interactions.
9.2 Mössbauer Spectroscopy
Mössbauer spectroscopy is one of the methods which gives the possibility to look at
the structure of the tested material from inside, from the point of view of the tested
nuclei. The fundamental of the method is an observation of recoilless emission and
resonant absorption of c-radiation by atomic nuclei. The resonant nuclear absorption is possible to be observed only if the given system is provided the amount of
energy equal the difference between lower and higher energy nuclear levels. This
can be possible between two the same atomic nuclei of which the first one is in the
excited state and the second in the ground state. The nucleus during the transition
from the excited to the ground state emits c quantum of energy precisely equal to
the difference in energy between those two states. The emitted quantum of energy
can be absorbed by the second nucleus which is in the ground state. The nucleus
absorbs the energy and is transferred to the excited state. This is the nuclear resonance transition between excited and ground states in the two nuclei. The process
is possible only if the energy difference between the excited and ground state is the
same for emitting and absorbing nuclei, and in this way a resonance condition is
achieved. Unfortunately, during the c quantum emission, the nucleus undergoes a
recoil process. Based on simple energy conservation rule, the emitting energy is less
by the recoil energy. The similar but opposite process is observed during the
absorption. The absorbing nucleus undergoes the recoil process, and the transferred
energy must be increased by the recoil energy. Thus, taking into account these two
processes, the energy of the c quantum should be higher by exactly twice the recoil
energy. The most well-known and frequently used Mössbauer isotope is
57 Fe for
which the c emission energy is 14.4 keV and the recoil energy is below
2 Â 10
−2 eV. Thus, to fulfill the resonance conditions in this case, the c quantum
energy should be increased by 4 Â 10
−2 eV. Although comparing these energies,
the difference is several orders, and the resonant condition cannot be observed. The
recoil energy is in inverse proportion to the mass of the system. If we were able to
somehow increase this mass, the recoil energy would be much smaller. Fortunately,
if we place the emitting and absorbing nuclei in a crystal lattice, there is a finite
probability that the momentum of the recoil accompanying the emission or
absorption of a photon is taken over by the crystal lattice. Thus, the mass in recoil
274
P. Stoch and A. Stoch