its coordination polyhedra (Fig. 9.4c). The [FeO 6 ] tilt is not able to fully compensate the ferroelectric distortion and Fe
3+ cations are also slightly shifted along
the c-axis. The displacements of Bi
3+ and Fe
3+ cations are 0.613(1) and 0.212(1) Å,
respectively [39]. This clearly shows that the displacement of Bi
3+ is about three
times larger than Fe
3+ and because of the formal charges of both cations are the
same, the Bi
3+ contributes to the total polarization about three times more. The total
unit cell polarization is along the c-axis.
Below Néel temperature, BFO has G-type antiferromagnetic moments alignment
(Fig. 9.4d). In this kind of alignment, each iron cation has as the nearest B-site iron
which magnetic moment is aligned opposite. Such behavior is a direct consequence
of the superexchange interaction. The Fe
3+ cations of formal configuration 3d
5 have
half-filled d-orbitals and they are separated by non-magnetic oxygen anions. In the
ideal perovskite structure, the Fe–O–Fe bond angle is 180°. Thus, a strongly antiferromagnetic superexchange interaction between nearest neighbor Fe spins occurs.
In the ideal regular case, this interaction would lead to full compensation of magnetic
moments and total magnetic moment of the net should be zero. In fact, BFO has
spatially modulated magnetic structure of a cycloid type with a period of modulation
of about 62 nm and exhibits at room temperature a residual moment arising from a
canted spin structure [36, 41, 42]. Therefore, it can be concluded that there should be
another interaction which has a tendency for parallel alignment of the magnetic
moments which is much weaker than Fe–O–Fe superexchange interaction [43, 44].
This interaction is anisotropic exchange interaction due to the relativistic spin-orbit
coupling called Dzyaloshinskii–Moriya (DM) interaction [45–47]. When the Fe–O–
Fe angle is linear, the DM interaction is zero but in BFO the FeO 6 octahedra are tilted
and it gives the possibility to turn on the interaction which is an order of magnitude
smaller than the superexchange. The DM interaction stabilizes spin canting and
induces an incommensurate magnetic structure with a spin cycloid propagating
along [1 1 0] with periodicity 62–78 nm. Additionally, the DM interaction can
stabilize the observed oxygen displacement which causes net electric polarization
what can be called as the inverse DM interaction [48]. Because of this, the interaction
can cause symmetry breaking rather than be caused by non-centrosymmetric bonds.
On the other hand, due to the inverse DM interaction, the opposite effect can take
place. Thus, electric polarization can induce magnetic polarization and vice versa
and magnetoelectric coupling can be achieved [28, 47, 49].
Bismuth ferrite can be the subject of Mössbauer effect measurements. One can
think that because of high iron concentration, the material is very good to measure
by this technique. Bismuth has a very high absorption coefficient of 14.4 keV
radiation and only very little resonant absorption could be obtained. The effect is a
very little what results in elongation time of measurement. Mössbauer spectroscopy
at first is used in checking the purity of the sample. This technique is very sensitive
to even small amounts of the secondary phase like unreacted Fe 2 O 3 or Bi 2 Fe 4 O 9
which is easily formed during the synthesis due to a strong evaporation of bismuth.
It was found that the magnetic hyperfine field extrapolated to 0 K is 54.6 T and
with increasing temperature is decreased. The temperature dependence of the field
which is proportional to iron magnetic moment fulfills the molecular field model
288
P. Stoch and A. Stoch
3+ cations are also slightly shifted along
the c-axis. The displacements of Bi
3+ and Fe
3+ cations are 0.613(1) and 0.212(1) Å,
respectively [39]. This clearly shows that the displacement of Bi
3+ is about three
times larger than Fe
3+ and because of the formal charges of both cations are the
same, the Bi
3+ contributes to the total polarization about three times more. The total
unit cell polarization is along the c-axis.
Below Néel temperature, BFO has G-type antiferromagnetic moments alignment
(Fig. 9.4d). In this kind of alignment, each iron cation has as the nearest B-site iron
which magnetic moment is aligned opposite. Such behavior is a direct consequence
of the superexchange interaction. The Fe
3+ cations of formal configuration 3d
5 have
half-filled d-orbitals and they are separated by non-magnetic oxygen anions. In the
ideal perovskite structure, the Fe–O–Fe bond angle is 180°. Thus, a strongly antiferromagnetic superexchange interaction between nearest neighbor Fe spins occurs.
In the ideal regular case, this interaction would lead to full compensation of magnetic
moments and total magnetic moment of the net should be zero. In fact, BFO has
spatially modulated magnetic structure of a cycloid type with a period of modulation
of about 62 nm and exhibits at room temperature a residual moment arising from a
canted spin structure [36, 41, 42]. Therefore, it can be concluded that there should be
another interaction which has a tendency for parallel alignment of the magnetic
moments which is much weaker than Fe–O–Fe superexchange interaction [43, 44].
This interaction is anisotropic exchange interaction due to the relativistic spin-orbit
coupling called Dzyaloshinskii–Moriya (DM) interaction [45–47]. When the Fe–O–
Fe angle is linear, the DM interaction is zero but in BFO the FeO 6 octahedra are tilted
and it gives the possibility to turn on the interaction which is an order of magnitude
smaller than the superexchange. The DM interaction stabilizes spin canting and
induces an incommensurate magnetic structure with a spin cycloid propagating
along [1 1 0] with periodicity 62–78 nm. Additionally, the DM interaction can
stabilize the observed oxygen displacement which causes net electric polarization
what can be called as the inverse DM interaction [48]. Because of this, the interaction
can cause symmetry breaking rather than be caused by non-centrosymmetric bonds.
On the other hand, due to the inverse DM interaction, the opposite effect can take
place. Thus, electric polarization can induce magnetic polarization and vice versa
and magnetoelectric coupling can be achieved [28, 47, 49].
Bismuth ferrite can be the subject of Mössbauer effect measurements. One can
think that because of high iron concentration, the material is very good to measure
by this technique. Bismuth has a very high absorption coefficient of 14.4 keV
radiation and only very little resonant absorption could be obtained. The effect is a
very little what results in elongation time of measurement. Mössbauer spectroscopy
at first is used in checking the purity of the sample. This technique is very sensitive
to even small amounts of the secondary phase like unreacted Fe 2 O 3 or Bi 2 Fe 4 O 9
which is easily formed during the synthesis due to a strong evaporation of bismuth.
It was found that the magnetic hyperfine field extrapolated to 0 K is 54.6 T and
with increasing temperature is decreased. The temperature dependence of the field
which is proportional to iron magnetic moment fulfills the molecular field model
288
P. Stoch and A. Stoch