magnetoelectrics is rather low because these two orders originate from different
kinds of ions [27, 29].
9.3.1 ABO 3 Perovskites
Most of the conventional ferroelectric oxides have perovskite structure, and also
there are hundreds of magnetic oxide perovskite. Therefore, these materials were
one of the first choices to look for the unique ones which would join both of the
groups in the same crystal phase and temperature.
Perovskites are a class of compounds with a structure related to the mineral
Perovskite (CaTiO 3 ) and can be characterized by general formula ABO 3 where A is
usually a large cation and B is usually a medium-sized cation. The idealized perovskite structure is cubic of Pm-3 m space group (No. 221). In the structure, large
A
2+ cation occupies Wyckoff position 1a (0, 0, 0) at the corners of the cubic unit
cell. The B
4+ ion lies at position 1b (0.5, 0.5, 0.5) at the center of the unit cell and is
surrounded by a regular octahedron of O
2− ions at 3c (0.5, 0.5, 0) positions. The
large A
2+ cations are coordinated to 12 O
2− anions. Thus, they are surrounded by a
cuboctahedral cage of O
2−
. The smaller B
4+ cations are placed in the middle of
[BO 6 ] octahedra which create a regular framework. All of the B
4+
–O
2− bond
lengths are equal, and the six O
2−
–B
4+
–O
2− bonds are linear. Thus, each B
4+ cation
has six neighbors in the B-sublattice. The ideal perovskite structure has no adjustable atomic position parameters, so any compositional change must be accommodated by a change in lattice parameter [30].
The ideal cubic perovskite structure is centrosymmetric what based on our
previous consideration about symmetry conditions in ferroelectrics and breaking the
spatial inverse symmetry leads to the conclusion that charge polarization in this
kind of materials cannot be observed. On the other hand, there are hundreds of
ferroelectrics in perovskite structure. There should exist a mechanism of cation
displacement which leads to structural distortion in order to obtain
non-centrosymmetric crystal lattice. This mechanism is the pseudo or second order
Jahn–Teller effect which is related to B
4+ ions with formal empty d-shell (d
0 ). The
effect is spontaneous symmetry breaking which is occurring in nondegenerate states
in the systems with sufficiently low-lying excited states. The driving force of this
distortion is an improvement of covalency. In result of this distortion, there is the
energy gain due to better covalence bonding between the atoms in the distorted
structure. To obtain a maximum degree of symmetry, cation displacement needs to
be realized along one of the symmetry axes of the octahedron. In case of ferroelectric materials, it is realized very often by transformation from ideal perovskite
cubic (Pm-3 m) structure at temperatures above Curie (paraelectric state) to
tetragonal which is stable below Curie temperature (ferroelectric phase). The cubic
cell expands slightly along c-axis and is compressed along a- and b-axes and adopts
P4 mm (No. 99) space group. The change leads to off-center movement of the
octahedrally coordinated B
4+ cation along c-axis. This elongation can be realized
9 Mössbauer Spectroscopy of Magnetoelectric Perovskite Oxides
285
kinds of ions [27, 29].
9.3.1 ABO 3 Perovskites
Most of the conventional ferroelectric oxides have perovskite structure, and also
there are hundreds of magnetic oxide perovskite. Therefore, these materials were
one of the first choices to look for the unique ones which would join both of the
groups in the same crystal phase and temperature.
Perovskites are a class of compounds with a structure related to the mineral
Perovskite (CaTiO 3 ) and can be characterized by general formula ABO 3 where A is
usually a large cation and B is usually a medium-sized cation. The idealized perovskite structure is cubic of Pm-3 m space group (No. 221). In the structure, large
A
2+ cation occupies Wyckoff position 1a (0, 0, 0) at the corners of the cubic unit
cell. The B
4+ ion lies at position 1b (0.5, 0.5, 0.5) at the center of the unit cell and is
surrounded by a regular octahedron of O
2− ions at 3c (0.5, 0.5, 0) positions. The
large A
2+ cations are coordinated to 12 O
2− anions. Thus, they are surrounded by a
cuboctahedral cage of O
2−
. The smaller B
4+ cations are placed in the middle of
[BO 6 ] octahedra which create a regular framework. All of the B
4+
–O
2− bond
lengths are equal, and the six O
2−
–B
4+
–O
2− bonds are linear. Thus, each B
4+ cation
has six neighbors in the B-sublattice. The ideal perovskite structure has no adjustable atomic position parameters, so any compositional change must be accommodated by a change in lattice parameter [30].
The ideal cubic perovskite structure is centrosymmetric what based on our
previous consideration about symmetry conditions in ferroelectrics and breaking the
spatial inverse symmetry leads to the conclusion that charge polarization in this
kind of materials cannot be observed. On the other hand, there are hundreds of
ferroelectrics in perovskite structure. There should exist a mechanism of cation
displacement which leads to structural distortion in order to obtain
non-centrosymmetric crystal lattice. This mechanism is the pseudo or second order
Jahn–Teller effect which is related to B
4+ ions with formal empty d-shell (d
0 ). The
effect is spontaneous symmetry breaking which is occurring in nondegenerate states
in the systems with sufficiently low-lying excited states. The driving force of this
distortion is an improvement of covalency. In result of this distortion, there is the
energy gain due to better covalence bonding between the atoms in the distorted
structure. To obtain a maximum degree of symmetry, cation displacement needs to
be realized along one of the symmetry axes of the octahedron. In case of ferroelectric materials, it is realized very often by transformation from ideal perovskite
cubic (Pm-3 m) structure at temperatures above Curie (paraelectric state) to
tetragonal which is stable below Curie temperature (ferroelectric phase). The cubic
cell expands slightly along c-axis and is compressed along a- and b-axes and adopts
P4 mm (No. 99) space group. The change leads to off-center movement of the
octahedrally coordinated B
4+ cation along c-axis. This elongation can be realized
9 Mössbauer Spectroscopy of Magnetoelectric Perovskite Oxides
285