Unfortunately, the effect in single-phase compounds is very small what makes it
difficult to register and limits its practical application. One of the candidates to
exhibit such phenomena are materials which are ferroelectrics with ferromagnetism.
Ferroelectricity is associated with a static charge distribution in a unit cell. Thus,
it needs the broken spatial inverse symmetry while the time reverse symmetry can
be invariant. It means that a spontaneous polarization would not appear unless a
structural distortion of the high-symmetry phase breaks the inversion symmetry.
Ferroelectric transition needs a change of symmetry in the system from a centrosymmetric (paraelectric) phase to a non-centrosymmetric (ferroelectric) one.
Most conventional ferroelectrics which are technologically important are perovskite
structure (ABO 3 ) oxides with the transition metal at B-site. These transition metal
ions should have an empty d-shell and have a formal configuration d
0 like Ti
4+ ,
Nb
5+ , Ta
5+ , W
6+ [26–28].
Magnetism is a dynamic effect which is related to spin order and needs the
broken time-reversal symmetry while spatial inverse symmetry may be invariant.
Indeed, most of conventional magnetic materials have a centrosymmetric crystal
structure. Additionally, magnetism requires transition metal ions with partially filled
d- or f-shells. It is because the spins of electrons on the completely filled shells add
to zero and no magnetic moment is observed and in this way they do not participate
in magnetic ordering [27].
Based on symmetry consideration, magnetoelectrics should have broken spatial
and time-reversal symmetry. Thus, among all of the 233 Shubnikov magnetic point
groups, only 13 point groups fulfill the requirements and allow the possibility to
observe spontaneous magnetic and electric polarization. This is one of explanation
why multiferroics are rare in nature and there is practically no overlap between
magnetic and ferroelectric oxides. Even there are hundreds of magnetic and ferroelectric oxides, separately [27].
One of the possibilities to overcome those problems is to synthesize materials
which have two different sublattices like in BiFeO 3 which is perovskite (ABO 3 )type oxide. The A-sites (Bi
3+ ) favor the stability of the ferroelectric distorted
structure, and the sublattice is responsible for electric polarization. At the same
time, the B-sites contain magnetic (Fe
3+ ) ions which provide magnetism. Thus,
ferroelectricity is induced by the ions at the A-sites, and the B-sites ions induce
magnetic order. In this way, the above exclusion rule of ferroelectricity and magnetism can be obeyed [26–28].
Another option is to mix both magnetic and ferroelectric active ions in the same
sublattice, e.g., Pb(Fe 0.5 Nb 0.5 )O 3 where at the B-sites Nb
5+ ions, which have empty
d-shell and are ferroelectric active, are partially substituted by Fe
3+ ions, which
have partially filled d-shell and are magnetically active. In this system, Nb
5+ stabilizes off-centrosymmetric distortion of the regular perovskite phase while Fe
3+
cations work in opposite way. Thus, the magnetic doping cannot be
over-concentrated. These systems are called independent. The dilution of the
electrical active system leads to a decrease of electric polarization and Curie temperature. In this system, rather low electric and magnetic ordering temperatures are
observed. The coupling between magnetic and ferroelectric order in this kind of
284
P. Stoch and A. Stoch
difficult to register and limits its practical application. One of the candidates to
exhibit such phenomena are materials which are ferroelectrics with ferromagnetism.
Ferroelectricity is associated with a static charge distribution in a unit cell. Thus,
it needs the broken spatial inverse symmetry while the time reverse symmetry can
be invariant. It means that a spontaneous polarization would not appear unless a
structural distortion of the high-symmetry phase breaks the inversion symmetry.
Ferroelectric transition needs a change of symmetry in the system from a centrosymmetric (paraelectric) phase to a non-centrosymmetric (ferroelectric) one.
Most conventional ferroelectrics which are technologically important are perovskite
structure (ABO 3 ) oxides with the transition metal at B-site. These transition metal
ions should have an empty d-shell and have a formal configuration d
0 like Ti
4+ ,
Nb
5+ , Ta
5+ , W
6+ [26–28].
Magnetism is a dynamic effect which is related to spin order and needs the
broken time-reversal symmetry while spatial inverse symmetry may be invariant.
Indeed, most of conventional magnetic materials have a centrosymmetric crystal
structure. Additionally, magnetism requires transition metal ions with partially filled
d- or f-shells. It is because the spins of electrons on the completely filled shells add
to zero and no magnetic moment is observed and in this way they do not participate
in magnetic ordering [27].
Based on symmetry consideration, magnetoelectrics should have broken spatial
and time-reversal symmetry. Thus, among all of the 233 Shubnikov magnetic point
groups, only 13 point groups fulfill the requirements and allow the possibility to
observe spontaneous magnetic and electric polarization. This is one of explanation
why multiferroics are rare in nature and there is practically no overlap between
magnetic and ferroelectric oxides. Even there are hundreds of magnetic and ferroelectric oxides, separately [27].
One of the possibilities to overcome those problems is to synthesize materials
which have two different sublattices like in BiFeO 3 which is perovskite (ABO 3 )type oxide. The A-sites (Bi
3+ ) favor the stability of the ferroelectric distorted
structure, and the sublattice is responsible for electric polarization. At the same
time, the B-sites contain magnetic (Fe
3+ ) ions which provide magnetism. Thus,
ferroelectricity is induced by the ions at the A-sites, and the B-sites ions induce
magnetic order. In this way, the above exclusion rule of ferroelectricity and magnetism can be obeyed [26–28].
Another option is to mix both magnetic and ferroelectric active ions in the same
sublattice, e.g., Pb(Fe 0.5 Nb 0.5 )O 3 where at the B-sites Nb
5+ ions, which have empty
d-shell and are ferroelectric active, are partially substituted by Fe
3+ ions, which
have partially filled d-shell and are magnetically active. In this system, Nb
5+ stabilizes off-centrosymmetric distortion of the regular perovskite phase while Fe
3+
cations work in opposite way. Thus, the magnetic doping cannot be
over-concentrated. These systems are called independent. The dilution of the
electrical active system leads to a decrease of electric polarization and Curie temperature. In this system, rather low electric and magnetic ordering temperatures are
observed. The coupling between magnetic and ferroelectric order in this kind of
284
P. Stoch and A. Stoch