Biomedical Engineering Reference
In-Depth Information
discovery of large ferroelectric polarization in epitaxially grown thin i lms
of BiFeO
3
and the discovery of strong magnetic and electric coupling in
orthorhombic TbMnO
3
and TbMn
2
O
5
, restimulated activity in the i eld of
multiferroics [18, 19].
13.1.3.2
Properties of Multiferroics
13.1.3.2.1 Reversal Symmetry
Ferromagnetic and ferroelectric properties have the same reversal symme-
tries as magnetic and electric i eld. From the Maxwell equations,
E
4
(13.1)
B
E
(13.2)
t
it is clear that electric i elds are invariant under time reversal but will get
a minus sign under spatial reversion, while magnetic i elds are invariant
under spatial reversion but will get a minus sign under time reversion; and
this totally opposite property in symmetry is one of the reasons that people
think ferromagnetism and ferroelectricity exclude each other. h e reversal
symmetries for ferroics are presented in Table 13.1.
13.1.3.2.2 Microscopic Double-Exchange Model
h e multiferroic materials exhibit microscopic double-exchange model
which contains:
• Electron hopping between sites
• Coulomb interaction between electrons
• Superexchange coupling between spins
• Electron-phonon coupling
Table 13.1
Reversal symmetries table for ferroics [20].
Characteristic
symmetry?
Spatial-inversion
symmetry
Time-reversal
Symmetry?
Ferroelastic
Yes
Yes
Ferroelectric
No
Yes
Ferromagnetic
Yes
No
