Abstract
Two microscopic mechanisms helping us to understand the multiferroic behavior
of distorted rare-earth manganites are here briefly reviewed. The original work was carried
out by means of Hamiltonian modeling and first-principles density functional simulations. Our
first topic concerns the link between the Dzyaloshinskii–Moriya interaction and ferroelectricity
in incommensurate magnets. We argue that the Dzyaloshinskii–Moriya interaction
may play a key role since (i) it induces ferroelectric displacements of oxygen atoms and (ii) it
favors the stabilization of a helical magnetic structure at low temperatures. Our second topic
concerns the prediction, based on Landau theory, that the symmetry of the zigzag spin chains
in the AFM-E (E-type antiferromagnetic) orthorhombic manganites (such as HoMnO3) allows
a finite polarization along the c axis. The microscopic mechanism at the basis of ferroelectricity
is interpreted through a gain in band energy of the eg electrons within the orbitally degenerate
double-exchange model. Related Monte Carlo simulations have confirmed that the polarization
can be much higher than what is observed in spiral magnetic phases. Density functional
calculations performed on orthorhombic HoMnO3 quantitatively confirm a magnetically induced
ferroelectric polarization up to ∼6 μC cm−2, the largest reported so far for improper magnetic
ferroelectrics. We find in HoMnO3, in addition to the conventional displacement mechanism,
a sizable contribution arising from the purely electronic effect of orbital polarization. The
relatively large ferroelectric polarization, present even with centrosymmetric atomic positions,
is a clear sign of a magnetism-induced electronic mechanism at play, which is also confirmed
by the large displacements of the Wannier function centers with respect to the corresponding
ions in AFM-E HoMnO3. The final polarization is shown to be the result of competing effects,
as shown by the opposite signs of the eg and t2g contributions to the ferroelectric polarization.
