The electronic structure and ferroelectric polarization of multiferroic TbMn${}_2$O${}_5$ are investigated using the generalized gradient approximation (GGA) and the GGA plus on-site Coulomb interaction (GGA$+U$) methods. We find an insulating charge-orbital ordered ground state driven by octahedral and pyramidal local structures. Associated with the observed charge ordering, the frustrated magnetic structure creates polarizations in the presence of magnetostriction effect. On-site $U$ leads to strong cancellations between the ionic and electronic part of polarizations, giving rise to a residual value of 83 nC/cm${}^2$ consistent with experimental data. By analyzing the contributions from individual species, we demonstrate that the main part of the polarizations results from the pyramidal Mn ions. Most importantly, we find clear evidence indicating that the $d_{z^2}$ orbital ordering on the pyramidal Mn${}^{3+}$ sublattice play important roles in the polarization.

• Received 17 November 2010

DOI:https://doi.org/10.1103/PhysRevB.84.024421