First-principles study of the lattice and electronic structure of TbMn₂O₅

The structural, electronic, and lattice dielectric properties of multiferroic TbMn₂O₅ are investigated using density-functional theory within the generalized gradient approximation. We use collinear spin approximations and ignore the spin-orbit coupling. The calculated structural parameters are in excellent agreement with the experiments. We confirm that the ground-state structure of TbMn₂O₅ is of space group Pb2₁m, allowing polarizations along the b axis. The spontaneous electric polarization is calculated to be 1187 nC cm^-2. The calculated zone-center optical phonon frequencies and the oscillator strengths of IR phonons agree very well with the experimental values. We then derive an effective Hamiltonian to explain the magnetically induced ferroelectricity in this compound. Our results strongly suggest that the ferroelectricity in TbMn₂O₅ is driven by the magnetic ordering that breaks the inversion symmetry, without invoking the spin-orbit coupling.