First-principles study of structural, vibrational, and lattice dielectric properties of hafnium oxide

Crystalline structures, zone-center phonon modes, and the related dielectric response of the three low-pressure phases of ${\mathrm{HfO}}_2$ have been investigated in density-functional theory using ultrasoft pseudopotentials and a plane-wave basis. The structures of low-pressure ${\mathrm{HfO}}_2$ polymorphs are carefully studied with both the local-density approximation (LDA) and the generalized gradient approximation. The fully relaxed structures obtained with either exchange-correlation scheme agree reasonably well with experiment, although LDA yields better overall agreement. After calculating the Born effective charge tensors and the force-constant matrices by finite-difference methods, the lattice dielectric susceptibility tensors for the three ${\mathrm{HfO}}_2$ phases are computed by decomposing the tensors into the contributions from individual infrared-active phonon modes.