First-principles study of the lattice and electronic structures of TbMn$_2$O$_5$

TL;DR

This study uses density functional theory to analyze the structural, electronic, and dielectric properties of multiferroic TbMn$_2$O$_5$, revealing its polarization and the magnetic origin of its ferroelectricity.

Contribution

It provides a first-principles analysis confirming the magnetic origin of ferroelectricity in TbMn$_2$O$_5$ without relying on spin-orbit coupling effects.

Findings

Structural parameters match experiments

Polarization along the b-axis is 1187 nC·cm$^{-2}$

Ferroelectricity is driven by magnetic ordering, not spin-orbit coupling

Abstract

The structural, electronic and lattice dielectric properties of multiferroic TbMn$_2$O$_5$ are investigated using density functional theory within the generalized gradient approximation (GGA). 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 TbMn$_2$O$_5$ is of space group $Pb2_1m$, allowing polarizations along the b-axis. The spontaneous electric polarization is calculated to be 1187 $nC\cdot$cm$^{-2}$. The calculated zone-center optical phonons 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 TbMn$_2$O$_5$ is driven by the magnetic ordering that breaks the the inversion symmetry, without invoking the spin-orbit coupling.