A first principle study of the electronic structure and electric polarization in multiferroic manganites of the type HoMn$_2$O$_5$

Compounds with general formula RMn$_2$O$_5$ (R=La, Y, Ho, Tb) have been studied since the late 1960`s for their unusual magnetic properties [1,2]. Recent studies of dielectric and magnetoelectric properties have indicated that RMn$_2$O$_5$ compounds are ferroelectric in their magnetically ordered state, with spontaneous polarization P being directed along the b axis of their unit cell [3,4]. These compounds are even more interesting because the spontaneous polarization is much smaller than in typical ferroelectric materials and experimentally there is very little evidence of structural transitions [5,6]. Experimental data showed that the structures of these compounds have space group Pbam [7] but it has been suspected that the actual symmetry group is Pb21m allowing polarization along the b axis [3,8] . From a theoretical point of view the interest in this class of materials lies in the coupling between magnetic and ferroelectric order parameters [9,10,11,12]. The aim of this project is to investigate by first principle calculations the electronic, magnetic properties of HoMn2O5 and its structural transition which leads to a spontaneous polarization. The calculations of the electronic ground state can be greatly simplified by theorem of Hohenberg and Kohn [13] upon which density functional theory (DFT) is based. We aim to perform density functional theory calculations using the Vienna Ab-Initio Simulation Package (VASP) [14]: it is a complex package for performing quantum-mechanical molecular dynamics simulations using the projector-augmented-wave (PAW) potentials and plane waves basis sets. In this work the PAW+U method [15] will be used to include the electron-electron correlations in the case of the Mn d electrons on a mean-field level. Within the PAW and PAW+U approaches an accurate method for computing the spontaneous polarization is the so called ?Berry-Phase?: in this approach, the electronic contribution to the polarization is calculated as a geometric phase, formally equivalent to the sum of the Wannier centers of the occupied bands [16].