Electronic structure, lattice dynamics, and magnetoelectric properties of double perovskite La$_{2}$CuTiO$_{6}$

The results of ab initio calculations of the electronic structure, vibrational properties, and the magnetoelectric effect in the La$_{2}$CuTiO$_{6}$ crystal with double perovskite structure are presented. The lattice dynamics calculation shows the presence of unstable modes in the phonon spectrum of the high-symmetry cubic phase with space group $Fm\bar3m$. Condensation of two most unstable modes belonging to the center and the boundary point $X$ of the Brillouin zone leads to the formation of a nonpolar stable phase with space group $P2_1/n$. The calculation taking into account spin polarization shows that the magnetic ground state is $E^*$-type antiferromagnetic with doubled magnetic cell and with the two spin-up and two spin-down configuration of magnetic moments of copper ions along the [010] crystallographic direction. Such ordering of magnetic moments leads to polar space group and polarization formation. The polarization magnitude is estimated as 71 $\mu$C/m$^2$.