Dielectric properties and spin-phonon coupling in multiferroic double perovskite Bi$_{2}$CoMnO$_{6}$ Satadeep Bhattacharjee, Olle Eriksson and Biplab Sanyal * Department of Physics and Astronomy, Box 516, 75120, Uppsala University, Uppsala, Sweden (Dated: October 26, 2018) First-principles electronic structure calculations have been performed for the double perovskite Bi$_{2}$CoMnO$_{6}$ in its non-centrosymmetric polar state using generalized gradient approximation plus Hubbard U approach. We find that while Co is in a high spin state, Mn is in a intermediate spin state. The calculated dynamical charge tensors are anisotropic reflecting a low-symmetry structure of the compound. Magnetic structure dependent phonon frequencies indicate the presence of spin- phonon coupling. Using Berry phase method, we obtain a spontaneous electronic polarization of 5.88 µC/cm 2 which is close to the experimental value observed for a similar compound, Bi$_{2}$NiMnO$_{6}$. PACS numbers: 75.50.Pp,75.70.-i,71.70.Gm Magnetic double perovskites with formula A$_{2}$BB $^{′}$O$_{6}$ (A is an alkaline rare-earth, B and B ′ are transition met- als) have attracted a lot of attention in the last decade due to their potential in spintronic applications specially since the discovery of low field magneto-resistance in Sr$_{2}$FeMoO$_{6}$ and Sr$_{2}$FeReO$_{6}$. $^{2}$. Depending on the sto- ichiometry and temperature, a number of double per- ovskites show inter-related magnetic, structural and elec- tronic phases. Although, many of these materials or- der ferromagnetically at high temperature, very few of them show ferroelectricity $^{3–7}$. A perpetual interest exists to identify materials having multiferroic properties with the simultaneous existence of ferroelectric and magnetic order $^{8}$. Here we have studied Bi$_{2}$ CoMnO$_{6}$ that crystal- lizes in the double perovskite structure. It is among a few, rare materials which show existence of both ferro- electric (FE) as well as ferromagnetic (FM) behavior. Due to the presence of 6s 2 lone pair of Bi $^{3+}$, there is a non-centrosymmetric (space group C2 (no. 5)) struc- tural distortion which leads to a FE transition temper- ature around 600 K $^{9}$, above which the centrosymmetric structure appears with space group C2 /m (no. 12). Be- low the magnetic ordering temperature of 95 K, ferro- magnetism appears due to the 180 ◦ cation-anion-cation ferromagnetic superexchange interaction 10 in the chain Co $^{+}$-O $^{−}$-Mn + where Co and Mn ions are ordered in a rock-salt configuration. A recent experimental study has claimed a strong dependence of T$_{c}$ on the mon- oclinic angle $^{11}$. In the present study, we concentrate on the C2 structure of Bi$_{2}$CoMnO$_{6}$ (BCMO) as first- principles calculations have not been reported in the liter- ature for either of the two structural phases. Calculations were performed using density functional theory (DFT) within the Perdew-Burke-Ernzerhof generalized gradient approximation (GGA) on the basis of the projector aug- mented wave method implemented in the Vienna ab ini- tio simulation package (VASP) $^{12}$. The wave function was expanded in plane waves using 500 eV energy cut-off. For Bi and Mn, we have used pseudopotentials with semi-core electrons. Brillouin zone integrations were carried out us- ing a 4 × 6 × 4 Monkhorst-Pack k -point mesh. To treat strong electron interaction effect in Co and Mn we have carried out GGA+U calculation in the Hubbard model framework with the choice of Coulomb parameter U=3 eV for Co-d and U=4 eV for Mn-d orbitals. The value of the exchange parameter J used was 1 eV for both the transition metals. The unit cell consists of four formula units in the C2 phase. In Wyckoff notations, the four Co atoms occupy 2a and 2b sites respectively while Bi, Mn and O occupy 4c sites. In Glazer’s notation, the tilt pat- tern of the octahedra is given by a $^{−}$b $^{0}$c − (Fig. 1) which imply that there is no tilting of octahedra along [010] direction, while the neighboring octahedra tilt in oppo- site directions to each other along both [100] and [001] directions. We have performed the structural optimiza- tion involving the relaxation of ionic positions as well as cell shape and volume. Forces were relaxed up to values smaller than 0.005 eV/ ˚ A. For the calculation of density of states we used a k -point mesh of 6 × 6 × 6 with 54 k-points in the irreducible Brillouin zone. The dielectric and dynamical properties such as Born effective charge (BEC) matrices and zon-center phonon frequencies were calculated using density functional perturbation theory (DFPT) $^{13}$. FIG. 1: (Color online) Crystal structure of BCMO, as viewed along the short-axis b , showing octahedral tilt patterns of CoO$_{6}$ (blue) and MnO$_{6}$ (red) octahedra along with Bi as pur- ple balls. arXiv:1001.0128v2 [cond-mat.mtrl-sci] 22 Oct 2010