Jahn-Teller distortions as a novel source of multiferroicity

The Jahn-Teller effect is a fascinating and ubiquitous phenomenon in modern quantum physics and chemistry. We propose a class of oxides with a melilite structure ${\mathrm{Ba}}_{2}T{\mathrm{Ge}}_2{\mathrm{O}}_7$ $(T=\text{V},\text{Ni})$ where Jahn-Teller distortions are mainly responsible for the appearance of electric polarization. At the heart of the proposed mechanism lies the lack of inversion symmetry displayed by tetrahedrally coordinated transition-metal ions, which allows for the condensation of polar Jahn-Teller distortions, at odds with octahedral coordination typical of conventional ferroelectric oxides with a perovskite structure. Since the noncentrosymmetric local environment of transition-metal ions also activates the proposed spin-dependent hybridization mechanism for magnetically induced electric polarization, proper multiferroic phases with intrinsic magnetoelectric interactions could be realized in this class of low-symmetry materials.

Figure 1

(a)–(d) Typical evolution of JT modes [shown in (e)–(h)] and energy as a function of the electronic angle $\phi$ for linear and quadratic couplings. The parameters have been chosen as $K_1=K_2=K_a/2=K_0/2=1\text{eV}/\AA {}^2,F_1=0.3\left(0.1\right)\text{eV}/\AA ,F_2=0.1\left(0.3\right)\text{eV}/\AA$ in the top (bottom) panels, corresponding to cases $a$ and $b$ discussed in the main text. Quadratic coupling constants are set to zero in the left panels [(a), (c)], while $L_1=L_2=0.9{\mathrm{eV}/\AA }^2$ and $G_1=G_2=0.5{\mathrm{eV}/\AA }^2$ in right panels [(b), (d)]. Arrows and vertical lines highlight the energy minima. (c)–(f) Schematic representation of the symmetrized displacements in each tetrahedral unit, corresponding to totally symmetric displacements with symmetry (e) $A_1$ and (f) $A_2$, and to nontotally symmetric displacements with symmetry (g) $B_1$ and (h) $B_2$.

Figure 2

(a) Melilite crystal structure of ${\mathrm{Ba}}_{2}T{\mathrm{Ge}}_2{\mathrm{O}}_7$ with $P\overline{4}{2}_{1}m$ symmetry, showing layers of ${\mathrm{Ge}}_2{\mathrm{O}}_7$ dimers linked by $T{\mathrm{O}}_4$ tetrahedra intercalated by Ba ions. The $T{\mathrm{O}}_4$ tetrahedra are compressed along the $c$ axis, resulting in different O-T-O angles $\alpha ,\beta$. (b) Top view of the crystal structure, highlighting two inequivalent $T{\mathrm{O}}_4$ tetrahedra which are rotated about the $c$ axis of $\pm \kappa$, respectively. (c) Level structure of the $T^{2+}$ metal ion in the melilite crystal. In the tetrahedral environment, $d$ orbitals split into lower $e_g$ and higher $t_{2g}$ manifolds; a tetragonal compression further splits the $e_g,t_{2g}$ levels, leaving only twofold degenerated $d_{yz},d_{zx}$ states. If these levels are half occupied, as in the case of $\text{Ni}\left(d^8\right)$ or $\text{V}\left(d^3\right)$, a JT distortion can take place, removing the only degeneracy left between the $d_{yz}\text{and}{d}_{zx}$ states. (d) Density of states (states/eV) decomposed into $d$-orbital states and calculated within the bare GGA approach. “Ni*” refers to the parent-compound structure, belonging to space group $P\overline{4}{2}_{1}m$, while the optimized distorted structure with $Cmm2$ symmetry is labeled by “Ni.”

Figure 3

Charge density plot (obtained within the GGA+$U$ approach, with $U=4$ eV) corresponding to the highest occupied state of the Ni-$d$ state hybridizing with tetrahedral O-$p$ states, (a) in perspective view in a local $xyz$ frame and (b) projected onto the $xy$ plane. (c) Distortion modes of tetrahedral O ions surrounding the Ni ion, projected onto the $xy$ plane, as obtained using the isodistort program [37].