Prediction of a multiferroic state with large electric polarization in tensile-strained TbMnO${}_3$

By performing first-principles calculations, we systematically explore the effect of epitaxial strain on the structure and properties of multiferroic TbMnO${}_3$. We show that, although the unstrained bulk TbMnO${}_3$ displays a noncollinear antiferromagnetic spin order, TbMnO${}_3$ can be ferromagnetic under compressive strain, in agreement with the experimental results on TbMnO${}_3$ grown on SrTiO${}_3$. By increasing the tensile strain up to 5$\%$, we predict that TbMnO${}_3$ transforms into a multiferroic state with a large ferroelectric polarization, two orders of magnitude larger than that in the unstrained bulk, and with a relatively high Néel temperature $E$-type antiferromagnetic order. We also find that the ferroelectric domain and antiferromagnetic domain are interlocked with each other, thus an external electric field can switch the ferroelectric domain and the antiferromagnetic domain simultaneously. Our work demonstrates that strain engineering can be used to improve the multiferroic properties of TbMnO${}_3$.

Figure 1

Calculated total energy and band gap (inset) vs strain. The circle, down triangle, and square represent $E$-AFM, $A$-AFM, and FM spin orders,respectively. The red, green, and blue colors label Pmc2${}_1$, Pmn2${}_1$, and Pbnm space groups, respectively. The red arrow highlights the situation where (001)-oriented TbMnO${}_3$ is epitaxially grown on the (001) plane of the cubic substrate SrTiO${}_3$. Note that all structures in this figure are in epitaxially strained states with |$a$| $=$ |$b$|. These strained structures are higher in energy than the free-standing bulk TbMnO${}_3$.

Figure 2

Partial density of states of TbMnO${}_3$ epitaxially grown on a SrTiO${}_3$ substrate. The left panel shows the Mn $d$-orbital partial density of states (PDOS). For simplicity, we plot the average $t_{2g}$ PDOS. The inset shows the MnO${}_6$ octahedron and electron configuration. The numbers give the Mn-O bond length in Å. The green vertical line gives the Fermi energy level. The right panel illustrates schematically the hybridization between $e_g$ orbitals in the FM (top) and AFM (bottom) cases. The half-filled circle represents half an electron. Spins are represented by arrows.

Figure 3

(a) Illustration of $E$-type zigzag chains (solid lines). The large violet and small red spheres represent Mn and oxygen, respectively. ${\alpha }_p$, ${\alpha }_{ap}$ bond angles (see text), short $\left(d_{\mathrm{short}}\right)$ and long $\left(d_{\mathrm{long}}\right)$ Mn-Mn bonds, and exchange paths are denoted. MnO${}_6$ octahedra of Pmc2${}_1$ TbMnO${}_3$ and bulk Pbnm HoMnO${}_3$ are shown in (b) and (c), respectively. (d) Evolution of ${\alpha }_p$, ${\alpha }_{ap}$ vs strain. (e) Evolution of $d_{\mathrm{short}}$ and $d_{\mathrm{long}}$ vs strain.