  By performing first-principles calculations, we systematically explore the
effect of epitaxial strain on the structure and properties of multiferroic
TbMnO3. We show that, although the unstrained bulk TbMnO3 displays a
non-collinear antiferromagnetic spin order, TbMnO3 can be ferromagnetic under
compressive strain, in agreement with the experimental results on TbMnO3 grown
on SrTiO3. By increasing the tensile strain up to 5%, we predict that TbMnO3
transforms into a new multiferroic state with a large ferroelectric
polarization,two orders of magnitude larger than that in the unstrained bulk,
and with a relatively high Neel 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 TbMnO3.
