Strain-induced ferroelectric phase transitions in incipient ferroelectric rutile TiO 2

Uniaxial strain induced ferroelectric phase transitions in rutile TiO 2 are investigated by first-principles calculations. The calculated results show that the in-plane tensile strain induces rutile TiO 2 , paraelectric phase with P 4-2/ mnm ( D 4 h ) space group, to a ferroelectric phase with P m ( C s ) space group, driven by the softening behaviour of the E u 1 mode. In addition, the out-of-plane tensile strain, vertical to the ab plane, leads to a ferroelectric phase with P 42 nm ( C 4 v ) space group, driven by the softening behaviour of the A 2u mode. The critical tensile strains are 3.7% in-plane and 4.0% out-of-plane, respectively. In addition, the in-plane compression strain, which has the same structure variation as out-of-plane tensile strain due to Poisson effect, leads the paraelectric rutile TiO 2 to a paraelectric phase with P nnm ( D 2 h ) space group driven by the softening behaviour of the B 1g mode. These results indicate that the sequence ferroelectric (or paraelectric) phase depends on the strain applied. The origin of ferroelectric stabilization in rutile TiO 2 is also discussed briefly in terms of strain induced Born effective charge transfer.