The investigation of Raman frequencies as well as optical response is a widely used non-destructive way to characterize crystalline solids and nanostructures. At ferroelectric domain walls, in particular, both the Raman intensity and the non-linear optical response strongly differ from the bulk. X-ray diffraction measurements have shown that domain walls in LiNbO₃ and LiTaO₃ behave like compressed bulk material [1]. Hence, knowledge of the dependence of Raman frequencies and optical response on uniaxial strain can help, i.a., to characterize domain walls in LiNbO₃ and LiTaO₃ crystals.

In our work, we model the vibrational properties of LiNbO₃ and LiTaO₃ crystals from first principles as a function of uniaxial compressive and tensile strain in 𝑥-, 𝑦- and 𝑧-direction. The calculations show a roughly linear dependence of the phonon frequencies on the applied strain, which is similar for LiNbO₃ and LiTaO₃ crystals and observed in experiments, as well. In particular, we observe a strong dependence on strain in 𝑥- and 𝑦-direction for the 𝐸 TO₅ and TO₆ modes which can be thus exploited as markers of the strain. While 𝐸 modes of unstrained LiNbO₃ and LiTaO₃ crystals are degenerate [2], we predict non-degenerate 𝐸 modes under strain, due to the breaking of rotational symmetry.

Additionally, linear and non-linear optical response of strained LiNbO₃ is calculated from first principles. This includes the calculation of the energy dependent second (SHG) and third harmonic generation (THG). Investigation of optical response of strained LiNbO₃ yields a spectroscopic signature of the domain walls.

[1] M. Rüsing et al., Phys. Rev. Mat. 2, 103801 (2018).

[2] S. Sanna et al., Phys. Rev. B 91, 224302 (2015).