Enhanced lattice polarization in ${\text{SrTiO}}_3/{\text{LaAlO}}_3$ superlattices measured using optical second-harmonic generation

Lattice polarization at the ${\text{SrTiO}}_3/{\text{LaAlO}}_3$ interface was investigated by optical second harmonic generation. Superlattices with varying periodicity were employed to study the evolution of interface polarization, while separating substrate contributions. We observed large perpendicular optical nonlinearity, which abruptly increases when the sublattice thickness goes above 3 unit cells. The polarization is primarily in ${\text{SrTiO}}_3$ and develops up to 8 unit cells from the interface.

Figure 1

(Color online) (a) Superlattice profiles in x-ray diffraction. (b) Temperature dependence of the SH intensity in $p_{in}\text{−}{p}_{out}$ geometry, together with that for a single $n$-type interface. The inset shows a representative topographic AFM image for the [STO(6)/LAO(6)]12 sample (a scale bar of $1\mu \text{m}$ is indicated). (c) Polar plots of the relative SH intensity for [STO(24)/LAO(24)]3 (dashed lines), [STO(12)/LAO(12)]6 (solid lines), and [STO(6)/LAO(6)]12 (dotted lines) in $p$-out and $s$-out geometry at 30 K.

Figure 2

(Color online) (a) Sublattice thickness dependence of the SH amplitude in $p_{in}\text{−}{p}_{out}$ geometry. Circles and triangles show the data at 300 and 30 K, respectively. (b) Relative phase of the SH field in $p_{in}\text{−}{p}_{out}$ geometry at 300 K (open circles) compared with that from the numerical calculation (open squares). A shaded thick line indicates the sublattice thickness between 3 and 4 uc.

Figure 3

(Color online) Numerical calculations assuming a constant $\chi$ for varying thickness of the STO in the SL with one nonlinear layer in the substrate (inset). (a) Dependence of the SH amplitude on the thickness of nonlinear region in the STO extending from $n$-type interfaces. The shaded line shows the normalized experimental data at 300 K. (b) Experimentally observed (filled circles) and retrieved (open circles) SH field in the complex plane. Transverse arrows indicate the contribution from the substrate.