Lengths of ferroelectric domains: The role of defects and random fields

Using noncollinear optical second-harmonic generation, the characteristic lengths of ferroelectric domains in strontium-barium niobate are determined. The role of the domain geometry in the random quasiphase matching process involved is elucidated by model calculations on different domain arrangements. The calculations prove that the domain geometries—especially the domain lengths—strongly affect the angular distribution of the generated second-harmonic light. The evaluation of the measured angular distributions in crystals with different doping concentrations shows that the domain lengths are distinctly albeit not drastically influenced by the dopant-induced random electric or strain fields.

Figure 1

(Color online) Experimental setup used (left) and momentum diagram for quasiphase matching (right). $\alpha$ and ${\alpha }^{\prime }$ are internal and external cone angles, respectively. See text for details.

Figure 2

(Color online) Left side: typical two-dimensional domain distributions, top: short domains, and bottom: long domains. Black and white denote the two possible domain orientations. Right side: corresponding density distributions of the momentum vector ${\mathbf{k}}_{\mathbf{g}}$ (blue granulated).

Figure 3

(Color online) Temperature dependence of a typical intensity profile—intensity of the second-harmonic light as function of temperature and angle. The bell-shaped curves are Gaussian fits for the angular-intensity profiles at the respective temperatures. For a better visual comparison, the fit curves are normalized to the same height and slightly shifted upwards, as indicated. Also sketched is the temperature dependence of the intensity maximum (blue line) which denotes the intensity decrease toward the phase-transition region.

Figure 4

(Color online) Intensity profile—intensity of the second-harmonic light as function of the cone angle $\alpha$ inside the crystal—for undoped and doped SBN.

Figure 5

(Color online) Mean domain lengths in SBN as a function of the doping concentration. The fit function includes the parameters derived from a fit of Eq. (3) to the experimental data.

Figure 6

(Color online) Model for the influence of random charges on the domain configuration in SBN.