Understanding gray track formation in KTP: ${\mathrm{Ti}}^{3+}$ centers studied from first principles

The magnetic signatures of ${\mathrm{Ti}}^{3+}$ centers in potassium titanyl phosphate (KTP) are studied within density-functional theory (DFT). The hyperfine tensor elements are very sensitive to the structural surrounding; the paramagnetic hyperfine splittings are used to evaluate the defect models. For each of the four experimentally observed electron paramagnetic resonance (EPR) spectra, we identify a defect model that reproduces the paramagnetic signature. All of them are electron donors, whereby one specific Ti atom can be identified, whose formal oxidation number is lowered from $4+$ in the ideal crystal to $3+$. The related charge redistribution leads to a strong polarization of the corresponding ${\mathrm{Ti}}^{3+}$ center. However, in three cases a second Ti atom, connected to the first by a mutual polarized O atom, is polarized too. Positively charged O vacancies at the lattice site O(10) are unique in leading to the formation of the only ${\mathrm{Ti}}^{3+}$ center that is stable at room temperature. This defect induces a defect state within the band gap, which may be excited during second harmonic generation (SHG) applications and thus is a plausible candidate to explain the so-called gray tracking, i.e., photochromic damage.

Figure 1

Schematic illustration [22] of exemplary point defects (i.e., a self-trapped electron, a trapped proton, and the O vacancy $V_{\mathrm{O}\left(10\right)}^{+1}$) within the KTP unit cell.

Figure 2

Magnetization density of the positively charged O vacancies $V_{\mathrm{O}\left(9\right)}^{+1}$ (left-hand side) and $V_{\mathrm{O}\left(10\right)}^{+1}$ (right-hand side). The position of the vacancy within the cell is shown schematically by the light gray ring. The yellow isosurfaces indicate areas where the majority spin dominates, while the cyan isosurfaces show those areas dominated by the minority spin. The ${\mathrm{Ti}}^{3+}$ caused by the latter can be attributed to the center $A_{\mathrm{flx}}$ [10] (also see Table 1).

Figure 3

Magnetization density as a direct measure of the trapped electron at the site Ti(1) (left-hand side) and Ti(2) (right-hand side). The ${\mathrm{Ti}}^{3+}$ caused by the former can be attributed to the center $I_{\mathrm{flx}}$ [10] (also see Table 2).

Figure 4

Magnetization density of the defect complex ${\mathrm{H}}_i^{\mathrm{O}\left(4\right)}$. The defect model can be attributed to the ${\mathrm{Ti}}^{3+}$ center $I_{\mathrm{hyd}}$ [10] (also see Table 3).

Figure 5

Magnetization density of the single trapped proton ${\mathrm{H}}_i$. The defect model can be attributed to the ${\mathrm{Ti}}^{3+}$ center $I{I}_{\mathrm{hyd}}$ [10] (also see Table 3).

Figure 6

Calculated $V_{\mathrm{O}\left(10\right)}$ formation energy in dependence on the Fermi level position using PBEsol [14] and $\mathrm{PBEsol}+U$ functionals.

Figure 7

Comparison between the magnetization densities of the O vacancies $V_{\mathrm{O}\left(10\right)}^{+1}$ and $V_{\mathrm{O}\left(10\right)}^0$. The additional electron leads to the formation of a chain of polarized Ti atoms. The binding energy of the second extra electron is larger than the first; see Table 5.