Figure 1

(a) Patterson function of the projected structure. Solid and dashed contours indicate positive and negative maxima, respectively. Maxima in $P(u,v)$ are labeled by $A$ to $F$. (b) Structure model of the ($2\times 1$) reconstructed unit cell projected along [001]. Atoms within the two top $\mathrm{Ti}{\mathrm{O}}_2$ layers are labeled from 1–8. O and Ti atoms are represented by red and gray spheres, respectively. Blue spheres represent Ba atoms as labeled. Dashed circles indicate the positions of Ti atom 5 in the unreconstructed ($1\times 1$) structure, which is shifted to the position ($\frac{1}{2}$, $\frac{1}{2}$) as indicated by the open arrow. (c) Perspective side view of the structure. Interatomic distances in Ångstrom units: 1-2, 1.82; 1-3, 2.01; 2-6, 1.88; 8-6, 2.00; 5-4, 2.30; 5-8, 2.29; 7-6, 2.01; Ba-O (in lane), 2.82; Ba-O (out of plane), 3.09.Reuse & Permissions

Figure 2

Measured (symbols) and calculated (lines) structure factor amplitudes for several fractional order rods. Curves are shifted for clarity. The inset lists the normalized in-plane structure factor amplitudes ($|F(hk0)|$) together with their standard deviations.Reuse & Permissions

Figure 3

Calculated total energy versus Ti-atom displacement. Labels ($7^{\prime }$), (5), and ($8^{\prime }$) correspond to the Ti position [see Fig. 1b] related to the ($\mathrm{BTO}\mathrm{\text{−}}(1\times 1)$, $\mathrm{BTO}\mathrm{\text{−}}(2\times 1)$, and the $\mathrm{STO}\mathrm{\text{−}}(2\times 1)$ structure, respectively (see text).Reuse & Permissions

Figure 4

Calculated spin-resolved density of states for $\mathrm{BTO}(001)\mathrm{\text{−}}(1\times 1)$ (a) and $\mathrm{BTO}(001)\mathrm{\text{−}}(2\times 1)$ (b) atomic labeling corresponds to the structure model in Figs. 1b, 1c Light colors indicate total spin-resolved DOS.Reuse & Permissions

Figure 5

Spin density and magnetic moments calculated for $\mathrm{BTO}(001)\mathrm{\text{−}}(2\times 1)$.Reuse & Permissions