Figure 1

(a) XSW intensity of BTO (001) Bragg reflection and z axis orientation, with \(z = 0\) at the sample surface. (b) Side view of the top two BTO unit cells with ferroelectric polarization \(\textrm{P}^\uparrow\) and \(\textrm{P}^\downarrow\), and Bragg spacing \(d_{001}\). In the \(\textrm{P}^{\uparrow }\) sketch, Ti and equatorial O atoms are offset by 0.05c, above and below the center of the unit cell, respectively, while apical O atoms are offset by \(-0.1c\). The same offsets in the opposite direction apply to the \(\textrm{P}^{\downarrow }\) sketch. Dashed lines indicate Ba planes, while solid lines refer to the Bragg diffraction planes and their absolute position with respect to the Ba plane is given by \(c(\beta _h + \varphi _0)/(2\pi )\) (Section Ba and Ti XSW). Here, \(\beta _h^{\uparrow }/(2\pi ) = 0.17\), \(\beta _h^{\downarrow }/(2\pi ) = 0.11\), and \(\varphi _0/(2\pi ) = 0.08\), which is the average of \(\varphi _0/(2\pi )\) found in the three samples (“Methods”, “Deformation phase calculation”) and is taken as an example. (c) Sketch of the experimental setup (top view) used at the beamline I09 of the Diamond Light Source, including sample, electron analyzer, and photodiode. The photodiode was located 10 mm away from the sample and was equipped with an Al mask in front to minimize the fluorescence background. The Bragg angle \(\theta\) and the photoelectron exit angle \(\gamma\) are shown, together with photoelectron exit angle ranges \(\gamma _1\), \(\gamma _2\) and \(\gamma _3\), incident \(\varvec{k}_0\) and Bragg-diffracted \(\varvec{k}_{\varvec{H}} = \varvec{k}_0 + \varvec{H}\) X-ray wavevectors.