The discovery of quasicrystals--crystalline structures that show order while lacking periodicity--forced a paradigm shift in crystallography. Initially limited to intermetallic systems, the observation of quasicrystalline structures has recently expanded to include 'soft' quasicrystals in the fields of colloidal and supermolecular chemistry. Here we report an aperiodic oxide that grows as a two-dimensional quasicrystal on a periodic single-element substrate. On a Pt(111) substrate with 3-fold symmetry, the perovskite barium titanate BaTiO3 forms a high-temperature interface-driven structure with 12-fold symmetry. The building blocks of this dodecagonal structure assemble with the theoretically predicted Stampfli-Gähler tiling having a fundamental length-scale of 0.69 nm. This example of interface-driven formation of ultrathin quasicrystals from a typical periodic perovskite oxide potentially extends the quasicrystal concept to a broader range of materials. In addition, it demonstrates that frustration at the interface between two periodic materials can drive a thin film into an aperiodic quasicrystalline phase, as proposed previously. Such structures might also find use as ultrathin buffer layers for the accommodation of large lattice mismatches in conventional epitaxy.

In the conventional Rashba model for an isotropic two-dimensional electron gas ͑2DEG͒, the electrons are spin-orbit split by a structural inversion asymmetry ͑SIA͒ perpendicular to the confinement plane. An additional SIA within the confinement plane leads to another contribution to the spin-orbit interaction which is investigated by means of a nearly-free electron model. The interplay of both contributions manifests itself as an enhanced splitting in the anisotropic 2DEG, as compared to the isotropic case. Further, the spin polarization of the electronic states is rotated out of the confinement plane. Both findings corroborate recent experimental and theoretical results for the ordered surface alloys Bi/ Ag͑111͒ and Pb/ Ag͑111͒.

We report on the first observation of an approximant structure to the recently discovered two-dimensional oxide quasicrystal. Using scanning tunneling microscopy, low-energy electron diffraction, and surface x-ray diffraction in combination with ab initio calculations, the atomic structure and the bonding scheme are determined. The oxide approximant follows a 3^{2}.4.3.4 Archimedean tiling. Ti atoms reside at the corners of each tiling element and are threefold coordinated to oxygen atoms. Ba atoms separate the TiO_{3} clusters, leading to a fundamental edge length of the tiling 6.7 Å.

This work focuses on the generation of ferromagnetism at the surface of anatase TiO 2 films by low-energy ion irradiation. Controlled Ar +-ion irradiation resulted in a thin (∼10) nm ferromagnetic surface layer. The intrinsic origin and robustness of the magnetic order has been characterized by x-ray magnetic circular dichroism at room temperature revealing that a Ti band is spin-polarized. These results, together with density functional theory calculations, indicate that Ti vacancy-interstitial pairs are responsible for the magnetic order. Superconducting quantum interference device measurements show the existence of a perpendicular magnetic anisotropy and a low remanent magnetization. Magnetic force microscopy reveals that this low remanence is due to oppositely aligned magnetic domains with magnetization vectors normal to the main surface. The weak domain-wall pinning, the magnetic anisotropy, together with the simplicity of the preparation method, open up interesting possibilities for future applications. As an example, single domain patterns of ∼1 μm width and several μm length can be easily prepared.

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