Search

We provide a geometric-combinatorial model for the category of coherent sheaves on the weighted projective line of type (2,2,n) via a cylindrical surface with n marked points on each of its upper and lower boundaries, equipped with an order 2 self-homeomorphism. A bijection is established between indecomposable sheaves on the weighted projective line and skew-curves on the surface. Moreover, by defining a skew-arc as a self-compatible skew-curve and a pseudo-triangulation as a maximal set of distinct pairwise compatible skew-arcs, we show that pseudo-triangulations correspond bijectively to tilting sheaves. Under this bijection, the flip of a skew-arc within a pseudo-triangulation coincides with the tilting mutation. As an application, we prove the connectivity of the tilting graph for the category of coherent sheaves.

The integration of ferroelectrics with semiconductors is crucial for developing functional devices, such as field-effect transistors, tunnel junctions, and nonvolatile memories. However, the synthesis of high-quality single-crystalline ferroelectric nitride perovskites has been limited, hindering a comprehensive understanding of their switching dynamics and potential applications. Here we report the synthesis and characterizations of epitaxial single-phase ferroelectric cerium tantalum nitride (CeTaN3) on both oxides and semiconductors. The polar symmetry of CeTaN3 was confirmed by observing the atomic displacement of central ions relative to the center of the TaN6 octahedra, as well as through optical second harmonic generation. We observed switchable ferroelectric domains in CeTaN3 films using piezo-response force microscopy, complemented by the characterization of square-like polarization-electric field hysteresis loops. The remanent polarization of CeTaN3 reaches approximately 20 uC/cm2 at room temperature, consistent with theoretical calculations. This work establishes a vital link between ferroelectric nitride perovskites and their practical applications, paving the way for next-generation information and energy-storage devices with enhanced performance, scalability, and manufacturability., Comment: 47 pages, 4 figures

We present a geometric model for the category of vector bundles over the weighted projective line of type (2,2,n). This model is based on the orbit space of an infinite marked strip under a specific group action. We establish a bijection between indecomposable bundles and orbits of line segments on the strip, which yields geometric interpretations for various aspects, including the Picard group action, vector bundle duality, dimension of extension group, projective cover and injective hull of extension bundle, etc., Comment: 29 pages, v2. Mainly made several changes to the Introduction. Comments welcome!

Releasing the epitaxial oxide heterostructures from substrate constraints leads to the emergence of various correlated electronic phases and paves the way for integrations with advanced semiconductor technologies. Identifying a suitable water-soluble sacrificial layer, compatible with the high-quality epitaxial growth of oxide heterostructures, is currently the key to the development of large-scale freestanding oxide membranes. In this study, we unveil the super-tetragonal Sr4Al2O7 (SAOT) as a promising water-soluble sacrificial layer. The distinct low-symmetric crystal structure of SAOT enables a superior capability to sustain epitaxial strain, thus allowing for broad tunability in lattice constants. The resultant structural coherency and defect-free interface in perovskite ABO3/SAOT heterostructures effectively restrain crack formations during the water-assisted release of freestanding oxide membranes. For a variety of non-ferroelectric oxide membranes, the crack-free areas can span up to a few millimeters in length scale. These compelling features, combined with the inherent high-water solubility, make SAOT a versatile and feasible sacrificial layer for producing high-quality freestanding oxide membranes, thereby boosting their potential for innovative oxide electronics and flexible device designs., Comment: 5 figures and SI, it is the second version of this manuscript

As a prototypical half-metallic ferromagnet, La0.67Sr0.33MnO3 (LSMO) has been extensively studied due to its versatile physical properties and great potential in spintronic applications. However, the weak perpendicular magnetic anisotropy (PMA) limits the controllability and detection of magnetism in LSMO, thus hindering the realization of oxide-based spintronic devices with low energy consumption and high integration level. Motivated by this challenge, we develop an experimental approach to enhance the PMA of LSMO epitaxial films. By cooperatively introducing 4d Ru doping and a moderate compressive strain, the maximum uniaxial magnetic anisotropy in Ru-doped LSMO can reach 3.0 to 1E5 J/m3 at 10 K. Furthermore, we find a significant anisotropic magnetoresistance effect in these Ru-doped LSMO films, which is dominated by the strong PMA. Our findings offer an effective pathway to harness and detect the orientations of magnetic moments in LSMO films, thus promoting the feasibility of oxide-based spintronic devices, such as spin valves and magnetic tunnel junctions.

In transition-metal-oxide heterostructures, the anomalous Hall effect (AHE) is a powerful tool for detecting the magnetic state and revealing intriguing interfacial magnetic orderings. However, achieving a larger AHE at room temperature in oxide heterostructures is still challenging due to the dilemma of mutually strong spin-orbit coupling and magnetic exchange interactions. Here, we exploit the Ru doping-enhanced AHE in LSMRO epitaxial films. As the B-site Ru doping level increases up to 20 percent, the anomalous Hall resistivity at room temperature can be enhanced from nOhmcm to uOhmcm scale. Ru doping leads to strong competition between ferromagnetic double-exchange interaction and antiferromagnetic super-exchange interaction. The resultant spin frustration and spin-glass state facilitate a strong skew-scattering process, thus significantly enhancing the extrinsic AHE. Our findings could pave a feasible approach for boosting the controllability and reliability of oxide-based spintronic devices.

Interfaces formed by correlated oxides offer a critical avenue for discovering emergent phenomena and quantum states. However, the fabrication of oxide interfaces with variable crystallographic orientations and strain states integrated along a film plane is extremely challenge by conventional layer-by-layer stacking or self-assembling. Here, we report the creation of morphotropic grain boundaries (GBs) in laterally interconnected cobaltite homostructures. Single-crystalline substrates and suspended ultrathin freestanding membranes provide independent templates for coherent epitaxy and constraint on the growth orientation, resulting in seamless and atomically sharp GBs. Electronic states and magnetic behavior in hybrid structures are laterally modulated and isolated by GBs, enabling artificially engineered functionalities in the planar matrix. Our work offers a simple and scalable method for fabricating unprecedented innovative interfaces through controlled synthesis routes as well as provides a platform for exploring potential applications in neuromorphics, solid state batteries, and catalysis., Comment: 38 pages, 4 main figures