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3D Gaussian splatting models, as a novel explicit 3D representation, have been applied in many domains recently, such as explicit geometric editing and geometry generation. Progress has been rapid. However, due to their mixed scales and cluttered shapes, 3D Gaussian splatting models can produce a blurred or needle-like effect near the surface. At the same time, 3D Gaussian splatting models tend to flatten large untextured regions, yielding a very sparse point cloud. These problems are caused by the non-uniform nature of 3D Gaussian splatting models, so in this paper, we propose a new 3D Gaussian splitting algorithm, which can produce a more uniform and surface-bounded 3D Gaussian splatting model. Our algorithm splits an $N$-dimensional Gaussian into two N-dimensional Gaussians. It ensures consistency of mathematical characteristics and similarity of appearance, allowing resulting 3D Gaussian splatting models to be more uniform and a better fit to the underlying surface, and thus more suitable for explicit editing, point cloud extraction and other tasks. Meanwhile, our 3D Gaussian splitting approach has a very simple closed-form solution, making it readily applicable to any 3D Gaussian model., Comment: 11 pages, 10 figures

The evolution of skyrmion crystal encapsulates skyrmion critical behaviors, such as nucleation, deformation and annihilation. Here, we achieve a tunable evolution of artificial skyrmion crystal in nanostructured synthetic antiferromagnet multilayers, which are comprised of perpendicular magnetic multilayers and nanopatterned arrays of magnetic nanodots. The out-of-plane magnetization hysteresis loops and first-order reversal curves show that the nucleation and annihilation of the artificial skyrmion can be controlled by tuning the diameter of and spacing between the nanodots. Moreover, when the bottom layer thickness increases, the annihilation of skyrmion shifts from evolving into a ferromagnetic spin texture to evolving into an antiferromagnetic spin texture. Most significantly, non-volatile multiple states are realized at zero magnetic field via controlling the proportion of the annihilated skyrmions in the skyrmion crystal. Our results demonstrate the tunability and flexibility of the artificial skyrmion platform, providing a promising route to achieve skyrmion-based multistate devices, such as neuromorphic spintronic devices.

One-dimensional (1D) confinement has been revealed to effectively tune the properties of materials in homogeneous states. The 1D physics can be further enriched by electronic inhomogeneity, which unfortunately remains largely unknown. Here we demonstrate the ultra-high sensitivity to magnetic fluctuations and the tunability of phase stability in the electronic transport properties of self-assembled electronically phase-separated manganite nanowires with extreme aspect ratio. The onset of magnetic nano-droplet state, a precursor to the ferromagnetic metallic state, is unambiguously revealed, which is attributed to the small lateral size of the nanowires that is comparable to the droplet size. Moreover, the quasi-1D anisotropy stabilizes thin insulating domains to form intrinsic tunneling junctions in the low temperature range, which is robust even under magnetic field up to 14 T, and thus essentially modifies the classic 1D percolation picture to stabilize a novel quantum percolation state. A new phase diagram is therefore established for the manganite system under quasi-1D confinement for the first time. Our findings offer new insight to understand and manipulate the colorful properties of the electronically phase-separated systems via dimensionality engineering.

In quantum matters hosting electron-electron correlation and spin-orbit coupling, spatial inhomogeneities, arising from competing ground states, can be essential for determining and understanding topological properties. A prominent example is Hall anomalies observed in SrRuO3 films, which were interpreted in terms of either magnetic skyrmion-induced topological Hall effect (THE) or inhomogeneous anomalous Hall effect (AHE). To clarify this ambiguity, we systematically investigated the AHE of SrRuO3 ultrathin films with controllable inhomogeneities in film thickness (tSRO). By harnessing the step-flow growth of SrRuO3 films, we induced microscopically-ordered stripes with one-unit-cell differences in tSRO. The resultant spatial distribution of momentum-space Berry curvatures enables a two-channel AHE, which shows hump-like anomalies similar to the THE and can be continuously engineered via sub-unit-cell control of tSRO. In these inhomogeneous SRO films, we microscopically identified a two-step magnetic switching and stripe-like ferromagnetic domains. These features are fingerprints for distinguishing the two-channel AHE from the skyrmion-induced THE., Comment: 24 pages, 6 figures, 4 figures in Supplementary Materials

Magnetic skyrmions are topologically non-trivial spin structure, and their existence in ferromagnetically coupled multilayers has been reported with disordered arrangement. In these multilayers, the heavy metal spacing layers provide an interfacial Dzyaloshinskii-Moriya interaction (DMI) for stabilizing skyrmions at the expense of interlayer exchanging coupling (IEC). To meet the functional requirement of ordered/designable arrangement, in this work, we proposed and experimentally demonstrated a scenario of skyrmion nucleation using nanostructured synthetic antiferromagnetic (SAF) multilayers. Instead of relying on DMI, the antiferromagnetic IEC in the SAF multilayers fulfills the role of nucleation and stabilization of skyrmions. The IEC induced skyrmions were identified directly imaged with MFM and confirmed by magnetometry and magnetoresistance measurements as well as micromagnetic simulation. Furthermore, the robustness of the proposed skyrmion nucleation scenario was examined against temperature (from 4.5 to 300 K), device size (from 400 to 1200 nm), and different lattice designs. Hence, our results provide a synthetic skyrmion platform meeting the functional needs in magnonic and spintronic applications.

The enigma of the emergent ferromagnetic state in tensile-strained LaCoO3 thin films remains to be explored because of the lack of a well agreed explanation. The direct magnetic imaging technique using a low-temperature magnetic force microscope (MFM) is critical to reveal new aspects of the ferromagnetism by investigating the lateral magnetic phase distribution. Here we show the experimental demonstration of the rare halved occupation of the ferromagnetic state in tensile-strained LaCoO3 thin films on SrTiO3 substrates using the MFM. The films have uniformly strained lattice structure and minimal oxygen vacancies (less than 2%) beyond the measurement limit. It is found that percolated ferromagnetic regions with typical sizes between 100 nm and 200 nm occupy about 50% of the entire film, even down to the lowest achievable temperature of 4.5 K and up to the largest magnetic field of 13.4 T. Preformed ferromagnetic droplets were still observed when the temperature is 20 K above the Curie temperature indicating the existence of possible Griffiths phase. Our study demonstrated a sub-micron level phase separation in high quality LaCoO3 thin films, which has substantial implications in revealing the intrinsic nature of the emergent ferromagnetism., Comment: Regular Article, 31 pages,9 figures