arXiv subjects

Weinan Lin

Publications and source records attributed to Weinan Lin.

10 recordsLinked to original sources

arXiv2024

Machine Proofs for Adams Differentials and Extension Problems among CW Spectra

In this document, we describe the process of obtaining numerous Adams differentials and extensions using computational methods, as well as how to interpret the dataset uploaded to Zenodo. Detailed proofs of the machine-generated results are also provided. The dataset includes information on 49 CW spectra, 180 maps, and 61 cofiber sequences. Leveraging these results, and with the addition of some ad hoc arguments derived through human insight, we successfully resolved the Last Kervaire Invariant Problem in dimension 126.

math.AT↗

arXiv2024

On the Last Kervaire Invariant Problem

We prove that the element $h_6^2$ is a permanent cycle in the Adams spectral sequence. As a result, we establish the existence of smooth framed manifolds with Kervaire invariant one in dimension 126, thereby resolving the final case of the Kervaire invariant problem. Combining this result with the theorems of Browder, Mahowald--Tangora, Barratt--Jones--Mahowald, and Hill--Hopkins--Ravenel, we conclude that smooth framed manifolds with Kervaire invariant one exist in and only in dimensions $2, 6, 14, 30, 62$, and $126$.

math.AT↗

arXiv2024

Product formulas for conjugated motivic milnor basis

We give explicit product formulas for the mod 2 motivic Steenrod algebra in the conjugated motivic Milnor basis. This provides an efficient tool for computing the E2-page of the motivic Adams spectral sequence

math.AT↗

arXiv2023

Noncommutative Gr\"obner Bases and Ext groups; Application to the Steenrod Algebra

We consider a theory of noncommutative Gr\"obner bases on decreasingly filtered algebras whose associated graded algebras are commutative. We transfer many algorithms that use commutative Gr\"obner bases to this context. As an important application, we implement very efficient algorithms to compute the Ext groups over the Steenrod algebra $\mathscr{A}$ at the prime $2$. Especially, the cohomology of the Steenrod algebra $Ext_{\mathscr{A}}^{*, *}(\mathbb{F}_2, \mathbb{F}_2)$, which plays an important role in algebraic topology, is calculated up to total degree of 261, including the ring structure in this range.

math.AT↗

arXiv2021

Epitaxial Growth of Ultraflat Bismuthene with Large Topological Band Inversion Enabled by Substrate-Orbital-Filtering Effect

Quantum spin Hall (QSH) systems hold promises of low-power-consuming spintronic devices, yet their practical applications are extremely impeded by the small energy gaps. Fabricating QSH materials with large gaps, especially under the guidance of design principles, is essential for both scientific research and practical applications. Here, we demonstrate that large on-site atomic spin-orbit coupling can be directly exploited via the intriguing substrate-orbital-filtering effect to generate large-gap QSH systems and experimentally realized on the epitaxially synthesized ultraflat bismuthene on Ag(111). Theoretical calculations reveal that the underlying substrate selectively filters Bi pz orbitals away from the Fermi level, leading pxy orbitals with nonzero magnetic quantum numbers, resulting in large topological gap of ~1 eV at the K point. The corresponding topological edge states are identified through scanning tunneling spectroscopy combined with density functional theory calculations. Our findings provide general strategies to design large-gap QSH systems and further explore their topology-related physics.

cond-mat.mes-hall↗

arXiv2020

On the May Spectral Sequence at the prime 2

We make a conjecture about the whole $E_2$ page of the May spectral sequence in terms of generators and relations and we prove it in a subalgebra which covers a large range of dimensions. We show that the $E_2$ page plays a universal role in the study of Massey products in commutative DGAs. We conjecture that the $E_2$ page is nilpotent free and also prove it in this subalgebra. We compute all the $d_2$ differentials of the generators in the conjecture and construct maps of spectral sequences which allow us to explore Adams vanishing line theorem to compute differentials in the May spectral sequence.

math.AT↗

arXiv2020

Magnetic asymmetry induced anomalous spin-orbit torque in IrMn

We demonstrate an anomalous spin-orbit torque induced by the broken magnetic symmetry in the antiferromagnet IrMn. We study the magnetic structure of three phases of IrMn thin films using neutron diffraction technique. The magnetic mirror symmetry M' is broken laterally in both L10-IrMn and L12-IrMn3 but not {\gamma}-IrMn3. We observe an out-of-plane damping-like spin-orbit torque in both L10-IrMn/permalloy and L12-IrMn3/permalloy bilayers but not in {\gamma}-IrMn3/permalloy. This is consistent with both the symmetry analysis on the effects of a broken M' on spin-orbit torque and the theoretical predictions of the spin Hall effect and the Rashba-Edelstein effect. In addition, the measured spin-orbit torque efficiencies are 0.61+-0.01, 1.01+-0.03 and 0.80+-0.01 for the L10, L12 and {\gamma} phases, respectively. Our work highlights the critical roles of the magnetic asymmetry in spin-orbit torque generation.

cond-mat.mtrl-sci↗

arXiv2020

Perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction at an oxide/ferromagnetic metal interface

We report on the study of both perpendicular magnetic anisotropy (PMA) and Dzyaloshinskii-Moriya interaction (DMI) at an oxide/ferromagnetic metal (FM) interface, i.e. BaTiO3 (BTO)/CoFeB. Thanks to the functional properties of the BTO film and the capability to precisely control its growth, we are able to distinguish the dominant role of the oxide termination (TiO2 vs BaO), from the moderate effect of ferroelectric polarization in the BTO film, on the PMA and DMI at the oxide/FM interface. We find that the interfacial magnetic anisotropy energy of the BaO-BTO/CoFeB structure is two times larger than that of the TiO2-BTO/CoFeB, while the DMI of the TiO2-BTO/CoFeB interface is larger. We explain the observed phenomena by first-principles calculations, which ascribe them to the different electronic states around the Fermi level at the oxide/ferromagnetic metal interfaces and the different spin-flip processes. This study paves the way for further investigation of the PMA and DMI at various oxide/FM structures and thus their applications in the promising field of energy-efficient devices.

cond-mat.mtrl-sci↗

arXiv2018

Electrical switching of perpendicular magnetization in L10 FePt single layer

Electrical manipulation of magnetization is essential for integration of magnetic functionalities such as magnetic memories and magnetic logic devices into electronic circuits. The current induced spin-orbit torque (SOT) in heavy metal/ferromagnet (HM/FM) bilayers via the spin Hall effect in the HM and/or the Rashba effect at the interfaces provides an efficient way to switch the magnetization. In the meantime, current induced SOT has also been used to switch the in-plane magnetization in single layers such as ferromagnetic semiconductor (Ga,Mn)As and antiferromagnetic metal CuMnAs with globally or locally broken inversion symmetry. Here we demonstrate the current induced perpendicular magnetization switching in L10 FePt single layer. The current induced spin-orbit effective fields in L10 FePt increase with the chemical ordering parameter (S). In 20 nm FePt films with high S, we observe a large charge-to-spin conversion efficiency and a switching current density as low as 7.0E6 A/cm2. We anticipate our findings may stimulate the exploration of the spin-orbit torques in bulk perpendicular magnetic anisotropic materials and the application of high-efficient perpendicular magnetization switching in single FM layer.

cond-mat.mtrl-sci↗

arXiv2014

Influence of oxygen pressure and aging on LaAlO3 films grown by pulsed laser deposition on SrTiO3 substrates

The crystal structures of LaAlO3 films grown by pulsed laser deposition on SrTiO3 substrates at oxygen pressure of 10-3 mbar or 10-5 mbar, where kinetics of ablated species hardly depend on oxygen background pressure, are compared. Our results show that the interface between LaAlO3 and SrTiO3 is sharper when the oxygen pressure is lower. Over time, the formation of various crystalline phases is observed while the crystalline thickness of the LaAlO3 layer remains unchanged. X-ray scattering as well as atomic force microscopy measurements indicate three-dimensional growth of such phases, which appear to be fed from an amorphous capping layer present in as-grown samples.

cond-mat.mtrl-sci↗