arXiv subjects

Gong Chen

Publications and source records attributed to Gong Chen.

100 records · Page 6Linked to original sources

arXiv2017

Multisolitons for the defocusing energy critical wave equation with potentials

We construct multisoliton solutions to the defocusing energy critical wave equation with potentials in $\mathbb{R}^{3}$ based on regular and reversed Strichartz estimates developed in \cite{GC3} for wave equations with charge transfer Hamiltonians. We also show the asymptotic stability of multisoliton solutions. The multisoliton structures with both stable and unstable solitons are covered. Since each soliton decays slowly with rate $\frac{1}{\left\langle x\right\rangle }$, the interactions among the solitons are strong. Some reversed Strichartz estimates and local decay estimates for the charge transfer model are established to handle strong interactions.

math.AP↗

arXiv2017

Significant Dzyaloshinskii-Moriya Interaction at Graphene-Ferromagnet Interfaces due to Rashba-effect

The possibility of utilizing the rich spin-dependent properties of graphene has attracted great attention in pursuit of spintronics advances. The promise of high-speed and low-energy consumption devices motivates a search for layered structures that stabilize chiral spin textures such as topologically protected skyrmions. Here we demonstrate that chiral spin textures are induced at graphene/ferromagnetic metal interfaces. This is unexpected because graphene is a weak spin-orbit coupling material and is generally not expected to induce sufficient Dzyaloshinskii-Moriya interaction to affect magnetic chirality. We demonstrate that graphene induces a new type of Dzyaloshinskii-Moriya interaction due to a Rashba effect. First-principles calculations and experiments using spin-polarized electron microscopy show that this graphene-induced Dzyaloshinskii-Moriya interaction can have similar magnitude as at interfaces with heavy metals. This work paves a new path towards two-dimensional material based spin orbitronics.

cond-mat.mtrl-sci↗

arXiv2016

Magnetism of epitaxial Tb films on W(110) studied by spin-polarized low-energy electron microscopy

Thin epitaxial films of Tb metal were grown on a clean W(110) substrate in ultra-high vacuum and studied in-situ by low-energy electron microscopy. Annealed films present magnetic contrast in spin-polarized low-energy electron microscopy. The energy dependence of the electron reflectivity was determined and a maximum value of its spin asymmetry of about 1\% was measured. The magnetization direction of the Tb films is in-plane. Upon raising the temperature, no change in the domain distribution is observed, while the asymmetry in the electron reflectivity decreases when approaching the critical temperature, following a power law $ \sim (1 - T/T_C)^β$ with a critical exponent $β$ of 0.39.

cond-mat.mtrl-sci↗

arXiv2016

Strichartz Estimates for Charge Transfer Models

In this note, we prove Strichartz estimates for scattering states of scalar charge transfer models in $\mathbb{R}^{3}$. Based on the idea of the proof of Strichartz estimates which follows \cite{CM,RSS}, we also show the energy of the whole evolution is bounded independently of time without using the phase space method, for example, in \cite{Graf}. One can easily generalize our argument to $\mathbb{R}^{n}$ for $n\geq3$. Finally, in the last section, we discuss the extension of these results to matrix charge transfer models in $\mathbb{R}^{3}$.

math.AP↗

arXiv2016

Non-divergence Parabolic Equations of Second Order with Critical Drift in Lebesgue Spaces

We consider uniformly parabolic equations and inequalities of second order in the non-divergence form with drift \[-u_{t}+Lu=-u_{t}+\sum_{ij}a_{ij}D_{ij}u+\sum b_{i}D_{i}u=0\,(\geq0,\,\leq0)\] in some domain $Q\subset \mathbb{R}^{n+1}$. We prove growth theorems and the interior Harnack inequality as the main results. In this paper, we will only assume the drift $b$ is in certain Lebesgue spaces which are critical under the parabolic scaling but not necessarily to be bounded. In the last section, some applications of the interior Harnack inequality are presented. In particular, we show there is a "universal" spectral gap for the associated elliptic operator. The counterpart for uniformly elliptic equations of second order in non-divergence form is shown in \cite{S10}.

math.AP↗

arXiv2016

Non-divergence Parabolic Equations of Second Order with Critical Drift in Morrey Spaces

We consider uniformly parabolic equations and inequalities of second order in the non-divergence form with drift \[-u_{t}+Lu=-u_{t}+\sum_{ij}a_{ij}D_{ij}u+\sum b_{i}D_{i}u=0\,(\geq0,\,\leq0)\] in some domain $Ω\subset \mathbb{R}^{n+1}$. We prove a variant of Aleksandrov-Bakelman-Pucci-Krylov-Tso estimate with $L^{p}$ norm of the inhomogeneous term for some number $p<n+1$. Based on it, we derive the growth theorems and the interior Harnack inequality. In this paper, we will only assume the drift $b$ is in certain Morrey spaces defined below which are critical under the parabolic scaling but not necessarily to be bounded. This is a continuation of the work in \cite{GC}.

math.AP↗

arXiv2015

Anatomy and giant enhancement of the perpendicular magnetic anisotropy of cobalt-graphene heterostructures

We report strongly enhanced perpendicular magnetic anisotropy (PMA) of Co films by graphene coating from both first-principles and experiments. Our calculations show that graphene can dramatically boost the surface anisotropy of Co films up to twice the value of its pristine counterpart and can extend the out-of-plane effective anisotropy up to unprecedented thickness of 25~Å. These findings are supported by our experiments on graphene coating on Co films grown on Ir substrate. Furthermore, we report layer-resolved and orbital-hybridization-resolved anisotropy analysis which help understanding the physical mechanisms of PMA and more practically can help design structures with giant PMA. As an example, we propose super-exchange stabilized Co-graphene heterostructures with a robust out-of-plane constant effective PMA and linearly increasing interfacial anisotropy as a function of film thickness. These findings point towards possibilities to engineer graphene/ferromagnetic metal heterostructures with giant magnetic anisotropy more than 20 times larger compared to conventional multilayers, which constitutes a hallmark for future graphene and traditional spintronic technologies.

cond-mat.mtrl-sci↗

arXiv2014

On Second Order Elliptic and Parabolic Equations of Mixed Type

It is known that solutions to second order uniformly elliptic and parabolic equations, either in divergence or nondivergence (general) form, are Hölder continuous and satisfy the interior Harnack inequality. We show that even in the one-dimensional case ($x\in R^1$), these properties are not preserved for equations of mixed divergence-nondivergence structure: for elliptic equations. \begin{equation*} D_i(a^1_{ij}D_ju)+a^2_{ij}D_{ij}u=0, \end{equation*} and parabolic equations \begin{equation*} p\partial_t u=D_i(a_{ij}D_ju), \end{equation*} where $p=p(t,x)$ is a bounded strictly positive function. The Hölder continuity and Harnack inequality are known if $p$ does not depend either on $t$ or on $x$. We essentially use homogenization techniques in our construction. Bibliography: 23 titles.

math.AP↗

arXiv2013

Real Space Imaging of the Verwey Transition at the (100) Surface of Magnetite

Effects of the Verwey transition on the (100) surface of magnetite were studied using scanning tunelling microscopy and spin polarized low-energy electron microsccopy. On cooling through the transition temperature Tv, the initially flat surface undergoes a roof-like distortion with a periodicity of ~0.5 um due to ferroelastic twinning within monoclinic domains of the low-temperature monoclinic structure. The monoclinic c axis orients in the surface plane, along the [001]c directions. At the atomic scale, the charge-ordered sqrt2xsqrt2R45 reconstruction of the (100) surface is unperturbed by the bulk transition, and is continuous over the twin boundaries. Time resolved low-energy electron microscopy movies reveal the structural transition to be first-order at the surface, indicating that the bulk transition is not an extension of the Verwey-like sqrt2xsqrt2R45 reconstruction. Although conceptually similar, the charge-ordered phases of the (100) surface and sub-Tv bulk of magnetite are unrelated phenomena.

cond-mat.mtrl-sci↗

arXiv2013

Room Temperature In-plane <100> Magnetic Easy Axis for Fe3O4/SrTiO3(001):Nb Grown by Infrared PLD

We examine the magnetic easy-axis directions of stoichiometric magnetite films grown on SrTiO3:Nb by infrared pulsed-laser deposition. Spin-polarized low-energy electron microscopy reveals that the individual magnetic domains are magnetized along the in-plane <100> film directions. Magneto-optical Kerr effect measurements show that the maxima of the remanence and coercivity are also along in-plane <100> film directions. This easy-axis orientation differs from bulk magnetite and films prepared by other techniques, establishing that the magnetic anisotropy can be tuned by film growth.

cond-mat.mtrl-sci↗