Department of Physics, University of Colorado, Boulder, Colorado 80309, USA.
Materials Science and Engineering Program, Soft Materials Research Center and Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA.
Phys Rev Lett. 2018 Nov 2;121(18):187201. doi: 10.1103/PhysRevLett.121.187201.
Two-dimensional topological solitons, commonly called Skyrmions, are extensively studied in solid-state magnetic nanostructures and promise many spintronics applications. However, three-dimensional topological solitons dubbed hopfions have not been demonstrated as stable spatially localized structures in solid-state magnetic materials. Here we model the existence of such static solitons with different Hopf index values in noncentrosymmetric solid magnetic nanostructures with a perpendicular interfacial magnetic anisotropy. We show how this surface anisotropy, along with the Dzyaloshinskii-Moriya interactions and the geometry of nanostructures, stabilize hopfions. We demonstrate knots in emergent field lines and computer simulate Lorentz transmission electron microscopy images of such solitonic configurations to guide their experimental discovery in magnetic solids.
二维拓扑孤子，通常称为斯格明子，在固态磁性纳米结构中得到了广泛研究，并有望在自旋电子学中得到广泛应用。然而，三维拓扑孤子，即霍普夫离子，在固态磁性材料中尚未被证明为稳定的空间局域结构。在这里，我们在具有垂直界面磁各向异性的非中心对称固态磁性纳米结构中，对具有不同霍普夫指标值的这种静态孤子的存在进行建模。我们展示了这种表面各向异性，以及狄亚洛斯基-莫里亚相互作用和纳米结构的几何形状，是如何稳定霍普夫离子的。我们展示了在新兴的磁场线中的结，并对这些孤子构型的洛伦兹透射电子显微镜图像进行了计算机模拟，以指导它们在磁性固体中的实验发现。
