标题： 有序和无序的斯格明子态在方形基底上 显示英文标题

标题： Ordered and Disordered Skyrmion States on a Square Substrate

摘要： 我们通过原子模拟研究了由各向异性调制产生的正方形基底与磁畴壁之间的排序。 我们考虑了在磁场和样品尺寸作为函数的每个势能最小值处的填充率{\it f}= 1.5、2.0、2.5、3.0 和 3.5 个磁畴壁。 对于填充率{\it f}= 2.0，我们发现了各种二聚体排序，例如倾斜的二聚体态，以及类似于在正方形基底上观察到的胶体二聚体排序的反铁磁排序。 磁畴壁改变形状或湮灭的能力会产生在胶体系统中不会出现的额外状态。 在某些参数下{\it f}= 2.0，一半的磁畴壁可以湮灭形成正方晶格，或者可以形成包含不同大小磁畴壁的三聚体和单体的超晶格。 在较低磁场下，可以出现有序的拉伸磁畴壁态，而在零磁场下，可能出现有序的条纹态。 对于{\it f}= 3.0，我们发现了铁磁有序的三聚体、倾斜晶格、柱状晶格和拉伸相。 对于填充率{\it f}= 1.5 和 2.5，我们发现了双子晶格、不同的有序和无序态，以及由挫败效应产生的几个扩展的无序区域。 显示英文摘要

摘要： We examine the ordering of skyrmions interacting with a square substrate created from a modulation of anisotropy using atomistic simulations. We consider fillings of {\it f} = 1.5, 2.0, 2.5, 3.0, and 3.5 skyrmions per potential minimum as a function of magnetic field and sample size. For a filling of {\it f} = 2.0, we find various dimer orderings, such as tilted dimer states, as well as antiferromagnetic ordering that is similar to the colloidal dimer ordering seen on square substrates. The ability of the skyrmions to change shape or annihilate produces additional states that do not occur in the colloidal systems. For certain parameters at {\it f} = 2.0, half of the skyrmions can annihilate to form a square lattice, or a superlattice of trimers and monomers containing skyrmions of different sizes can form. At lower fields, ordered stretched skyrmion states can appear, and for zero field, there can be ordered stripe states. For {\it f} = 3.0, we find ferromagnetic ordered trimers, tilted lattices, columnar lattices, and stretched phases. For fillings of {\it f} = 1.5 and 2.5, we find bipartite lattices, different ordered and disordered states, and several extended disordered regions produced by frustration effects.