The driving force in materials to spontaneously form states with magnetic or electric order is of fundamental importance for basic research and device technology. The macroscopic properties and functionalities of these ferroics depend on the size, distribution and morphology of domains; that is, of regions across which such uniform order is maintained¹. Typically, extrinsic factors such as strain profiles, grain size or annealing procedures control the size and shape of the domains^2,3,4,5, whereas intrinsic parameters are often difficult to extract due to the complexity of a processed material. Here, we achieve this separation by building artificial crystals of planar nanomagnets that are coupled by well-defined, tuneable and competing magnetic interactions^6,7,8,9. Aside from analysing the domain configurations, we uncover fundamental intrinsic correlations between the microscopic interactions establishing magnetically compensated order and the macroscopic manifestations of these interactions in basic physical properties. Experiment and simulations reveal how competing interactions can be exploited to control ferroic hallmark properties such as the size and morphology of domains, topological properties of domain walls or their thermal mobility.

材料自发形成具有磁或电有序状态的驱动力对于基础研究和器件技术具有根本重要性。这些铁的宏观性质和功能取决于域的大小、分布和形态；也就是说，保持这种统一秩序的区域¹。通常，应变分布、晶粒尺寸或退火程序等外在因素控制着域^2,3,4,5的大小和形状，而由于加工材料的复杂性，内在参数通常难以提取。在这里，我们通过构建平面纳米磁铁的人造晶体来实现这种分离，这些晶体通过明确、可调谐和竞争性的磁相互作用耦合^6,7,8,9. 除了分析域配置之外，我们还揭示了建立磁补偿顺序的微观相互作用与这些相互作用在基本物理性质中的宏观表现之间的基本内在相关性。实验和模拟揭示了如何利用竞争相互作用来控制铁质标志特性，例如畴的大小和形态、畴壁的拓扑特性或其热迁移率。