Ferrotoroidicity—the fourth form of primary ferroic order—breaks both space and time-inversion symmetry. So far, direct observation of ferrotoroidicity in natural materials remains elusive, which impedes the exploration of ferrotoroidic phase transitions. Here we overcome the limitations of natural materials using an artificial nanomagnet system that can be characterized at the constituent level and at different effective temperatures. We design a nanomagnet array as to realize a direct-kagome spin ice. This artificial spin ice exhibits robust toroidal moments and a quasi-degenerate ground state with two distinct low-temperature toroidal phases: ferrotoroidicity and paratoroidicity. Using magnetic force microscopy and Monte Carlo simulation, we demonstrate a phase transition between ferrotoroidicity and paratoroidicity, along with a cross-over to a non-toroidal paramagnetic phase. Our quasi-degenerate artificial spin ice in a direct-kagome structure provides a model system for the investigation of magnetic states and phase transitions that are inaccessible in natural materials.

铁环形——初级铁序的第四种形式——打破了空间和时间反演对称性。迄今为止，对天然材料中铁磁环性的直接观察仍然难以捉摸，这阻碍了对铁磁环相变的探索。在这里，我们使用人造纳米磁体系统克服了天然材料的局限性，该系统可以在成分水平和不同的有效温度下进行表征。我们设计了纳米磁体阵列来实现直接戈薇旋转冰。这种人造自旋冰表现出强大的环形矩和准简并基态，具有两个不同的低温环形相：铁环形和副环形。使用磁力显微镜和蒙特卡罗模拟，我们展示了铁磁环形和副环形之间的相变，以及与非环形顺磁相的交叉。我们的直接戈薇结构中的准简并人造自旋冰为研究天然材料中无法达到的磁态和相变提供了一个模型系统。