标题： 对称破缺的磁-环形人工自旋冰：磁化状态和动力学 显示英文标题

标题： Symmetry-broken magneto-toroidal artificial spin ices: magnetization states and dynamics

摘要： 磁电环形人工自旋冰（MT-ASIs）是由纳米磁体排列而成的结构，表现出自发的环形磁化。 铁环形序可能对自旋波在这一人工自旋冰中的传播产生影响，包括拓扑边缘模式的发展。 在这里，我们数值研究了具有和不具有空间对称性破缺的MT-ASI的磁化动力学。 通过微磁模拟，我们计算了四个最低阶态的能量和铁磁共振谱，这些态表现出铁环形性、反铁环形性和无环形性。 如预期的那样，我们发现当空间对称性被打破时，共振模式会分裂。 为了确定我们的系统是否表现出拓扑保护的边缘模式，我们进行了半解析计算，首先估计铁磁共振，然后计算带结构。 我们的结果表明，对称性破缺的MT-ASIs可以通过磁场协议进行重新配置，且其带结构依赖于磁化状态。 陈数的计算表明，在所有情况下，带结构都是拓扑平凡的，这表明动态磁耦合较弱。 非零陈数的缺失证明了在ASIs中的动态耦合较弱，这必须得到解决，以释放其在自旋电子学应用中的全部潜力。 显示英文摘要

摘要： Magneto-toroidal artificial spin ices (MT-ASIs) are arrangements of nanomagnets that exhibit spontaneous toroidization. A ferrotoroidic order could have implications on the propagation of spin waves through this artificial spin ice, including the development of topological edge modes. Here, we numerically investigate the magnetization dynamics of an MT-ASI with and without spatial symmetry breaking. Through micromagnetic simulations, we compute the energies and ferromagnetic resonance spectra of the four lowest-order states, which exhibit ferrotoroidicity, antiferrotoroidicity, and no toroidicity. As expected, we find that the resonant modes split when spatial symmetry is broken. To determine whether our system exhibits topologically protected edge modes, we perform semi-analytical calculations to first estimate the ferromagnetic resonance and then compute the band structure. Our results show that symmetry-broken MT-ASIs are reconfigurable by magnetic field protocols, and that their band structures depend on magnetization state. Calculation of the Chern number indicates that the bands are topologically trivial in all cases, suggesting that the dynamic magnetic coupling is weak. The absence of a non-zero Chern number is proof of the weak dynamic coupling in ASIs, which must be addressed to unlock their full potential in magnonics applications.