Non-Hermitian and topological magnonics with interacting artificial spin ices for reconfigurable microwave devices

半导体定义了我们的技术领域，开启了一个大数据计算的时代。随着设备接近其极限，为特定应用寻求替代和节能的解决方案。磁性材料提供了一种节能的替代方案，因为它们的自然运行时间尺度为纳秒（十亿分之一秒），并且减少了热量损失。这种操作依赖于电磁波或“磁振子”的激发，磁振子在材料中传播，可以与光子学和CMOS器件相连接。然而，磁振子衰减很快，在微米（百万分之一米）尺度上的可探测传播限制了它们的性能。本文介绍了一类新的支持磁振子沿其边缘传播的磁性材料。这种模式的空间约束保证了单向运动和更长的传播长度。此外，所提出的由强耦合纳米级磁铁组成的材料是“功能性的”，因为它们的性质可以主动地、非破坏性地重新配置，甚至可以切换。该项目的成功将为具有优异性能的可重构微波器件开辟新的途径。该项目将为磁学前沿的研究生和本科生提供研究机会。外联活动将使社区参与进来，提高人们对科学进步及其对社会的影响的认识。该项目将允许研究生和本科生领导专门为K-12学生设计的外展示范装置的开发，并扩大代表性不足群体的参与。这里提出的功能材料旨在结合磁振学领域，其中磁振子被操纵，以及人工自旋冰领域，其中二维晶格表现出可重构状态。这样，就有可能利用两种不同的物理现象进行潜在的微波应用。“磁环自旋冰”依赖于稳定的手性磁态来诱导磁振子带结构的拓扑结构。在这种情况下，边缘模式预计是拓扑保护，因此，单向的。非厄米系统将利用强层间耦合和不可避免的损耗来支持基于pt对称守恒的单向模式。为了模拟这些功能材料，该项目引入了一种新的分析形式，能够基于哈密顿形式来处理任意磁性超晶格。然后将形式主义应用于两种不同的数值方案：特征值求解器和时间相关模拟。本征值求解器将提供计算磁振子带结构的手段，这是迄今为止其他数值方法无法有效解决的问题。一个时间相关的模拟是一个独特的工具，将桥梁哈密顿形式主义大规模数值模拟。通过结合几何、耦合和拓扑，该项目有望激发对社区中更大类别的功能磁性材料的研究，包括三维几何和纳米尺度图案材料。该项目还将通过为其建模和随后的实验实现提供分析和数值工具，从而实现可重构微波磁振子器件和半导体类器件的下一步。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Semiconductors have defined the landscape of our technology, enabling an era of big-data computing. As devices approach their limits, alternative and energy-efficient solutions are sought for specific applications. Magnetic materials offer an energy-efficient alternative because of their natural operation timescales of nanoseconds (one billionth of a second) and reduced energy losses through heat. This operation relies on the excitation of magnetic waves, or “magnons”, that propagate through the material and can be interfaced with photonics and CMOS devices. However, magnons decay quickly, with detectable propagation in the micrometer (one-millionth of a meter) scale that limits their performance. In this proposal, a new class of magnetic materials supporting magnons constrained to propagate along their edges is introduced. The spatial constraint on such modes ensures both unidirectional motion and longer propagation lengths. Additionally, the proposed materials composed of strongly coupled nanosized magnets are “functional” in the sense that their properties can be actively and non-destructively reconfigured and even toggled. The success of this project will open a new pathway toward reconfigurable microwave devices with superior performance. This project will provide research opportunities for a diverse graduate and undergraduate student population at the forefront of magnetism. Outreach activities will engage the community and bring awareness to scientific advances and their impact on society. This project will allow graduate and undergraduate students to lead the development of an outreach demonstration setup specifically designed for K-12 students and to broaden the participation of underrepresented groups.The functional materials proposed here aim to combine the field of magnonics, where magnons are manipulated, and the field of artificial spin ices, where two-dimensional lattices exhibit reconfigurable states. In doing so, it will be possible to harness two distinct physical phenomena for potential microwave applications. The “magneto-toroidal spin ice” relies on a stable chiral magnetic state to induce topology in the magnon band structure. In this case, edge modes are expected to be topologically protected and, therefore, unidirectional. The non-Hermitian systems will make use of strong inter-layer coupling and the unavoidable losses to support unidirectional modes based on the conservation of PT-symmetry. To model these functional materials, this project introduces a new analytical formalism that will be able to tackle arbitrary magnetic super-lattices based on a Hamiltonian formalism. The formalism will be then applied to two distinct numerical schemes: an eigenvalue solver and a time-dependent simulation. The eigenvalue solver will provide the means to compute the magnon band structure, which has not been efficiently solved by other numerical methods to date. A time-dependent simulation is a unique tool that will bridge the Hamiltonian formalism to large-scale numerical modeling. By combining geometry, coupling, and topology, this project is expected to spark the investigation of a larger class of functional magnetic materials in the community, including three-dimensional geometries and nanoscale-patterned materials. The project will also enable the next step towards the realization of reconfigurable microwave magnon-based devices and semiconductor-like devices by providing the analytical and numerical tools for their modeling and subsequent experimental realization.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.