Multi-Scale Magnonic Crystals and Fractional Schr?dinger Equation-Governed Dynamics

Nontechnical Abstract:

This project focuses on the design of advanced materials utilizing the geometries of nature. Nature, unlike geometry class in high school, is not composed of smooth lines, planes, and spheres, but rather bumpy, wrinkled, jagged curves like DNA wrapped up in the cell, surfaces like a mountainous landscape, and volumes like the porous nature of soil in the water table.

Fractional derivatives have been used to describe these geometries of nature, but no one has built such geometries from the ground up, element by element. Using textured thin magnetic films, the team will build such geometries as the basis for a new class of materials intermediate between order and disorder. These materials will control transport of information in the form of waves of magnetism, called spin waves, moving through our textured thin film slower (sub-diffusive) or faster (super-diffusive) than possible in simple geometries used up till now.

Construction of this new artificial material will be the first experimental realization of a quantum fractional derivative, because spin waves follow the same equations as the wave physics of quantum mechanics, in this case the fractional Schrödinger equation, up till now a purely theoretical idea. A key facet of this work is cross-training of graduate students between theory and experiment, producing a more robust workforce that can work in multiple modalities to solve new problems not tractable otherwise.

Fields in which the work force can excel with this knowledge include battery technology, based on porous, fractional materials; the spread of contaminants in soil and the water table; and vascular structures for transport in biological matter, including self-healing materials based on biological ideas.

Technical Abstract:

Fractional derivatives describe the bumpy, wrinkled, and jagged geometries of nature, where an integer derivative leads to divergent results rendering traditional definition of a derivative inapplicable, due to a rapid increase in the tangent and curvature with decreasing “ruler size”. Such natural geometries in the quantum context have been theoretically described with the fractional Schrӧdinger equation but never experimentally studied.

The team will explore the fractional Schrӧdinger equation-governed fundamental physics in multi-scale materials that consist of magnetic thin film–based, spatially modulated magnonic crystals. They will design and measure tunable sub-diffusive and super-diffusive transport in this artificial lattice as clear evidence of fractional Schrӧdinger equation dynamics.

The design builds on a new order-disorder lattice modulation axis, with an ordered lattice at one extreme and a disordered lattice giving rise to Anderson localization at the other. The project will provide a general basis for generating fractional partial differential equations, and lead to a deeper understanding of the present highly empirical approach to porous and other fractional media ranging from battery applications to biomimetic Murray materials to spread of contaminants in soil and the water table.

The program will be carried out through tight, integral collaborations between Mingzhong Wu's experimental group at Colorado State University and Lincoln Carr's theoretical group at Colorado School of Mines. Working together as an integrated team encompassing experimental and theoretical condensed matter physics, they propose a multi-faceted approach to meet broader impact goals, centrally themed on blending experiment and theory to train our graduate and undergraduate student to become well-rounded scientists.

This DMR grant supports research on fundamental understanding of quantum materials and especially exploring principles that cross-cuts many other condensed matter systems with funding from the Condensed Matter Physics (CMP) Program in the Division of Materials Research of the Mathematical and Physical Sciences Directorate.

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.