On the Christmas Eve of 2011, Mark Hoefer received an email linking one of his theories to experiments taking place in Gothenburg, Sweden. It was a momentous occasion. During his time with the National Institute of Standards and Technology (NIST) as a postdoctoral fellow, Professor Hoefer and colleagues had proposed a hypothesis surrounding the existence of dissipative droplet solitons. He felt strongly he was correct, but lacked part of the puzzle, the physical observations. On the other side of the world, Ezio Iacocca鈥檚 former PhD advisor gave a lecture on his research. Afterward, an audience member brought Professor Hoefer鈥檚 hypothesis to the speaker鈥檚 attention, a discussion that ultimately led to the momentous Christmas Eve email. Theory and experiment had at last intersected. Now a Swedish International Postdoctoral Fellow in 抖阴旅行射 Boulder鈥檚 Applied Mathematics Department, Dr. Iacocca works closely with Professor Hoefer and, with their associates, continue their exciting findings.
聽聽聽聽聽聽聽聽聽聽聽 In 2013, they published 鈥溾�� in , one of the world鈥檚 top academic journals. The paper spurred excitement among the academic community, and the project maintained its momentum.聽 A new paper, 鈥溾�� has been published in , another widely recognized and prestigious academic journal.
This publication discusses dissipative droplets, which are magnetic solitons that Professor Hoefer and colleagues theoretically predicted to exist in materials where dispersion, anisotropy, dissipation, and forcing balance each other. This balance is possible to achieve experimentally using ferromagnetic materials with perpendicular magnetic anisotropy (PMA) and a current-induced forcing known as spin transfer torque. In addition to their novel physical features, these solitons may be useful for spintronic applications where the electron鈥檚 spin, in addition to its charge, is used for signal and information processing.聽 In this paper, the dissipative droplet鈥檚 condition for existence, or nucleation boundary, is derived analytically and measured experimentally. This is achieved by weakly nonlinear stability analysis of the Landau-Lifshitz magnetic equations of motion including dissipation and forcing. From a uniform state, localized forcing excites plane waves when spatially uniform dissipation is balanced or exceeded. However, in materials with PMA, the uniform state exhibits a subcritical Hopf bifurcation.聽 The corresponding plane waves that compose this bifurcation are modulationally unstable, a nonlinear instability that results in the coalescence of waves and, ultimately the formation of a large amplitude dissipative droplet. In contrast, the corresponding equation without PMA exhibits a supercritical Hopf bifurcation and the formation of a stable, weakly nonlinear time-periodic solution.聽 Looking for instability and taking into account asymmetries present in the experiment, an analytical expression for the nucleation boundary as a function of applied fields and current (forcing) is obtained. Experiments show a remarkable agreement and fits to the analytical expression enable the in-situ determination of relevant material parameters such as the spin torque efficiency and asymmetry, with good accuracy.聽 These results reconcile different nucleation trends previously observed experimentally under a single, closed-form expression.
Written by Danielle Hawley