How can this be studied through the nonlinear magnetization dynamics of coupled ferromagnetic nanowires? Michael Cottam and Zahra Haghshenasfard take us through their fascinating recent work in Journal of Physics: Condensed Matter.
In recent years, the nonlinear properties of spin waves (SWs) or magnons in confined geometries have been a topic of intense interest. Investigations have included parametric instabilities of these modes under microwave pumping in nanostructures composed (for example) of thin ﬁlms, wires, rings, etc, and the demonstration of the Bose-Einstein condensation (BEC) of interacting magnons at room temperature. Studies of periodic arrays of these elements have been important in the field of magnonic crystals. To a large extent this interest has been a result of progress in the fabrication of high quality nanostructured magnetic materials and arrays with smaller sizes and sharper interfaces, but there is always the continuing need for a proper understanding of the nonlinear magnetization dynamics at surfaces and interfaces on the sub-micron length scale.
In this paper, we develop a microscopic (or Hamiltonian-based) formalism for the quantum statistics of bosonic excitations in a two-mode magnon system, motivated by previous studies of two-mode systems in quantum optics and their relevance for optical communications. An essential difference, however, in the magnon case arises from the effects of a microwave pumping field considered to be applied along the magnetization direction, as well as from the forms of the magnon dispersion relations and the four-magnon interactions. The Hamiltonian for the magnon systems includes the role of the short-range exchange and the long-range magnetic dipole-dipole interactions, as well as the Zeeman term for an external applied field. A coherent magnon state representation is used to study the time development of the magnon occupation numbers and other quantum-statistical properties of the two-mode system. In particular, a collapse-and-revival phenomenon for the temporal evolution of the magnon numbers was highlighted (broadly analogous to Rabi oscillations in quantum optics), which could be effectively controlled through the amplitude and frequency of the pumping field. Also the four-magnon interactions were shown to play an interesting role for the cross correlation between the two magnon modes under pumping, e.g., with the development of anti-correlation effects in some cases when coherent states are used for the magnons.
As a physical realization of a two-mode magnon system, we propose a simple model consisting of a ferromagnetic nanowire geometry formed by two interacting lines of spins, and numerical applications were made using parameters appropriate to Permalloy (or Ni80Fe20). Examples are given in the figure. Adaptations of the current work could lead to a theory of magnon-BEC in nanowires and in nanowire magnonic arrays, by contrast with the experiments to date on ferromagnetic films.
About the Authors
This work was carried out at the Department of Physics & Astronomy at the University of Western Ontario in London, Ontario, Canada. Michael Cottam is an emeritus professor of physics and Zahra Haghshenasfard is close to completing her second PhD degree. The focus of research in the group is the quantum theory of nanostructured materials, particularly the optical and magnetic dynamical properties. Current interests include magnonic materials, nonlinear magnetization dynamics, quantum statistics, and topological modes in graphene-based nanomaterials.
This work is licensed under a Creative Commons Attribution 3.0 Unported License