Magnonics is an emerging field of modern magnetism, which can be considered a subfield of modern solid-state physics. Magnonics combines the study of waves and magnetism. Its main aim is to investigate the behaviour of spin waves in nano-structured elements. In essence, spin waves are a propagating re-ordering of the magnetisation in a material and arise from the precession of magnetic moments. Magnetic moments arise from the orbital and spin moments of the electron; most often, it is this spin moment that contributes to the net magnetic moment. Following the success of the modern hard disk, there is significant current interest in future magnetic data storage and using spin waves for things such as 'magnonic' logic and data storage. Similarly, spintronics aims to utilize the inherent spin degree of freedom to complement the already successful charge property of the electron used in contemporary electronics. Modern magnetism is concerned with deepening the understanding of the behaviour of the magnetisation on very small (sub-micrometre) length scales and very fast (sub-nanosecond) timescales, and how this can be applied to improving existing or generating new technologies and computing concepts. A magnon torque device was invented and later perfected at the National University of Singapore's Electrical & Computer Engineering department, which is based on such potential uses, with results published on November 29, 2019, in Science. A magnonic crystal is a magnetic metamaterial with alternating magnetic properties. Like conventional metamaterials, their properties arise from geometrical structuring, rather than their band structure or composition directly. Small spatial inhomogeneities create an effective macroscopic behaviour, leading to properties not readily found in nature. By alternating parameters such as the relative permeability or saturation magnetisation, there exists the possibility to tailor 'magnonic' band gaps in the material. By tuning the size of this bandgap, only spin wave modes able to cross the bandgap would be able to propagate through the media, leading to the selective propagation of certain spin wave frequencies. See Surface magnon polariton.
Theory
Spin waves can propagate in magnetic media with magnetic ordering, such as ferromagnets and antiferromagnets. The frequencies of the precession of the magnetisation depend on the material and its magnetic parameters. In general, precession frequencies are in the microwave from 1–100 GHz, exchange resonances in particular materials can even see frequencies up to several THz. This higher precision frequency opens new possibilities for analogue and digital signal processing. Spin waves themselves have group velocities on the order of a few km per second. The damping of spin waves in a magnetic material also causes the amplitude of the spin wave to decay with distance, meaning the distance freely propagating spin waves can travel is usually only several 10's of μm. The damping of the dynamical magnetisation is accounted for phenomenologically by the Gilbert damping constant in the Landau–Lifshitz–Gilbert equation (LLG equation), the energy loss mechanism itself is not completely understood, but is known to arise microscopically from magnon–magnon scattering, magnon–phonon scattering, and losses due to eddy currents. The Landau–Lifshitz–Gilbert equation is the 'equation of motion' for the magnetisation. All of the properties of the magnetic systems, such as the applied bias field, the sample's exchange, anisotropy, and dipolar fields, are described in terms of an 'effective' magnetic field that enters the Landau–Lifshitz–Gilbert equation. The study of damping in magnetic systems is an ongoing modern research topic. The LL equation was introduced in 1935 by Landau and Lifshitz to model the precessional motion of magnetization M {\displaystyle \mathbf {M} } in a solid with an effective magnetic field H e f f {\displaystyle \mathbf {H} _{\mathrm {eff} }} and with damping. Later, Gilbert modified the damping term, which in the limit of small damping yields identical results. The LLG equation is,
∂ m ∂ t = − γ m × H e f f + α m × ∂ m ∂ t . {\displaystyle {\frac {\partial {\textbf {m}}}{\partial t}}\,=\,-\gamma \,{\textbf {m}}\times {\textbf {H}}_{\mathrm {eff} }\,+\,\alpha \,{\textbf {m}}\times {\frac {\partial {\textbf {m}}}{\partial t}}\,.\qquad }
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