Abstract
The role of three-dimensionality in a ferromagnetic medium in ruling the propagation properties of spin-waves (SW) has been one of the main focuses of the research activity in recent years. In this context, we investigate the evolution of the SW dispersion (frequency vs wave vector) induced by a progressive vertical undulation of a ferromagnetic film. The geometric undulation is taken along a single direction and is periodic with constant period, while the amplitude (differential maximum height with respect to the film thickness) is gradually increased from 0 to 60 nm. We study the characteristic modification of the internal effective field and link it to the resulting SW dispersions and spatial profile. These systems display at once features both of a planar film and a discretized medium, and the dispersion curves change not only when SWs propagate along the undulation direction, but also perpendicular to it. We discuss the geometric and magnetic conditions for having either the invariance of the SW group velocity with respect to even major changes in the undulation, or a large group velocity for some edge modes. We address a potential dual-band activity, namely the simultaneous propagation of two independent SW-signals, with separated frequency bands and disjoint oscillation regions.
Highlights
The role of three-dimensionality in a ferromagnetic medium in ruling the propagation properties of spin-waves (SW) has been one of the main focuses of the research activity in recent years
We find out how special edge modes, forming in a specific 3D structure, show a frequency bandwidth comparable to or even larger than the bulk wave ones, allowing an additional channel for simultaneous information delivery
As discussed in section “Methods”, we use a micromagnetic simulator to compute the equilibrium magnetic configuration, and the dynamical matrix method (DMM) to get the spin waves (SWs) frequency and profile at any given wavevector value and direction: both calculation tools are based on the discretization of the sample into a tridimensional mesh of prisms
Summary
The role of three-dimensionality in a ferromagnetic medium in ruling the propagation properties of spin-waves (SW) has been one of the main focuses of the research activity in recent years. We study the characteristic modification of the internal effective field and link it to the resulting SW dispersions and spatial profile These systems display at once features both of a planar film and a discretized medium, and the dispersion curves change when SWs propagate along the undulation direction, and perpendicular to it. When propagating along waveguides consisting of artificial magnetic materials with properties periodically varied in space (magnonic crystals), SWs undergo Bragg diffraction and acquire new properties, absent in bulk materials, due to the formation of frequency bands and band gaps Since these properties depend on geometry and applied magnetic field, they can be designed and reconfigured. We discuss the coexistence, in the same system, of periodic waves together with non-periodic waves, and, on the other side, of bulk waves together with edge waves when the magnetization is not uniform
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