Mapping the magnonic landscape in patterned magnetic structures

Abstract

We report the development of a hybrid numerical / analytical model capable of mapping the spatially-varying distributions of the local ferromagnetic resonance (FMR) frequency and dynamic magnetic susceptibility in a wide class of patterned and compositionally modulated magnetic structures. Starting from the numerically simulated static micromagnetic state, the magnetization is deliberately deflected orthogonally to its equilibrium orientation, and the magnetic fields generated in response to this deflection are evaluated using micromagnetic software. This allows us to calculate the elements of the effective demagnetizing tensor, which are then used within a linear analytical formalism to map the local FMR frequency and dynamic magnetic susceptibility. To illustrate the typical results that one can obtain using this model, we analyze three micromagnetic systems boasting non-uniformity in either one or two dimensions, and successfully explain the spin-wave emission observed in each case, demonstrating the ubiquitous nature of the Schlömann excitation mechanism underpinning the observations. Finally, the developed model of local FMR frequency could be used to explain how spin waves could be confined and steered using magnetic non-uniformities of various origins, rendering it a powerful tool for the mapping of the graded magnonic index in magnonics.

Broadband conversion of microwaves into propagating spin waves in patterned magnetic structures

“…A more detailed account of the method and the discussion of its advantages and limitations can be found in Ref. 35. The ground state micromagnetic configuration of the transversely-magnetized stripe is shown in Fig.…”

Magnetic interfaces as sources of coherent spin waves

“…whereχ A(B) are the susceptibility tensors of the media. We note that, since we have allowed the magnetic parameters of the two media to vary in space, both m A(B),U andχ A(B) are also functions of the coordinates and should be treated as local functions [22]. This is not a problem, however, for the present calculation since we will only need their values at the interface boundaries.…”

“…For the same reason, no spin-wave emission is possible if the source term = (14) becomes equal to zero for any other reason. Depending on the problem, the local microwave susceptibility tensorsχ A(B) in the vicinity of the interface can be calculated analytically [23] or from micromagnetic simulations [22,24]. The most efficient emission is expected when the source term is strongest.…”

“…When the coupling is strong, i.e., when A AB can be considered as a large parameter, Eqs. (22) predict that the dependence of the amplitudes of the emitted spin waves on the coupling strength saturates, so that the amplitudes approach asymptotically constant values:…”

Towards magnonic devices based on voltage-controlled magnetic anisotropy

“…In principle, any patterned magnetic micro-or-nanostructure shows nonuniformity in magnetization. However, the desired nonuniformity in magnetization can be created through proper design of sample structure by using single or multiple magnetic materials, and can be controlled through dynamic demagnetizing field with the help of an external magnetic field 81 . Very recently, the theoretical work by Krivoruchko et al have shown that an external electric field, applied along a direction perpendicular to SW wavevector and magnetization, can induce Dzyaloshinskii-Moriya-like (DM-like) interaction 82 , known as Aharanov-Casher effect.…”