1D and 2D magnonic crystals

A magnonic crystal (MC) is formed through a periodically modulated magnetic material. This might be obtained through a magnetic superlattice or array of neighboring magnetic nanowires (one-dimensional MCs), a periodic array of nanomagnets or holes in a ferromagnetic thin-film (two-dimensional MC), or a three-dimensional arrangement of magnetic nanostructures ("artificial solid"). The period of the "superstructure" is larger than the lattice constant of the given magnetic material. The artificially introduced periodicity modifies the energy spectrum of magnons. Depending on the absolute value of the period the energy of dipolar or exchange dominated spin waves will be altered. A frequency gap (stop band) might open such that magnon propagation through the MC is forbidden for a specific frequency range. Such stop band properties might be useful for spin wave filters, spin wave guiding and storage devices which are tailored through the artificially created superstructure and not through the specific magnetic material. This functionality is different from early microwave devices such as circulators and insulators which were prepared from bulk magnetic materials, like garnets and ferrites. There a spin-wave resonance was, e.g., tuned through a biasing magnetic field.

Left: Nanotrenches subdivide a ferromagnetic thin film in an array of nanowires. If the magnetization of neighboring wires is anti-parallel the size of the stop band is tuned via an in-plane magnetic field without shifting the center of the same stop band. The field is collinear with the long axis of the wires. Spin waves propagating in transverse direction experience the stop band .
  [full article (pdf): click here. Copyright by American Physical Society]  
We have found recently that an array of densely packed magnetic nanowires forms a new class of artificial crystal. It allows one to "reprogram" the band structure in one and the same device in a remanent state.This offers new perspectives in magnonics and solid state research (see section: reprogrammable magnonic crystal).

Right: (a) to (d) Time evolution in a simulated spin-wave propagation experiment. The antidot lattice is subject to an in-plane magnetic field H generating an inhomogeneous internal field. The pulse-like broadband excitation of spin waves takes place in a circular area within the array. Importantly the propagation is highly anisotropic, going beyond the anisotropy known from plain films. After about 2 ns spin waves have mainly propagated in a direction perpendicular to H. There is almost no propagation collinear with H. We attribute this to localized spin-wave modes which form in the magnonic waveguides being orientated along H.

We have investigated two-dimensional arrays of holes in, both, micromagnetic simulations and experiments. Antidot lattices were prepared from ferromagnetic permalloy films. Using focused ion beam patterning we generated 250 nm wide circular holes on an rectangular lattice with a lattice constant of about 500 nm. In a further study we used a nanopatterned template, i.e. an anodic aluminium oxide membrane, to generate square-like holes with an edge length of 80 nm. The lattice constant was 180 nm. The animated illustration in the header reflects the spin-wave excitations in such an antidot lattice for different orientations of an in-plane magnetic field. Further experiments on 2D magnonic crystals have recently shown that coherently coupled egde modes form allowed minibands for spin waves which exhibit relatively large propagation velocities of about 5 km/s. We have found this for an antidot lattice consisting of holes with a diameter of 120 nm etched into a thin permalloy film. The lattice constant of the square lattice was 300 nm.

Simulations: Spin waves entering an antidot lattice (left) for H collinear with (center) and perpendicular to (right) wave vector k of propagating spin waves. The excitation takes place at the top with a magnetic field pulse, i.e., the excited spin waves cover a broad frequency and wave vector range. In the right graph, spin waves propagate through the perodic array of holes in the Permalloy film. We attribute this to extended modes that form in vertical direction due to the orientation of the applied field. After crossing the antidot lattice the spin waves exhibit a charactistic wave vector. Rotating the field by 90 (central graph) blocks the spin wave propagation. The animation covers about 2 ns. The left graph depicts the layout of the Permalloy film (white) and holes (dark).

S. Neusser, G. Duerr, S. Tacchi, M. Madami, M.L. Sokolovskyy, G. Gubbiotti, M. Krawczyk, and D. Grundler:
"Magnonic minibands in antidot lattices with large spin-wave propagation velocities",

Phys. Rev. B. 84, 094454 (2011).
[abstract: click here]  
J. Topp, D. Heitmann, M.P. Kostylev, and D. Grundler:
"Making a Reconfigurable Artificial Crystal by Ordering Bistable Magnetic Nanowires",

Phys. Rev. Lett. 104, 207205 (2010).
[full article (pdf): click here. Copyright by American Physical Society] 
[3] S. Neusser, B. Botters, M. Becherer, D. Schmitt-Landsiedel, and D. Grundler:
"Spin wave localization between nearest and next-nearest neighboring holes in an antidot lattice",

Appl. Phys. Lett. 93, 122501 (2008).
[abstract: click here]  
S. Neusser, B. Botters, and D. Grundler: "Localization, confinement, and field-controlled propagation of spin waves in antidot lattices",
Phys. Rev. B 78, 054406 (2008).
[full text (pdf): click here]

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