Role of internal demagnetizing field for the dynamics of a surface-modulated magnonic crystal

Abstract

Magnonic crystals with locally alternating properties and specific periodicities exhibit interesting effects, such as a multitude of different spin-wave states and large band gaps. This work aims for demonstrating and understanding the key role of local demagnetizing fields in such systems. To achieve this, hybrid structures are investigated consisting of a continuous thin film with a stripe modulation on top favorable due to the adjustability of the magnonic effects with the modulation size. For a direct access to the spin dynamics, a magnonic crystal was reconstructed from 'bottom-up', i.e., the structural shape as well as the internal field landscape of the structure were experimentally obtained on the nanoscale using electron holography. Subsequently, both properties were utilized to perform dynamic response calculations. The simulations yield the frequency-field dependence as well as the angular dependence of spin waves in a magnonic crystal and reveal the governing role of the internal field landscape around the backward-volume geometry. The complex angle-dependent spin-wave behavior is described for a 360• in-plane rotation of an external field by connecting the internal field landscape with the individual spin-wave localization.

Spin-wave non-reciprocity in magnetization-graded ferromagnetic films

“…One of the scientific interests is based on promising applications for signal processing devices, since the SW wavelength is shorter than those of electromagnetic waves in the GHz frequency range [2,5], allowing for better prospects for the miniaturization of magnonic devices [6]. This, added to the fact that the magnon bandstructure can be enriched with the artificial modulation of the magnetic media [7][8][9][10][11][12][13][14][15][16][17][18], has stimulated experimental and theoretical advances in the emerging field of magnonics. Recently, it has been theoretically predicted and subsequently proven experimentally, that such waves in FM thin films can couple to a heavy-metal layer with strong spin-orbit coupling, as evidenced by a considerable frequency non-reciprocity due to the interfacial Dzyaloshinskii-Moriya interaction [19][20][21][22][23][24][25][26].…”

Dipolar interaction induced band gaps and flat modes in surface-modulated magnonic crystals

“…SWs in MCs exhibit adjustable frequency band gaps (BGs), which can be optimized by modulating the magnetic parameters or changing the geometry and arrangement of periodic scattering centers . The design of MCs has wide versatility since these media can be created by artificial modulation of the magnetic properties, either in the form of dipolarly coupled nanowires [21], bicomponent magnonic crystals [12][13][14], width-modulated waveguides [30,32], antidot lattices [34,35], or modulated thickness films [36][37][38][39][40][41] or by means of ion implantation [42,43]. Also, reconfigurable magnonic crystals with a periodic induction of perpendicular magnetic anisotropy have been designed [44].…”

“…However, experimentally defining material parameters such as magnetization or exchange length with laterally well defined periodicities often is not straightforward and suffers from limitations of the range in which variations are possible for a given material. A periodic surface modulation of a ferromagnetic (FM) thin film is an interesting alternative to creating magnonic structures and devices, where the periodic properties are attributed to the size of the modulation [38][39][40][41]45,46,[50][51][52][53][54][55]. For instance, yttrium iron garnet (YIG) films with periodic arrays of micrometer-sized etched grooves have been synthesized [45,46,50,51,[53][54][55], while FM films with nanometric grooves have been created by means of ion implantation [42,43] and electron-beam lithography [40].…”

Controlling the three dimensional propagation of spin waves in continuous ferromagnetic films with an increasing out of plane undulation

“…Moreover, the variation in frequency is experienced by spin waves independently of the propagation direction or the magnetization configurations, because the geometric changes influence the whole system energetics. In other words, the undulation changes vary the whole system total energy, which in turn can make the system either more stable (stiffer), determining a general frequency increase, or less stable (softer), determining a general frequency decrease 50 , 51 . Interestingly, due to the specific symmetry of the primitive cell that we chose, we do not have any frequency gap across the first and second Brillouin zone for any propagating spin wave.…”