Narrow Magnonic Waveguides Based on Domain Walls

The channeling of spin waves with domain walls in ultrathin ferromagnetic films is demonstrated theoretically and through micromagnetics simulations. It is shown that propagating excitations localized to the wall, which appear in the frequency gap of bulk spin wave modes, can be guided in curved geometries and propagate in close proximity to other channels. For Néel-type walls arising from a Dzyaloshinskii-Moriya interaction, the channeling is strongly nonreciprocal and group velocities can exceed $1\mathrm{km}/\mathrm{s}$ in the long wavelength limit for certain propagation directions. The channeled modes represent an unusual analogy of whispering gallery waves that are one dimensional and nonreciprocal with this interaction. Moreover, a sufficiently strong Dzyaloshinskii-Moriya interaction can create a degeneracy of channeled and propagating modes at a critical wave vector.

Figure 1

A magnonic waveguide based on a domain wall (DW). (a) Geometry for spin wave propagation along the center of the wall, where a radio frequency antenna generating an alternating field $h_{\text{rf}}$ excites spin waves that propagate along the ($x$). (b),(d) Dispersion relation for channeled Bloch [(b), red curve], ${\mathrm{\Omega }}_k^B$, and Néel [(d), blue curve], ${\mathrm{\Omega }}_k^N$, domain wall spin wave modes in comparison with bulk spin waves (black curve), ${\mathrm{\Omega }}_k^u$. For the Néel wall case, $D=1.5\mathrm{mJ}/{\mathrm{m}}^2$. (c),(e) Simulation results of propagating modes for excitation field frequencies in the bulk (50 GHz) and in the gap (10 GHz) for Bloch (c) and Néel (e) walls. These driving frequencies are shown as dashed lines in (b),(d).

Figure 2

Simulated dispersion relation for channeled and bulk spin waves. ${\mathrm{\Omega }}_k^u$ indicate bulk modes. The channeled modes for Bloch-type (${\mathrm{\Omega }}_k^B$) and Néel-type (${\mathrm{\Omega }}_k^{N\pm }$) walls are computed, where $D=3\mathrm{mJ}/{\mathrm{m}}^2$ for the latter and the sign indicates propagation relative to the wall chirality. The points represent simulated values and lines are based on Eqs. (2), (3), and (4). The inset shows the three-domain geometry with two parallel domain wall channels.

Figure 3

(a) Spin wave channeling around a curved track through two Néel-type domain walls ($D=1\mathrm{mJ}/{\mathrm{m}}^2$). Fluctuations in the $m_z$ magnetization component are shown as a color code for a microwave excitation frequency of 5 GHz, where the simulated microwave antenna is situated at the top of the track. The area of the simulated region is $1600\mathrm{nm}\times 1600\mathrm{nm}$. The width of the wire is 200 nm and the thickness is 1 nm. (b) Equilibrium configuration of the curved track comprising three domains. The inset shows a schematic of the magnetization profile in a cross section at the top of the track.

Figure 4

(a) Group velocity for the channeled and bulk spin waves. ${\mathrm{\Omega }}_k^u$ indicate bulk modes. The channeled modes for Bloch-type (${\mathrm{\Omega }}_k^B$) and Néel-type (${\mathrm{\Omega }}_k^{N\pm }$) walls ($D=1\mathrm{mJ}/{\mathrm{m}}^2$) are computed, where the sign for the latter indicates propagation relative to the wall chirality. The inset shows the $k\to 0$ limit of the group velocity for the two Néel wall modes as a function of the Dzyaloshinskii-Moriya constant, $D$. (b) Wave packets in a Néel wall channel ($D=3\mathrm{mJ}/{\mathrm{m}}^2$) at three instants after generation by a sinusoidal pulse with ${\nu }_p=7.5\mathrm{GHz}$.