Creation of magnetic rogue waves

Rogue waves, first discovered in the ocean, are extraordinarily large amplitude waves which can form in relatively calm environments. Magnetic materials also support waves, but with a completely different set of underlying physics. We demonstrate the possibility of generating magnetic rogue waves by applying an abstract form of time reversal. Magnetic systems have important differences from the other media which admit rogue waves; they are inherently anisotropic and have many tunable parameters such as the magnitude and direction of an applied field. We investigate the role of anisotropy and these tunable parameters in the formation and properties of magnetic rogue waves. Through analytic calculations, we identify the important wave vectors and frequencies, typically ranging from 10 to 25 GHz, of the spin waves involved in the creation of magnetic rogue waves. We then correlate this information with the overall efficiency of the rogue wave generation process.

Figure 1

Out-of-plane angle measurements (degrees) during the recording and reemission phases of a simulated magnetic rogue wave reconstructed through time reversal. (a) Initial rogue wave whose decay is recorded by sensors positioned throughout the material. (b) Anisotropic decay of the initial rogue wave. (c) End of the recording phase after significant damping. (d) Reemission of sensor data. (e) Constructive and destructive interference. (f) Reconstruction of the magnetic rogue wave at the end of the reemission phase.

Figure 2

Anisotropic decay of a magnetic rogue wave calculated for Permalloy films with thicknesses of (a) 5 nm and (b) 30 nm. For both thicknesses, an external field, $H$, is applied in plane along the $x$ axis.

Figure 3

Analytic calculations of the isofrequency curves for a (a) 5 nm film and a (b) 30 nm film. The red shaded area indicates the typical wave vectors involved in the decay of a magnetic rogue wave. Strong self-focusing and caustics occur in directions perpendicular to where the isofrequency curves have near zero curvature.

Figure 4

Peak-to-noise ratio (PNR) as a function of the angle, $\theta$, between the direction of the external field, $H$, and a line drawn between two sensors positioned equidistant from a magnetic rogue wave (MRW) source calculated for Permalloy films with thicknesses of 5 and 30 nm.

Figure 5

Peak and noise amplitudes measured in degrees out of plane as functions of external field strength for a reconstructed magnetic rogue wave calculated for Permalloy films with thicknesses of 5 and 30 nm.