Chaotic dynamics of magnetic domain walls in nanowires

The nonlinear dynamics of a transverse domain wall (TDW) in permalloy and nickel nanostrips with two artificially patterned pinning centers is studied numerically up to rf frequencies. The phase diagram frequency-driving amplitude shows a rich variety of dynamical behaviors depending on the material parameters and the type and shape of pinning centers. We find that T-shaped traps (antinotches) create a classical double well Duffing potential that leads to a small chaotic region in the case of nickel and a large one for Py. In contrast, the rectangular constrictions (notches) create an exponential potential that leads to larger chaotic regions interspersed with periodic windows for both Py and Ni. The influence of temperature manifests itself by enlarging the chaotic region and activating thermal jumps between the pinning sites while reducing the depinning field at low frequency in the notched strips.

Figure 1

Simulated structures: planar nanowire with two symmetric double notches (a) and with two symmetric antinotches (b). The equilibrium position of a pinned DW is shown in each case. The arrows indicate the direction of magnetization. Normalized potential pinning energy for notches (c) and antinotches (d) is shown for two different materials (Ni and Py) as determined by micromagnetic simulations.

Figure 2

Normalized Lyapunov phase diagram for a DW at $T=0$ K in a Py (a) and Ni (e) nanostrip with two symmetric antinotches. Dark color represents chaotic motion. The frequency $f$ is given in units of ${\gamma }_0{M}_s$, which corresponds to an absolute scale of 0–3 GHz. The amplitude of the applied field $h$ is given in units of $M_s$, that corresponds to 0–50 Oe in an absolute scale. Bifurcation diagrams are shown in (b) and (c) computed at 500 MHz and 1 GHz, respectively, for Py. (d) Example of strange attractor obtained at $H=50$ Oe from (c). (f) Bifurcation diagram for Ni at 500 MHz. (g) Strange attractor for a field of $H=6$ Oe from (f). The bifurcation diagrams and the strange attractor are computed with a 1D analytical model (upper panels) and by 3D micromagnetic simulations (lower panels). (h) Frequency response spectrum with jump phenomena for Py at $H=10$ Oe and for Ni at $H=20$ Oe.

Figure 3

Normalized Lyapunov phase diagram for a DW at $T=0$ K in a Py (a) and Ni (d) nanostrip with two double notches. Dark color represents chaotic motion. The frequency $f$ is given in units of ${\gamma }_0{M}_s$, which corresponds to an absolute scale of 0–3 GHz. The amplitude of the applied field $h$ is given in units of $M_s$, that corresponds to 0–50 Oe in an absolute scale for Py and to 0–30 Oe for Ni. Bifurcation diagrams are shown in (b) and (e) computed at 2.5 GHz for Py and 500 MHz for Ni, respectively. (c) Example of strange attractor obtained at $H=30$ Oe from (b). (f) Strange attractor for a field of $H=6$ Oe from (e). The bifurcation diagrams and the strange attractor are computed with a 1D analytical model (upper panels) and by 3D micromagnetic simulations (lower panels).

Figure 4

Frequency-current phase diagram for a DW at $T=0$ K in a Py nanostrip with two double notches.

Figure 5

Comparison between the DW motion at 0 (full line) and 300 K (dotted line) for the Py antinotched strip (a) and (c), Ni antinotched strip (e), and Ni notched strip (g). The control parameters are (a) 15.7 Oe, 600 MHz, (c) 22.6 Oe, 600 MHz, (e) 18 Oe, 400 MHz, and (g) 17.2 Oe, 800 MHz. The power spectrum at 300 K is shown in (b), (d), and (h) corresponding to (a), (c), and (g), respectively. (f) Phase-space plot of the DW motion from (e). The thick line corresponds to 0 K.