Modes of Periodic Domain Wall Motion in Ultrathin Ferromagnetic Layers

Magnetization reversal in a periodic magnetic field is studied on an ultrathin, ultrasoft ferromagnetic $\mathrm{Pt}/\mathrm{Co}(0.5\mathrm{nm})/\mathrm{Pt}$ trilayer exhibiting weak random domain wall (DW) pinning. The DW motion is imaged by polar magneto-optic Kerr effect microscopy and monitored by superconducting quantum interference device susceptometry. In close agreement with model predictions, the complex linear ac susceptibility corroborates the dynamic DW modes segmental relaxation, creep, slide, and switching.

Figure 1

(a) Schematic plot of the DW velocity, $v$ vs dc field $H$, which does not report on the high-field behavior, exhibiting depinning at $H=H_p$ and slide (marked as SL) at $T=0$ (broken line) and—additionally—creep (C) at $T>0$ (solid line). (a) Schematic Cole-Cole plot of the susceptibility components, ${\chi }^{\prime \prime }$ vs ${\chi }^{\prime }$, due to a randomly pinned DW in ac driving fields, exhibiting relaxation (R), creep (C), slide (SL), and switching (SW).

Figure 2

Upper panel: $P$-MOKE micrographs (size $200\times 150\mu {\mathrm{m}}^2$) of a $\mathrm{Pt}/\mathrm{Co}(0.5\mathrm{nm})/\mathrm{Pt}$ trilayer taken at time distances $\Delta t=2.5\mathrm{s}$ during 1.4 periods of an ac excitation at $f=0.1\mathrm{Hz}$ with ${\mu }_0{H}_0=0.45\mathrm{mT}$ and $f=0.1\mathrm{Hz}$. Lower panel: Oscillating magnetic field ${\mu }_{0}H$ and magnetization $\Delta M$ vs $t$ with time labels 1–5 corresponding to the images in the upper panel.

Figure 3

Spectra of the real, ${\chi }^{\prime }$, and imaginary part, ${\chi }^{\prime \prime }$, of the ac susceptibility vs. frequency, $f$, at $T=325$ (a),(b) and 350 K (d),(e) for ac amplitudes, ${\mu }_{0}H=0.42$ (black circles), 0.2 (red squares) and 0.1 mT (blue triangles), and the corresponding Cole-Cole plots, ${\chi }^{\prime \prime }$ vs ${\chi }^{\prime }$ (c),(f). Bold solid lines mark the power-law creep spectra in (c) and the switching quarter circles in (f). Arrows in (b),(c) mark the relaxation-to-creep crossover. Thin solid lines are guides to the eye.