Domain Wall Creep in Magnetic Wires

The dynamics of a 1D domain wall (DW) in magnetic wires patterned in 2D ultrathin Co films is studied as a function of the wire width $w_0$. The DW velocity $v(H)$ is hugely reduced when $w_0$ is decreased, and its field dependence is consistent with a creep process with a critical exponent $\mu =1/4$. The effective critical field scales as ($1/w_0$). Measurements of $v(H)$ in wires with controlled artificial defects show that this arises from the edge roughness introduced by patterning. We show that the creep law can be renormalized by introducing a topologically induced critical field proportional to $(1/w_0)$.

Figure 1

Time dependence of the longitudinal voltage $V_R$ during magnetization reversal. The first (second) step corresponds to the DW moving inside the first (second) cross. The inset shows the sketch of voltage measurement and a MO image indicating a single domain nucleation in the large magnetic area ($t_{\mathrm{Co}}=1\mathrm{nm}$).

Figure 2

(a) Average DW velocity as a function of $H^{1/4}$ for 1.5, 1, 0.6, and $0.5\mu \mathrm{m}$ wide wires patterned in a 1 nm thick Co layer. (b) Effective critical field $H_c^{\mathrm{eff}}$ as a function of $(1/w_0)$.

Figure 3

(a) DW propagating in a wire where the lateral width is varying as $w(x)=w_0+2a|\sin (kx)|$ and scanning electron microscopy (SEM) image after the resist writing process of a wire with artificial ER of form $w(x)$ ($a=200\mathrm{nm}$; $p=1\mu \mathrm{m}$). (b) Average DW velocity inside a wire of $1\mu \mathrm{m}$ with natural ER ($a=10\mathrm{nm}$; $p=200\mathrm{nm}$) and with artificially induced ER (a) patterned in the same 0.5 nm thick Co layer, compared to the DW velocity inside the large reservoir.

Figure 4

Typical potential landscape $(H_{cw}/H{)}^{1/4}$ vs $x$ (for $H=200\mathrm{Oe}$ and $H_c\sim 400\mathrm{Oe}$) for the wire of natural roughness of Fig. 3b. The dashed line represents the potential without ER.