Pinning-Dependent Field-Driven Domain Wall Dynamics and Thermal Scaling in an Ultrathin $\mathrm{Pt}/\mathrm{Co}/\mathrm{Pt}$ Magnetic Film

Magnetic-field-driven domain wall motion in an ultrathin $\mathrm{Pt}/\mathrm{Co}(0.45\mathrm{nm})/\mathrm{Pt}$ ferromagnetic film with perpendicular anisotropy is studied over a wide temperature range. Three different pinning dependent dynamical regimes are clearly identified: the creep, the thermally assisted flux flow, and the depinning, as well as their corresponding crossovers. The wall elastic energy and microscopic parameters characterizing the pinning are determined. Both the extracted thermal rounding exponent at the depinning transition, $\psi =0.15$, and the Larkin length crossover exponent, $\varphi =0.24$, fit well with the numerical predictions.

Figure 1

Variation of the domain wall velocity in the $\mathrm{Pt}/\mathrm{Co}(0.45\mathrm{nm})/\mathrm{Pt}$ film with $H$ for different temperatures. The big black filled and half-filled symbols correspond to boundaries between the creep and TAFF regimes, $H_{C\text{−}T}$, and TAFF and depinning regimes, $H_{\text{dep}}$, respectively. The straight line represents the predicted asymptotic high-field flow limit at 300 K for $m=0.085\mathrm{m}/\mathrm{s}\mathrm{Oe}$. Inset: Domain wall displacement (in black) from a nucleus (in red) produced by a $1\mu s$ field pulse of amplitude $H=865\mathrm{Oe}$, at 150 K.

Figure 2

Field-dependent domain wall velocity. (a) Plot of $\ln v$ vs $H^{-1/4}$ to evidence the creep regime and its upper boundary $H_{C\text{−}T}$ (creep). Inset: creep prefactor $v_{\text{creep}}^0$ deduced from an extrapolation of the creep law (straight line) to $H^{-1/4}=0$. (b) Plot of $\ln v$ vs $H$ reveals the TAFF regime and its two boundaries $H_{C\text{−}T}$ (TAFF) and $H_{\text{dep}}$ (TAFF).

Figure 3

(a) $\psi$ as a function of $T$ calculated from the crossover at $H=H_{\text{dep}}$ between the TAFF and thermal rounding regimes, $v_{\mathrm{TAFF}}^0/(m{H}_{\text{dep}})=(T/T_{\text{dep}}{)}^{\psi }$. (b) Universal scaling plot of the depinning transition using $\psi =0.15$, $\beta =0.25$ and the parameters of Table 1. With the reduced coordinates $x=[(H-H_{\text{dep}})/H_{\text{dep}}](T/T_{\text{dep}}{)}^{-\psi /\beta }$ and $y=[v/(m{H}_{\text{dep}})](T/T_{\text{dep}}{)}^{-\psi }$, the velocity curves (cf. Fig. 1) are superimposed in the vicinity of the depinning transition ($x=0$), as expected from Eq. (3).

Figure 4

(a) Temperature variation of the elastic energy density, ${\epsilon }_{\text{el}}$, and the pinning energy density, ${\epsilon }_{\text{pin}}$. We used the value of $\xi (=19.3\mathrm{nm})$, obtained for $T=300\mathrm{K}$. (b) Temperature dependence of the wall width parameter, $\mathrm{\Delta }$, and of the Larkin length, $L_c$. In the inset, $L_c$ is plotted versus $T/T_{\text{dep}}$ . The line is the fit of Eq. (8) used for determining the $\varphi$ exponent.