Asymmetric magnetic bubble expansion under in-plane field in Pt/Co/Pt: Effect of interface engineering

We analyze the impact of growth conditions on the asymmetric magnetic bubble expansion under an in-plane field in ultrathin Pt/Co/Pt films. Specifically, using sputter deposition, we vary the Ar pressure during the growth of the top Pt layer. This induces a large change in the interfacial structure as evidenced by a factor three change in the effective perpendicular magnetic anisotropy. Strikingly, a discrepancy between the current theory for domain-wall propagation based on a simple domain-wall energy density and our experimental results is found. This calls for further theoretical development of domain-wall creep under in-plane fields and varying structural asymmetry.

Figure 1

(a) Saturation magnetization $M_S$ as a function of $p_{\mathrm{top}}$. (b) Effective anisotropy field ${\mu }_0{H}_{K,\mathrm{eff}}$ as function of $p_{\mathrm{top}}$. (c) Polar MOKE loops for different $p_{\mathrm{top}}$. (d) Effective anisotropy field ${\mu }_0{H}_{K,\mathrm{eff}}$ as a function of $p_{\mathrm{top}}^{-1}$, the red dash line is a linear fit to the data for $p_{\mathrm{top}}^{-1}<1.19$ ${\mathrm{Pa}}^{-1}$. The blue line indicates a transitions between the “layered growth” and “alloying” regime.

Figure 2

(a) Typical example of a symmetrically expanding bubble with $H_x=0$ mT driven by an out-of-plane magnetic field $H_{z,P}$ of 5.39 mT with a duration of $t_P=9.93$ ms for the $p_{\mathrm{top}}=0.29$ Pa sample. (b) Typical velocity $v$ vs ${\mu }_0{H}_z$, black symbols and left-bottom axis and $ln\left(v\right)$ versus ${\left({\mu }_0{H}_z\right)}^{-1/4}$, blue symbols and right-top axis for $p_{\mathrm{top}}=0.29$ Pa. The red dashed lines are a fit to the creep law. (c) $ln\left(v\right)$ vs ${\left({\mu }_0{H}_z\right)}^{-1/4}$ for all samples. (d) Creep law scaling constant $\chi$ vs $p_{\mathrm{top}}$ (black symbols and right/bottom axis). Effective anisotropy field as function of $p_{\mathrm{top}}$ (red symbols and right/bottom axis). The left inset shows the creep law prefactor $v_0$ as a function of $p_{\mathrm{top}}$. The right inset plot $\chi$ vs $K_{\mathrm{eff}}$ indicating the $\chi \sim K_{\mathrm{eff}}^{5/8}$ proportionality. (e) Top left panel shows a Bloch bubble where we have indicated the magnetization angle inside the DW defining the bubble. The top right panel shows a Néel type bubble where the chirality of the DW depends on the sign of the DMI interaction. Bottom two panels show the orientation when the DWs magnetization is saturated along the applied in-plane field direction and the thickness of the arrows indicate the increase in energy of the DWs for different $D$, the white dotted circles in the bottom right panel accentuate the change when the in-plane field is reversed. (f) Bubble expansion [same scaling as in (a)] in the $p_{\mathrm{top}}=1.40$ Pa grown sample while applying an in-plane field, the inset shows the expansion with inverted $H_z$ showing identical, but mirrored in the $y$ axis, expansion.

Figure 3

(a)–(f) DW velocity profiles for $\mathrm{L}+\mathrm{R}-,\mathrm{L}-\mathrm{R}+,\mathrm{U}+\mathrm{D}-$, and $\mathrm{U}-\mathrm{D}+$ on a logarithmic scale as a function of $H_x$ for all $p_{\mathrm{top}}$. Note the different ranges of the $v$ scale used, i.e., the velocity variation increases with increasing pressure $p_{\mathrm{top}}$. (g)–(l) $\mathrm{L}+\mathrm{R}-$ velocity profiles as a function of $H_x$ for all $p_{\mathrm{top}}$ and different $|H_z|$ as indicated in the panels. (m)–(r) $ln\left(v_0\right)$ and $\chi$ as a function of $H_x$ for all $p_{\mathrm{top}}$ as extracted from the data shown in (g)–(l). The cyan line in the $ln{v}_0$ graph indicates the symmetric behavior relative to $H_x$ = 0.