Enhanced domain wall velocity near a ferromagnetic instability

Assuming a Fermi liquid behavior for $s$-conduction electrons, we rewrite the extended Landau-Lifshitz-Gilbert (LLG) equation renormalized by interactions through the Landau parameters $F^{a}_{l}$ ($l=0,1,2 \cdots$) in an explicit form to describe the dynamic of a domain wall (DW) due to spin transfer torque phenomenon. The interaction between spins of the \textit{s}-conduction electrons explains qualitatively the DW velocity experimental observations in $\mathrm{Ni_{81}}\mathrm{Fe_{19}}$ (Permalloy) recalculated by us without defects or impurity hypothesis. Close to Stoner ferromagnetic instability point where $F^{a}_{0} \approx -0.99$, the DW velocity becomes high ($v^{*}_{DW}\approx 600$ $ms^{-1}$) and critical spin current density becomes reduced ($j^{*}_{c}\approx1\times10^{12}$ $Am^{-2}$) when compared to that calculated by nonadiabatic approach. At the critical point, the DW velocity diverges while critical spin current density at the same point goes to zero. Our theory also provides a prediction to looking for materials in which is possible applies a smallest critical spin current density and observes higher DW velocity.