Global existence of the $s$-Schrödinger maps in $n\ge 5$

We study the $s$-Schrödinger map equation $$\{\begin{array}{l}{\mathrm{\partial }}_{t}u=-u\wedge (-\mathrm{\Delta }{)}^{s}u\text{on }{\mathbb{R}}^n\times \mathbb{R}\\ u:{\mathbb{R}}^n\times \mathbb{R}\to {\mathbb{S}}^2\\ u(x,0)=u_0\mathrm{.}\end{array}$$ For $s\in (1\mathrm{/}2,1)$ and $n\ge 5$ we prove that for small initial data $u_0$ in the critical Besov space one can obtain a global solution.