On absolute continuity of the spectrum of a periodic magnetic Schr\"odinger operator

We consider the Schr"odinger operator in ${\mathbb{R}}^n$, $n\ge 3$, with the electric potential $V$ and the magnetic potential $A$ being periodic functions (with a common period lattice) and prove absolute continuity of the spectrum of the operator in question under some conditions which, in particular, are satisfied if $V\in L_{\mathrm{l}\mathrm{o}\mathrm{c}}^{n\mathrm{/}2}({\mathbb{R}}^n)$ and $A\in H_{\mathrm{l}\mathrm{o}\mathrm{c}}^q({\mathbb{R}}^n;{\mathbb{R}}^n)$, $q>(n-1)\mathrm{/}2$.