Strong coupling between magnetic and structural order parameters in SrFe2As2

X-ray and Neutron diffraction as well as muon spin relaxation and M\"ossbauer experiments performed on SrFe$_2$As$_2$ polycrystalls confirm a sharp first order transition at $T_0 = 205$,K corresponding to an orthorhombic phase distortion and to a columnar antiferromagnetic Fe ordering with a propagation vector (1,0,1), and a larger distortion and larger size of the ordered moment than reported for BaFe$_2$As$_2$. The structural and the magnetic order parameters present an remarkable similarity in their temperature dependence from $T_0$ down to low temperatures, showing that both phenomena are intimately connected. Accordingly, the size of the ordered Fe moments scale with the lattice distortion when going from SrFe$_2$As$_2$ to BaFe$_2$As$_2$. Full-potential band structure calculations confirm that the columnar magnetic order and the orthorhombic lattice distortion are intrinsically tied to each other.