Surface Broken Symmetry on Orthorhombic Double-layer Sr$_{3}$(Ru$_{1-x}$Mn$_{x})_{2}$O$_{7}$

The surface of double-layered ruthenate Sr$_{3}$Ru$_{2}$O$_{7}$ exhibits octahedra tilt distortion and an enhanced rotational distortion caused by the broken symmetry. Previous LEED IV calculation reveals that the tilt angle is (2.5\textpm 1.7)\textdegree at 80 K (B. Hu \textit{et. al.}, Physical Review B 81, 184104 (2010)). A glideline symmetry and a mirror symmetry along this direction are both broken. Results from LEED IV simulations show that both broken symmetries originate from the emergence of surface tilt. The degree of broken symmetry is more sensitive to the tilt angle, thus producing a smaller error than from conventional LEED IV calculation. When Mn doping is induced into the compound, the tilt is removed and the symmetry of the LEED pattern returns to what is expected for rotation, two glide planes and four-fold symmetry.