Atomic scale observation of C$_{\mathrm{4}}$-plaquette antiferromagnetic order coexisting with superconductivity in iron-based superconductor Sr$_{\mathrm{2}}$VO$_{\mathrm{3}}$FeAs

The symmetry requirement and the origin of magnetic orders coexisting with superconductivity have been strongly debated issues of iron-based superconductors (FeSCs): it has been argued that the $C_{2}$-symmetric magnetism is a pre-requisite for the superconductivity in FeSCs. $C_{4}$-symmetric antiferromagnetism in superconducting ground state indeed has never been observed in real-space yet, likely due to the onset of $C_{2}$ structural orthorhombicity. The superconducting material Sr$_{\mathrm{2}}$VO$_{\mathrm{3}}$FeAs with its magnetism ($T_{N}$ \textasciitilde 50 K) and superconductivity ($T_{c}$ \textasciitilde 37 K) coexisting at parent state, has no reported structural orthorhombic distortion and thus makes a perfect system to look for some of the theoretically expected $C_{4}$ magnetisms. In this work, we studied the magnetic ground state and its phase transition using spin-polarized scanning tunneling microscopy. We observed $C_{4}$-symmetric plaquette antiferromagnetic order coexisting with superconductivity in tetragonal Fe spin lattice, and confirmed that the plaquette order can only be explained by Fe local moments picture. Furthermore, the inconsistency of its modulation $Q$ vectors from the nesting condition implies that the nesting-based $C_{2}$-symmetric magnetism is not a unique pre-requisite of high-$T_{c}$ FeSC.