I. Plaquette antiferromagnetic order coexisting with iron superconductivity
The symmetry requirement and the origin of magnetic orders coexisting with superconductivity have been strongly debated issues of iron-based superconductors (FeSCs). Observation of C₄-symmetric antiferromagnetism in violation of the inter-band nesting condition of spin-density waves in superconducting ground state will require significant change in our understanding of the mechanism of FeSC. The superconducting material Sr₂VO₃FeAs, a bulk version of monolayer FeSC in contact with a perovskite layer with its magnetism (T_N ~ 50 K) and superconductivity (T_C ~ 37 K) coexisting at parent state, has no reported structural orthorhombic distortion and thus makes a perfect system to look for theoretically expected C₄ magnetisms. Based on variable temperature spin-polarized scanning tunneling microscopy (SPSTM) with newly discovered imaging mechanism that removes the static surface reconstruction (SR) pattern by fluctuating it rapidly with spin-polarized tunneling current, we could visualize underlying C₄ symmetric (2×2) magnetic domains and its phase domain walls coexisting with superconductivity. We find that this magnetic order is perfectly consistent with the plaquette antiferromagnetic order in tetragonal Fe spin lattice expected from theories based on the Heisenberg exchange interaction of local Fe moments and the quantum order by disorder. The inconsistency of its modulation Q vectors from the nesting condition also implies that the nesting-based C₂ symmetric magnetism is not a unique prerequisite of high-Tc FeSC. Furthermore, the plaquette antiferromagnetic domain wall dynamics under the influence of small spin torque effect of spin-polarized tunneling current are shown to be consistent with theoretical simulation based on the extended Landau-Lifshitz-Gilbert equation. (ArXiv:1608.00884, under review in Nat. Mat.)

II. Enhancement of superconductivity by interfacial phonons
The physics at the interface between monolayer iron-based superconductor (FeSC) and perovskite substrate has received considerable attention due to the unusually high Tc of ~100 K found recently in monolayer FeSe on SrTiO₃ substrate. It has been suggested that forward-scattering interfacial phonons coupled with the Fe-layer electrons can enhance superconductivity from almost any kind of pre-existing electron-based pairing, initiating the quest for perovskite-clad FeSC monolayer and its bulk heterostructure with higher coupling efficiency with interfacial phonons. Here we report a spectroscopic imaging scanning tunneling microscopy (SI-STM) study on a parent-compound superconductor Sr₂VO₃FeAs, the only currently known self-assembled bulk example of FeSC monolayers on perovskite layers with substantially high T_C ~ 37 K. It shows clear signatures of forward-scattering phonons with unprecedentedly strong coupling close to 1 probably due to doubled interfaces per FeSC monolayer. Our masked quasiparticle interference (QPI) analysis based on the superconducting gap map and the V-Fe hybridization strength map shows clear positive correlations between all pairs, which is the hallmark of pairing enhancement due to electron-phonon coupling with interfacial phonons. With the possibility of massive number of parallel superconducting layers and the stronger electron-phonon coupling achieved, perovskite-clad FeSC monolayers may become a building block of the next generation Fe-based high-Tc superconductors with significantly enhanced Tc and current carrying capacity. (ArXiv:1608.00886, under review in Nat.)