Atomic scale visualization of novel magnetic phase transitions in Fe-based superconductor Sr$_{\mathrm{4}}$V$_{\mathrm{2}}$O$_{\mathrm{6}}$Fe$_{\mathrm{2}}$As$_{\mathrm{2}}$

Sr$_{\mathrm{4}}$V$_{\mathrm{2}}$O$_{\mathrm{6}}$Fe$_{\mathrm{2}}$As$_{\mathrm{2}}$ consists of superconducting FeAs layers and Mott insulating Sr$_{\mathrm{2}}$VO$_{\mathrm{3}}$ layers, and exhibits superconductivity with T$_{\mathrm{c}}$ near 30 K despite being a parent compound material. Unlike normal Fe-based superconductors, the magnetism of Sr$_{\mathrm{4}}$V$_{\mathrm{2}}$O$_{\mathrm{6}}$Fe$_{\mathrm{2}}$As$_{\mathrm{2}}$ has complexity due to the presence of two magnetic atomic layers of V and Fe; therefore, the issue of magnetism has been actively debated. In this work, we studied the orbital and magnetic phase transitions in the range of 4 K to 180 K using spin-polarized scanning tunneling microscope. We directly observed the changes of charge density waves of V atomic layer related to the nematicity at 150 K, and spin density waves of V atomic layer resulting from spin ordering of underlying Fe atomic layer below 50 K. Moreover, controlling the sample bias voltage, the hysteresis of magnetic domain is observed at 4 K. Our results show key clues to solve controversy about the magnetism of Sr$_{\mathrm{4}}$V$_{\mathrm{2}}$O$_{\mathrm{6}}$Fe$_{\mathrm{2}}$As$_{\mathrm{2}}$.