Visualization of the magnetic flux structure in phosphorus-doped EuFe$_2$As$_2$ single crystals

Magnetic flux structure on the surface of EuFe$_2$(As$_{1-x}$P$_x$)$_2$ single crystals with nearly optimal phosphorus doping levels $x=0.20$ and $x=0.21$ is studied by low-temperature magnetic force microscopy and decoration with ferromagnetic nanoparticles. The studies are performed in a broad temperature range. It is shown that the single crystal with $x=0.21$ in the temperature range between the critical temperatures $T_{\mathrm{SC}}=22$ K and $T_{\mathrm{C}}=(18\pm0.3)$ K of the superconducting and ferromagnetic phase transitions, respectively, has the vortex structure of a frozen magnetic flux, typical for type-II superconductors. The magnetic domain structure is observed in the superconducting state below $T_{\mathrm{C}}$. The nature of this structure is discussed.