Direct observation of vortex and Meissner domains in a ferromagnetic superconductor EuFe$_2$(As$_{0.79}$P$_{0.21}$)$_2$ single crystal

A spontaneous vortex structure in magnetic domains (vortex domains) has been visualized by the decoration technique near the ferromagnetic transition temperature ($T_{\mathrm{C}} = 18$ K) in a ferromagnetic superconductor EuFe$_2$(As$_{0.79}$P$_{0.21}$)$_2$ single crystal with the superconducting transition temperature ($T_{\mathrm{SC}} = 22$ K). Meissner domains previously observed by magnetic force microscopy have also been observed in a narrow temperature range ($\Delta T\sim1$ K) near $T_{\mathrm{C}}$. A domain structure with the alternating direction of the magnetic flux has been observed upon cooling below $T_{\mathrm{C}}$. Experimental results are in reasonable agreement with a theoretical estimate of the periods of domain structures and the temperature interval below $T_{\mathrm{C}}$ in which they are observed.