Unconventional Magnetic Domains in Triple-layered Sr$_{4}$Ru$_{3}$O$_{10}$

A plethora of fascinating phenomena including p-wave superconductivity in Sr$_{2}$RuO$_{4}$ (n=1) and hybrid improper ferroelectricity in Ca$_{3}$Ru$_{2}$O$_{7}$ (n=2) have been observed in Ruddlesden-Popper ruthenates (Ca, Sr)$_{n+1}$Ru$_{n}$O$_{3n+1}$. The triple-layered Sr$_{4}$Ru$_{3}$O$_{10}$ (n=3) is believed to have an intriguing complex magnetic state, compared with its neighboring bi-layered meta-magnetic Sr$_{3}$Ru$_{2}$O$_{7}$(n=2) and ferromagnetic SrRuO$_{3}$ (n=$\infty$). The phase competition nature associated with this complexity is considered to be responsible for its novel properties such as coupled anisotropic magnetism and transport, low frequency quantum oscillations and sharp magneto-resistivity steps, which are still not well understood yet. To better understand its microscopic mechanism, we studied the magnetic domain structure on Sr$_{4}$Ru$_{3}$O$_{10}$ using low-temperature magnetic force microscopy. The observed unique domain structures in Sr$_{4}$Ru$_{3}$O$_{10}$ may shed lights on its microscopic phase competition nature and lead to a deeper understanding on its relations with other layered ruthenates.