Evidence of in-plane ferromagnetic order probed by planar Hall effect in the geometry-confined ruthenate Sr4Ru3O10

The magnetic structure in the strongly correlated ruthenate $\mathrm{S}{\mathrm{r}}₄\mathrm{R}{\mathrm{u}}₃{\mathrm{O}}₁₀$ has been debated for a long time and still remains elusive. Here, we perform a systematically planar Hall effect study on a single-crystalline $\mathrm{S}{\mathrm{r}}₄\mathrm{R}{\mathrm{u}}₃{\mathrm{O}}₁₀$ nanostripe with a thickness of less than 100 nm. Large sharp switching behavior is observed in the planar Hall resistance, unambiguously indicating a strong anisotropic in-plane ferromagnetic order in the nanostripe, which is in contrast to the bulk system. Temperature-dependent evolution of the in-plane magnetism reveals that the in-plane spin order transforms from a single-domain state below a Curie temperature ${T}_C$ into a multidomain state below a critical temperature ${T}_M$, probably due to the inherent strong spin-orbit coupling driven reconfiguration of spins between the $c$ axis and the $ab$ plane.