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Sr$_4$Ru$_3$O$_{10}$, the $n$ = 3 member of the Ruddlesden-Popper typeruthenate Sr$_{n+1}$Ru$_n$O$_{3n+1}$, is known to exhibit a peculiarmetamagnetic transition in an in-plane magnetic field. However, the nature ofboth the temperature- and field-dependent phase transitions remains as a topicof debate. Here, we have investigated the magnetic transitions ofSr$_4$Ru$_3$O$_{10}$ via single-crystal neutron diffraction measurements. Atzero field, we find that the system undergoes a ferromagnetic transition withboth in-plane and out-of-plane magnetic components at $T_{c}$ ~ 100 K. Below$T^{*}$ ~ 50 K, the magnetic moments incline continuously toward theout-of-plane direction. At $T$ ~ 1.5 K, where the spins are nearly alignedalong the $c$ axis, a spin reorientation occurs above a critical field $B_c$,giving rise to a spin component perpendicular to the plane defined by the fielddirection and the $c$ axis. We suggest that both the temperature- andfield-driven spin reorientations are associated with a change in themagnetocrystalline anisotropy, which is strongly coupled to the lattice degreesof freedom. This study elucidates the long-standing puzzles on the zero-fieldmagnetic orders of Sr$_4$Ru$_3$O$_{10}$ and provides new insights into thenature of the field-induced metamagnetic transition.

Temperature- and field-driven spin reorientations in triple-layer ruthenate Sr$_4$Ru$_3$O$_{10}$