The coupling of spin and orbital degrees of freedom in the trilayer ${\mathrm{Sr}}_4{\mathrm{Ru}}_3{\mathrm{O}}_{10}$ sets a long-standing puzzle due to the peculiar anisotropic coexistence of out-of-plane ferromagnetism and in-plane metamagnetism. Recently, the induced magnetic structure by in-plane applied fields was investigated by means of spin-polarized neutron diffraction, which allowed the extraction of a substantial orbital component of the magnetic densities at Ru sites. It has been argued that the latter is at the origin of the evident layer-dependent magnetic anisotropy, where the inner layers carry larger magnetic momenta than the outer ones. We present a spin-polarized neutron diffraction study in order to characterize the nature of the ferromagnetic state of ${\mathrm{Sr}}_4{\mathrm{Ru}}_3{\mathrm{O}}_{10}$ in the presence of a magnetic field applied along the $c$ axis. The components of the magnetic densities at the Ru sites reveal a vanishing contribution of the orbital magnetic moment which is unexpected for a material system where orbital and spin degeneracies are lifted by spin-orbit coupling and ferromagnetism. We employ a model that includes the Coulomb interaction and spin-orbit coupling at the Ru site to address the origin of the suppression of the orbital magnetic moment. The emerging scenario is that of nonlocal orbital degrees of freedom playing a significant role in the ferromagnetic phase, with a Coulomb interaction that is crucial to making an antialigned orbital moment at short distance, resulting in a ground state with vanishing local orbital moments.

• Received 30 January 2019
• Revised 31 July 2019

DOI:https://doi.org/10.1103/PhysRevB.100.104440