The Consequences of Spin-Orbit Coupling on the 5d$^{\mathrm{3}}$ Electronic Configuration

The impact of spin-orbit coupling on collective properties of matter is of considerable interest. The most intensively investigated materials in this regard are Iridium-based transition metal oxides which exhibit a host of interesting ground states that originate from a 5d$^{\mathrm{5}}$ J$_{\mathrm{eff}}=$1/2 electronic configuration. Moving beyond the J$_{\mathrm{eff}}=$1/2 paradigm to other electronic configurations where spin-orbit coupling plays a prominent role is a key objective of ongoing research. Here we focus on several Osmium-based transition metal oxides such as NaOsO$_{\mathrm{3}}$, Cd$_{\mathrm{2}}$Os$_{\mathrm{2}}$O$_{\mathrm{7}}$, Ca$_{\mathrm{3}}$LiOsO$_{\mathrm{6}}$, Sr$_{\mathrm{2}}$ScOsO$_{\mathrm{6}}$, Ba$_{\mathrm{2}}$YOsO$_{\mathrm{6}}$, and Sr$_{\mathrm{2}}$FeOsO$_{\mathrm{6}}$, which are nominally in the 5d$^{\mathrm{3}}$ electronic configuration. Within the LS coupling picture and a strong octahedral crystal field, the 5d$^{\mathrm{3}}$ configuration is expected to be an orbital singlet and spin-orbit effects should be minimal. Nevertheless, our neutron and x-ray scattering investigations of these materials as well as investigations by other groups show dramatic effects of spin-orbit coupling including reduced moment magnetic order, enhanced spin-phonon coupling, and large spin gaps. In particular, the anisotropy induced by spin-orbit coupling tips the balance of the frustrated interactions and drives the selection of particular magnetic ground states. To understand the mechanism driving the spin-orbit effects, we have explored the ground state t$_{\mathrm{2g}}$ manifold with resonant inelastic x-ray scattering and observe a spectrum inexplicable by an LS coupling picture. On the other hand, an intermediate coupling approach reveals that the ground state wave function is a J$=$3/2 configuration which answers the question of how strong spin-orbit coupling effects arise in 5d$^{\mathrm{3}}$ systems.