Local site behavior of the $5d$ and $4f$ ions in the frustrated pyrochlore ${\mathrm{Ho}}_2{\mathrm{Os}}_2{O}_7$

The pyrochlore osmate ${\mathrm{Ho}}_2{\mathrm{Os}}_2{O}_7$ is a candidate material for a fragile $J=0$ local singlet ground state; however little is known regarding the single-ion behavior of either the Os or Ho ions. To address this we present polarized neutron powder diffraction (PNPD) and RIXS measurements that separately probe the local site behavior of the Os and Ho ions. The PNPD results are dominated by ${\mathrm{Ho}}^{3+}$ scattering and the analysis reveals local site susceptibility behavior consistent with spin-ice materials. Complementary unpolarized neutron powder diffraction shows an ordered spin-ice ground state in an applied magnetic field. To isolate the ${\mathrm{Os}}^{4+}$ single-ion behavior we present resonant inelastic x-ray scattering (RIXS) measurements at the osmium $L$ edge. Analysis of the RIXS spectra parametrizes the spin-orbit coupling (0.35 eV), Hund's coupling (0.27 eV), and trigonal site distortion $(-0.17 \mathrm{eV})$. The results are considered within the context of a $J=0$ model and possible departures from this through structural distortions, excitonic interactions, and $5d\text{−}4f$ interactions between the Os ion and the surrounding Ho lattice. The experimental methodology employed highlights the complementary information available in rare-earth-based $5d$ pyrochlores from distinct neutron and x-ray scattering techniques that allow for the isolation and determination of the behavior of the different ions.