Unanticipated spin gap measured in the frustrated quasi-FCC $d^3$ double perovskites $La_2LiXO_6$ (X = Ru, Os)

There is much current interest in the influence of strong spin-orbit (SO) interactions on exotic ground state selection in new 4d and 5d magnets, particularly involving 4d$^5$ Ir. Here we consider double perovskites of the form $A_2BB'O_6$ which are based on heavy 4d or 5d magnetic ions, where the SO interaction is expected to be significant as it increases as $\sim Z^4$. The double perovskite structure can accommodate a variety of magnetic ions on the B' site, providing a playground for systematic studies of the exotic ground states stabilized by strong SO coupling. Here, we report inelastic neutron scattering (INS) measurements conducted on the frustrated monoclinic magnets, La$_2$LiXO$_6$ (X = Ru, Os), wherein the magnetic moments decorate a quasi face-centered-cubic lattice. Our results show the development of a spin gap in the spin excitation spectrum of size $\Delta_{Os}$ = 8 meV and $\Delta_{Ru}$ = 2.5meV concomitant with $T_N$, which is unexpected for orbitally quenched $d^3$ systems. We liken these results to INS results obtained for Ba$_2$YXO$_6$ and La$_2$NaXO$_6$, which were also shown to exhibit spin gaps that correlate with $T_N$. We shall discuss trends observed in these three d$^3$ double perovskite families which correlate strong SO coupling, spin gap and T$_N$.