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Exotic magnetism on the quasi-FCC lattices of the $d^3$ double perovskites La$_2$NaB$'$O$_6$ (B$'$ $=$ Ru, Os)

We find evidence for long-range and short-range ($ζ$ $=$ 70 Å~at 4 K) incommensurate magnetic order on the quasi-face-centered-cubic (FCC) lattices of the monoclinic double perovskites La$_2$NaRuO$_6$ and La$_2$NaOsO$_6$ respectively. Incommensurate magnetic order on the FCC lattice has not been predicted by mean field theory, but may arise via a delicate balance of inequivalent nearest neighbour and next nearest neighbour exchange interactions. In the Ru system with long-range order, inelastic neutron scattering also reveals a spin gap $Δ$ $\sim$ 2.75 meV. Magnetic anisotropy is generally minimized in the more familiar octahedrally-coordinated $3d^3$ systems, so the large gap observed for La$_2$NaRuO$_6$ may result from the significantly enhanced value of spin-orbit coupling in this $4d^3$ material.