Verify the susceptibility correspondence under strong spin-orbit coupling

Determine whether the one-to-one correspondence between the total-moment susceptibility χ_J and the low-energy correlation factor z_L remains valid in systems with strong spin-orbit coupling, where total angular momentum rather than spin is the appropriate degree of freedom.

Background

In the presence of strong spin-orbit coupling, the paper explains that electrons are more naturally described in a total-moment J_tot basis and that z_L should be compared with the susceptibility χ_J of total angular momentum rather than the ordinary spin susceptibility. Although BaOsO₃ results appear consistent with the proposed framework, the authors explicitly leave open whether the one-to-one susceptibility–z_L correspondence established without strong spin-orbit coupling survives in this setting.

References

In such case, the $z_L$ should rather be compared to the $\chi_{J}$, the susceptibility for $J_{\mathrm{tot}$ than the spin susceptibility. Thus the spin-degree-of-freedom effectiveness should be modified based on $J_{tot}$, and whether the 1-to-1 correspondence between the $\chi_{J}$ and $z_L$ will be kept needs further verification.

— Universal Signature of Hundness and Its Quantification  (2608.14480 - Kim et al., 14 Aug 2026) in Supplementary Material, Section “Hundness with strong spin-orbit coupling”