Spin anisotropy due to spin-orbit coupling in optimally hole-doped Ba${}_{0.67}$K${}_{0.33}$Fe${}_2$As${}_2$

We use polarized inelastic neutron scattering to study the temperature and energy dependence of spin space anisotropies in the optimally hole-doped iron pnictide Ba${}_{0.67}$K${}_{0.33}$Fe${}_2$As${}_2$ ($T_{\mathrm{c}}=38$ K). In the superconducting state, while the high-energy part of the magnetic spectrum is nearly isotropic, the low-energy part displays a pronouced anisotropy, manifested by a $c$-axis polarized resonance. We also observe that the spin anisotropy in superconducting Ba${}_{0.67}$K${}_{0.33}$Fe${}_2$As${}_2$ extends to higher energies compared to electron-doped BaFe${}_{2-x}T{M}_x$As${}_2$ ($TM=$Co, Ni) and isovalent-doped BaFe${}_2$As${}_{1.4}$P${}_{0.6}$, suggesting a connection between $T_{\mathrm{c}}$ and the energy scale of the spin anisotropy. In the normal state, the low-energy spin anisotropy for optimally hole- and electron-doped iron pnictides onset at temperatures similar to the temperatures at which the elastoresistance deviate from Curie-Weiss behavior, pointing to a possible connection between the two phenomena. Our results highlight the relevance of the spin-orbit coupling to the superconductivity of the iron pnictides.