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We use polarized inelastic neutron scattering to study the temperature andenergy dependence of spin space anisotropies in the optimally hole-doped ironpnictide Ba$_{0.67}$K$_{0.33}$Fe$_{2}$As$_{2}$ ($T_{{\rm c}}=38$ K). In thesuperconducting state, while the high-energy part of the magnetic spectrum isnearly isotropic, the low-energy part displays a pronouced anisotropy,manifested by a $c$-axis polarized resonance. We also observe that the spinanisotropy in superconducting Ba$_{0.67}$K$_{0.33}$Fe$_{2}$As$_{2}$ extends tohigher energies compared to electron-doped BaFe$_{2-x}TM_{x}$As$_{2}$ ($TM=$Co,Ni) and isovalent-doped BaFe$_{2}$As$_{1.4}$P$_{0.6}$, suggesting a connectionbetween $T_{\rm c}$ and the energy scale of the spin anisotropy. In the normalstate, the low-energy spin anisotropy for optimally hole- and electron-dopediron pnictides onset at temperatures similar to the temperatures at which theelastoresistance deviate from Curie-Weiss behavior, pointing to a possibleconnection between the two phenomena. Our results highlight the relevance ofthe spin-orbit coupling to the superconductivity of the iron pnictides.

Spin anisotropy due to spin-orbit coupling in optimally hole-doped Ba$_{0.67}$K$_{0.33}$Fe$_{2}$As$_{2}$