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We use polarized inelastic neutron scattering (INS) to study spin excitationsof optimally hole-doped superconductor Ba$_{0.67}$K$_{0.33}$Fe$_2$As$_{2}$($T_c=38$ K).  In the normal state, the imaginary part of the dynamic susceptibility,$\chi^{\prime\prime}(Q,\omega)$, shows magnetic anisotropy for energies below$\sim$7 meV with c-axis polarized spin excitations larger than that of thein-plane component. Upon entering into the superconducting state, previousunpolarized INS experiments have shown that spin gaps at $\sim$5 and 0.75 meVopen at wave vectors $Q=(0.5,0.5,0)$ and $(0.5,0.5,1)$, respectively, with abroad neutron spin resonance at $E_r=15$ meV. Our neutron polarization analysisreveals that the large difference in spin gaps is purely due to different spingaps in the c-axis and in-plane polarized spin excitations, resulting resonancewith different energy widths for the c-axis and in-plane spin excitations. Theobservation of spin anisotropy in both opitmally electron and hole-dopedBaFe$_2$As$_2$ is due to their proximity to the AF ordered BaFe$_2$As$_2$ wherespin anisotropy exists below $T_N$.

Magnetic anisotropy in hole-doped superconducting Ba 0.67K 0.33Fe 2As2 probed by polarized inelastic neutron scattering