We use polarized inelastic neutron scattering (INS) to study spin excitations of 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, $chi^{primeprime}(Q,omega)$, shows magnetic anisotropy for energies below $sim$7 meV with c-axis polarized spin excitations larger than that of the in-plane component. Upon entering into the superconducting state, previous unpolarized INS experiments have shown that spin gaps at $sim$5 and 0.75 meV open at wave vectors $Q=(0.5,0.5,0)$ and $(0.5,0.5,1)$, respectively, with a broad neutron spin resonance at $E_r=15$ meV. Our neutron polarization analysis reveals that the large difference in spin gaps is purely due to different spin gaps in the c-axis and in-plane polarized spin excitations, resulting resonance with different energy widths for the c-axis and in-plane spin excitations. The observation of spin anisotropy in both opitmally electron and hole-doped BaFe$_2$As$_2$ is due to their proximity to the AF ordered BaFe$_2$As$_2$ where spin anisotropy exists below $T_N$.
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