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A planar Mott insulator with easy plane N\'eel order can be mapped onto aGutzwiller-projected spin Hall state. The in-plane substitution of Zn$^{2+}$and Li$^{+}$ for Cu$^{2+}$ brings zero modes around the spin vacancy. TheGutzwiller projection precludes single particle excitations, however, preservesthe zero modes which have a local spin moment for Zn$^{2+}$ and a local chargedhole for Li$^{+}$, respectively. While the local spin moment for Zn$^{2+}$ isscreened by the long-range spin correlations, the active charge degree offreedom for Li$^{+}$ impurity twists the spin background with long rangeddisturbances. This proposal explains the very different roles of the Zn$^{2+}$and Li$^{+}$ impurities on the magnetic perturbations in the CuO$_2$ plane inthe undoped cuprate compounds.

Different roles of Zn$^{2+}$ and Li$^{+}$ impurities in the CuO$_2$ plane in undoped cuprate compounds