Impurity induced frustrations in a non-frustrated antiferromagnet

Zn substitution for Cu in La$_2$CuO$_4$ is thought to be an ideal example for a simple site dilution of the antiferromagnetic $S=1/2$, square lattice non-frustrated nearest-neighbor Heisenberg model. We show that starting from the microscopic three-band Hubbard model one obtains quite different, counterintuitive result. Namely, the spinless impurity generates {\it frustrating} interactions around itself. This is because the oxygen orbitals around Zn impurity site can be still engaged in the virtual transitions which produce substantial superexchange interactions between the Cu spins {\it across} the impurity site. This effect can explain noticeable discrepancies between the experimental data and theoretical results for the simple site- diluted Heisenberg model.