Compass Impurity Model of Tb Substitution in Sr2IrO4

We show that upon Tb substitution the interaction between the magnetic moments on the impurity Tb${}^{4+}$ ion and its surrounding Ir${}^{4+}$ ions is described by a “compass” model, i.e., Ising-like interaction favoring the magnetic moments across each bond to align along the bond direction. Such interaction nucleates quenched magnetic vortices near the impurities and drives a reentrant transition out of the antiferromagnetic ordered phase at low temperatures hence quickly suppresses the N'eel temperature consistent with the experiment [Phys. Rev. B $\mathbf{\text{92}}$, 214411 (2015)]. As a by-product, we propose that the compass model can be realized in ordered double perovskites composed of the spin-orbital-coupled $d^5$ ions and the half-closed-shell $f^7$ ions.