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Ferromagnetism of magnetic impurities coupled indirectly via conduction electrons: Insights from various theoretical approaches

The magnetic ground-state properties of the periodic Anderson model with a regular depletion of the correlated sites are analyzed within different theoretical approaches. We consider the model on the one-dimensional chain and on the two-dimensional square lattice with hopping between nearest neighbors. At half-filling and with correlated impurities present at every second site, the depleted Anderson lattice is the most simple system where the indirect magnetic coupling mediated by the conduction electrons is ferromagnetic. We discuss the underlying electronic structure and the possible mechanisms that result in ferromagnetic long-range order. To this end, different numerical and analytical concepts are applied to the depleted Anderson and also to the related depleted Kondo lattice and are contrasted with each other. This includes numerical approaches, i.e. Hartree-Fock theory, density-matrix renormalization and dynamical mean-field theory, as well as analytical concepts, namely a variant of the Lieb-Mattis theorem and the concept of flat-band ferromagnetism, and finally perturbative approaches, i.e. the effective RKKY exchange in the limit of weak and the "inverse indirect magnetic exchange" in the limit of strong coupling between the conduction band and the impurities.