Magnetic exchange in Kondo lattice systems is of the Ruderman-Kittel-Kasuya-Yosida type, whose sign depends on the Fermi wave vector, $k_F$ . In the simplest setting, for small $k_F$ , the interaction is predominately ferromagnetic, whereas it turns more antiferromagnetic with growing $k_F$. It is remarkable that even though $k_F$ varies vastly among the rare-earth systems, an overwhelming majority of lanthanide magnets are in fact antiferromagnets. To address this puzzle, we investigate the effects of a p-wave form factor for the Kondo coupling pertinent to nearly all rare-earth intermetallics. We show that this leads to interference effects which for small kF are destructive, greatly reducing the size of the RKKY interaction in the cases where ferromagnetism would otherwise be strongest. By contrast, for large $k_F$, constructive interference can enhance antiferromagnetic exchange. Based on this, we propose a new route for designing ferromagnetic rare-earth magnets.
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