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 $k_F$ 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 route for designing ferromagnetic rare-earth magnets.

• Received 24 September 2017
• Revised 4 August 2018

DOI:https://doi.org/10.1103/PhysRevB.98.054420