Magnetic impurities in an altermagnetic metal

We study the physics of dilute magnetic impurities in a two-dimensional altermagnetic metal. We first discuss the Kondo problem. Although the spin degeneracy is broken in an altermagnetic metal, we show that the antiferromagnetic Kondo coupling still flows to the strong coupling regime at low energies in terms of the one-loop renormalization-group equation. To study the ground-state properties, we employ the variational wavefunction approach. We find that the impurity spin is completely screened at long distances, in contrast to the usual antiferromagnet. The $d$-wave nature of the Fermi surface in an altermagnetic metal is reflected in the correlation between the impurity and conduction electron spins, which exhibits the $C_{4z}$ symmetry of the altermagnet at long distances. The spin correlation decays as $1/r^3$ at long distances, and its amplitude oscillates with four different periods due to the anisotropic Fermi surfaces. Moreover, the values of these periods depend on the direction of observation. Next, we calculate the RKKY interaction which is of an anisotropic Heisenberg type. This anisotropic RKKY interaction also exhibits the $C_4$ symmetry at long distances due to the $d$-wave nature of the Fermi surface. In addition, the transverse and longitudinal components of the RKKY interactions posses distinct periods of oscillations.