RKKY interaction in Rashba altermagnets

TL;DR

This paper investigates the RKKY interaction in altermagnetic materials, revealing unique anisotropic and oscillatory behaviors influenced by spin-orbit coupling and Zeeman fields, which differ fundamentally from ferromagnetic systems.

Contribution

It provides a detailed analysis of the RKKY interaction in 2D and 3D altermagnets, including effects of Rashba spin-orbit coupling and Zeeman fields, highlighting qualitative differences from ferromagnets.

Findings

RKKY interaction in altermagnets shows anisotropic and oscillatory behavior.

The Ising component exhibits a Fermi surface-dependent beating pattern.

Short-range interactions include rapidly oscillating non-collinear terms.

Abstract

The interaction between two impurity spins provides vital information about the host system and has been suggested to form a building block in quantum computation and spintronic devices. We here determine this Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in recently discovered altermagnetic materials, including the presence of a Zeeman field, in a two- and three-dimensional altermagnet. In two dimensions, we also study the effect of Rashba spin-orbit coupling. Our results reveal that the momentum-resolved spin-polarization of the itinerant carriers in the altermagnet changes the RKKY interaction qualitatively from the isotropic spin-splitting in a ferromagnet. The Ising-contribution directed parallel with the altermagnetism is found to exhibit a beating pattern reflecting the shape of the Fermi surface of the system and may thus be further influenced by an out-of-plane Zeeman field. However, the exchange interaction for in-plane impurity spins deviates only slightly from that of a normal metal. On shorter length scales, we find that the Ising, the Dzyaloshinskii-Moriya terms, and other non-collinear interaction terms in the RKKY interaction acquire a rapidly oscillating behavior as a function of the relative angle between the impurity spins, which is not present in the ferromagnetic case. We determine how this new length scale depends on the system parameters analytically. Our results show that the RKKY interaction in altermagnets is qualitatively different from that of ferromagnets despite both breaking time-reversal symmetry.