RKKY interaction in altermagnets with adiabatic electron-phonon coupling

TL;DR

This paper theoretically explores how slow phonons influence RKKY magnetic interactions in two-dimensional altermagnets, revealing tunable anisotropic and chiral couplings via electron-phonon interactions and spin-orbit effects.

Contribution

It introduces a comprehensive model showing how static lattice distortions can control RKKY interaction properties in altermagnets, including magnitude, anisotropy, phase, and chirality.

Findings

Static lattice distortions tune RKKY magnitude and anisotropy.

Moderate EPC causes phase shifts and sign reversals in RKKY components.

Enhanced oscillatory complexity with altermagnetic order, RSOC, and doping.

Abstract

Altermagnets, characterized by time-reversal symmetry breaking without net magnetization and momentum-dependent spin-split bands, offer a promising platform for spintronics due to their anisotropic spin textures and potential for tunable magnetic interactions. Here, we theoretically investigate the slow phonon-renormalized Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in two-dimensional Rashba $d$-wave altermagnets, incorporating arbitrary Rashba spin-orbit coupling (RSOC) strength and spin-dependent static-Holstein electron-phonon coupling (EPC). Using a continuum model Hamiltonian that captures altermagnetic anisotropy, RSOC, and adiabatic lattice distortions, we compute the noncollinear RKKY exchange tensor via second-order perturbation theory and numerical momentum-space integration. Our results reveal that static lattice distortions provide a versatile tuning knob for engineering the magnitude, anisotropy, and chirality of RKKY couplings: moderate EPC suppresses long-range coherence while inducing component-specific phase shifts and sign reversals, particularly in Dzyaloshinskii-Moriya and compass-like terms, enabling control over ferromagnetic/antiferromagnetic alignments and clockwise/counterclockwise chiralities. Systematic parameter scans demonstrate enhanced oscillatory complexity with altermagnetic order, RSOC, and doping. These findings establish slow phonons as a low-energy tuning knob that systematically controls the magnitude, anisotropy, phase, and chirality of noncollinear RKKY couplings - even at arbitrary Rashba strength - thereby providing a practical route to engineer ferromagnetic/antiferromagnetic alignments and clockwise/counterclockwise DM chiralities in altermagnet-based heterostructures.