RKKY interaction as a probe of valley-dependent spin splitting and odd-parity nature in Floquet collinear magnets

Abstract

Odd-parity magnets were recently proposed to emerge in collinear antiferromagnets (AFMs) via Floquet engineering, with valley-dependent spin splitting underlying the odd-parity spin polarization. This proposal brings about two key challenges: detecting the spin splitting to verify the generation mechanism of these magnets, and identifying such polarization to confirm the odd-parity nature. Here, we show that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction provides a unified magnetic probe for both tasks. Taking collinear $f$-wave magnets as a representative example, we find that the RKKY interaction yields distinct magnetic signals of the spin splitting---including a magnetism reversal in the Heisenberg/Ising terms and a sign alternation of the Dzyaloshinskii-Moriya (DM) term---that enable clear discrimination of collinear $f$-wave magnets from other related AFMs. Moreover, the DM term exhibits an $f$-wave shape with odd-parity symmetry, satisfying $J^{αβ}_{DM}(\mathbf{R}) = -J^{αβ}_{DM}(C_{2q}\mathbf{R})$ ($q=3$), which directly reflects the odd-parity spin polarization $S_z(\mathbf{k}) = -S_z(C_{2q}\mathbf{k})$ in momentum space. This behavior persists in $p$-wave magnets ($q=1$), demonstrating the generality of our approach. Our work establishes the RKKY interaction as a versatile probe for detecting band features of collinear odd-parity magnets, with predictions accessible to existing experimental techniques such as spin-polarized scanning tunneling spectroscopy.