Nonreciprocal RKKY Interactions and Chiral Phases in Voltage-Biased Metals

Driving a conducting bath out of equilibrium allows it to mediate intrinsically nonreciprocal interactions between localized degrees of freedom—such as spins—even though the underlying system remains Hamiltonian. We show that applying a dc bias voltage eV across a ballistic metal realizes precisely such a setting, where electron-mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between embedded classical spins become nonreciprocal. Exploiting the oscillatory range dependence of the RKKY interaction, we model a d ≤ 3 bipartite lattice of XY spins with alternating bond lengths along the bias. In the weak-coupling limit, the resulting effective theory exhibits reciprocal intra-sublattice couplings and antagonistic, bias-dependent inter-sublattice couplings—a paradigmatic platform for nonreciprocal phase transitions. Within a mean-field treatment, we obtain a dynamic phase diagram in the eV–k_BT plane and identify the onset of a PT–broken time-dependent phase. We further propose transport diagnostics revealing how the transition imprints on the steady-state current. This establishes a simple, tunable route to engineer and detect nonreciprocity in metallic spin arrays. Extending this framework to the Kondo regime—where bias can disrupt local moment screening—emerges as a natural next step.