The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction across a tunneling junction out of equilibrium

TL;DR

This paper investigates how a nonequilibrium bias across a tunneling junction influences the RKKY interaction between magnetic impurities, revealing tunable magnetic coupling and altered interaction range out of equilibrium.

Contribution

It introduces a method to analyze the nonequilibrium RKKY interaction using Keldysh formalism, showing bias-dependent tuning of magnetic coupling and interaction range.

Findings

Bias induces interference of oscillations in RKKY interaction.

Magnetic coupling can be tuned from ferromagnetic to antiferromagnetic by bias.

Interaction energy scales extensively with slab thickness under bias.

Abstract

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic $s$-$d$ spin impurities across a tunneling junction is studied when the system is driven out of equilibrium through biasing the junction. The nonequilibrium situation is handled with the Keldysh time-loop perturbation formalism in conjunction with appropriate coupling methods for tunneling systems due to Caroli and Feuchtwang. We find that the presence of a nonequilibrium bias across the junction leads to an interference of several fundamental oscillations, such that in this tunneling geometry, it is possible to tune the interaction between ferromagnetic and antiferromagnetic coupling at a fixed impurity configuration, simply by changing the bias across the junction. Furthermore, it is shown that the range of the RKKY interaction is altered out of equilibrium, such that in particular the interaction energy between two slabs of spins scales extensively with the thickness of the slabs in the presence of an applied bias.