THE RKKY INTERACTION ACROSS A TUNNELING JUNCTION OUT OF EQUILIBRIUM IN RELATION TO THE SPIN CURRENT

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magne tic spin impurities across a tunnelling junction is studied when the s ystem is driven out of equilibrium through biasing the junction. The n onequilibrium situation is handled with the Keldysh time-loop perturba tion formalism in conjunction with appropriate coupling methods for tu nnelling systems due to Caroli and Feuchtwang. We find that the presen ce of a nonequilibrium bias across the junction leads to an interferen ce of several fundamental oscillations: such that in this tunnelling g eometry, it is possible to tune the interaction between ferromagnetic and antiferromagnetic coupling at a fixed impurity configuration, simp ly by changing the bias across the junction. Furthermore, it is shown that the range of the RKKY interaction is altered out of equilibrium s uch that in particular the interaction energy between two slabs of spi n scales extensively with the thickness of the slabs in the presence o f an applied bias. The spin current has been calculated for this syste m and it is shown that it is proportional to the long-range interactio n. Other aspects of the relationship of the current to the spin geomet ry are explored. (C) 1998 Elsevier Science B.V. All rights reserved.