Dynamic Ruderman-Kittel-Kasuya-Yosida indirect interaction

We consider the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two spins, when they are affected by a frequency-dependent magnetic field. It is shown that the RKKY indirect interaction, i.e., value of the coupling, its spatial dependence, and the periods of spatial oscillations, in the three-dimensional free-electron gas for transversal component of the spins depends on the frequency. For the high-frequency range h omega less than or equal to epsilon(F) three main uncommensurable periods of oscillations k(F), (1 + root 2)k(F), (root 2 - 1)k(F) are found. The spatial dependence of the coupling for large k(F)r contains terms proportional to r(-1) and r(-2). The value of the coupling is of the order (k(F)r)(2) as much as in the static case. For the frequency range h omega much less than epsilon(F) the dynamic RKKY interaction contains the terms whose values and spatial periods are determined by the frequency of the magnetic field. It is shown that there is a frequency-dependent anisotropy of the dynamic RKKY interaction.