Effects of electron-electron interaction and electron spin correlations on the exchange coupling in mesoscopic rings

Using the formalism of Lobo, Singwi, and Tosi (LST), we study the effect of electron-electron interaction and electron spin correlations on the indirect exchange interaction between two nuclear spins embedded in a mesoscopic metallic ring, threaded by an Aharonov-Bohm magnetic flux. We first calculate the spin local field correction and the spin-density response function of the ring in a self-consistent manner. Then, we employ the Ruderman-Kittel-Kasuga-Yosida (RKKY) theory to determine the variation of the exchange coupling as a function of the magnetic flux and the angular distance between the two nuclear spins. The LST approach predicts a reach behavior for the exchange coupling as a function of the magnetic flux. Our numerical results show that due to the electron-electron interaction and the electron spin-correlations the exchange coupling can change sign as a function of the magnetic flux, contrary to the prediction of the random phase approximation. Furthermore, the exchange coupling beside its usual oscillatory behavior acquires an oscillatory envelope which brings about strong RKKY interaction between the two nuclear spins even at far distances on the ring.