Long-Range Exchange Interaction Between Ferromagnetic Nanoparticles Embedded in Carbon Nanotubes

Indirect exchange coupling mediated by the conduction electrons (Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange) is studied in the multiwall carbon nanotubes (MWCNTs) of diameters of tens of nanometers with single domain ferromagnetic nanoparticles (FNPs) embedded inside. By adapting the Klinovaja-Loss (KL) model [Phys. Rev. B 87, 045422 (2013)] for single-wall carbon nanotube (CNT) and applying the parameters of MWCNTs, we show that the static spin susceptibility can propagate up to tens of micrometers. The main condition for the long-range exchange interaction is the adjustment of the Fermi level to the gap opened by the spin–orbit interaction (SOI). At typical diameters of the inner shell of MWCNTS of 20–30 nm, the required shift of the Fermi level is much smaller than that for single-wall CNT and does not exceed tens of meV. The proposed approach allows evaluating the energy of the exchange interaction between FNPs belonging to the same CNT. The obtained results open up good opportunities for the realization and implementation of MWCNT-based spintronic devices.