Abstract
In our publication from eight years ago (Kogan, E. 2011, vol. 84, p. 115119), we calculated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities adsorbed on graphene at zero temperature. We show in this short paper that the approach based on Matsubara formalism and perturbation theory for the thermodynamic potential in the imaginary time and coordinate representation which was used then, can be easily generalized, and calculate RKKY interaction between the magnetic impurities at finite temperature.
Highlights
IntroductionMore than 60 years ago, it was understood that localized spins in metals can interact by means of the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism [1,2,3]
More than 60 years ago, it was understood that localized spins in metals can interact by means of the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism [1,2,3]. This indirect exchange between two magnetic impurities in a non–magnetic host coupling is mediated by the conduction electrons and is traditionally calculated as the second order perturbation with respect to exchange interaction between the magnetic impurity and the itinerant electrons of the host
RKKY interaction has been investigated in materials of different nature such as disordered metals [4], superconductors [5,6,7], topological insulators [8,9,10,11,12,13,14,15], carbon nanotubes [16,17], semiconducting wires [18], in Weyl and Dirac semimetals [19,20,21,22,23,24], but most thoroughly in graphene [25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46]
Summary
More than 60 years ago, it was understood that localized spins in metals can interact by means of the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism [1,2,3]. This indirect exchange between two magnetic impurities in a non–magnetic host coupling is mediated by the conduction electrons and is traditionally calculated as the second order perturbation with respect to exchange interaction between the magnetic impurity and the itinerant electrons of the host. In the previous publication we consider two magnetic impurities sitting on top of carbon atoms in graphene lattice, which is from our point of view the most interesting case. Where H is the Hamiltonian of the electron system, Si is the spins of the impurity and si is the spin of itinerant electrons at site i
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