RKKY Interaction in a One-Dimensional Crystal Taking into Account Disorder and Temperature
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D MATTER
RKKY Interaction in a One-Dimensional Crystal Taking into Account Disorder and Temperature K. A. Baryshnikova, * and I. V. Krainova a
Ioffe Institute, Russian Academy of Science, St. Petersburg, 194021 Russia *e-mail: [email protected] Received April 18, 2020; revised May 3, 2020; accepted May 4, 2020
An analytical expression for the energy of indirect exchange interaction of two magnetic impurities in a onedimensional crystal has been obtained taking into account both disorder and temperature. The inclusion of even a weak disorder in a one-dimensional crystal leads to the localization of charge carriers in it and, as a result, to the suppression of the long-range indirect exchange interaction (RKKY interaction) between two magnetic impurities at the localization length of charge carriers. An increase in the temperature, in turn, causes the disappearance of electron density coherence, which provides the RKKY interaction. It has been shown that these two effects are independent of each other and exponentially suppress the exchange interaction with an increase in the distance between the impurities. Another important manifestation of disorder is a change in the power dependence on the distance between the impurities: the RKKY interaction decreases with distance faster than 1/r. DOI: 10.1134/S0021364020120061
Currently, progress in nanotechnology has aroused great interest in theoretical and experimental studies of the properties of one-dimensional systems with magnetic impurities [1–6]. The key issue is the interaction and ordering of such centers. Indirect exchange interaction (Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction) [7] is one of the main mechanisms of interaction between magnetic centers in metals and semiconductors. It is well studied for systems with an ideal degenerate electron gas of various dimensions [8] for both the quadratic spectrum and the linear spectrum in graphene [9, 10] and in carbon nanotubes [11]. The RKKY interaction appears because of the spindependent scattering of electrons on magnetic centers in the crystal and interference of scattered waves at other centers. In this context, an important condition for the presence of such an interaction is the coherence of the electron spin density at different crystal points. However, this condition begins to be violated when the temperature spreading of states in the system appears and the inclusion of disorder significantly changes the interference of scattered waves. Disorder in a one-dimensional crystal is critical for interference effects, since it leads to the localization of all charge carriers [12, 13]. While the RKKY interaction in the absence of disorder is long-range and decreases with distance as 1/r, localization causes a sharp weakening of the interaction of magnetic centers with the increase in the distance between them, which was shown by numerical calculation of the susceptibility of magnetic centers in such crystals [14]. One-
dimensional systems are very different from systems with a larger dimension. Averaging
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