ИСТИНА

An intensive study of magnetic properties of single-atomic chains has begun after the discovery of the giant magnetic anisotropy energy (MAE) of Co atoms and Co atomic chains on the Pt(997) [1,2]. Ferromagnetic Co chains can grow on the step edges of Pt(997) surface as a result of self-organization process at low concentrations of Co atoms and low temperatures. The analogous effect was observed for Fe atomic chains on the Cu(111) surface [3]. The applications of atomic chains in spintronics, quantum communications, quantum computing, and other fields have been discussed in literature. Strong DMI in atomic chains also can lead to some interesting phenomena. For example, biatomic Fe chains on the Ir(001)(5×1) surface have a DMI-induced noncollinear magnetic ground state [3]. Also DMI can significantly change the energies of excited states even if the ground state of an atomic chain is collinear. Using ab initio calculations the significant DMI in Co and Fe chains on Pt(664) surface has been predicted [4]. It has been shown that the infinitely long Co and Fe chains have the collinear ferromagnetic ground state, but DMI changes the energies of the excited states. The magnetic properties of the atomic chains can be satisfactorily described in the framework of some effective theory including the exchange interaction, the magnetic anisotropy energy (MAE), DMI, and the interaction with the external fields. The parameters of the effective theory have been taken from Ref. [4]. For the numerical calculations the geodesic nudged elastic band (GNEB) method [5] is employed. For analytical calculations the continuous XY-model is used. The main goal of the presented work is detailed comparison of the analytical results obtained in the framework of XY-model and the numerical results obtained with GNEB method. The following physical values are under the consideration: energy barriers for magnetization reversal, average magnetization reversal times [6] and coercivity of the finite-size Co and Fe chains. It is shown that the most of the numerical results can be satisfactorily explained in the framework of the XY-model. The limitations of the XY-model are also discussed. Finally, the influence of the long-range dipole-dipole interaction on the energy barriers for the magnetization reversal is investigated. The research is carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University [7]. The investigation is supported by the Russian Science Foundation (Project No. 21-72-20034).