Energy Barriers for the Spontaneous Magnetization Reversal of Atomic Co Chains on the Surface Pt(664) in the Model of Dzyaloshinskii–Moriya Interaction

Within the framework of the continuous XY model, analytical expressions are derived to calculate the time of the spontaneous magnetization reversal of finite-length atomic chains on the surface of a metal. The interaction of magnetic moments of atoms is described by the classical Hamiltonian, which includes the Heisenberg exchange interaction, the Dzyaloshinskii–Moriya interaction, and the magnetic-anisotropy energy. Using the example of the Co/Pt(664) system, it is demonstrated that the proposed method exhibits good agreement with the results of numerical simulations for both short and long atomic chains. For atomic chains of intermediate length, it can be utilized to obtain an upper bound on the time of spontaneous magnetization reversal. We obtained dependences of the time of spontaneous magnetization reversal for finite-length Co atomic chains, taking into account the exchange integral, parameters characterizing the magnetic anisotropy, and the projection of the Dzyaloshinskii vector onto the axis perpendicular to the plane containing the magnetic moments of atoms. The proposed method is applicable over a wide range of temperatures and values of physical parameters that characterize the magnetic properties of atomic chains. Thus, it can be employed not only for the Co/Pt(664) system but also for other similar systems.