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

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Abstract

The analytical approach has been developed in the framework of the continuous XY-model. This approach allows calculating the spontaneous magnetization reversal time of finite-length atomic chains on the metallic surface. The interaction of the 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 Co/Pt(664) system as an example, it has been shown that the proposed method is in a good agreement with the results of the numerical simulation in the limit of short and long atomic chains. And for atomic chains of intermediate length, it can be used to estimate an upper bound on the spontaneous magnetization reversal time. We obtained the dependences of the spontaneous magnetization reversal time of finite-length Co chains the value of the exchange integral, parameters of the magnetic anisotropy, and also on the value of the projection of the Dzyaloshinskii vector onto the axis perpendicular to the plane containing the magnetic moments of the atoms. It is shown that the proposed method has a wide range of applicability both in terms of temperature and the values of the physical parameters characterizing the magnetic properties of the atomic chains.

About the authors

S. V. Kolesnikov

Lomonosov Moscow State University, Faculty of Physics

Author for correspondence.
Email: kolesnikov_s_v_@mail.ru
Russian Federation, Moscow

E. S. Sapronova

Lomonosov Moscow State University, Faculty of Physics

Email: kolesnikov_s_v_@mail.ru
Russian Federation, Moscow

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2. Fig. 1. Energy barriers ΔE1 (1) and ΔE2 (2) for the remagnetization of a chain of N Co atoms on the Pt(664) surface. The dots show the values found numerically by the geodesic elastic tape method [22], the lines show the theoretical values obtained in the framework of the XY model

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3. Fig. 2. Dependence of the time τ of spontaneous remagnetization of the Co/Pt(664) atomic chain on the exchange integral J (a), the magnetic anisotropy constants K (b) and E (c), and the projection of the Dzialoszynski vector Dz (d). The theoretical dependences obtained within the XY-model for chains of 10 and 100 atoms are depicted by lines. The dots show the values calculated using energy barriers obtained using the geodesic elastic band method [22]

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