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Ground and excited states of the finite-size Fe chains on Pt(664) surface

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Abstract

The energy barriers for magnetization reversal of the finite-size Fe chains on Pt(664) surface have been calculated using the geodesic nudged elastic band method. The Dzyaloshinskii–Moriya interaction and the dipole–dipole interaction have been taken into account. It has been found that the ground states of Fe/Pt(664) atomic chains are non-collinear at the ends. The magnetization reversal of short atomic chains occurs without the formation of the domain walls. While the magnetization reversal of the long atomic chains occurs via the formation of the domain walls. The interplay between the magnetic anisotropy energy and the Dzyaloshinskii–Moriya interaction leads to the rotation of the domain wall plane. As a result, the domain walls in Fe/Pt(664) atomic chains are intermediate configurations between Bloch and Néel walls. The dipole–dipole interaction weakly influences the value of the energy barriers and may be neglected. It is shown that the presented results can be explained in the framework of the classical continuous model. The constructed approximate functions correctly describe all features of the ground states and the saddle points. The structure of the domain walls and the dependencies of the energy barriers on the parameters of the model are different from the case of the Co/Pt(664) system investigated recently.

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Data will be made available on reasonable request.

Notes

  1. Here we neglect the symmetric anisotropic exchange interaction following to Ref. [30].

  2. All angles are measured in radians.

  3. More exact calculations of the critical temperature are beyond the scope of the paper.

  4. The angle \(\beta \) is the same as the angle \(\phi _i\) in Fig. 1a. We use a different notation to emphasize that all magnetic moments in the domain wall lie in the same plane (\(\phi _i=\beta \) for all i).

  5. The difference between the energy barriers is related to the inversion symmetry breaking.

  6. Eq. (15) gives the value of \(\Delta N=5.080\) and \(N_0=4\Delta N\). Unfortunately, the direct comparison of \(\Delta N\) with the numerical results for the discrete model is not possible, because \(\Delta N\) is not integer. However, the good agreement between the GNEB results and theoretical approximation in Fig. 2 indicates that the estimation (15) of the \(\Delta N\) is quite well.

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Acknowledgements

The research is carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University [59, 60]. The investigation is supported by the Russian Science Foundation (Project No 21-72-20034). E.S. Sapronova also acknowledges financial support of the Theoretical Physics and Mathematics Advancement Foundation “BASIS”.

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  1. Ekaterina S. Sapronova and Inna N. Kolesnikova contributed equally to this work.

Authors and Affiliations

  1. Faculty of Physics, Lomonosov Moscow State University, Leninskie Gory, Moscow, 119991, Russian Federation

    Sergey V. Kolesnikov & Ekaterina S. Sapronova

  2. Department of Chemistry, Lomonosov Moscow State University, Leninskie Gory, Moscow, 119991, Russian Federation

    Inna N. Kolesnikova

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Kolesnikov, S.V., Sapronova, E.S. & Kolesnikova, I.N. Ground and excited states of the finite-size Fe chains on Pt(664) surface. Eur. Phys. J. B 96, 163 (2023). https://doi.org/10.1140/epjb/s10051-023-00634-8

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