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# Atomistic spin simulations of electric-field-assisted nucleation and annihilation of magnetic skyrmions in Pd/Fe/Ir(111)

Title: Atomistic spin simulations of electric-field-assisted nucleation and annihilation of magnetic skyrmions in Pd/Fe/Ir(111)
Author:

Date: 2022-06-27
Language: English
Scope: 214435
University/Institute: Háskóli Íslands
University of Iceland
School: Verkfræði- og náttúruvísindasvið (HÍ)
School of Engineering and Natural Sciences (UI)
Department: Raunvísindastofnun (HÍ)
Science Institute (UI)
Series: Physical Review B;105(21)
ISSN: 2469-9950
2469-9969
DOI: 10.1103/PhysRevB.105.214435
Subject: Master equation; Heisenberg model; Ultrathin films; Noncollinear magnets; Skyrmions; Magnetoelectric effect; Frustrated magnetism
URI: https://hdl.handle.net/20.500.11815/3978

### Citation:

Goerzen, M.A., von Malottki, S., Kwiatkowski, G., Bessarab, P. & Heinze, S. (2022). Atomistic spin simulations of electric-field-assisted nucleation and annihilation of magnetic skyrmions in Pd/Fe/Ir(111). Physical Review B 105(214435). https://doi.org/10.1103/PhysRevB.105.214435

### Abstract:

We provide a theoretical background for electric-field-assisted thermally activated writing and deleting of magnetic skyrmions in ultrathin transition-metal films. We apply an atomistic spin model, which includes the exchange interaction, the Dzyaloshinskii-Moriya interaction, and the magnetocrystalline anisotropy energy. The strengths of the magnetic interactions are taken from density functional theory (DFT) calculations for a Pd/Fe bilayer on the Ir(111) surface. We systematically vary all magnetic interactions up to $\pm10$~\% reating the magnetoelectric effect in linear response. The critical magnetic fields marking the onset of the skyrmion phase and the field-polarized phase shift considerably upon varying the interaction constants due to the electric field. Based on harmonic transition state theory, we calculate the transition rates for skyrmion nucleation and annihilation, which are in good agreement with experimental values for Pd/Fe/Ir(111). The field-dependent variation of energy barriers and preexponential factors leads to large changes of the transition rates, which are accompanied by changes in skyrmion radii. Finally, we simulate the electric-field-dependent writing and deleting of magnetic skyrmions in Pd/Fe/Ir(111) based on the master equation and transition rates obtained using the magnetic interactions calculated via DFT for electric fields of ${\cal E}= \pm 0.5$~V/{\AA}. The magnetic-field-dependent skyrmion probability follows a Fermi-Dirac distribution function of the free energy difference of the skyrmion state and the ferromagnetic (FM) state. The probability function for the opposite electric field directions is in striking agreement with experimental results [Romming {\it et al.}, Science {\bf 341}, 636 (2013)].