Two-dimensional skyrmion lattice in a nanopatterned magnetic film

M. V. Sapozhnikov and O. L. Ermolaeva

Phys. Rev. B 91, 024418 – Published 20 January 2015

Abstract

We study the possibility of a two-dimensional (2D) skyrmion crystal stabilization in a magnetic film with perpendicular anisotropy in the absence of Dzyaloshinskii-Moriya interaction by creating the regular array of blind holes or stubs. By micromagnetic simulation we demonstrate that skyrmions can be stable in the patterned films with the parameters of ordinary materials such as CoPt, FePt, or FePd. The skyrmion lattices can be initialized in the system by simple magnetization in the uniform external magnetic field. At the zero external field the skyrmion helicity depends on the geometry of the blind hole or stub but also can be tuned by applying the field. The suggested method makes it possible to create dense enough (with the period less than 100 nm) skyrmion lattices which are important to carry out transport measurements.

Received 4 April 2014
Revised 18 December 2014

DOI:https://doi.org/10.1103/PhysRevB.91.024418

Authors & Affiliations

M. V. Sapozhnikov and O. L. Ermolaeva

Institute for Physics of Microstructures RAS, Nizhny Novgorod 603950, GSP-105, Russiaand N. I. Lobachevskii State University, Nizhny Novgorod 603950, Russia

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Issue

Vol. 91, Iss. 2 — 1 January 2015

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Images

Figure 1
The geometry of the proposed skyrmion system. (a) The regular array of the blind holes, arrows denote the direction of the magnetization inside and outside the blind holes in the presence of the skyrmion lattice. (b) The cross section of the blind hole, the geometry parameters used in micromagnetic simulations are shown: $h_{1}$ is the thickness of the initial film, $D$ is the diameter of the blind hole, $h_{2}$ is the thickness of its bottom, and $h_{3}$ is its depth. (c) The regular array of the stubs. (d) Corresponding geometrical parameters.
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Figure 2
(a) Calculated phase diagram for the skyrmion stability in the blind hole (see Fig. 1 for the geometry parameters, $h_{1} = 20$ nm, $h_{1} = h_{2} + h_{3}$ ). The stars shows the skyrmion with the helicity $γ = π$ , solid circles represent skyrmion with the helicity $γ < π$ , and open circles are for the skyrmion instability. (b) The dependence of the helicity of the skyrmion in the blind hole ( $h_{1} = 30$ nm, $h_{2} = 5$ nm, $h_{3} = 25$ nm, and $D = 40$ nm) on the external magnetic field. (c) The external field range when the skyrmion is stable in the conical blind hole depending on the cone slope, $h_{1} = 20$ nm, $h_{3} = 15$ nm, the average cone diameter is 50 nm.
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Figure 3
(a) The magnetization curve in the perpendicular magnetic field for the $300 nm \times 300 nm \times 30 nm$ plate with the stub ( $D = 50$ nm, $h_{3} = 25$ nm) in the center. Left graph axis shows the absolute value of the magnetic moment of the system. The thick parts of the curve correspond to the skyrmionlike magnetization distribution in the stub. (b) Calculated phase diagram for the skyrmion stability of the stub (see Fig. 1 for the geometry parameters, $h_{1} = 20$ nm, $h_{1} = h_{2} + h_{3}$ ). The stars shows the skyrmion with the helicity $γ = π$ , solid circles represent skyrmion with the helicity $γ < π$ , and open circles are for the skyrmion instability. (c) The dependence of the skyrmion helicity in the stub ( $h_{1} = 30$ nm, $h_{2} = 5$ nm) on the relative position of the film and stub in the general case $(h_{1} \neq h_{2} + h_{3})$ for the zero external field. (d) The scheme of the demagnetizing fields and magnetization distribution for different geometries of the system.
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Figure 4
The typical magnetization curve of the hexagonal array (the period is 110 nm) of the blind holes (the diameter is 60 nm, the depth is 25 nm) in 30 nm thick film. (b) Close view of the part of the magnetization curve showing the range of the stability of the skyrmion lattices with different symmetries. The black circles represents blind holes with reversed magnetization, i.e., skyrmions. (c) The devil-staircase-like shape of the magnetization curve caused by the effective antiferromagnetic magnetostatic interaction between skyrmions.
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Figure 5
(a) Magnetization distribution in the skyrmion lattice on the blind hole array at $H = 0$ , part of the simulated system is shown. Dotted lines denote the blind hole edges. (b) Calculated local skyrmion density $ϕ$ per unit cell for the same skyrmion lattice. (c) The dependence of the skyrmion density $ϕ$ distribution on the external magnetic field. The red circle denotes the size of the blind hole, $D = 60$ nm.
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Figure 6
Left: The typical magnetization curve of the hexagonal array (the period is 120 nm) of the cylindrical stubs (the diameter is 60 nm, the height is 25 nm) on the surface of the 5 nm thick film. Pairs of the capital letters ${A − A}^{'}$ , ${B − B}^{'}$ , ${C − C}^{'}$ , etc. indicate the ranges of the stability of the skyrmion lattices denoted by the same lowercase letters a, b, c which are schematically represented in the middle. Middle: Some (the most symmetrical) of the possible skyrmion lattices consequently arising during the magnetization of the array of the stubs. The black color (for the stubs) and gray color (for the film) denote the up-directed magnetization, the white is for down-magnetized regions of the system. The arrows indicate the possible transitions between the states caused by applied external field. Right: The devil-staircase-like shape of the magnetization curve between $B^{'}$ and $E^{'}$ is presented.
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