Stability of Neel skyrmions in ultra-thin nanodots considering Dzyaloshinskii-Moriya and dipolar interactions

Abstract

An analytical expression for the energy of Néel skyrmions in ultra-thin nanodots considering exchange, uniaxial anisotropy, Dzyaloshinskii-Moriya, and dipolar contributions has been obtained. In particular, we have proposed for the Néel skyrmion, a general ansatz for the component of the magnetization perpendicular to the dot, given by mz(r) = [1 − (r/Rs) n ]/[1 + (r/Rs) n ], where Rs is the radius of the skyrmion and n is an integer and even number. As proof of concept, we calculate the energy of a Néel skyrmion in an ultra-thin Co/Pt dot, and we find that the dipolar contribution cannot be neglected and that both Dzyaloshinskii-Moriya interaction and anisotropy play an important role to stabilize the skyrmion. Additionally, we have obtained a good agreement between our analytical calculations and previously published micromagnetic simulations for n = 10. For this reliable value of n, we have obtained that for a Dzyaloshinski Moriya constant D = 5.5 (mJ/m 2 ), it is possible to stabilize a Néel skyrmion for Ku in the range, 0.4 (M J/m 3 ) < Ku < 1.3 (M J/m 3 ), whereas for Ku = 0.8 (M J/m 3 ), the skyrmion stabilizes for 5.0 (mJ/m 2 ) < D < 6.0 (mJ/m 2 ). Thus, this analytical equation can be widely used to predict stability ranges for the Néel skyrmion in spintronic devices. arXiv:1705.03778v1 [cond-mat.mes-hall] 10 May 2017 2

Geometrically Tailored Skyrmions at Zero Magnetic Field in Multilayered Nanostructures

“…This corresponds to a weak dependence of the normalized size d s sk /w on magnetic parameters [e.g., D/A; Fig. 5(b)], consistent with recent multilayer simulations by other groups [28,37]. However, such insensitivity of d s sk to magnetic parameters is in stark contrast with our MFM data [ Fig.…”

“…This observation, while incongruous with N i = 1 simulations for κ > 1 [ Fig. 5(a)] [5,24,37], is consistent with the behavior of multiskyrmion states [ Fig. 5(d)].…”

“…S4 within the Supplemental Material [33] [4], thermodynamically stable entities for material parameter κ > 1, where κ = π D/4 √ AK eff [1,3,10]. Moreover, the presence of interlayer dipolar coupling in multilayer stacks [28,37,38] and long-range intralayer dipolar interactions [8] can also play a role-the latter being key to stabilizing larger (>200 nm) skyrmion bubbles [7][8][9]28,32]. Notably, confined geometries can shape the ground state [8,24,29,30,37,39], potentially favoring ZF stabilization of skyrmions [5,24].…”

“…The stability and size of confined skyrmions would be markedly influenced by magnetic interactions and geometric parameters [24,28,37]. Multilayer [Ir(10)/Fe(x)/Co(y)/ Pt(10)] 20 stacks (layer thicknesses in angstroms in parentheses), wherein magnetic interactions can be tailored by the Fe(x)/Co(y) composition, are a suitable platform for establishing confined Néel-textured skyrmion phenomenology [34].…”

Forming individual magnetic biskyrmions by merging two skyrmions in a centrosymmetric nanodisk

“…To support the above analytical considerations, we performed micromagnetic simulations for a thin magnetic nanodisk with out-of-plane anisotropy. These disks have been in the focus of skyrmion-related research in many recent publications [40][41][42][43][44][45] . The considered disk and its surfaces exhibit negligibly small DMI, so that only the dipole-dipole interaction (included in the demagnetization field) could stabilize a biskyrmion.…”