An analytical expression for the energy of Neel skyrmions in ultra-thin nanodots considering exchange, uniaxial anisotropy, Dzyaloshinskii-Moriya, and dipolar contributions has been obtained. In particular, we have proposed for the Neel skyrmion, a general ansatz for the component of the magnetization perpendicular to the dot, given by m(z)(r) = [1 - (r/R-s)(n)]/[1 + (r/R-s)(n)], where R-s is the radius of the skyrmion and n is an integer and even number. As proof of concept, we calculate the energy of a Neel 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 Neel skyrmion for K-u in the range 0.4 (MJ/m(3)) < K-u < 1.3 (MJ/m(3)), whereas for K-u = 0.8 (MJ/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 Neel skyrmion in spintronic devices. (C) 2017 Elsevier B.V. All rights reserved.
