14 Topology in Magnetism
375
Fig. 14.12 a–d The D (a), A (b), K (c) and B (d) dependence of the skyrmion size R (the left axis)
and wall width w (the right axis). Model parameters are A = 15 pJ/m, K = K u − μ 0 M 2
s /2 = 0.588
MJ/m 3 , D = 3.7 mJm −2 , and B = 0. In each subfigure, one of these four parameters is treated
as a tuning parameter, and the other three parameters are fixed to above values. The symbols
are the micromagnetic simulation data. The solid lines are exact analytic results obtained from
minimising E of (14.23). The dashed lines are approximate results of R = π D
A
16AK 2 −π 2 D 2 K
,
w =
π D
4K [subfigures a–c] and solution of (14.25)(14.26) [subfigure d]. Vertical dashed lines are the
upper (lower) bound of parameters above (below) which a stable skyrmion cannot exist. e–h The
comparison of the skyrmion size R for the micromagnetic simulation (the black dots), our formula
(14.27) [or solution of (14.25) (14.26) for non-zero B] (the red lines), and previous studies [78]
(the green lines), [80] (the blue lines). Figure redrawn using the results in [84]
375
Fig. 14.12 a–d The D (a), A (b), K (c) and B (d) dependence of the skyrmion size R (the left axis)
and wall width w (the right axis). Model parameters are A = 15 pJ/m, K = K u − μ 0 M 2
s /2 = 0.588
MJ/m 3 , D = 3.7 mJm −2 , and B = 0. In each subfigure, one of these four parameters is treated
as a tuning parameter, and the other three parameters are fixed to above values. The symbols
are the micromagnetic simulation data. The solid lines are exact analytic results obtained from
minimising E of (14.23). The dashed lines are approximate results of R = π D
A
16AK 2 −π 2 D 2 K
,
w =
π D
4K [subfigures a–c] and solution of (14.25)(14.26) [subfigure d]. Vertical dashed lines are the
upper (lower) bound of parameters above (below) which a stable skyrmion cannot exist. e–h The
comparison of the skyrmion size R for the micromagnetic simulation (the black dots), our formula
(14.27) [or solution of (14.25) (14.26) for non-zero B] (the red lines), and previous studies [78]
(the green lines), [80] (the blue lines). Figure redrawn using the results in [84]