Pinning of magnetic domain walls to structural defects in thin layers within a Heisenberg-type model

The interaction between domain walls and structural defects in equiatomic $L{1}_0$ FePt, antiphase boundaries and microtwins, was investigated by numerical simulations at atomic scale based on a Heisenberg model. It was shown that domain walls are strongly pinned, with depinning fields reaching a few teslas for the thickest microtwins. The potential well of the domain wall pinned in the microtwin is found to be asymmetric as a result of the pinning process. This results in depinning fields depending on the direction of propagation of the wall.

Figure 1

(Color online) Geometry of a six atomic layer thick microtwin (left) and of an APB (right) at the top of a $L{1}_0$ FePt thin film.

Figure 2

(Color online) (a) Bloch wall with Néel’s caps far from a microtwin. (b) Domain wall pinned in the microtwin (the line indicates the middle of the wall, where the magnetization is along $x$). (c) Pinned configuration with an antiphase boundary.

Figure 3

(Color online) Potential-energy wells for a domain wall pinned in an antiphase boundary (top) or in a six atomic layer thick microtwin (bottom) in the case of a 40 atomic planes thick film. The variation of the energy between the pinned and the free configuration, normalized by the energy of a Bloch wall corresponding to a surface energy density $4\sqrt{AK}$, is plotted as a function of the position of the domain wall, deduced from the $z$ component of magnetization. This position is set to zero when the domain wall is pinned in the defects with no applied field.

Figure 4

(Color online) Variation of the absolute value of the depinning field as a function of the microtwin’s thickness (in atomic layers), with the hypothesis that the domain wall comes from the left of the system. Results are shown for dipolar term omitted (depinning on the left: ▵ and on the right: ▿) and included (depinning on the left: + and on the right: ×). The layers contain 80 atomic planes.

Figure 5

(Color online) Magnetic configuration for low vertical coupling, just below the depinning field (left, $H_r^{-}$) and at the beginning of the depinning (right, $H_r^{+}$). It can be noticed that the magnetization is entirely in the plane of the figure (the color is a guide to the eye and the lines are the location where the magnetization is perpendicular to the field).