16 Antiferromagnetic Skyrmions and Bimerons
451
As a result, adopting the magnetic anisotropy gradient to drive the skyrmion in
pure antiferromagnets, the skyrmion can move at high speeds (up to 500 m/s) without
any transverse drift. It is worth mentioning that using the anisotropy gradient as a
driving source can be introduced to antiferromagnetically coupled bilayer systems,
as reported by Qiu et al. [64]. The above results may open an alternative way
for the design of antiferromagnetic skyrmion-based devices, such as the horizontal
racetrack-type memory [65]. In addition, when these devices are chained together,
it can also be used to build the antiferromagnetic skyrmion-based diode [66].
16.6 Pinning and Depinning of Antiferromagnetic
Skyrmions
To understand more antiferromagnetic skyrmion physics and use it in future
nanoscale magnetic data storage and logic devices, it is essentially important to
know the pinning and depinning of antiferromagnetic skyrmions to defects. In this
section, we discuss the effect of defects caused by the local variation of perpendicular magnetic anisotropy on the current-induced dynamics of an antiferromagnetic
skyrmion under the framework of micromagnetics.
From [67], the local magnetic anisotropy value in the defect area is specified
by K = K 0
1.0 + λ/exp(|r − r d |/R d )
2
, where K 0 is the magnetic anisotropy
constant in the homogeneous area, |λ| denotes the amplitude of variation referred
as the strength of the defect, R d represents its characteristic size (i.e., the radius) and
r d is the position vector of the defect center. Such an anisotropy profile to describe
the inhomogeneity induced by potential impurity sites, might be more realistic than
a simple step-like defect or a defect with a linear variation of anisotropy, and is
analogous to the model proposed by Kronmüller [68]. In addition, similar distribution of exchange interaction J ex has also been used to discuss the skyrmion-defect
interaction in ferromagnetic film [69, 70]. In all simulations, the coordinate of the
antiferromagnetic skyrmion center is represented by (R x , R y ) with the initial position
(0, 0).
First let us consider the effect of the defect on the antiferromagnetic skyrmion
without any external driving force. The simulation results show that when the
skyrmion is placed at the area where the defect can interact with it, the skyrmion
will spontaneously move and eventually stop at the center or off-center of the defect.
Moreover, for the same defect, the skyrmion always be pinned at the same position. In
particular, the final pinned position depends strongly on the ratio of skyrmion size to
the defect size and is not sensitive to the strength of the defect. As shown in Fig. 16.8a,
when the radius R d of defect is smaller than the antiferromagnetic skyrmion radius
R sk , the skyrmion stops at the off-center of the defect, and the distance L gradually
decreases as R d increases. When R d is close to or exceeds R sk , L drops sharply and
approaches 0, and the skyrmion will stay at the center of the defect. Such dynamic
pinning processes are also similar to those of ferromagnetic skyrmions [71].
451
As a result, adopting the magnetic anisotropy gradient to drive the skyrmion in
pure antiferromagnets, the skyrmion can move at high speeds (up to 500 m/s) without
any transverse drift. It is worth mentioning that using the anisotropy gradient as a
driving source can be introduced to antiferromagnetically coupled bilayer systems,
as reported by Qiu et al. [64]. The above results may open an alternative way
for the design of antiferromagnetic skyrmion-based devices, such as the horizontal
racetrack-type memory [65]. In addition, when these devices are chained together,
it can also be used to build the antiferromagnetic skyrmion-based diode [66].
16.6 Pinning and Depinning of Antiferromagnetic
Skyrmions
To understand more antiferromagnetic skyrmion physics and use it in future
nanoscale magnetic data storage and logic devices, it is essentially important to
know the pinning and depinning of antiferromagnetic skyrmions to defects. In this
section, we discuss the effect of defects caused by the local variation of perpendicular magnetic anisotropy on the current-induced dynamics of an antiferromagnetic
skyrmion under the framework of micromagnetics.
From [67], the local magnetic anisotropy value in the defect area is specified
by K = K 0
1.0 + λ/exp(|r − r d |/R d )
2
, where K 0 is the magnetic anisotropy
constant in the homogeneous area, |λ| denotes the amplitude of variation referred
as the strength of the defect, R d represents its characteristic size (i.e., the radius) and
r d is the position vector of the defect center. Such an anisotropy profile to describe
the inhomogeneity induced by potential impurity sites, might be more realistic than
a simple step-like defect or a defect with a linear variation of anisotropy, and is
analogous to the model proposed by Kronmüller [68]. In addition, similar distribution of exchange interaction J ex has also been used to discuss the skyrmion-defect
interaction in ferromagnetic film [69, 70]. In all simulations, the coordinate of the
antiferromagnetic skyrmion center is represented by (R x , R y ) with the initial position
(0, 0).
First let us consider the effect of the defect on the antiferromagnetic skyrmion
without any external driving force. The simulation results show that when the
skyrmion is placed at the area where the defect can interact with it, the skyrmion
will spontaneously move and eventually stop at the center or off-center of the defect.
Moreover, for the same defect, the skyrmion always be pinned at the same position. In
particular, the final pinned position depends strongly on the ratio of skyrmion size to
the defect size and is not sensitive to the strength of the defect. As shown in Fig. 16.8a,
when the radius R d of defect is smaller than the antiferromagnetic skyrmion radius
R sk , the skyrmion stops at the off-center of the defect, and the distance L gradually
decreases as R d increases. When R d is close to or exceeds R sk , L drops sharply and
approaches 0, and the skyrmion will stay at the center of the defect. Such dynamic
pinning processes are also similar to those of ferromagnetic skyrmions [71].