Altering critical depinning current via domain wall pile-up in magnetic nanowires
Introduction
Domain walls in magnetic nanowires attract great attentions for their applications in advanced logic and memory devices [1], [2]. Manipulation of domain walls by electric current is an essential component of domain wall devices and is under intensive study [3], [4]. Pinning and depinning of domain walls is a critical issue for domain wall manipulation where pinning sites are usually turning corners, bends, joints, and notches in magnetic circuits [5], [6]. Reducing the critical depinning current is important for technological application, in order to lower the power and to avoid increased nanowire temperature hindering reliable domain wall manipulation [7]. Finding an effective means to reduce and tune the critical depinning current will have a significant impact on the operation of domain wall devices. In this paper we present a micromagnetic simulation study of current-driven domain wall behaviors in thin film-patterned planar magnetic nanowires, which demonstrates a new mechanism for substantial reduction and effective tuning of the critical current for depinning domain walls in magnetic circuit. It is worth noting that micromagnetic simulation has been widely used to understand various factors that affect the critical current for domain wall depinning in magnetic nanowires, including edge roughness [8], [9], thermal perturbation [10], magnetic anisotropy [11], [12] and saturation magnetization [13], applied magnetic field [14], and notch shape [15]. The new mechanism revealed in this work is based on domain wall pile-up, in analogy to the well-known dislocation pile-up mechanism responsible for the Hall–Petch effect in mechanical strength.
Since the pinning strength of a pinning site depends on its geometrical shape, the depinning current can be modified by changing the geometrical shape of the pinning site. For example, decreasing the curvature of a bend would reduce its pinning strength [6] and thus lower the critical depinning current. However, changing geometrical shape is constrained by other functional requirements of the pinning site being a part of the magnetic circuit, thus the changeable range of the critical depinning current is limited. Here we show that utilizing domain wall pile-up enables not only a drastic reduction in the critical depinning current but also an effective programing of the current-driven pinning and depinning operations of domain walls. As shown in Fig. 1(a), a domain wall pile-up is formed in magnetic nanowire when a set of 180° and/or 360° domain walls of the same chirality are pushed against a barrier (an s-shape pinning site here). For convenience of discussion, such a domain wall pile-up will be named after its total magnetization rotation angle, nπ-pileup, where n is an integer greater than 2 (n=1 and 2 correspond respectively to 180° and 360° domain wall). A 360° domain wall is highly stable [16] unless an antiparallel magnetic field is applied, under which it dissociates into two 180° domain walls. Unlike stable 180° domain wall and relatively stable 360° domain wall [17], an nπ-pileup is not stable under magnetic field, dissociating into a set of discrete 360° and 180° domain walls, as exemplified in Fig. 1(b). However, an nπ-pileup under spin-polarized current does not dissociate, but instead moves as a whole in the nanowire, as demonstrated in Fig. 1(c). When the current-driven motion of an nπ-pileup encounters a barrier in its moving direction, interesting domain wall pinning and depinning phenomena take place, as will be discussed in the following. It is worth noting that a set of 180° and/or 360° domain walls of the same chirality (needed for formation of domain wall pile-up) can be conveniently generated in magnetic nanowires [18], [19], [20].
Section snippets
Micromagnetic modeling
Before discussing the important role of domain wall pile-up in current-driven domain wall depinning in nanowires, we first describe the micromagnetic simulation method used in this study. In micromagnetic modeling, magnetic domain structure is described by the magnetization direction unit vector field m(r), which is set to zero outside the magnetic nanowire. The evolution of the magnetic domain structure driven by spin-polarized current and magnetic field is described by the modified
Results and discussion
Computer simulation starts from the generation of multiple domain walls of the same chirality to be used for formation of domain wall pile-up. A magnetic nanowire shown in Fig. 2(a) is considered, which combines an s-shape bend as pinning site and a nanowire loop as domain wall generator [20]. Under counterclockwise rotating magnetic field, one 180° domain wall is generated per half cycle in the alternating sequence of head-to-head and tail-to-tail types. All the generated domain walls possess
Conclusions
In summary, this paper reports an important role of magnetic domain wall pile-up in current-driven domain wall depinning behaviors in magnetic nanowires, which is analogous to the crucial role of dislocation pile-up in determining the mechanical strength of polycrystalline materials (Hall–Petch effect). The critical current for domain wall depinning can be drastically reduced and effectively tuned by simply controlling the number of domain walls in the pile-up. It is shown that domain wall
Acknowledgments
Support from NSF under Grant no. DMR-1409317 is acknowledged. Simulations were performed on XSEDE supercomputers.
References (24)
- et al.
J. Magn. Magn. Mater.
(2010) - et al.
Science
(2005) - et al.
Science
(2008) Adv. Phys.
(2005)- et al.
Science
(2008) - et al.
J. Appl. Phys.
(2008) - et al.
Appl. Phys. Lett.
(2009) - et al.
Appl. Phys. Lett.
(2005) - et al.
Europhys. Lett.
(2005) - et al.
J. Appl. Phys.
(2009)
Phys. Rev. B
Appl. Phys. Lett.
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