Geometrically Constrained Magnetic Wall

Abstract

The structure and properties of a geometrically constrained magnetic wall in a constriction separating two wider regions are studied theoretically. They are shown to differ considerably from those of an unconstrained wall, so that the geometrically constrained magnetic wall truly constitutes a new kind of magnetic wall, besides the well known Bloch and Néel walls. In particular, the width of a constrained wall can become very small if the characteristic length of the constriction is small, as is actually the case in an atomic point contact. This provides a simple, natural explanation for the large magnetoresistance observed in ferromagnetic atomic point contacts. PACS numbers: 75.60.Ch, 75.70.Kw, 75.70.Pa The investigation of magnetic nanostructures is one of the major current subjects in magnetism. This interest is stimulated, on one hand, by the great progress in nanofabrication techniques and magnetic characterization methods and, on the other hand, by the perspective of technological applications for magnetic storage of information of unprecedented density.A major question to be addressed in this field of research is: How does the micromagnetic structure (i.e., domains, walls, etc.) respond to geometrical constraints on the nanometer scale?In an unconstrained system such as in a bulk ferromagnet, as first pointed out by Bloch, the wall structure is determined by a competition between exchange and anisotropy energies [1]. The exact structure of the Bloch wall has been calculated by Landau and Lifshitz [2]. In a ferromagnetic thin film with in-plane easy magnetization axis, as shown by Néel [3], the dipolar interaction leads to a new kind of wall, known as a Néel wall, in which the structure is determined by a competition between exchange, anisotropy, and dipolar energies.In this Letter, I consider the problem of the structure and energy of a magnetic wall in a constriction separating two regions of wider cross section. This encompasses various situations of great physical interest such as a narrow constriction fabricated in a magnetic ultrathin film by lithographic techniques, or a constriction in a wire.I point out that when the cross section of the constriction is much smaller than that of the wide region, the structure of the wall becomes almost independent of the material parameters such as magnetization, exchange stiffness, and anisotropy constant and is determined mostly by the geometry of the constriction. The wall energy consists mostly of exchange energy. Thus, geometrically constrained magnetic walls appear as a new kind of magnetic walls, with properties completely different from those of Bloch and Néel walls. In particular, the width of the geometrically constrained magnetic walls is essentially given by the length of the constriction, which can be considerably smaller than the width of a Bloch or Néel wall.In the limit of a point contact of atomic dimensions, the width of the wall would also be of atomic dimensions. This fact has important physical consequences: in particular, the contribution ...

Current driven dynamics of domain walls constrained in ferromagnetic nanopillars

“…In this paper however we do not make any assumptions on the origin of the pinning, which can be achieved in other ways. One example could be a ferromagnetic body, made by two regions connected through a small constriction: a domain wall is developed in the constriction, when the wider regions are magnetized in opposite directions 9,10 .…”

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“…If Eq. (2) has a DW solution of a boundary condition ∂m/∂n = 0, where n is the normal direction of the wire boundary, it means that a DW is pinned [4,28]. Mathematically, the depinning field is the minimal external field at which Eq.…”

“…Thus, a trap potential as a function of one variable like the DW center is ill defined. A seminal analytical work by Bruno [4] suggests that the pinning can only occur at narrower parts of a constrained nanowire. Thus, it cannot explain DW pinning by an antinotch [18].…”

Fabrication and simulation of nanostructures for domain wall magnetoresistance studies on nickel

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