Domain wall motion in nanowires using moving grids (invited)

Förster, H.; Schrefl, T.; Suess, Dieter; Scholz, W.; Tsiantos, V.; Dittrich, R.; Fidler, J.

doi:10.1063/1.1452189

Cited by 74 publications

(59 citation statements)

References 23 publications

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“…Results of our simulations and previous results in wires 7,8,9,10 show three main idealized types of MR, where M changes from one of its two energy minima (M = M 0ẑ , with energy E F ) to the other (M = −M 0ẑ , with energy E F ) by a path such that the energy barrier is the difference between the energy maximum (E max ) and the energy minimum. These mechanisms are illustrated in Fig.…”

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confidence: 99%

“…An important problem is to establish the way and conditions for reversing the orientation of the magnetization. Although the reversal process is well known for ferromagnetic nanowires, 6,7,8,9,10 the equivalent phenomenon in nanotubes has been poorly explored so far in spite of some potential advantages over solid cylinders. Nanotubes exhibit a core-free magnetic configuration leading to uniform switching fields, guaranteeing reproducibility, 4,5 and due to their low density they can float in solutions making them suitable for applications in biotechnology (see [1] and refs.…”

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Reversal modes in magnetic nanotubes

Landeros

Allende

Escrig

et al. 2007

Applied Physics Letters

217

200

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The magnetic switching of ferromagnetic nanotubes is investigated as a function of their geometry. Two independent methods are used: Numerical simulations and analytical calculations. It is found that for long tubes the reversal of magnetization is achieved by two mechanism: The propagation of a transverse or a vortex domain wall depending on the internal and external radii of the tube.During the last decade, interesting properties of magnetic nanowires have attracted great attention. Besides the interest in their basic properties, there is evidence that they can be used in the production of new devices. More recently magnetic nanotubes have been grown 1,2,3,4 motivating a new research field. Magnetic measurements, 3 numerical simulations 4 and analytical calculations 5 on such tubes have identified two main states: an in-plane magnetic ordering, namely the fluxclosure vortex state, and a uniform state with all the magnetic moments pointing parallel to the axis of the tube. An important problem is to establish the way and conditions for reversing the orientation of the magnetization. Although the reversal process is well known for ferromagnetic nanowires, 6,7,8,9,10 the equivalent phenomenon in nanotubes has been poorly explored so far in spite of some potential advantages over solid cylinders. Nanotubes exhibit a core-free magnetic configuration leading to uniform switching fields, guaranteeing reproducibility, 4,5 and due to their low density they can float in solutions making them suitable for applications in biotechnology (see [1] and refs. therein).Let us consider a ferromagnetic nanotube in a state with the magnetization M along the tube axis. A constant and uniform magnetic field is then imposed antiparallel to M. After some delay time the magnetization reversal (MR) will start at any end. MR or magnetic switching can occur by means of different mechanisms, depending on the geometrical parameters of the tube. In this paper we will focus on the reversal process by means of two different but complementary approaches: numerical simulations and analytical calculations. Their mutual agreement sustains the results reported in this study.Numerical Simulations. Geometrically, tubes are characterized by their external and internal radii, R and a respectively, and height, H. It is convenient to define the ratio β ≡ a/R, so that β = 0 represents a solid cylinder and β → 1 correspond to a very narrow tube. The internal energy, E, of a nanotube with N magnetic moments can be written aswhere E ij is the dipolar energy given by E ij = µ i · µ j − 3(µ i ·n ij )(µ j ·n ij ) /r 3 ij , with r ij the distance between the magnetic moments µ i and µ j ,μ i the unit vector along the direction of µ i andn ij the unit vector along the direction that connects µ i and µ j . J ij = J is the exchange coupling constant between nearest neighbors and J ij = 0 otherwise. E a = − N i=1 µ i · H a is the contribution of the external magnetic field. In this paper we are interested in soft magnetic materials, in which case anisotropy can be s...

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confidence: 99%

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confidence: 99%

Reversal modes in magnetic nanotubes

Landeros

Allende

Escrig

et al. 2007

Applied Physics Letters

217

200

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“…Bloch points have also been predicted to exist at rest in magnetic nanowires with a compact cross-section such as cylindrical. In nanowires two types of DWs have indeed been predicted to exist: the transverse wall (TW) and the Bloch-Point wall(BPW) [14,15] (Fig. 1c-d).…”

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“…Nevertheless, each type of DW should exist as a metastable state over a significant range of diameters. The existence of BPWs would have practical macroscopic consequences: micromagnetic simulation predicts that the topological protection of the BPW prevents its transformation into other types of domain walls (DWs) during its motion [14,15]. As a consequence domainwall speeds beyond 1 km/s should be reachable, opening the way to new physics such as the spin-Cherenkov effect through interaction of the domain wall with standing spin-waves [16].…”

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Observation of Bloch-point domain walls in cylindrical magnetic nanowires

Col

Jamet²,

Rougemaille³

et al. 2014

Phys. Rev. B

171

151

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Topological protection is an elegant way of warranting the integrity of quantum and nanosized systems. In magnetism one example is the Bloch-point, a peculiar object implying the local vanishing of magnetization within a ferromagnet. Its existence had been postulated and described theoretically since several decades, however it has never been observed. We confirm experimentally the existence of Bloch points, imaged within domain walls in cylindrical magnetic nanowires, combining surface and transmission XMCD-PEEM magnetic microscopy. This opens the way to the experimental search for peculiar phenomena predicted during the motion of Bloch-point-based domain walls.There is a rising interest for physical systems providing topological protection. The interest is both fundamental to elucidate the underlying physical phenomena, and applied as a mean to provide robustness to a state against external perturbations and decoherence pathways. For example, the peculiar topology of the band structure of carbon nanotubes and graphene forbids backscattering of charge carriers [1], an effect which is often invoked to explain the high mobilities up to room temperature [2]. A similar effect occurs at the surface of so-called topological insulators, together with a locking of the spin of charge carriers; this provides spin currents protected against depolarization [3]. A photonic analogue was also designed by combining helical wave guides on a lattice with a graphene-like honeycomb topology, removing time-reversal symmetry and thereby preventing backscattering of light [4].In systems displaying a directional order parameter such as liquid crystals and ferromagnets, interesting phenomena are associated with the slowly-varying texture of the order field (magnetization for a ferromagnet). The requirement of local continuity of a vector field with fixed magnitude provides a topological protection against the transformation of the texture. A prototypical case in magnetism is skyrmions, which are essentially local two-dimensional chiral spin textures stabilized by the Dzyaloshinskii-Moriya interaction, embedded in an otherwise uniformly-magnetized surrounding. Despite these surroundings skyrmions cannot unwind continuously as explained by the above continuity constraints of the magnetization field, explaining their topological protection. Skyrmions have first been predicted theoretically [5], then confirmed experimentally in both bulk [6] and thin film forms [7].Bloch points are yet another type of topologicallyprotected magnetic texture which cannot be unwound, however of a three-dimensional nature. Bloch points are such that given the distribution of magnetization set on a closed surface like a sphere, the enclosed volume cannot be mapped with a continuous magnetization field of finite magnitude. This occurs e.g. for hedge-hog configurations, or more generally whenever all directions of magnetization are mapped on the closed surface (Fig. 1a-b). Such boundary conditions imply the local cancellation of the modulus of magnetization on a...

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“…Dense arrays of vertical wires would be the natural geometry to implement the proposal of a 3D magnetic race-track memory 3 . For wires, theory and simulations [5][6][7] suggested the existence of two types of DWs: the transverse wall and the Bloch-point wall. The features of their motion under field [5][6][7] or current 8 were predicted to be even more simple than in strips, mostly precessional in its azimuth in the former case, and purely translational for the second case with speed around 1 km/s, and absence of Walker instabilities.…”

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confidence: 99%