Neel Walls Research Articles

Magnetic domain walls in constrained geometries

Magnetic domain walls have been studied in micrometer-sized Fe20Ni80 elements containing geometrical constrictions by spin-polarized scanning electron microscopy and numerical simulations. By controlling the constriction dimensions, the wall width can be tailored and the wall type modified. In particular, the width of a 180 degree Neel wall can be strongly reduced or increased by the constriction geometry compared with the wall in unconstrained systems.

Magneto-optical Kerr effect in Fe21Ni79 films on Si(100): Quantum behavior for film thicknesses below ∼6 nm

The magneto-optical Kerr effect (MOKE) has been observed and characterized in 1–80 nm thick Fe21Ni79 films deposited onto Si(100), for an external magnetic field (variable in strength up to 400 G) oriented parallel or orthogonal to the magnetization axis of the film. A measurable response is observed for film thicknesses (d) as small as 2 nm and, if the external magnetic field lies in the plane of the film, two-dimensional quantum behavior is evident for d≲6 nm. A precipitous decline in the magnitude of the MOKE response is accompanied by an increase in the coercivity and, when the external field is perpendicular to the film magnetization axis, a rapid rise in the saturation field. Experiments also confirm the existence of a component of the film magnetization oriented out of the plane of the film, a result consistent with the prediction of computational studies [T. Trunk et al., J. Appl. Phys. 89, 7606 (2001)] that the transition between Bloch and Néel wall domain structure occurs in FeNi films for film thicknesses of ≈30 nm.

Structure dependent stray fields from domain walls in permalloy films

Magnitudes and distributions of stray magnetic fields from a single domain wall in a Permalloy film are calculated for film thickness from 10 nm to 2.5 /spl mu/m, using direct integration of the Landau-Lifshitz-Gilbert equation in a Cartesian lattice. This thickness range supports a Neel wall whose magnetization rotates in the plane of the film, a symmetric Bloch wall whose magnetization rotates out of the plane, and an asymmetric Bloch wall whose magnetization rotates simultaneously in and out of the plane of the film at the surfaces and inside the film, respectively. The stray field magnitude is largest for films with a Neel wall rather than film with a Bloch wall. The stray field magnitude varies linearly with thickness for films with Neel walls. The field distribution has a Neel-dominant character, i.e., it lies in a plane perpendicular to the plane of the wall, parallel to the plane of the film, and is dominated by the transverse component of the field. For films with a Bloch-type component, the stray field is lower. The field distribution has a Bloch-dominant character, i.e., it lies in a plane perpendicular to the plane of the wall, normal to the plane of film, and is dominated by the normal component of the field. At thickness larger than 1 /spl mu/m, the stray field appears independent of thickness and is relatively constant at 15 Oe.

Magnetic domains and domain-wall structure in Ni/Cu(001) films imaged by spin-polarized low-energy electron microscopy

manuscript received 28 May 2003; published 25 August 2003) The magnetic domain microstructure of four- to eight-monolayer- (ML-) thick Ni/Cu(001) films deposited at 100 K and 300 K was studied at both temperatures by spin-polarized low-energy electron microscopy. Domain structures remain stable during deposition: large in-plane domains of several 10 μm diameter persist at both temperatures throughout the thickness range. The position of the domain walls is not significantly correlated with topographic features (step bunches, terraces) which were imaged simultaneously. The structure of 180° Neel walls in the films was determined by using the spin manipulator of the electron illumination system to measure image contrast as a function of polar and azimuthal polarization of the illuminating beam. We find that in 8-ML films at 300 K, the Neel walls are 400 nm wide and wall segments with both expected chiralities were identified.

패턴된 이중박막의 자구벽 특성조사

The magnetic domain walls at the edges of a large patterned and exchanged-biased NiO(10-60 nm)/NiFe(10 nm) bilayers and their motions with applied field were investigated by magnetic force microscopy. Three kinds of domain walls, namely, head-to-head zig-zag and tail-to-tail zig-zag Bloch walls and straight Neel walls were found at specific edges of the unidirectional biased NiO(30 nm)/NiFe(10 nm) bilayer having the exchange biasing field (Hex/) of 21 Oe. No walls were observed for the strong exchange-biased bilayer (60 nm NiO, Hex/

The Logarithmic Tail of Néel Walls

We study the multiscale problem of a parametrized planar 180° rotation of magnetization states in a thin ferromagnetic film. In an appropriate scaling and when the film thickness is comparable to the Bloch line width, the underlying variational principle has the form where the reduced stray-field operator 𝒮 Q approximates (−Δ)1/2 as the quality factor Q tends to zero. We show that the associated Neel wall profile u exhibits a very long logarithmic tail. The proof relies on limiting elliptic regularity methods on the basis of the associated Euler-Lagrange equation and symmetrization arguments on the basis of the variational principle. Finally we study the renormalized limit behavior as Q tends to zero.

Repulsive Interaction of Néel Walls, and the Internal Length Scale of the Cross-Tie Wall

Neel walls and cross-tie walls are two structures commonly seen in ferromagnetic thin films. They are interesting because their internal length scales are not determined by dimensional analysis alone. This paper studies (a) the repulsive interaction of one-dimensional Neel walls and (b) the internal length scale of the cross-tie wall. Our analysis of (a) is mathematically rigorous; it provides, roughly speaking, the first two terms of an asymptotic expansion for the energy of a pair of interacting walls. Our analysis of (b) is heuristic, since it rests on an analogy between the cross-tie wall and an ensemble of Neel walls. This analogy, combined with our results on Neel walls and a judicious choice of parameter regime, yields a specific prediction for the internal length scale of a cross-tie wall. This prediction is consistent with the experimentally observed trends.

Cross-tie walls in thin permalloy films

Cross-tie walls in permalloy films have been simulated as a function of thickness in the range 10-70 nm using direct integration of the Landau-Lifshitz-Gilbert equation in a Cartesian lattice with periodic boundary conditions along the length of the wall. A cross-tie wall is a Bloch-like transition along the wall [or vertical Bloch line (VBL)] between Neel Walls of opposite chirality in a film with in-plane magnetization. This transition is a low-energy state, which allows the long tails of Neel walls to partially close their magnetic flux in the vicinity of the walls. The magnetization configuration of these transitions is either elliptical (vortex) or hyperbolic (antivortex). The pi-VBL transitions are 50 nm in diameter and the distance from each other increases with film thickness. The cross-tie wall energy per unit area was lower than that of a pure Neel or Bloch wall between 15 and 50 nm film thickness.

Thickness dependent wall mobility in thin Permalloy films

Domain wall mobility in Permalloy films has been calculated as a function of thickness at 10, 80, and 160 nm which reflects the structure change of Néel, symmetric Bloch and C-shaped (asymmetric Bloch) domain walls. The mobility has been derived from the dynamics of a single nonperiodic domain wall using direct integration of the Landau–Lifshitz–Gilbert equation in a Cartesian lattice. This investigation allows for a detailed examination of spin precession, wall motion and overall magnetization distortion as the wall is moved in the presence of fields ranging from 0.5 to 5 Oe applied in the easy axis direction. At 10-nm-thick films, the mobility of a Néel wall is 30 m/s Oe. Wall motion takes place without noticeable distortion in the magnetization distribution in the vicinity of the Néel wall. For 80 nm-thick films, the mobility of a symmetric Bloch wall is 5 m/s Oe, or 20% less than the theoretical prediction for the mobility of a 180° domain wall model. At dynamic equilibrium, the symmetric Bloch wall has been slightly distorted into a C-shaped wall. For 160 nm-thick films, the mobility of a C-shaped wall is 12 m/s Oe, or 29% less than the theoretical predicted value. Shearing-type magnetization distortion is observed in this composite structure of a Bloch component at the center and Néel caps of opposite chirality at the surfaces.

Domain walls in elastically soft crystals

The properties of domain walls in ferromagnets that are elastically soft are considered. The wall energy is comprised of exchange, anisotropy, elastic, and magnetoelastic terms. Results are given for the energy and profile of a model crystal with [100] easy axes and large tetragonal magnetostriction. The wall energy is calculated for Neel walls propagating in [010] and [110] directions. It is shown that the [110] wall has lower energy for all values of magnetostriction. It is argued that these walls should be observable in crystals with magnetoelastic energy large enough to overcome demagnetizing effects. Candidate materials include Fe1−xGax alloys, rare earth–zinc compounds, and certain martensitic materials in their cubic phases.

Domain wall induced switching of whisker-based tunnel junctions

The magnetization behavior of a single-crystalline [Fe-whisker/MgO (20 ML)/Fe-film (20 ML)] sandwich (ML denotes monolayer) was studied by depth-selective Kerr microscopy. Residual stray fields of the whisker domain wallswere identified to be responsible for complex magnetization processes in the iron film. A 180° wall in the whisker magnetizes the film transversally to the wall direction, depending on the internal rotation alignment of the whisker wall and not on its surface rotation. We also found that 360° walls can be formed in the film for pure topological reasons if Neel walls of certain rotation alignments are facing each other.

Bloch walls in strongly driven easy-plane ferromagnets

We show that the action of strong rapidly oscillating transverse magnetic field in easy-plane ferromagnet gives rise to the appearance of effective biaxial magnetic anisotropy and new soliton solutions in the form of Bloch and Neel domain walls. Exact analytical expressions describing the conversion of a Neel wall into the stationary Bloch wall under dissipation are derived on the ground of the adiabatic approximation which are in good agreement with the numerical simulations of the basic strongly perturbed Landau-Lifshitz equation.

Thermal and quantum fluctuations of a domain wall in a fine magnetic wire

The effect of thermal fluctuations on the structure of a domain wall (DW) in a fine magnetic wire is analyzed. It is shown that the polarization of a DW in a magnetic nanowire is changed spontaneously as a result of thermal and quantum fluctuations. There is a critical diameter of the wire below which a transformation analogous to the superparamagnetic transition occurs, with the result that the Neel wall is transformed into a Ginzburg-Bulaevski $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} $$ wall.

Néel and Cross-Tie Wall Energies for Planar Micromagnetic Configurations

We study a two-dimensional model for micromagnetics, which consists in an energy functional over S 2 -valued vector fields. Bounded-energy configurations tend to be planar, except in small regions which can be described as vortices (Bloch lines in physics). As the characteristic “exchange-length” tends to 0, they converge to planar divergence-free unit norm vector fields which jump along line singularities. We derive lower bounds for the energy, which are explicit functions of the jumps of the limit. These lower bounds are proved to be optimal and are achieved by one-dimensional profiles, corresponding to Neel walls, if the jump is small enough (less than π/2 in angle), and by two-dimensional profiles, corresponding to cross-tie walls, if the jump is bigger. Thus, it provides an example of a vector-valued phase-transition type problem with an explicit non-one-dimensional energy-minimizing transition layer. We also establish other lower bounds and compactness properties on different quantities which provide a good notion of convergence and cost of vortices.

Domain formation in Fe–N multilayers

We prepared a series of sputtered FeN single layer films, and bilayer and multilayer films laminated with alumina, in which both the Fe–N thickness and the alumina interlayer thickness varied. The films were characterized by quantitative magneto-optical Kerr-microscopy and inductive measurements. We found a strong influence of interlayer coupling and FeN thickness on the domain formation in these layers. For single layers a transition from cross-tie walls to Bloch-type walls for increasing ferromagnetic layer thickness was observed. The multilayer films displayed a wide range of different types of coupled Neel walls depending on interlayer thickness. These include superimposed, compensated, and 360° walls. The change in domain wall structure strongly influences the coercivity of the thin film systems. The relative coupling strength between the magnetic films is calculated from the domain wall width of the superimposed Neel walls. Magnetic in-plane deviation strongly depends on the sign of magnetostriction. The observed magnetic dispersion leads to an increase in the minimum magnetic switching time. The observed micromagnetic structures result in unwanted irregular domain patterns in structured samples. Both are indicating limitations for applications in thin film recording heads.

Micromagnetic simulation of 360° domain walls in thin Co films

A moving mesh finite element technique is applied to simulate the formation and annihilation of 360° wall structures in thin Co films. Adaptive refinement and coarsening of the finite element mesh controls the discretization error during the simulation of domain wall movement. Elements are refined in regions with high variation of the magnetization, whereas elements are taken out where the magnetization is uniform. The calculated Neel walls have very wide tails and have an extension of about 15–20 nm. The motion of domain walls through the sample gives rise to the formation of 360° domain walls. They are formed when a Bloch line in a domain wall is caught at a nonmagnetic defect in the sample. Pinholes with an extension greater than 6 nm are sufficient to trap a Bloch line. The width of the 360° walls is found to be in the range of 40 to 50 nm. The stability of the 360° walls depends on the strength of the pinning of the Bloch lines. The field required to annihilate the 360° walls increases linearly with the size of the nonmagnetic defect.

Magnetic ground state of a thin-film element

By means of three-dimensional numerical calculations we studied possible micromagnetic configurations in a rectangular Permalloy-like thin-film element. The parameters were chosen to be compatible with the so-called micromagnetic standard problem 1. We demonstrate that for these parameters a diamond domain pattern is the lowest energy state that replaces cross-tie patterns favorable in larger elements. Only at smaller sizes does the originally envisaged Landau pattern form the ground state. The transition to high-remanence structures (or what would be comparable to a single-domain state) is found for lateral sizes that are an order of magnitude smaller than the benchmark parameters. The transitions among the different domain patterns become plausible in view of the energy of symmetric Neel walls in extended thin films. The features of the high-remanence structures can be derived from the principle of uniform charge distribution.

Excitations of domain walls pinned at F/AF interface steps

We study rigid displacement excitations of a Neel wall of a thin uniaxial ferromagnetic film on a two-sublattice antiferromagnetic substrate. An interface step defect pins the domain wall and provides the restoring force that stabilizes the domain wall oscillations. The frequency of the rigid displacement domain wall modes is shown to be of the same order of magnitude as that of the uniform domain modes of the ferromagnetic film, for a wide range of interface exchange energy values.

Geometrically Constrained Magnetic Wall

The structure and properties of a geometrically constrained magnetic wall in a constriction separating two wider regions are investigated theoretically. They are shown to differconsiderably 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 Neel walls. In particular, the width of a constrained wall cann 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.

Role of boundary conditions and dimensions on the micromagnetics of a cobalt point contact

We have calculated the micromagnetic structure of a Co point contact, for applied magnetic fields parallel (H∥) and perpendicular (H⊥) to the device’s electrodes. Different boundary conditions and dimensions have been examined. In most situations a Néel wall is formed in the constriction. When the size of the device is reduced (or the exchange stiffness is increased), then the energy barrier between the state with and without the Néel wall is increased. The domain wall magnetoresistance (DWMR) and anisotropic MR (AMR) have been estimated, and they show a maximum in the DWMR for both field directions of the applied magnetic field and a maximum and minimum in the AMR for H∥ and H⊥, respectively.