Bloch Domain Walls Research Articles

Dynamics of domain walls in magnetically multiaxial films in the thickness range corresponding to the Bloch-Néel transformations of the structure

The numerical minimization of the total energy functional and the solution of the nonlinear Landau-Lifshitz equation have been performed exactly taking into account the fundamental (including dipole-dipole) interactions in terms of the two-dimensional magnetization distribution. The equilibrium structure, energy, mobility, and scenario of the dynamic transformation of the domain walls (in their non- steady-state motion) have been determined as a function of the film thickness b and external magnetic field H for two different ((010) and (110)) orientations of the surfaces of magnetically triaxial films. The range of film thicknesses, including the thickness b = b N, for which the Neel domain walls can be transformed into the Bloch domain walls, has been investigated. The phenomena of anisotropy of the domain-wall energy, the domain-wall mobility, and the period of dynamic transformations of the domain walls have been analyzed as a function of the film thickness b and external magnetic field H. The range of film thicknesses has been determined, in which the non-steady-state motion of the Neel domain walls is accompanied by the creation and annihilation of vortex-like structures despite the one-dimensional character of the magnetization distribution in these walls.

Supercurrent enhancement in Bloch domain walls

Conventional spin-singlet Cooper pairs convert into spin-triplet pairs in ferromagnetic Josephson junctions in which the superconductor/ferromagnet interfaces (S/F) are magnetically inhomogeneous. Although much of the theoretical work describing this triplet proximity effect has considered ideal junctions with magnetic domain walls (DW) at the interfaces, in practice it is not easily possible to isolate a DW and propagate a supercurrent through it. The rare-earth magnet Gd can form a field-tuneable in-plane Bloch DW if grown between non-co-linearly aligned ferromagnets. Here we report supercurrents through magnetic Ni-Gd-Ni nanopillars: by field annealing at room temperature, we are able to modify the low temperature DW-state in Gd and this result has a striking effect on the junction supercurrent at 4.2 K. We argue that this result can only be explained in terms of the interconversion of triplet and singlet pairs, the efficiency of which depends on the magnetic helicity of the structure.

Current induced domain wall dynamics in the presence of a transverse magnetic field in out-of-plane magnetized materials

An analytical model was developed to describe the current induced domain wall (DW) dynamics of a Bloch DW in the presence of an external transverse magnetic field. The model takes into account the DW deformation and the magnetization tilting in the domain. The model is compared to the results of micromagnetic simulation and an excellent agreement is obtained. In the steady state regime, the model shows that the domain tilting does not change the DW mobility. An external or current induced transverse magnetic field such as the Oersted or Rashba field can prevent the Walker breakdown leading to a higher domain wall velocity.

Micromagnetic study of flux-closure states in Fe dots using quantitative Lorentz microscopy

A micromagnetic study of epitaxial micron-sized iron dots is reported through the analysis of Fresnel contrast in Lorentz Microscopy. Their use is reviewed and developed through analysis of various magnetic structures in such dots. Simple Landau configuration is used to investigate various aspects of asymmetric Bloch domain walls. The experimental width of such a complex wall is first derived and its value is discussed with the help of micromagnetic simulations. Combination of these two approaches enables us to define what is really extracted when estimating asymmetric wall width in Lorentz Microscopy. Moreover, quantitative data on the magnetization inside the dot is retrieved using phase retrieval as well as new information on the degrees of freedom of such walls. Finally, it is shown how the existence and the propagation of a surface vortex can be characterized and monitored. This demonstrates the ability to reach a magnetic sensitivity a priori hidden in Fresnel contrast, based on an original image treatment and backed-up by the evaluation of contrasts obtained from micromagnetic simulations.

Symmetry theory of the flexomagnetoelectric effect in the Bloch lines

It was shown that there are 48 magnetic point groups of the Bloch lines including 22 (11 time-invariant and 11 time-noninvariant) enantiomorphic and 26 non-enantiomorphic groups. The Bloch lines with the time-noninvariant enantiomorphism have identical types (parities) of the magnetization and polarization dependences. The list of soliton-like Bloch lines is derived from the symmetry classification. The tip electrode method of the creation of these Bloch lines is suggested for the potential applications in the magnetoelectric memory devices. The method of the experimental determination of the flexomagnetoelectric properties of the Bloch lines carried by the Bloch domain wall has been suggested. New type of the flexomagnetoelectric coupling, which is determined by the spatial derivatives of the electric polarization, can be found in the vicinity of the Curie temperature or compensation point of the ferrimagnets. The multi-state Bloch line magnetoelectric/multiferroic memory is proposed. It can be considered as a concept of the magnetoelectric enhancement of existing Bloch line memory invention.

Magnetic properties of sputtered Permalloy/molybdenum multilayers

In this work, we report the magnetic properties of sputtered Permalloy (Py: Ni80Fe20)/molybdenum (Mo) multilayer thin films. We show that it is possible to maintain a low coercivity and a high permeability in thick sputtered Py films when reducing the out-of-plane component of the anisotropy by inserting thin film spacers of a non-magnetic material like Mo. For these kind of multilayers, we have found coercivities which are close to those for single layer films with no out-of-plane anisotropy. The coercivity is also dependent on the number of layers exhibiting a minimum value when each single Py layer has a thickness close to the transition thickness between Neel and Bloch domain walls.

Externally driven collisions of domain walls in bistable systems near criticality

Multidomain solutions to the time-dependent Ginzburg-Landau equation in the presence of an external field are analyzed using the Hirota bilinearization method. Domain-wall collisions are studied in detail considering different regimes of the critical parameter. I show the dynamics of the Ising and Bloch domain walls of the Ginzburg-Landau equation in the bistable regime to be similar to that of the Landau-Lifshitz domain walls. Domain-wall reflections lead to the appearance of bubble and pattern structures. Above the Bloch-Ising transition point, spatial structures are determined by the collisions of fronts propagating into an unstable state. Mutual annihilation of such fronts is described.

Ferromagnetic resonance, magnetic susceptibility, and transformation of domain structure in CoFeB film with growth induced anisotropy

Field dependence of magnetic susceptibility in nanocrystalline CoFeB film was studied in a wide frequency range from 500 kHz to 15 GHz. Anomalies of the susceptibility were detected exciting CoFeB film with a solenoidal coil, microwave strip line, in the tunable microwave cavity as well as employing magneto-optical domains imaging. Critical spin fluctuations in the form of “soft” modes were observed in a whole range of orientations of magnetic field perpendicular to the “easy” magnetic axis. A sequence of domain structure transformations was extensively examined in a “hard” direction in in-plane magnetic field reduced below the field of uniaxial anisotropy Hp = 535 Oe. At first, uniformly magnetized state in CoFeB film transforms to stripe domains separated by low angle Néel domain walls (DWs) parallel to the “hard”-axis. Then, at critical field Hcr = 232 Oe, Néel DWs gradually convert to the“easy”-axis oriented Bloch DWs loaded with vertical Bloch lines (VBLs). After field reversal at H = −Hcr, backward conversion of VBL-loaded Bloch DWs to Néel DWs results in instantaneous energy release and sharp anomaly of magnetic susceptibility. Appearance of critical spin fluctuations accomplishes domains transformation to the uniformly magnetized state at H = −535 Oe.

Nonequilibrium density operator approach to domain wall resistivity

We derive the static resistivity due to the Bloch domain wall using the nonequilibrium density operator technique by Zubarev in the ballistic limit of electronic transport.

Link of microscopic and macroscopic fields in nematodynamics

We have found an unusual and unexpected link between micro- (nematic director) and macro- (velocity) fields in nematodynamics, which exhibits itself in extended defects of a new type. In particular, we have shown that black lines (BLs) observed in electroconvection of a homeotropically aligned nematic layer are simultaneously Bloch's domain walls for the director field and lines of zero velocity intersecting a roll pattern for the convection. A detailed experimental study revealing the fine structure of BLs and their point defects is presented.

Diffusion limit of a generalized matrix Boltzmann equation for spin-polarized transport

The aim of the present paper is the mathematical study of a linear Boltzmann equation with different matrix collision operators, modelling the spin-polarized, semi-classical electron transport in non-homogeneous ferromagnetic structures. In the collision kernel, the scattering rate is generalized to a hermitian, positive-definite $2\times2$ matrix whose eigenvalues stand for the different scattering rates of, for example, spin-up and spin-down electrons in spintronic applications. We identify four possible structures of linear matrix collision operators that yield existence and uniqueness of a weak solution of the Boltzmann equation for a general Hamilton function. We are able to prove positive-(semi)definiteness of a solution for an operator that features an anti-symmetric structure of the gain respectively the loss term with respect to the occurring matrix products. Furthermore, in order to obtain matrix drift-diffusion equations, we perform the diffusion limit with one of the symmetric operators assuming parabolic spin bands with uniform band gap and in the case that the precession frequency of the spin distribution vector around the exchange field of the Hamiltonian scales with order $\epsilon^2$. Numerical simulations of the here obtained macroscopic model were carried out in non-magnetic/ferromagnetic multilayer structures and for a magnetic Bloch domain wall. The results show that our model can be used to improve the understanding of spin-polarized transport in spintronics applications.

Phase-controlled proximity effect in ferromagnetic Josephson junctions: Calculation of the density of states and the electronic specific heat

We study the thermodynamic properties of a dirty ferromagnetic S$\mid$F$\mid$S Josephson junction with s-wave superconducting leads in the low-temperature regime. We employ a full numerical solution with a set of realistic parameters and boundary conditions, considering both a uniform and non-uniform exchange field in the form of a Bloch domain wall ferromagnetic layer. The influence of spin-active interfaces is incorporated via a microscopic approach. We mainly focus on how the electronic specific heat and density of states (DOS) of such a system is affected by the \textit{proximity effect}, which may be tuned via the superconducting phase difference. Our main result is that it is possible to \textit{strongly modify the electronic specific heat} of the system by changing the phase difference between the two superconducting leads from 0 up to nearly $\pi$ at low temperatures. An enhancement of the specific heat will occur for small values $h\simeq\Delta$ of the exchange field, while for large values of $h$ the specific heat is suppressed by increasing the phase difference between the superconducting leads. These results are all explained in terms of the proximity-altered DOS in the ferromagnetic region, and we discuss possible methods for experimental detection of the predicted effect.

Field-driven creep motion of a composite domain wall in a Pt/Co/Pt/Co/Pt multilayer wire

We have studied the field-driven motion of a pair of coupled Bloch domain walls in a perpendicular magnetic anisotropy Pt/Co/Pt/Co/Pt multilayer Hall bar. The nucleation of an isolated but coincident pair of walls in the two Co layers, observed by Kerr microscopy, took place at an artificial nucleation site created by Ga + ion irradiation. The average velocity v of the wall motion was calculated from time-resolved magnetotransport measurements at fixed driving field H, where the influence of the extraordinary Hall effect leads to the observation of voltages at the longitudinal resistance probes. We observed a good fit to the scaling relation ln v ∝ H − 1 / 4 , consistent the motion of a single 1-dimensional wall moving in a 2-dimensional disordered medium in the creep regime: the two walls are coupled together into a 1-dimensional composite object.

10.1007/s11448-008-3012-2

The magnetoresistance effects in the bi- and trilayer hybrid planar superconductor/ferromagnet (S/F) structures based on Py (permalloy) and Nb near the superconducting transition temperature T C are considered. It has been experimentally shown that the sign of the observed magnetoresistance peaks in the bilayer S/F systems changes from negative to positive at the permalloy layer thickness corresponding to the change in the type of domain walls from Néel to Bloch. For the Néel walls at the ferromagnet coercive fields, the negative magnetoresistance effect, which is due to a decrease in the depairing action of the exchange field E ex, is observed in the S/F bilayers. For the Bloch domain walls, the magnetoresistance of the bilayer S/F structures is determined by the dissipative motion of Abrikosov vortices in the superconducting layer. In the trilayer F/S/F structures, the magnetoresistance is mainly due to the suppression of the superconducting order parameter in the superconducting layer under the action of the accumulation of the spin-polarized carriers near the S/F interfaces.

Magnetic recording on domain walls in a single crystal film

The existing magnetic data recording media employ polycrystalline tracks, on which data are encoded using domains with different orientations of magnetic moments. We have numerically simulated data recording on the track in a single crystal film, in which the domain structure is formed using an intrinsic magnetostatic field of the crystal and the Bloch domain walls play the role of information bits.

Ferromagnetic resonance in a plate with a stripe domain structure with allowance for the inhomogeneity of the demagnetizing field

A numerical simulation of ferromagnetic resonance (FMR) in the absence of an external magnetic field has been performed for a plate with a high quality factor. A domain structure with Bloch domain walls (DWs) has been studied. It has been shown that the allowance for the inhomogeneity of the intrinsic demagnetizing field leads to the appearance of additional peaks in the FMR spectrum. With decreasing plate thickness, there occurs a displacement of the resonance-curve peaks into the region the low frequencies. An increase in the size of one of the domains at the expense of another in the periodic domain structure leads to an increase in the amplitude of the susceptibility of the low-frequency FMR mode and its shift into the region of low frequencies. Accordingly, the amplitude of the susceptibility of the high-frequency mode decreases and is shifted into the region of high frequencies. Furthermore, in the presence of resonance, in the plate with unequal domains the peak of the resonance curve that corresponds to the high-frequency mode is observed also upon the excitation of oscillations by an external ac field perpendicular to the DW, and the peak corresponding to the low-frequency mode, upon the excitation by an ac field parallel to the DW. These features of the FMR are explained by the corresponding changes in the inhomogeneous demagnetizing field.

Contacting individual Fe(110) dots in a single electron-beam lithography step

We report on a new approach, entirely based on an electron-beam lithography technique, tocontact electrically, in a four-probe scheme, single nanostructures obtained by self-assembly.In our procedure, nanostructures of interest are located and contacted in the samefabrication step. This technique has been developed to study the field-inducedreversal of an internal component of an asymmetric Bloch domain wall observed inelongated structures such as Fe(110) dots. We have focused on the control, using anexternal magnetic field, of the magnetization orientation within Néel caps thatterminate the domain wall at both interfaces. Preliminary magneto-transportmeasurements are discussed demonstrating that single Fe(110) dots have been contacted.

Hysteresis and noise in ferromagnetic materials with parallel domain walls

We investigate dynamic hysteresis and Barkhausen noise in ferromagnetic materials with a huge number of parallel and rigid Bloch domain walls. Considering a disordered ferromagnetic system with strong in-plane uniaxial anisotropy and in-plane magnetization driven by an external magnetic field, we calculate the equations of motion for a set of coupled domain walls, considering the effects of the long-range dipolar interactions and disorder. We derive analytically an expression for the magnetic susceptivity related to the effective demagnetizing factor and show that it has a logarithmic dependence on the number of domains. Next, we simulate the equations of motion and study the effect of the external field frequency and the disorder on the hysteresis and noise properties. The dynamic hysteresis is very well explained by means of the loss separation theory.

Controlled Switching of Néel Caps in Flux-Closure Magnetic Dots

While magnetic hysteresis usually considers magnetic domains, the switching of the core of magnetic vortices has recently become an active topic. We considered Bloch domain walls, which are known to display at the surface of thin films flux-closure features called Néel caps. We demonstrated the controlled switching of these caps under a magnetic field, occurring via the propagation of a surface vortex. For this we considered flux-closure states in elongated micron-sized dots, so that only the central domain wall can be addressed, while domains remain unaffected.

Sudden critical current drops induced in S/F structures

In the search for new physical properties of S/F structures, we have found that the superconductor critical current can be controlled by the domain state of the neighboring ferromagnet. The superconductor is a thin wire of thickness d_{s} ~ 2 xi_{S}. Nb/Co and Nb/Py (Permalloy Ni_{80}Fe_{20}) bilayer structures were grown with a significant magnetic anisotropy. Critical current measurements of Nb/Co structures with ferromagnet thickness d_{F} > 30nm show sudden drops in two very defined steps when the measurements are made along the hard axes direction (i.e. current track parallel to hard anisotropy axes direction). These drops disappear when they are made along the easy axis direction or when the ferromagnet thickness is below 30nm. The drops are accompanied by vortex flux flow. In addition magnetorestistance measurements close to Tc show a sharp increase near saturation fields of the ferromagnet. Similar results are reproduced in Nb/Py bilayer structure with the ferromagnet thickness d_{F} ~ 50nm along the easy anisotropy axes. These results are explained as being due to spontaneous vortex formation and flow induced by Bloch domain walls of the ferromagnet underneath. We argue these Bloch domain walls produce a 2D vortex-antivortex lattice structure.