Planar Domain Wall Research Articles

Magnetic field driven domain-wall propagation in magnetic nanowires

The mechanism of magnetic field induced magnetic domain-wall (DW) propagation in a nanowire is revealed: A static DW cannot exist in a homogeneous magnetic nanowire when an external magnetic field is applied. Thus, a DW must vary with time under a static magnetic field. A moving DW must dissipate energy due to the Gilbert damping. As a result, the wire has to release its Zeeman energy through the DW propagation along the field direction. The DW propagation speed is proportional to the energy dissipation rate that is determined by the DW structure. The negative differential mobility in the intermediate field is due to the transition from high energy dissipation at low field to low energy dissipation at high field. For the field larger than the so-called Walker breakdown field, DW plane precesses around the wire, leading to the propagation speed oscillation.

Discrimination between coupling and anisotropy fields in exchange-biased bilayers

In the framework of models that assume planar domain wall formed at the antiferromagnetic part of the interface of exchange-biased bilayers, one cannot distinguish between the cases of high or low ratios between the coupling and the antiferromagnet’s anisotropy fields by using hysteresis loop measurement, ferromagnetic resonance, anisotropic magnetoresistance, or ac susceptibility techniques applied on one and the same sample. The analysis of the experimental data obtained on a series of FeMn/Co films indicated that once the biasing is established the variation in the coercivity with the FeMn layer thickness could be essential for solving this problem. If the coercivity decreases with the thickness then the interlayer exchange coupling is the parameter that varies while the domain-wall energy of the antiferromagnet remains practically constant.

Effect of a planar magnetic field on the domain wall dynamics in a double-layer uniaxial magnetic film

Motion of an isolated domain wall in a double-layer uniaxial magnetic film, where the film layers differ in characteristic length, saturation magnetization and damping parameter, is investigated by solving the Slonczewski equation. A planar magnetic field is applied normal to the domain-wall plane. The dependences of the threshold field and limiting velocity of disruption of the steady-state motion of the domain wall on the planar magnetic field value are obtained.

Influence of Surface Layers Modified by Proton Exchange on Domain Kinetics of Lithium Niobate

The abnormal domain kinetics in congruent lithium niobate single crystals caused by surface modification using proton exchange was studied experimentally. The dependence of domain kinetics on polarity of the growing domains at the surface with proton exchange was revealed. The abnormal smooth motion of irregularly shaped domain walls with finger-like features and correlated nucleation was observed for growth of domains with Z + at surface with proton exchange. Such behavior drastically differs from jump-like motion of plane domain walls oriented along Y directions observed both in conventional lithium niobate and for growth of domains with Z – at surface with proton exchange.

Mechanism of chirality reversal for planar interface domain walls in exchange-coupled hard/soft magnetic bilayers

The mechanism of chirality reversal for a planar interface domain wall in a hard/soft magnetic bilayer has been identified by combining magnetoresistance measurements, modeling, and direct magnetic domain observations. The reversal occurs through IDW nucleation and lateral domain wall propagation. Over an unpredicted wide range of applied magnetic fields, the chirality transition takes place by an unwinding followed by a rewinding of the IDW. The chirality transition mechanism of phase transition could be identified from a micromagnetic analysis of the lateral magnetic domain wall orientation. Up to three magnetization phases coexist in the uniaxial material during reversal.

Magnetoresistance and magnetization studies through a Cu interlayer in spin valves of NiFe/Cu/NiFe/FeMn

The influence of the Cu layer thickness on the magnetic and magnetotransport properties has been investigated in Ta/NiFe/Cu/NiFe/FeMn spin valves. The magnetization and magnetoresistance measurements were carried out for magnetic field applied along the easy-axis direction. A phenomenological model, which assumes formation of a planar domain wall at the anti-ferromagnetic side of the interfaces as well as bilinear coupling between the ferromagnetic layers, was used to derive the anisotropy characteristics and orientation of each NiFe layer magnetization. The anisotropy and spin valve magnetoresistance were simulated numerically and compared with the experiment. It was found that the anisotropy magnetoresistance is negligible and that there is a poor agreement for the spin-valve one, which was attributed to the model (valid for ferromagnetic layers in single-domain state only) used for its calculation. It was found that the increase of the Cu layer thickness provokes a decrease of the interdiffusion between the NiFe and FeMn layers, and, as consequence, changes of the uniaxial anisotropy of the pinned NiFe layer, of the exchange interaction between the pinned NiFe layer and the FeMn ones, as well as of the exchange-bias field of the pinned NiFe layer.

Charge contrast of ferroelectric domain walls in ferroelastic terbium molybdate

An extraordinary potential contrast of a plane domain wall forming in the case of excess negative charging of a ferroelastic-ferroelectric Tb2(MoO4)3 sample with a two-domain structure has been detected using a scanning electron microscope. Conditions and features of the formation of this potential contrast (called charge contrast) in the domain wall region are determined. It is shown that the surface is charged at a lower rate in the domain wall region, which is an elastically strained crystal region. The smallest domain wall width determined by the charge-contrast image was 1.6 μm on the average.

THICK PLANAR DOMAIN WALL: ITS THIN WALL LIMIT AND DYNAMICS

We consider a planar gravitating thick domain wall of the λϕ4 theory as a space–time with finite thickness glued to two vacuum space–times on each side of it. Darmois junction conditions written on the boundaries of the thick wall with the embedding space–times reproduce the Israel junction condition across the wall in the limit of infinitesimal thickness. The thick planar domain wall located at a fixed position is then transformed to a new coordinate system in which its dynamics can be formulated. It is shown that the wall's core expands as if it were a thin wall. The thickness in the new coordinates is not constant anymore and its time dependence is given.

Magnetostatic field in a thin plate with a stripe-domain structure

Magnetostatic fields inside and outside of a plate with a stripe-domain structure have been calculated based on the formulas derived depending on the domain and domain-wall parameters and the plate thickness. In a plate with equal-size domains, the induction B z perpendicular to the plate surface nearly repeats the magnetization (without extremes) in thick samples, while in a thin plate, the maximum B z values correspond to domain-wall edges. It has been shown that the maximum value of the field component H x perpendicular to the domain-wall plane is, on the order of magnitude, close to the logarithm of the ratio of the wall thickness to the period of the domain structure; for thin domain walls, it can exceed the saturation magnetization by several times.

Theory of current-driven domain wall dynamics

The motion of a planar domain wall in a nanoscale ferromagnetic wire under electric current is studied, based on a microscopic description. In the adiabatic case, the domain wall is driven by spin torque (spin transfer), and there is an intrinsic pinning arising from hard-axis anisotropy energy. Effects of extrinsic pinning and spin relaxation (β-term) on the threshold current are discussed.

Influence of lateral domains and interface domain walls on exchange-bias phenomena inGbFe∕TdFebilayers

The effect of lateral magnetic domains on exchange-bias phenomena in a soft/hard Gd 40 Fe 60 100 nm / Tb 12 Fe 88 50 nm bilayer with antiferromagnetic interface exchange coupling is investigated. At low temperature , domains in the hard TbFe layer are found to behave independently of each other and to give rise to their own exchange-bias fields. Double hysteresis loops are observed when the sample is cooled with domains present in both the hard TbFe layer and the soft GdFe layer, whereas single hysteresis loops are observed when domains are only present in the hard layer. These features are understood by taking into account the presence of both lateral domains and planar interface domain walls in this strongly coupled system.

Field-dependent anisotropic magnetoresistance and magnetization measurements of NiFe/FeMn exchange-biased bilayers

The exchange-bias effect was investigated through the analyses of the magnetic hysteresis loops and anisotropic magnetoresistance measurements of NiFe/FeMn bilayers. The angular variations of the exchange-bias field and coercivity were fitted in the framework of a domain-wall formation model which assumes formation of a planar domain wall at the antiferromagnetic side of the interface. The anisotropy parameters of both layers were extracted from the fits and were also used to obtain the orientation of the NiFe magnetization for different magnetic field in-plane directions. The angular dependence of the anisotropic magnetoresistance was then calculated and a comparison with the experimental measurements was made. The agreement between these curves was good for magnetic field much higher than the exchange-bias field and only reasonable for magnetic field of the order of or lower than the exchange-bias field.

Deaging in Gd2(MoO4)3 by cyclic motion of a single planar domain wall

The motion of a single planar 180° domain wall was studied in single-crystalline gadolinium molybdate, Gd2(MoO4)3. The switching current and the instantaneous wall positions were recorded using polarized light in an optical microscope and subsequent image processing. A pronounced deaging (wake-up) effect is observed represented by an increase of domain-wall shift during cyclic switching at constant voltage amplitude. The experimental data are compared to computer simulations taking into account the kinetic imprint effect under ac cycling. The latter is the change of the spatial distribution of the internal bias field during cycling. It is shown that deaging (wake-up) arises for aged (screened) initial states. After long enough cycling, the spatial distribution of the internal bias field becomes steady state and the wall motion becomes reproducible in all its details. The final distribution of the internal bias field does not depend on the initial state of the sample. The activation energies for deaging and aging are equal within the experimental uncertainty and thus very likely stem from the same micromechanism.

Magnetization-induced second-harmonic generation of light by exchange-coupled magnetic layers

A longitudinal magneto-optical Kerr effect and magnetization-induced second-harmonic generation (MSHG) of light (at 2omega) have been measured in a SiO2/Fe96Si4/Dy30Fe58Co12/glass exchange-coupled magnetic bilayer system with competitive anisotropies. Theoretical MSHG predictions in this structure that give rise to an effect proportional to magnetization components and that are allowed by an electric dipole mechanism are reported and discussed. The magnitude of the MSHG effect depends on the electric field of the incoming radiation at each interface and on the corresponding incoming (at omega) and outgoing (at 2omega) Fresnel coefficients. It is demonstrated that transverse pp MSHG selectively probes the magnetization of the first SiO2/Fe96Si4 interface, while transverse sp and longitudinal ps MSHG is sensitive, but less selectively, to the Fe96Si4/Dy30Fe58Co12 interface that supports a planar magnetic domain wall. (p and s are the usual parallel and perpendicular polarizations to the plane of incidence.) The contribution to MSHG by gradient magnetization terms is negligible.

Creation of an antiferromagnetic exchange spring.

We present evidence for the creation of an exchange spring in an antiferromagnet due to exchange coupling to a ferromagnet. X-ray magnetic linear dichroism spectroscopy on single crystal Co/NiO(001) shows that a partial domain wall is wound up at the surface of the antiferromagnet when the adjacent ferromagnet is rotated by a magnetic field. We determine the interface exchange stiffness and the antiferromagnetic domain wall energy from the field dependence of the direction of the antiferromagnetic axis, the antiferromagnetic pendant to a ferromagnetic hysteresis loop. The existence of a planar antiferromagnetic domain wall, proven by our measurement, is a key assumption of most exchange bias models.

The dynamics of the sandwich domain structure in 3%Si–Fe sheets

Two types of the domain walls motion equations have been derived in which a step-like movement character and polarization of the domain walls parallel to the magnetic sheet plane and forming a sandwich domain structure were take into account. The deduced equations permit to calculate the domain walls coordinates x ̄ (τ) in this structure and the damping coefficient β( x ̄ ) or the demagnetizing field H d ( x ̄ ) in each domain wall plane during one cycle of the dynamic magnetization reversal accompanied by the Matteucci emf appearance. The steps shape of the moving domain walls is non-essential for these equations. With the help of the derived equations it has been discovered that the interaction of the 3%Si–Fe two sheets by means of the transverse magnetic stray fields leads to formation of the sandwich domain structure in each sheet during dynamic (200 Hz) magnetization reversal. The appearance, the movement direction, the velocity and annihilation of the magnetization reversal fronts in each sheet are determined by local demagnetizing fields and by the magnetic fields of eddy currents. The first front appears in each sheet at the beginning of each semiperiod of the magnetization reversal close to the contact surface of sheets. In Δτ≈0.8 ms on an opposite surface of each sheet the second magnetization reversal front appears and it moves toward the first one. Before the collision of the fronts close to the sheet middle the first front changes the movement direction and both fronts move to the contact surface of the sheets. The simultaneous one way movement of the fronts is accompanied by the decrease of their mutual distance.

Onset of exchange bias in ultrathin antiferromagnetic layers

Current theoretical explanations of exchange biasing are based upon magnetic domains in the antiferromagnetic layer being responsible for the phenomenon. Both the ideas of planar and perpendicular domain walls have been developed in explaining the various observed effects. Here the exchange bias (H e x ) has been investigated as a function of the antiferromagnetic (AF) layer thickness (t A F ) in IrMn/Co and FeMn/Co exchange biased systems. The results indicate that the onset of biasing occurs for t A F which appears to be far too low (∼ 10 A) to accommodate planar domain walls (∼200 A) within the AF layer. From these results it is inferred that planar domain walls cannot therefore be responsible for biasing, and that theoretical calculations involving perpendicular domain walls in the antiferromagnetic layers appear to be the more plausible explanation.

The Dynamics of Domain Walls Determined from Acoustic Emission Measurements

The field-induced jump-like dynamics of a single planar domain wall in single crystalline uniaxial ferroelectric-ferroelastic Gd 2 (MoO 4 ) 3 and needle domains in the perovskite BaTiO 3 are compared. Acoustic emission as well as ferroelectric Barkhausen pulse measurements were performed in order to investigate time coincidences with optically observed jumps. In both crystals significant amounts of acoustic emissions occur. The coincidences of both event types in Gd 2 (MoO 4 ) 3 are determined by the particular character of extended defects in the crystal and the relative orientation of the acoustic sensor. Hardly any Barkhausen pulses but huge amounts of acoustic pulses are observed for the annihilation of needle domains. The underlying microscopic mechanisms are discussed.

Interaction of light waves with an isolated domain wall in a ferrodielectric

The specific features of the reflection and transmission of light waves through a planar domain wall in a ferrodielectric are investigated with due regard for the linear and quadratic magneto-optical coupling. The polarization and intensity-related characteristics of the reflected and transmitted light waves are determined at an arbitrary angle of incidence of a normal mode of the uniformly magnetized medium.

Switching current noise and relaxation of ferroelectric domains

We simulate field-induced nucleation and switching of domains in a three-dimensional model of ferroelectrics with quenched disorder and varying domain sizes. We study (1) bursts of the switching current at slow driving along the hysteresis loop (electrical Barkhausen noise) and (2) the polarization reversal when a strong electric field was applied and back-switching after the field was removed. We show how these processes are related to the underlying structure of domain walls, which in turn is controlled by the pinning at quenched local electric fields. When the depolarization fields of bound charges are properly screened we find that the fractal switching current noise may appear with two distinct universal behaviors. The critical depinning of plane domain walls determines the universality class in the case of weak random fields, whereas for large randomness the massive nucleation of domains in the bulk leads to different scaling properties. In both cases the scaling exponents decay logarithmically when the driving frequency is increased. The polarization reverses in the applied field as a power-law, while its relaxation in zero field is a stretch exponential function of time. The stretching exponent depends on the strength of pinning. The results may be applicable for uniaxial relaxor ferroelectrics, such as doped SBN:Ce.