Consistency between domain wall oscillation modes and spin wave modes in nanostrips

Investigations on domain wall(DW) and spin wave(SW) modes in a series of nanostrips with different widths and thicknesses have been carried out using micromagnetic simulation. The simulation results show that the frequencies of SW modes and the corresponding DW modes are consistent with each other if they have the same node number along the width direction. This consistency is more pronounced in wide and thin nanostrips, favoring the DW motion driven by SWs.Further analysis of the moving behavior of a DW driven by SWs is also carried out. The average DW speed can reach a larger value of ~ 140 m/s under two different SW sources. We argue that this study is very meaningful for the potential application of DW motion driven by SWs.

Ferroelectric domain wall memory

Ferroelectric domain walls appear as sub-nanometer-thick topological interfaces separating two adjacent domains in different orientations,and can be repetitively created,erased,and moved during programming into different logic states for the nonvolatile memory under an applied electric field,providing a new paradigm for highly miniaturized low-energy electronic devices.Under some specific conditions,the charged domain walls are conducting,differing from their insulating bulk domains.In the past decade,the emergence of atomic-layer scaling solid-state electronic devices is such demonstration,resulting in the rapid rise of domain wall nano-electronics.This review aims to the latest development of ferroelectric domain-wall memories with the presence of the challenges and opportunities and the roadmap to their future commercialization.

Electronic states of domain walls in commensurate charge density wave ground state and mosaic phase in 1T-TaS_(2)

Domain walls(DWs)in the charge-density-wave(CDW)Mott insulator 1T-TaS_(2)have unique localized states,which play an important role in exploring the electronic properties of the material.However,the electronic states in DWs in 1TTaS_(2)have not been clearly understood,mostly due to the complex structures,phases,and interlayer stacking orders in the DW areas.Here,we explored the electronic states of DWs in the large-area CDW phase and mosaic phase of 1T-TaS_(2)by scanning tunneling spectroscopy.Due to the different densities of DWs,the electronic states of DWs show distinct features in these phases.In the large area CDW phase,both the domain and the DWs(DW1,DW2,DW4)have zero conductance at the Fermi level;while in the mosaic phase,they can be metallic or insulating depending on their environments.In areas with a high density of DWs,some electronic states were observed both on the DWs and within the domains,indicating delocalized states over the whole region.Our work contributes to further understanding of the interplay between CDW and electron correlations in 1T-TaS_(2).

Multi-segmented nanowires for vortex magnetic domain wall racetrack memory

A vortex domain wall's(VW) magnetic racetrack memory's high performance depends on VW structural stability,high speed, low power consumption and high storage density. In this study, these critical parameters were investigated in magnetic multi-segmented nanowires using micromagnetic simulation. Thus, an offset magnetic nanowire with a junction at the center was proposed for this purpose. This junction was implemented by shifting one portion of the magnetic nanowire horizontally in the x-direction(l) and vertically(d) in the y-direction. The VW structure became stable by manipulating magnetic properties, such as magnetic saturation(M_(4)) and magnetic anisotropy energy(K_(u)). In this case, increasing the values of M_(4) ≥ 800 kA/m keeps the VW structure stable during its dynamics and pinning and depinning in offset nanowires,which contributes to maintenance of the storage memory's lifetime for a longer period. It was also found that the VW moved with a speed of 500 m/s, which is desirable for VW racetrack memory devices. Moreover, it was revealed that the VW velocity could be controlled by adjusting the offset area dimensions(l and d), which helps to drive the VW by using low current densities and reducing the thermal-magnetic spin fluctuations. Further, the depinning current density of the VW(J_(d)) over the offset area increases as d increases and l decreases. In addition, magnetic properties, such as the M_(4) and K_(u),can affect the depinning process of the VW through the offset area. For high storage density, magnetic nanowires(multisegmented) with four junctions were designed. In total, six states were found with high VW stability, which means three bits per cell. Herein, we observed that the depinning current density(J_(d)) for moving the VW from one state to another was highly influenced by the offset area geometry(l and d) and the material's magnetic properties, such as the M_(4) and K_(u).

Domain wall dynamics in magnetic nanotubes driven by an external magnetic field

We use the Landau-Lifshitz-Gilbert equation to investigate field-driven domain wall propagation in magnetic nan- otubes. We find that the distortion is maximum as the time becomes infinite and the exact rigid-body solutions are obtained analytically. We also find that the velocity increases with increasing the ratio of inner radius and outer radius. That is to say, we can accelerate domain wall motion not only by increasing the magnetic field, but also by reducing the thickness of the nanotubes.

Cu-doping induced ferromagnetic insulating behavior and domain wall pinning effects in LaMnO_3

A systematic study on the structural, magnetic, and electrical transport properties was performed for the LaMnlxCUxO3 system. A single phase of orthorhornbic perovskite structure was formed for x = 0.05-0.40. A striking paramagnetic-ferromagnetic transition and a considerable magnetoresistance effect were observed at the ferromagnetic ordering temperature Tc, but no insulator-metal transition induced by Cu-doping was observed. Below Tc, a visible unexpected drop was observed in the ac susceptibility and zero-field-cooled dc magnetization for the dilute doped samples with x≤0.10, which was proven to be associated with domain wall pinning effects by milling the bulk material into single domain particles. It is validated that there is no exchange interaction between Cu and Mn, and double exchange interactions between Mn^3＋ and Mn^4＋ are induced by Cu-doping in the anti-ferromagnetic LaMnO3 matrix, whereas the severe distortion and disorder caused by occupied-dopant prohibits charge carriers from hopping.

Dependence of domain wall structures on repetition n in[Pt(0.5 nm)/Co(0.4 nm)]_n/NiO(1.1 nm)/[Co(0.4 nm)/Pt(0.5 nm)]_n multilayers

The magnetic force microscopy and a sample vibrating magnetometer have been used to investigate the domain structure in two antiferromagnetically coupled Co/Pt multilayers.In the antiferromagnetic coupled[Pt（0.5 nm）/Co（0.4 nm）]n/NiO（1.1 nm）/[Co（0.4 nm）/Pt（0.5 nm）]n multilayers with perpendicular anisotropy,the antiferromagnetic interlayer coupling strength increases linearly with the repetition number n in Co/Pt multilayers.In demagnetized states,relatively shifted domain walls in the two Co/Pt multilayers are observed,with net ferromagnetic stripes formed between them for the repetition number n less than 5,and the stripe width decreases with the increase of n.The occurrence of these features can be attributed to the competition between the interlayer coupling and magnetostatic energies.

Magneto-elastic waves in the orthoferrite plates induced by solitary domain wall

Dynamics of domain walls(DWs) was studied in transparent thin orthoferrite samples with weak ferromagnetic ordering at subsonic and supersonic speeds.Direct measurements were made of flexural vibration amplitude in the samples studied,which were induced by a solitary DW with periodic actions of a driving magnetic field.The values of the amplitude reached 7 nm at a resonance.The formation of magnetoelastic solitons was observed and their dynamics was studied at a resonance between an elastic and a spin subsystems.Solitons lag behind the DW at the moment when the DW surpasses the sound barrier and are ahead of it at the subsonic motion.

Generation of high-energy dual-wavelength domain wall pulse with low repetition rate in an HNLF-based fiber ring laser

The generation of high-energy dual-wavelength domain wall pulse with a low repetition rate is demonstrated in a highly nonlinear fiber （HNLF）-based fiber ring laser. By introducing the intracavity birefringence-induced spectral filtering effect, the dual-wavelength lasing operation can be achieved. In order to enhance the cross coupling effect between the two lasing beams for domain wall pulse formation, a 215-m HNLF is incorporated into the laser cavity. Experimentally, it is found that the dual-wavelength domain wall pulse with a repetition rate of 77.67 kHz could be efficiently obtained through simply rotating the polarization controller （PC）. At a maximum pump power of 322 mW, the 655-nJ single pulse energy in cavity is obtained. The proposed configuration provides a simpler and more efficient way to generate high energy pulse with a low repetition rate.

Influence of spin–orbit coupling on spin-polarized electronic transport in magnetic semiconductor nanowires with nanosized sharp domain walls

Influence of spin–orbit coupling on spin-polarized electronic transport in magnetic semiconductor nanowires with nanosized sharp domain walls is investigated theoretically.It is shown that the Rashba spin–orbit coupling can enhance significantly the spin-flip scattering of charge carriers from a nanosized sharp domain wall whose extension is much smaller than the carrier＇s Fermi wavelength.When there are more than one domain wall presented in a magnetic semiconductor nanowire,not only the spin-flip scattering of charge carriers from the domain walls but the quantum interference of charge carriers in the intermediate domain regions between neighboring domain walls may play important roles on spin-polarized electronic transport,and in such cases the influences of the Rashba spin–orbit coupling will depend sensitively both on the domain walls＇ width and the domain walls＇ separation.

Drinfeld twist and the domain wall partition function of the eight-vertex model

With the help of the F-basis provided by the Drinfeld twist or factorising F-matrix for the spatial optical soliton model associated with the eight-vertex model, we calculate the partition function for the eight-vertex model on an N ×N square lattice with domain wall boundary condition.

Model of hybrid interfacial domain wall in ferromagnetic/antiferromagnetic bilayers

A general model of a hybrid inteffacial domain wall （HIDW） in ferromagnetic/antiferromagnetic exchange biased bilayers is proposed, where an inteffacial domain wall is allowed to extend into either the ferromagnetic or antiferromagnetic layer or across both. The proposition is based on our theoretical investigation on thickness and field dependences of ferromagnetic domain wall （FMDW） and antiferromagnetic domain wall （AFDW）, respectively. Good match of the simulation to the hysteresis loops of a series of NiFe/FeMn exchange-biased bilayers confirms the existence of the HIDW, where the AFDW part is found to preferentially occupy the entire antiferromagnetic layer while the FMDW shrinks with the increased magnetic field as expected. The observed asymmetry between the ascending and descending branches of the hysteresis loop is explained naturally as a consequence of different partition ratios between AFDW and FMDW.

Thick Domain Walls in Lyra Geometry with Bulk Viscosity

In this paper, we evaluate the general solutions for plane-symmetric thick domain walls in Lyra geometry in presence of bulk viscous fluid. Expressions for the energy density and pressure of domain walls are derived in both cases of uniform and time varying displacement field β. Some physical consequences of the models are also given. Finally, the geodesic equations and acceleration of the test particle are discussed.

Investigation of Domain Wall Velocity to External Fields for High-Quality Waveguide-Type Periodically Poled LiNbO_(3) Fabrication

The Ti-doped waveguide-type periodically poled LiNbO_(3)(PPLN)were fabricated and the dependence of domain wall velocity on an external field applied for domain inversion was investigated.The whole polarization reversal process was computer-controlled to regulate domain wall expansion at a feedback time shorter than 5μs.The coercive voltage and several values of excess voltage were applied on 500μm-thick wafers serially connected to a 1-MOhm external resistor which had an effect of the poling current reduction,i.e.the deceleration of domain wall expansion.The domain wall velocity is sensitive to the poling voltage,precisely speaking,to the excess voltage.The domain wall velocities were 28.70,16.02 and 5.75μm·s^(-1)under poling field of 23.5,22.0 and 21.0 kV·mm^(-1),respectively.Moreover,average duty cycle of PPLN is about 49.93%.

Spin waves and transverse domain walls driven by spin waves: Role of damping

Based on the uniform,helical and spiral domain-wall magnetic configurations,the excited spin waves are studied with emphasis on the role of damping.We find that the damping closes the gap of dispersion,and greatly influences the dispersion in the long-wave region for the spin waves of spiral wall and helical structure.For the uniform configuration,the Dzyaloshinskii-Moriya interaction determines the modification of dispersion by the damping.Furthermore,we investigate the interaction between spin waves and a moving spiral domain wall.In the presence of damping,the amplitude of spin wave can increase after running across the wall for small wave numbers.Driving by the spin waves,the wall propagates towards the spin-wave source with an increasing velocity.Unlike the case without damping,the relation between the wall velocity and the spin-wave frequency depends on the position of wall.

Asymmetric dynamic behaviors of magnetic domain wall in trapezoid-cross-section nanostrip

Field-driven magnetic domain wall propagation in ferromagnetic nanostrips with trapezoidal cross section has been systematically investigated by means of micromagnetic simulation. Asymmetric dynamic behaviors of domain wall, depending on the propagation direction, were observed under an external magnetic field. When the domain walls propagate in the opposite direction along the long axis of the nanostrip, the Walker breakdown fields as well as the average velocities are different. The asymmetric landscape of demagnetization energies, which arises from the trapezoidal geometry, is the main origin of the asymmetric propagation behavior. Furthermore, a trapezoid-cross-section nanostrip will become a nanotube if it is rolled artificially along its long axis, and thus a two-dimensional transverse domain wall will become a three-dimensional one. Interestingly, it is found that the asymmetric behaviors observed in two-dimensional nanostrips with trapezoidal cross section are similar with some dynamic properties occurring in three-dimensional nanotubes.

Chirped Domain Wall Arrays and Solitary Waves in a Generalized Nonlinear Schrodinger Equation

We study a generalized nonlinear Schrodinger equation, and obtain some exact solutions, including domain wall arrays （periodic solutions in terms of elliptic functions）, fronts, bright and dark solitons. In certain parameter domains, fundamental bright and dark solitons show directionality and hence are chiral, and the propagation direction is determined by the sign of the self-steepening parameter. Moreover, the chirping reversal phenomena of bright and dark solitons are found.

Anomalous Josephson current in quantum anomalous Hall insulator-based superconducting junctions with a domain wall structure

We theoretically study the Josephson effect in a quantum anomalous Hall insulator(QAHI)nanoribbon with a domain wall structure and covered by the superconductor.The anomalous Josephson current,the nonzero supercurrent at the zero superconducting phase difference,appears with the nonzero magnetization and the suitable azimuth angle of the domain wall.Dependent on the configuration of the domain wall,the anomalous current peaks in the Bloch type but disappears in the Néel type because the y-component of magnetization is necessary to break symmetry to arouse the anomalous current.The phase shift of the anomalous current is tunable by the magnetization,the azimuth angle,or the thickness of the domain wall.By introducing a bare QAHI region in the middle of the junction which is not covered by the superconductor,the anomalous Josephson effect is enhanced such that the phase shift can exceedπ.Thus,a continuous change between 0 andπjunctions is realized via regulating the configuration of the domain wall or the magnetization strength.As long as an s-wave superconductor is placed on the top of the QAHI with a domain wall structure,this proposal can be experimentally fabricated and useful for the phase battery or superconducting quantum bit.

RC-Circuit-Like Dynamic Characteristic of the Magnetic Domain Wall in Flat Ferromagnetic Nanowires

We investigate the dynamic behavior of the magnetic domain wall under perpendicular magnetic field pulses in fiat ferromagnetic nanowires using micromagnetic simulations. It is found that the perpendicular magnetic field pulse can trigger the magnetic domain wall motion, where all the field torques axe kept on the plane of nanowire strip. The speed of magnetic domain walls faster than several hundreds of meters per second is predicted without the Walker breakdown for the perpendicular magnetic driving field stronger than 200mT. Interestingly, the dynamic behavior of the moving magnetic domain wall driven by perpendicular magnetic field pulses is explained by charging- and discharging-like behaviors of an electrical RC-circuit model, where the charging and the discharging of magnetic charges on the nanowire planes are considered. The concept of the RC-model-like dynamic characteristic of the magnetic domain wall might be promising for the applications in spintronic functional devices based on the magnetic domain wall motion.

Current-Driven Domain Wall Motion: Velocity, Current and Phase Transition

The relation between domain wall motion and intensity of driven current is examined in a phenomenological theory where the kinetic energy is expanded as a series of polynomial function of current density just as the Landau phase transition theory. The dependency of velocity on current density is square root which degenerates into linear if the current is much higher than the critical value. The theory result is consistent with several previous experiments and also can explain the change of critical current in the presence of temperature. The role of temperature playing in the dynamics of domain wall motion is also discussed. The phase transition theory in terms of current density is employed to explain the critical behavior of domain wall motion.