Bloch-type Domain Walls Research Articles

Influence of Stress on the Chiral Polarization and Elastrocaloric Effect in BaTiO3 with 180° Domain Structure

The polarization and elastrocaloric effect of chiral barium titanate (BaTiO3) with an Ising–Bloch-type domain wall under stress was investigated using the Landau–Ginzburg–Devonshire (LGD) theory. It has been shown that tensile stresses increase the magnitude of the Ising polarization component in barium titanate, together with a decrease in the domain wall width. Compressive stresses cause a reduction in the Ising polarization component and an increase in the domain width. Under compressive stress, barium titanate exhibits a negative elastrocaloric effect and temperature changes with increasing stress, while BaTiO3 exhibits a positive elastrocaloric effect under tensile stress. Bloch polarization shows angle-dependent polarization under external force, but the temperature change from the elastrocaloric effect is smaller than that of Ising polarization under stress. This work contributes to the understanding of polarization evolution under tension in ferroelectrics with chiral structure.

Propagation dynamics of the Bloch-type domain wall on CoFeB nanostripes driven by a nanosecond magnetic pulse

Despite the abundance of research on the dynamics of magnetic domain walls (DW) on thin-film media, in-depth discussions regarding the behavior around the so-called Walker breakdown phenomenon are still scarce. In this work, propagation dynamics of the Bloch-type DW on CoFeB nanostripes with perpendicular anisotropy driven by a nanosecond magnetic pulse are investigated using micromagnetic simulation. It is found that on smaller nanostripes, the Walker breakdown corresponds with the oscillatory motion of the DW. On larger nanostripes, the formation of a Bloch-line with previously unreported behavior can be observed for magnetic pulses above HWB. Using a nanosecond field pulse instead of a continuous external field may allow for more direct control over the oscillatory DW motion and nucleation of the Bloch-line. A deeper understanding of the dynamics of the Bloch-type DW and its correlation to the applied nanosecond pulse may lead to better control of the DW for future spintronic devices.

Influence of an external electric field on the structure and properties of domain walls in a (111)-oriented ferrite-garnet film

In this study, the features of the manifestation of the flexomagnetoelectric effect in a (111)-oriented ferrite garnet film were investigated. It has been shown that, in such magnets, two types of domain walls with magnetization in domains with are possible: a Bloch-type domain wall and a wall with a quasi-Bloch structure. The evolution of each type of domain wall in an increasing electric field with is revealed, and the characteristic stages of transformation of their structures were determined. Critical fields for their rearrangement and the corresponding values of differential and integral polarizations were found. It has been established that the presence of cubic anisotropy in a (111)-oriented film weakens the degree of manifestation of the flexomagnetoelectric effect in it.

Magnetic bubbles with alternating chirality in domain walls

In magnetic multilayers with perpendicular anisotropy, the competition of short-range and long-range interactions gives rise to the stability of cylindrical magnetic domains, also known as magnetic bubbles. The presence of Dzyaloshinsky-Moriya interaction induced by asymmetric interfaces between magnetic and nonmagnetic layers may lead to the formation of cylindrical bubble domains with Neel-type domain walls across the whole thickness of the multilayer. Such domain walls produce no contrast in Lorentz TEM under the normal incidence of the electron beam to the film. The latter is often used as an argument for the presence of Dzyaloshinskii-Moriya interaction in the system. Here we show that in magnetic multilayers, the absence of the Lorentz TEM contrast might also have another origin. In particular, in the absence of interfacial Dzyaloshinskii-Moriya interaction and weak interlayer exchange coupling, the magnetic bubbles might have Bloch-type domain walls of alternate chirality in adjacent layers. Such domain walls also do not produce magnetic contrast in Lorentz TEM at normal incidence of the electron beam. We show that, in the absence of interlayer exchange coupling, the magnetic bubble domains with the domain walls of fixed and alternate chirality have nearly identical energies and can coexist in the same range of magnetic fields. Using the geodesic nudged elastic band method, we prove that these states are separated by finite energy barriers. Furthermore, we demonstrate that magnetic multilayers with only dipolar coupling, besides the magnetic bubbles with nontrivial topology in all layers, can accommodate solutions with trivial topology within the internal layers.

Phase shifter based on voltage-controlled magnetic domain walls

A controllable phase shifter is an essential part of spin-wave (SW) logic devices. Magnetic domain walls (DWs) as magnonic waveguides have been used to study SW propagation in ultrathin ferromagnetic films. In this study, we present a channel for SW propagation that relies on magnetic DWs as natural waveguides and realize phase manipulation by voltage-controlled magnetic anisotropy (VCMA) at a lower excitation frequency with micromagnetic simulations. The system model is a double-layer magnetic film structure, containing two oppositely magnetized domains and an upper layer (Co20Fe60B20) coupled with the lower layer ([Co/Pd]) through exchange interaction. The pinning structure can effectively maintain the state of the waveguide during later operation without an additional magnetic field. By numerical micromagnetic simulation, we can clearly see that the exchange-dominated isotropic magnetostatic forward volume like SWs are confined in the Bloch-type DW. The phase accumulation by a propagating SW depends on the accumulated phase wave vector (k) and the distance traveled. Therefore, SWs accumulate more phase through DW waveguides covered by electrodes with different lengths. The phase of the SW is shifted after the SW passes through the voltage region, compared with the waveguide where a voltage is unapplied. As a result, the established phase shifter shows a phase difference of 2π by applying a voltage (E = 1 V/nm), and the length of the applied electrode is about 644 nm.

Channeling of spin waves in antiferromagnetic domain walls

We theoretically calculated ultrafast propagations of spin waves channeled in antiferromagnetic Bloch-type domain walls based on a phenomenological theory developed by Hals et al. [Phys. Rev. Lett. 106, 107206 (2011)]. Our analytical derivation demonstrates that the dispersion relation of such channeled spin waves exhibits an extremely high group velocity, up to \ensuremath{\sim}18.7 km/s, without any forbidden gap. Further, such electromagnetic-wave-like dispersion relation allows for dispersionless and translational transmission of trains of low-frequency, long-wavelength digital signals in the channel. Our results offer guidelines for the development of ultrafast information signal processing in nanoscale magnonic circuits composed of antiferromagnetic domain walls.

General treatment of off-specular resonant soft x-ray magnetic scattering using the distorted-wave Born approximation: Numerical algorithm and experimental studies with hybrid chiral domain structures

We present a numerical algorithm for the simulation of resonant x-ray magnetic scattering in reflection geometry for an arbitrary three-dimensional magnetization distribution over a multilayer sample utilizing the distorted-wave Born approximation. Our approach takes the medium boundary matrix approach for specular reflection, and the Born approximation typically used for off-specular reflection, combines the two, and adds the contribution from transmission through the sample before and after a reflection event. The algorithm is then tested on experimental data from an ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$/Co/Pt multilayer sample with hybrid N\'eel/Bloch/N\'eel domain walls at incidence angles at and near multilayer Bragg angles, and photon energies near the Co ${L}_{3}$ absorption edge, achieving high levels of agreement with experimental data. Incorporating the transmission components into the algorithm was found to explain the dichroism observed in scattering from Bloch-type domain walls, and uncovered the likely importance of diffuse scattering in transmission from the polycrystalline grain walls along the optical path of the x rays in the sample---a theme which deserves further investigation.

Nanometre imaging of Fe3GeTe2 ferromagnetic domain walls

Fe3GeTe2 is a layered crystal which has recently been shown to maintain its itinerant ferromagnetic properties even when atomically thin. Here, differential phase contrast scanning transmission electron microscopy is used to investigate the domain structure in a Fe3GeTe2 cross-sectional lamella at temperatures ranging from 95 to 250 K and at nanometre spatial resolution. Below the experimentally determined Curie temperature (T C) of 191 K, stripe domains magnetised along 〈0001〉, bounded with 180◦ Bloch type domain walls, are observed, transitioning to mixed Bloch−Néel type where the cross-sectional thickness is reduced below 50 nm. When warming towards T C, these domains undergo slight restructuring towards uniform size, before abruptly fading at T C. Localised loss of ferromagnetic order is seen over time, hypothesised to be a frustration of ferromagnetic order from ambient oxidation and basal cracking, which could enable selective modification of the magnetic properties for device applications.

Meissner currents induced by topological magnetic textures in hybrid superconductor/ferromagnet structures

Topological spin configurations in proximity to a superconductor have recently attracted great interest due to the potential application of the former in spintronics and also as another platform for realizing non-trivial topological superconductors. Their application in these areas requires precise knowledge of the existing exchange fields and/or the stray-fields which are therefore essential for the study of these systems. Here, we determine the effective stray-field and the Meissner currents in a Superconductor/Ferromagnet/Superconductor (S/F/S) junction produced by various nonhomogenous magnetic textures in the F. The inhomogeneity arises either due to a periodic structure with flat domain walls (DW) or is caused by an isolated chiral magnetic skyrmion (Sk). We consider both Bloch- and N\'{e}el-type Sk and also analyze in detail the periodic structures of different types of DW's-- that is Bloch-type DW (BDW) and N\'{e}el-type DW (NDW) of finite width with in- and out-of-plane magnetization vector. The spatial dependence of the fields and Meissner currents are shown to be qualitatively different for the case of Bloch- and N\'{e}el-type magnetic textures. While the spatial distributions in the upper and lower S are identical for Bloch-type Sk and DW's they are asymmetric for the case of N\'{e}el-type magnetic textures. The depairing factor, which determines the critical temperature and which is related to vector potential of the stray-field, can have its maximum at the center of a magnetic domain but also, as we show, above the DW. For Sk's the maximum is located at a finite distance within the Sk radius. Based on this, we study the nucleation of superconductivity in the presence of DW's. Because of the asymmetry for N\'{e}el-type structures, the critical temperature in the upper and lower S is expected to be different. The obtained results can also be applied to S/F bilayers.

Chiral Magnonics: Reprogrammable Nanoscale Spin Wave Networks Based on Chiral Domain Walls.

SummarySpin waves offer promising perspectives as information carriers for future computational architectures beyond conventional complementary metal-oxide-semiconductor (CMOS) technology, owing to their benefits for device minimizations and low-ohmic losses. Although plenty of magnonic devices have been proposed previously, scalable nanoscale networks based on spin waves are still missing. Here, we demonstrate a reprogrammable two-dimensional spin wave network by combining the chiral exchange spin waves and chiral domain walls. The spin-wave network can be extended to two dimensions and offers unprecedented control of exchange spin waves. Each cell in the network can excite, transmit, and detect spin waves independently in the chiral domain wall, and spin-wave logics are also demonstrated. Our results open up perspectives for integrating spin waves into future logic and computing circuits and networks.

Giant caloric effects enhanced by the helix polarization at the 180° domain wall in tetragonal BaTiO3

The electrocaloric and elastocaloric properties at the 180° domain wall in the tetragonal BaTiO3 are studied using the Landau–Ginzburg–Devonshire model as a function of the domain wall rotation angle α. The Ising-Bloch character is predicted at the 180° domain wall in tetragonal BaTiO3 under the flexoelectric effect. The electric field-induced adiabatic temperature change (ΔTE) which is induced by the Bloch-type polarization component depends on α, and a giant positive ΔTE appears at α = (π + 12n)/24 where n is an integer. The asymmetry of ΔTE is found around the Bloch-type domain wall. The Bloch-type polarization component has a little contribution to the stress-induced adiabatic temperature change. This calculation indicates a contribution of helix polarization at the domain wall on the caloric effects (CEs) in the ferroelectric materials.

Динамика взаимодействия блоховских доменных границ в двумерной нелинейной сигма-модели

Динамика взаимодействия блоховских доменных границ в двумерной нелинейной сигма-модели

Observation of spin textures in La1−xSrxMnO3 (x = 0.175)

We have investigated topological spin textures in the ferromagnetic metallic phase of La0.825Sr0.175MnO3 with the centrosymmetric crystal structure by small-angle electron diffraction (SmAED) and low-temperature Lorentz transmission electron microscopy (TEM) experiments. In-situ Lorentz TEM and SmAED experiments revealed that type-I and type-II magnetic bubbles evolved from magnetic stripe domains with the Bloch-type domain wall by applying vertical magnetic field. Type-I magnetic bubbles with left-handed and right-handed spin helicity were randomly distributed and simultaneously type-II magnetic bubbles are formed locally. The important point about type-I and type-II magnetic bubbles is that their emergence depends strongly on whether perpendicular magnetic field is applied parallel to the magnetic easy axis along the [001] direction. Our experimental results suggested that the stabilization of magnetic bubbles should originate from the long-range dipole-dipole interactions, as opposed to the Dzyaloshinskii-Moriya interaction in helical magnets.

Interaction Between Spin Wave Packets and Domain Wall With Various Propagation Modes and Wall Structures

The interaction between the spin wave (SW) packet and the domain wall (DW) have been numerically studied for various spin wave modes and the DW structures. Micromagnetic simulations reveal that the Neel type DW causes practically similar phase shift Δφ (0.4π ~ 0.6π) for all of the three different SW modes, while the Δφ is considerably enhanced in the case of the interaction with the Bloch type DW. The inductive detection of the DW induced phase shift in the SW, emitted with a pulsed microwave current, is also demonstrated.

Unconventional Magnetic Domain Structure in the Ferromagnetic Phase of MnP Single Crystals

We have studied ferromagnetic (FM) structures in the FM phase of MnP single crystals by low-temperature Lorentz transmission electron microscopy and small-angle electron diffraction analysis. In Lorentz Fresnel micrographs, striped FM domain structures were observed at an external magnetic field less than 10 Oe in specimens with the a b -plane in their plane. From real- and reciprocal-space analyses, it was clearly identified that striped FM domains oriented to the c -axis appear with Bloch-type domain walls in the b -direction and order regularly along the a -axis with a constant separation less than 100 nm. Moreover, the magnetic chirality reverses in alternate FM domain walls. These specific spin configuration of striped FM domains will affect the magnetic phase transition from the FM phase to the proper screw spiral phase at low temperature or to the FAN phase in magnetic fields in MnP.

Nonlinear magneto-optical diffraction from periodic domain structures in magnetic films

The nonlinear optical diffraction in magnetic films with a laminar domain structure and Bloch-type domain walls is investigated for both s and p polarization of incident light. It is shown that the contribution of magnetic domains and domain walls to the nonlinear diffraction can be separated by a polarization analysis of the scattered light.

Coupling of YCo2 thin films in a macroscopic ferrimagnet

We study here the behavior of YCo 2 thin films when they are decoupled or when they are 3d-coupled in a macroscopic ferrimagnet (MF). The latter consists of YCo 2 /GdCo 2 /YCo 2 , the thickness of each layer (100 nm) being higher than the optical penetration depth. Such a study was done by means of the transverse magneto optic Kerr effect (TMOKE) hysteresis loops and their evolution upon applying a dc field perpendicularly to the easy axis of magnetization. We observe clear differences between magnetically decoupled layers and layers coupled in the MF. The latter case may be understood taken into account that the exchange interaction in the MF is controlled by the existence of a Bloch-type domain wall extending through the layered system.

Structure and properties of domain walls in a (111)-oriented plate of crystals with combined anisotropy

We theoretically study the physical properties of magnetic domain wall inhomogeneities in crystals possessing both natural cubic and induced uniaxial anisotropies (combined anisotropy). The structure and stability of Bloch type domain walls (DWs) has been investigated for plates with (111)-oriented surfaces in the anisotropy constant range in which bubbles exist. We have shown the possibility of hysteresis phenomena during reorientation the DWs relative to crystallographic axes. Dynamic characteristics of steady and oscillatory motion have been found to be functions of sample material parameters and their peculiarities are examined in the vicinity of spin-reorientation phase transition as well as in the vicinity of the DW reorientation line phase transition relative to crystallographic axes. The dynamic DW parameter values are shown to be affected by temperature and external stresses.

Micromagnetic model of an exchange-coupled NiFe-TbCo bilayer (abstract)

A micromagnetic model for NiFe-TbCo exchange-coupled bilayers which can quantitatively predict and explain the major macroscopic features observed in measured M-H characteristics is presented. Comparison of theoretical and experimental results shows conclusively that the strong interfacial exchange coupling in NiFe-TbCo is essentially indistinguishable from that of a perfect, homogeneous interface. Commonly invoked assumptions concerning the existence or origin of a substantially weakened exchange coupling at a highly imperfect interface are neither necessary, nor even consistant with experimental measurements. The mechanism of the unidirectional exchange anisotropy is the formation of Bloch-type domain walls in an ≂0.08-μm-thick TbCo sublayer of uniaxial, in-plane anisotropy adjacent to the NiFe interface. The manner in which the observable magnetic behavior of NiFe-TbCo bilayers depends on film thicknesses, TbCo anisotropy, interfacial exchange coupling strength, as well as the previously unconsidered large hysteretic effects due to the small net magnetization in ferrimagnetic TbCo, are discussed in detail. It is demonstrated, for a strongly coupled system such as NiFe-TbCo, that the often used single parameter ‘‘exchange field’’ description of a shifted NiFe M-H loop is inadequate. A quantitatively accurate description requires that one take into account the spatial variations in the micromagnetic magnetization distributions of both layers.

Two-Dimensional Bloch-Type Domain Walls in Ferromagnetic Films

The structure of a two-dimensional 180° Bloch-type domain wall in a ferromagnetic film has been generated directly from an iterative micromagnetic energy minimization. The resultant magnetization distribution (which varies through the thickness of the film as well as in the plane of the film perpendicular to the wall) is observed to be significantly different from previous one-dimensional models. The equilibrium wall structure is characterized by extensive flux closure internal to the film, very low pole densities on the film surfaces, asymmetry in the magnetization distribution perpendicular to the wall, and an approximately linear dependence of the over-all wall width on film thickness. Finally, it is found that the total wall energy in this two-dimensional model is less than one-half the comparable value predicted from the most accurate one-dimensional treatment for 1000 Å Permalloy films and less than one-third the corresponding one-dimensional value at 2000 Å.