Domain Wall Width Research Articles

Effective anisotropy due to the surface of magnetic nanoparticles

Analytical solution has been found for the second-order effective anisotropy of magnetic nanoparticles of a cubic shape due to the surface anisotropy (SA) of the N\'eel type. Similarly to the spherical particles, for the simple cubic lattice the grand-diagonal directions $\left(\pm1,\pm1,\pm1\right)$ are favored by the effective cubic anisotropy but the effect is twice as strong. Uniaxial core anisotropy and applied magnetic field cause screening of perturbations from the surface at the distance of the domain-wall width and reduce the effect of SA near the energy minima. However, screening disappears near the uniaxial energy barrier, and the uniform barrier state of larger particles may become unstable. For these effects the analytical solution is obtained as well, and the limits of the additive formula with the uniaxial and effective cubic anisotropies for the particle are established. Thermally-activated magnetization-switching rates have been computed by the pulse-noise technique for the stochastic Landau-Lifshitz equation for a system of spins.

Periodic boundary conditions for the simulation of 3D domain patterns in tetragonal ferroelectric material

Periodic domain patterns in tetragonal ferroelectrics are explored using a phase field model calibrated for barium titanate. In this context, we discuss the standard periodic boundary condition and introduce the concept of reverse periodic boundary conditions. Both concepts allow the assembly of cubic cells in accordance with mechanical and electrical conditions. However, application of the reverse periodic boundary condition is due to an increased size of the RVE and enforces more complex structures compared to the standard condition. This may be of particular interest for other multiphysics simulations. Additionally, we formulate mechanical side conditions with minimal spherical (hydrostatic) stress, or conditions with controlled average strain. It is found that in sufficiently small periodic cells, only a uniform single domain, or the simplest stripe domains constitute equilibrium states. However, once the periodic cells are of order 20 domain wall widths in size, more complex, 3-dimensional patterns emerge. Some of these patterns are known from prior studies, but we also identify other domain patterns with long, ribbon-like domains threaded through them and some vortex-like structures.

Magnetic domain structure in nanocrystalline nickel electrodeposits

The correlation between the crystal/defect and the magnetic domain structure of nanocrystalline (nc) bulk nickel produced by electrodeposition was investigated. By means of conventional and high resolution transmission electron microscopy, an average grain size of 23 nm was determined; nano-grains surrounded by low angle and high angle boundaries and the presence of nanotwins and stacking faults were observed. The nc nickel exhibited soft magnetic properties. Lorentz TEM (LTEM) in the Fresnel mode revealed magnetic domains of various sizes in the micrometer range extending over many grains, with a few random pinning sites, exhibiting a magnetic ripple structure and vortices. The LTEM was used to investigate the motion of domain walls driven by an external in situ magnetic field and to determine the domain wall width. Domain wall movement was observed at very small magnetic fields along the hysteresis loop. The correlation of the grain size and magnetic properties shows good agreement with the Herzer random anisotropy model for nanocrystalline materials, although the nc nickel studied here has no traces of an amorphous phase.

Direct imaging of antiferromagnetic domains in Mn2Au manipulated by high magnetic fields

In the field of antiferromagnetic (AFM) spintronics, information about the N\'eel vector, AFM domain sizes, and spin-flop fields is a prerequisite for device applications but is not available easily. We have investigated AFM domains and spin-flop induced changes of domain patterns in Mn2Au(001) epitaxial thin films by X-ray magnetic linear dichroism photoemission electron microscopy (XMLD-PEEM) using magnetic fields up to 70 T. As-prepared Mn$_2$Au films exhibit AFM domains with an average size $\sim$ 1 $\mu$m. Application of a 30T field, exceeding the spin-flop field, along a magnetocrystalline easy axis, dramatically increases the AFM domain size with N\'eel vectors perpendicular to the applied field direction. The width of N\'eel type domain walls (DW) is below the spatial resolution of the PEEM and therefore can only be estimated from an analysis of the DW profile to be smaller than 80 nm. Furthermore, using the values for the DW width and the spin-flop field, we evaluate an in-plane anisotropy constant ranging between 1 and 17 $\mu$eV/f.u.

Precise control of nanodomain size in LiNbO3

It is still a gap to precisely control nanodomian size in ferroelectric nanoscale periodically poled structures, which is needed in nonlinear optics and quantum optics. In particular, when the lateral nanodomain size is comparable to the domain wall width in ferroelectrics, the optical properties of the domain or the electrical properties of the domain wall strongly depend on the lateral domain size, which is worthy to be noticed in nonlinear optical applications or domain wall electronics. However, the present experimental results about the nanodomian fabrication in widely-used lithium niobate crystal can not meet the need for precisely controlling nanodomian size, because high duty cycle, imprecise period or instability in domain structures fabricated by these techniques can not be ignored. In this paper we report on our experiment to precisely control the lateral nanodomain size in 1D PPMgLN. The SEM image shows that the average period and the standard deviation are 267 nm and 6 nm, respectively. The average duty cycle and the standard deviation are 52% and 2%, respectively. The depth of inverted domain is about 1.2 μm and meantime, the domain structure is stable within 30-day observation period. At last, we discuss the possibility to fabricate ultrahigh-Q Photonic crystal (PhC) cavities based upon our poling method. To the best of our knowledge, it is the first time to precisely control the lateral nanodomain size and reduce it down to near domain wall width in 1D PPMgLN.

Enhancement of exchange bias in ferromagnetic/antiferromagnetic core-shell nanoparticles through ferromagnetic domain wall formation

The spin configuration in the ferromagnetic part during the magnetization reversal plays a crucial role in the exchange bias effect. Through Monte Carlo simulation, the exchange bias effect in ferromagnetic-antiferromagnetic core-shell nanoparticles is investigated. Magnetization reversals in the ferromagnetic core were controlled between the coherent rotation and the domain wall motion by modulating ferromagnetic domain wall width with parameters of uniaxial anisotropy constant and exchange coupling strength. An anomalous monotonic dependence of exchange bias on the uniaxial anisotropy constant is found in systems with small exchange coupling, showing an obvious violation of classic Meiklejohn-Bean model, while domain walls are found to form close to the interface and propagate in the ferromagnetic core with larger uniaxial anisotropy in both branches of the hysteresis. The asymmetric magnetization reversal with the formation of a spherical domain wall dramatically reduces the coercive field in the ascending branch, leading to the enhancement of the exchange bias. The results provide another degree of freedom to optimize the magnetic properties of magnetic nanoparticles for applications.

Domain Walls in the Early Universe and Generation of Matter and Antimatter Domains

We present a model where it is possible to generate cosmologically large domains of matter and antimatter separated by cosmologically large distances. Domain walls existed only in the early universe and later they disappeared. So the problem of domain walls in this model does not exist. These features are achieved through a postulated form of interaction between inflaton and a new scalar field. This scenario inspired a study of the related problem - evolution of the domain wall width in expanding universe. According to classical results there is a region of parameter space where the solutions with constant physical width exist. Numerical study of the problem demonstrates that initial configurations tend to these solutions with time. However, we have found that the wall width can grow exponentially outside of that parameter region.

Tailoring the structural and magnetic properties of masked CoPt thin films using ion implantation

The effects of ion implantations through a mask on the structural and magnetic properties of Co80Pt20 films were investigated. The mask was patterned using the self-assembly of diblock copolymers. For implantation, high (40 keV for 14N+ and 100 keV for 40Ar+) and low (7.5 keV for 14N+ and 4.5 keV for 40Ar+) energy 14N+ and 40Ar+ ions were used to modify the structural and magnetic properties of these films. X-ray diffraction and TRIM simulations were performed for understanding the structural changes due to ion implantations. These results revealed the intermixing of Co atoms in lower layers and lattice expansion in Co80Pt20 magnetic and Ru layers. A lateral straggling of Co caused an increase in the exchange coupling in the masked region. Depletion of Co atoms in Co80Pt20 layer caused a decrease in the anisotropy constant, which were further confirmed by the alternating gradient force magnetometer and magnetic force microscopy results. The magnetic force microscopy images showed an increase in domain width and domain wall width confirming the above-mentioned effects.

Remarkably enhanced current-driven 360\xb0 domain wall motion in nanostripe by tuning in-plane biaxial anisotropy

By micromagnetic simulations, we study the current-driven 360° domain wall (360DW) motion in ferromagnetic nanostripe with an in-plane biaxial anisotropy. We observe the critical annihilation current of 360° domain wall can be enhanced through such a type of anisotropy, the reason of which is the suppression of out-of-plane magnetic moments generated simultaneously with domain-wall motion. In details, We have found that the domain-wall width is only related to Ky − Kx, with Kx(y) the anisotropy constant in x(y) direction. Taking domain-wall width into consideration, a prior choice is to keep Ky ≈ Kx with large enough K. The mode of domain-wall motion has been investigated as well. The traveling-wave-motion region increases with K, while the average DW velocity is almost unchanged. Another noteworthy feature is that a Walker-breakdown-like motion exists before annihilation. In this region, though domain wall moves with an oscillating behavior, the average velocity does not reduce dramatically, but even rise again for a large K.

2D magnetic domain wall ratchet: The limit of submicrometric holes

The study of ratchet and crossed-ratchet effects in magnetic domain wall motion through 2D arrays of asymmetric holes is extended in this article to the submicrometric limit in hole size (small size regime). Therefore, the gap has been closed between the 2D ratchets in the range of tens-of-micrometers (large size regime) and the small size regime 1D ratchets based on nanowires. The combination of Kerr microscopy, X-ray PhotoEmission Electron Microscopy and micromagnetic simulations has allowed a full magnetic characterisation of both the domain wall (DW) propagation process over the whole array and the local DW morphology and pinning at the holes. It is found that the 2D small size limit is driven by the interplay between DW elasticity and half vortex propagation along hole edges: as hole size becomes comparable to DW width, flat DW propagation modes are favoured over kinked DW propagation due to an enhancement of DW stiffness, and pinned DW segments adopt asymmetric configurations related with Néel DW chirality. Nevertheless, both ratchet and crossed-ratchet effects have been experimentally found, and we propose a new ratchet/inverted-ratchet effect in the submicrometric range driven by magnetic fields and electrical currents respectively.

Selective multiple domain wall injection using spin-orbit torque

We demonstrate from both simulation and experiment a simple scheme for selective injection of multiple domain walls in a magnetic nanowire. The structure consists of a side-contact misaligned Hall bar made of ferromagnet/heavy metal bilayers. The combination of current-induced spin-orbit torque and an external magnetic field allows for the formation of localized domains with specific magnetization direction and length, thereby creating domain walls in predetermined locations. With the side contacts at two sides misaligned for a distance that is comparable to the contact width, it is possible to create densely packed domains by simply applying current between different pairs of side contacts. Simulation results show that the proposed scheme is scalable to a large number of domains with their dimension limited only by the domain wall width.

Comparison between collective coordinate models for domain wall motion in PMA nanostrips in the presence of the Dzyaloshinskii-Moriya interaction

Lagrangian-based collective coordinate models for magnetic domain wall (DW) motion rely on an ansatz for the DW profile and a Lagrangian approach to describe the DW motion in terms of a set of time-dependent collective coordinates: the DW position, the DW magnetization angle, the DW width and the DW tilting angle. Another approach was recently used to derive similar equations of motion by averaging the Landau-Lifshitz-Gilbert equation without any ansatz, and identifying the relevant collective coordinates afterwards. In this paper, we use an updated version of the semi-analytical equations to compare the Lagrangian-based collective coordinate models with micromagnetic simulations for field- and STT-driven (spin-transfer torque-driven) DW motion in Pt/CoFe/MgO and Pt/Co/AlOx nanostrips. Through this comparison, we assess the accuracy of the different models, and provide insight into the deviations of the models from simulations. It is found that the lack of terms related to DW asymmetry in the Lagrangian-based collective coordinate models significantly contributes to the discrepancy between the predictions of the most accurate Lagrangian-based model and the micromagnetic simulations in the field-driven case. This is in contrast to the STT-driven case where the DW remains symmetric.

Thermal stability and magnetization reversal mechanism in granular L1 FePt thin films

The relationship between coercivity HC and magneto-crystalline anisotropy field HK of L10 FePt granular alloy thin films is investigated as a function of film thickness in the range of 3.5–12.5 nm. While HK exhibits a decrease from 82 kOe to 71 kOe with increasing film thickness, HC displays a pronounced peak at a critical film thickness of tCR ≅ 7 nm. In order to explain the non-monotonic behavior of HC as a function of film thickness, the time dependence of HC at ambient temperature (TRT = 300 K) and the temperature dependence of the AC susceptibility in the range TRT – 800 K are measured as a function of film thickness and interpreted in the frame of the Stoner–Wohlfarth model of coherent rotations. It is demonstrated that the HC decrease with increasing film thickness above tCR is a consequence of a transition from coherent to an incoherent magnetization reversal mechanism in isolated grains. For a 7 nm thick film (tCR), the average grain size of ∼7.4 nm is comparable with the film thickness, suggesting that the domain-wall (DW) width δ ≅ tCR. Previous theoretical work has demonstrated a strong dependence of δ on the orientation of the DW with respect to the (001) planes of an L10 FePt lattice. By using the values of the micromagnetic exchange coupling A theoretically evaluated for parallel and vertical DW orientation with respect to the (001) planes, one obtains δ = 5.2 nm for parallel and δ = 6.7 nm for vertical DWs. The latter is closer to the experimental value of δ, suggesting that the nucleation of vertical DWs inside the grains (probably at grain boundaries) is the dominant mechanism responsible for the incoherent magnetization reversal evidenced in the investigated films.

Material Developments and Domain Wall-Based Nanosecond-Scale Switching Process in Perpendicularly Magnetized STT-MRAM Cells

We investigate the Gilbert damping and the magnetization switching of perpendicularly magnetized FeCoB-based free layers embedded in tunnel junctions adequate for spin-torque operated memories. We study the influence of the boron content in MgO / FeCoB /Ta systems alloys on their Gilbert damping after crystallization annealing. Increasing the boron content from 20 to 30\% increases the crystallization temperature, thereby postponing the onset of elemental diffusion within the free layer. This reduction of the interdiffusion of the Ta atoms helps maintaining the Gilbert damping at a low level of 0.009 without any penalty on the anisotropy and the magneto-transport properties up to the 400$^\circ$C annealing required in CMOS back-end of line processing. In addition, we show that dual MgO free layers of composition MgO/FeCoB/Ta/FeCoB/MgO have a substantially lower damping than their MgO/FeCoB/Ta counterparts, reaching damping parameters as low as 0.0039 for a 3 \r{A} thick Tantalum spacer. This confirms that the dominant channel of damping is the presence of Ta impurities within the FeCoB alloy. On optimized tunnel junctions, we then study the duration of the switching events induced by spin-transfer-torque. We focus on the sub-threshold thermally activated switching in optimal applied field conditions. From the electrical signatures of the switching, we infer that once the nucleation has occurred, the reversal proceeds by a domain wall sweeping though the device at a few 10 m/s. The smaller the device, the faster its switching. We present an analytical model to account for our findings. The domain wall velocity is predicted to scale linearly with the current for devices much larger than the wall width. The wall velocity depends on the Bloch domain wall width, such that the devices with the lowest exchange stiffness will be the ones that host the domain walls with the slowest mobilities.

Domain wall structure in metals: A new approach to an old problem

The Monte Carlo Simulated Annealing (MCSA) method is used for performing micromagnetic simulations, in particular the determination of the domain wall structure originated from the energy’s minimization of known micromagnetic hamiltonians. Beside the new theoretical approach, we also discuss the influence of different models for the exchange energy on the wall structure. It was found that the existence of long range exchange, like the RKKY interactions, can significantly affects the domain wall width when compared to the results obtained for the typical Heisenberg like exchange, whose range is restricted to the nearest neighbors. The calculations also indicate that especially for phases with high magnetocrystalline anisotropy the modeling should be performed at atomistic level or, in other words, the Bloch wall continuum model is not valid.

The effect of film thickness on Curie temperature distribution and magnetization reversal mechanism for granular L10 FePt films

Structural and magnetic properties of granular L10 FePt films are investigated as a function of film thickness in the range 3–11 nm. Scanning transmission electron microscopy observations indicate an increasing contribution of in-plane variants to the L10 FePt crystalline structure with increasing film thickness, which may explain the noticed degradation of the perpendicular anisotropy. The temperature dependence of coercivity suggests a progressive deviation of the magnetization reversal mechanism from coherent rotations with increasing film thickness above ~6 nm, corresponding to a domain-wall width. The anisotropy field distribution (〈HK〉, ) is estimated using Monte Carlo (MC) simulations of AC transverse susceptibility (ACTS). The average anisotropy field 〈HK〉 displays a similar temperature dependence to (MS)1.1, where MS is the film saturation magnetization, consistent with the theoretical predictions for L10 FePt. The Curie temperature distribution (〈TC〉, ) is evaluated using two methods: fast (ns) thermal erasure (ThEr) of remanent magnetization and MC modeling of the temperature dependence of AC susceptibility (ACS). The values evaluated by the two methods are in agreement, indicating an increase of in the range 2–6% with decreasing film thickness. The observed increase of 〈TC〉 in the range 620–680 K with increasing film thickness is explained using the finite-size scaling law with the critical exponent set to the theoretical value for L10 FePt. A general procedure to extract 〈TC〉 and using MC modeling of ACS, essentially independent of the magnetization reversal mechanism, is proposed. MC simulations of ACS confirm the deviation of the magnetization reversal mechanism from coherent rotations with increasing film thickness above ~6 nm.

Nanoscale thermoelectrical detection of magnetic domain wall propagation

In magnetic nanowires with perpendicular magnetic anisotropy (PMA) magnetic domain walls (DW) are narrow and can move rapidly driven by current induced torques. This enables important applications like high-density memories for which the precise detection of the position and motion of a propagating DW is of utmost interest. Today's DW detection tools are often limited in resolution, or acquisition speed, or can only be applied on specific materials. Here, we show that the anomalous Nernst effect provides a simple and powerful tool to precisely track the position and motion of a single DW propagating in a PMA nanowire. We detect field and current driven DW propagation in both metallic heterostructures and dilute magnetic semiconductors over a broad temperature range. The demonstrated spatial resolution below 20 nm is comparable to the DW width in typical metallic PMA systems.

Accurate model of the stripe domain phase of perpendicularly magnetized multilayers

We develop an accurate analytical model for the stray field energy of parallel stripe domains in multilayer films with perpendicular magnetic anisotropy, taking into account the effects of finite domain wall width and variable domain wall angle. By minimizing the total energy, we predict the domain width, the domain wall width, and the domain wall angle for given material parameters. We show how the domain wall width depends on the film thickness and the domain size. We explore the domain wall angle as a function of Dzyaloshinskii-Moriya interaction (DMI) and derive a threshold value ${D}_{\text{thr}}$ beyond which the system is in a N\'eel state. We find that thicker films require larger values of DMI to stabilize the N\'eel state. Finally, we test the effective medium theory, which allows treating multilayers as effective single layer films, and provide criteria for the applicability of the model in the presence of both surface and volume stray fields. Our results are supported by micromagnetic simulations, which indicate that the predictions are still precise even if the system is in a labyrinthine domain state. Using our model, otherwise inaccessible magnetic parameters, such as the DMI constant or the exchange constant, can now be obtained straightforwardly from static measurements of the stripe domain width in such films.

Magnetic order and noncollinear spin transport of domain walls based on zigzag graphene nanoribbons

Considering exotic spintronic properties, we propose by first-principles calculations that the domain walls (DWs) can form in zigzag graphene nanoribbon (ZGNR). The calculations based on the density functional theory and the non-equilibrium Green's function show that both abrupt and spiral DWs can exist in ZGNR depending on the initial magnetization conditions which can be implemented by the external magnetic field in experiments. Moreover, as the width of DW is small, a spiral DW is preferred. More importantly, the transmission at the Fermi level remains almost unchanged even when the relative angle (θ) between magnetization direction of two leads is up to 135°. Such a characteristic indicates that the slight change in the direction of magnetization of ZGNR-based spintronic devices will not alter the conductance. On the other hand, as the width of DW is large, the magnetization distribution of DW is of spiral nature at small θ, but it will change from the spiral-like to abrupt-like when θ increases.

Synergistic effect of carbonaceous reinforcements on microstructural, electrochemical, magnetic and tribological properties of electrophoretically deposited nickel

Abstract Mutilation of various industrial devices like rechargeable-batteries, magnetic-recording heads from corrosion and wear can be protected by carbon coatings on nickel surface. This article presents a comprehensive study of the corrosion, magnetic and tribological behaviour of electrophoretically deposited Ni with the carbonaceous reinforcements, i.e. diamond (Ni-D), carbon nanotubes (Ni-CNT) and graphene (Ni-Gr). Enhanced corrosion resistance of Ni-D coating (1920 Ω cm 2 ) than that of pure Ni (552 Ω cm 2 ) and permanent magnetism with higher magnetic coercivity (413.56 Oe), compared to that of Ni-CNT (132.91 Oe), Ni-Gr (124.63 Oe) and pure Ni (129.07 Oe) coatings, is linked through the interfacial anchoring via distribution of the reinforcements. Enhanced magnetic coercivity and remanence of Ni-D coating is attributed to a wider domain wall width (1.65 μm) which has enhanced magnetostatic energy per unit area near the surface (3.16 erg/cm 2 ) compared to that of CNT (2.25 erg/cm 2 ) and graphene (0.94 erg/cm 2 ). Moreover, compressive stress (−611 MPa) existing in Ni-D coating have shown to seal the micro-cavities restricting the onset of corrosion and wear. With an enhanced corrosion resistance, magnetism and frictional resistance (reduced coefficient-of-friction, scratch wear volume and high scratch hardness), Ni-D coatings can be effectually applicable for batteries, marine, automotive and aerospace industries.