Domain Wall Energy Density Research Articles

The Effect of Temperature and Film Thickness on Domain Wall Energy Density, Coercivity Force, and Magnetostriction of Galfenol Films

The Effect of Temperature and Film Thickness on Domain Wall Energy Density, Coercivity Force, and Magnetostriction of Galfenol Films

Effects of surface acoustic waves on reversal of magnetic domains in patterned films with perpendicular magnetic anisotropy

In this work, the magnetization reversal of patterned Pt/Co/Pt multilayers influenced by surface acoustic waves is investigated. For each patterned cell, the magnetization reversal involves formation of a reversal nucleus followed by rapid motion of a domain wall. The nucleation probability of the reversal nucleus increases with the power of the applied surface acoustic wave, which is explained by the magnetic droplet model, and fitting the experimental results with this model gives important parameters such as the domain-wall energy density and the reduction rate of local perpendicular anisotropy. The fitting results for different patterned cells are consistent with the experimental results, which validates this model for dealing with such issues.

Controlling magnetic skyrmion nucleation with Ga+ ion irradiation

In this paper, we show that magnetic skyrmion nucleation can be controlled using ${\mathrm{Ga}}^{+}$ ion irradiation, which manipulates the magnetic interface effects (in particular, the magnetic anisotropy and Dzyaloshinskii-Moriya interaction) that govern the stability and energy cost of skyrmions in thin-film systems. We systematically and quantitatively investigate what effect these changes have on the nucleation of magnetic skyrmions. Our results indicate that the energy cost of skyrmion nucleation can be reduced up to $26%$ in the studied dose range and that it scales approximately linearly with the square root of the domain wall energy density. Moreover, the total number of nucleated skyrmions in irradiated devices after nucleation was found to depend linearly on the ion dose and could be doubled compared to nonirradiated devices. These results show that ion irradiation cannot only be used to enable local nucleation of skyrmions but also allows for fine control of the threshold and efficiency of the nucleation process.

Magnetic Domain Structure of Galfenol at Elevated Temperatures

Galfenol (iron–gallium) has a great potential in MEMS applications owing to its high magnetostriction constant, low saturation field, and resilience to bending, compressive, and tensile loading. Here, we report on the expansion/shift of the topography and the expansion/shift of the magnetic domain structure of galfenol observed at high temperatures via atomic force microscopy (AFM) and magnetic force microscopy (MFM). The maze-like domain pattern and stripe-like domain pattern are observed in the perpendicular and parallel surfaces. The spike and reverse domains are observed in 3-D view via XEI imaging software. A MATLAB-based stereological method was used to obtain the domain width and domain wall energy density. An increase in domain width and decrease in domain wall energy density was identified when temperature increased from room temperature to 150 °C.

Local control of magnetic interface effects in chiral Ir|Co|Pt multilayers using Ga+ ion irradiation

Skyrmions are topologically protected chiral spin textures that have shown promise as data carriers in future spintronic applications. They can be stabilized by the interfacial Dzyaloshinskii-Moriya interaction (iDMI) in material systems with inversion asymmetry and spin-orbit coupling, such as Ir$|$Co$|$Pt multilayers. The ability to locally tune such interface interactions, and hence the skyrmion energy, could greatly enhance the nucleation and control of skyrmions in racetrack type devices. In this work, we investigate local tuning of the iDMI and perpendicular magnetic anisotropy (PMA) using focussed Ga$^{+}$ ion beam irradiation, in an Ir$|$Co$|$Pt multilayer system. We show that the magnitude of the interface contribution to both effects can be significantly reduced by the irradiation with Ga$^{+}$ ions. This leads to a reduction by a factor two of the domain wall energy density, while still preserving the N\'{e}el character of the domain walls. Hence, we postulate that Ga$^{+}$ ion irradiation is an effective way to locally reduce the energy barrier for skyrmion nucleation, providing a novel pathway for targeted skyrmion nucleation in racetrack type devices.

Skyrmion Stabilization at the Domain Morphology Transition in Ferromagnet/Heavy Metal Heterostructures with Low Exchange Stiffness

AbstractHerein, the experimental observation of micrometer‐scale magnetic skyrmions at room temperature in several Pt/Co‐based thin film heterostructures designed to possess low exchange stiffness, perpendicular magnetic anisotropy, and a modest interfacial Dzyaloshinskii–Moriya interaction (iDMI) is reported. It is found both experimentally and by micromagnetic and analytic modeling that a low exchange stiffness and modest iDMI eliminates the energetic penalty associated with forming domain walls in thin films. When the domain wall energy density approaches negative values, the remanent morphology transitions from a uniform state to labyrinthine stripes. A low exchange stiffness, indicated by a sub‐400 K Curie temperature, is achieved in Pt/Co, Pt/Co/Ni, and Pt/Co/Ni/Re structures by reducing the Co thickness to the ultrathin limit (<0.3 nm). Similar effects occur in thicker Pt/Co/NixCu1−x structures when the Ni layer is alloyed with Cu. At this transition in domain morphology, skyrmion phases are stabilized by small (<1 mT), perpendicular magnetic fields, and skyrmion motion in response to spin–orbit torque is observed. While the temperature and thickness‐induced morphological phase transitions observed are similar to the well‐studied spin reorientation transition that occurs in the ultrathin limit, the underlying energy balances are substantially modified by the presence of an iDMI.

Scaling of Dzyaloshinskii-Moriya interaction with magnetization in Pt/Co(Fe)B/Ir multilayers

Magnetic multilayers with perpendicular anisotropy and an interfacial Dzyaloshinskii-Moriya interaction (DMI) contain chiral domain walls and skyrmions that are promising for applications. Here, we measure the temperature dependence of the DMI in Pt/CoFeB/Ir and Pt/CoB/Ir multilayers by means of static domain imaging. First, the temperature dependences of saturation magnetization $({M}_{\mathrm{S}})$, exchange stiffness $(A)$, and intrinsic perpendicular anisotropy $({K}_{\mathrm{u}})$ are determined. Then the demagnetized domain pattern in each multilayer is imaged by wide-field Kerr microscopy in the temperature range 9--290 K, and the characteristic domain period at each temperature is determined. We calculate the DMI constant $D$ from an analytical expression for the domain wall energy density that treats the multilayer as a uniform medium. Scaling laws for ${K}_{\mathrm{u}}$ and $D$ with the magnetization are established from the experiments. While the scaling of ${K}_{\mathrm{u}}$ is consistent with Callen-Callen theory, we find that the scaling of $D$ is like that of $A$ predicted theoretically $(\ensuremath{\sim}1.8)$.

Ultra-thin interfacial domain wall less than 1 nm based on TbxCo100−x/Cu/[Co/Pt]2 heterostructures for multi-level magnetic pillar memory

We propose a new pillar type of multi-level memory with TbxCo100−x/Cu/[Co/Pt]2 heterostructures to achieve high storage density and controllable domain wall position in-memory applications. The structure consists of amorphous ferrimagnetic Tb–Co alloy films and ferromagnetic Co/Pt multilayers separated by less than one monolayer of Cu. Here, we observe that the interfacial domain wall energy density can be controlled by changing the interlayer thickness of Cu and Tb–Co composition. We also observe two competing mechanisms, one leading to an increase and the other to a decrease, corresponding to the effect of Tb content on saturation magnetization and coercivity of heterostructures. Theoretical and experimental results show that by tuning the Tb–Co composition, we were able to decrease domain wall (DW) width and precisely control the DW position of the multilayer structure. The interfacial domain wall width is significantly decreased to less than 1 nm compared to other reports. Moreover, controlling the DW position and width offers a novel multi-level magnetic memory with high performance compared to conventional memory applications.

Influence of thermal annealing on the morphology and magnetic domain structure of Co thin films

Centimeter scale cobalt films with various thicknesses (8 nm ∼ 100 nm) were deposited by electron beam evaporation (EBE) and then annealed in a gas mixture of Ar and H2 at temperatures ranging from 200 °C to 500 °C. Advanced characterization techniques (e.g., XRD, SEM, AFM and MFM) were employed to investigate the influence of annealing on the morphology, crystal structures and magnetic domain structures of Co thin films. The results of SEM and AFM suggest that there is no obvious change in the morphology of Co film before and after annealing especially for thicker films and the root-mean-square roughness of Co film surface is slightly reduced after annealing. The influence of thermal annealing on the magnetic domain structure of EBE Co thin films was investigated by magnetic force microscopy (MFM) for the first time. It is found that even if there is no clear domain structure in the as-deposited films, it is possible to obtain periodic stripe domains with perpendicular magnetic anisotropy (PMA) by thermal annealing owing to the development of HCP Co phase, which was confirmed by XRD analysis. The correlations between the film morphology, thickness and magnetic domain structure are discussed qualitatively. Based on the periodic stripe magnetic domains, the domain-wall energy density of annealed cobalt films is calculated and this study found that the annealing has almost no effect on the energy density of the domain-wall. This work provides an effective way to obtain the perpendicular magnetic anisotropy (PMA) for practical applications.

Quantitative analysis of pinning-hardened intrinsic coercivity of Sm(CoFeCuZr)z (z = 7.0–7.8) high-temperature permanent magnets

SmCo-based permanent magnets possessing high Curie temperature and outstanding magnetocrystalline anisotropy are of great scientific and technological value on high temperature applications. It is widely accepted the coercivity mechanism as well as its temperature dependence is closely related to the microstructure and microchemistry. However, direct domain wall pinning observation with Lorentz microscopy is extremely difficult to explore the strength of domain wall pinning under high temperature and strong magnetic field. The quantitatively understanding of coercivity mechanism such as micromagnetic simulations cannot be carried out without the intrinsic magnetism of 1:5H and 2:17R inside the cellular microstructure of SmCo sintered magnets. Up to nowadays, there are no methods to directly measure the intrinsic magnetism of nanometer scale 1:5H and 2:17R, which retards the exploring of coercivity mechanism especially at high temperature. Herein, we prepared Sm(CoCuFeZr)z high-temperature permanent magnets with the ratio z values ranging from 7.0 to 7.8 and measured the microchemistry of 1:5H and 2:17R phases with transmission electron microscopy. Then single-phase solid solution samples with the same composition as 1:5H and 2:17R phases were prepared and the high temperature magnetic properties are measured directly. The coercivity mechanism can be well explained based on the difference of domain wall energy density qualitatively, including the abnormal temperature dependence of coercivity. More importantly, the quantitatively calculated coercivity according to the pinning-hardened coercivity theory with the obtained intrinsic parameters were found to agree well with the experiment results. Our work on the intrinsic magnetism of 1:5H and 2:17R phases at varying temperatures may offer important guidance for compositions design of the magnets with higher performance.

Surface microstructural design to improve mechanical and giant magneto-impedance properties of melt-extracted CoFe-based amorphous wires

The influence of surface microstructural regulation mechanisms on the mechanical and giant magneto-impedance (GMI) properties of as-cast melt-extracted CoFe-based wires has been systematically researched based on morphology, phase distribution and domain structure parameters. A series of statistical models were applied to analyze the mechanical properties and followed by mapping the curve of cumulative failure rate for wire application. It was found that the average and highest fracture strengths, average tensile strain increased with Cu substitution and reached peaks of ~3725 MPa, ~4250 MPa and ~2.7%, respectively. Verified structure-simulation experiments revealed that surface Rayleigh waves effectively split the main crack and the diffusely distributed nanocrystalline in surface area acted as a pinning point to impede the crack growth, enhancing the mechanical properties. The GMI ratio displayed similar variations and attained a maximum value of 700 ± 5% as well as the resistance and reactance ratios improved to ~687% and ~2206%, respectively. The enhanced relative dielectric permeability μs resulting from the increased domain wall energy density and the decreased surface domain width. The unique synchronous enhancement of CoFe-based wires satisfies the demand for emerging magnetoelectric sensor applications, e.g. flexible and wearable sensors, equipment self-monitoring sensors, and array robotic skin sensors under harsh working environments.

Exploring the high-performance (1-x)BaTiO3-xCaZrO3 piezoceramics with multiphase coexistence (R-O-T) from internal lattice distortion and domain features

Although the multiphase coexistence has made great achievements in improving the piezoelectric properties of barium titanate-based (BT) ceramics, the problems such as internal lattice distortion and external physical mechanism at the phase boundary still remain. Here, we have studied the phase structure, atomic parameters and domain structure of (1-x)BaTiO3-xCaZrO3 (abbreviated as BT-xCZ) ceramics. By regulating the phase transition temperatures, the rhombohedral-orthorhombic-tetragonal (R-O-T) multiphase coexistence (x = 0.06) is realized at room temperature. Notably, high piezoelectric constant of d33 ∼ 445 ± 20 pC/N and large electromechanical coupling factor of kp = 55% are obtained at x = 0.06. With the doping of CaZrO3 (CZ), the lattice of ceramics is distorted, thereby increasing the ferroelectricity and piezoelectricity. Importantly, the domain structure of BT-xCZ ceramics observed by the acid etching technology further proves that the high piezoelectricity is attributed to the multiphase coexistence and reduction of the domain wall energy density.

Quasi-one-dimensional ferroelectricity and piezoelectricity in WOX4 halogens

A series of oxytetrahalides WO$X_4$ ($X$: a halogen element) that form quasi-one-dimensional chains is investigated using first-principles calculations. The crystal structures, electronic structures, as well as ferroelectric and piezoelectric properties are discussed in detail. Group theory analysis shows that the ferroelectricity in this family originates from an unstable polar phonon mode $\Gamma_1^-$ induced by the W's $d^0$ orbital configuration. Their polarization magnitudes are found to be comparable to widely used ferroelectric perovskites. Because of its quasi-one-dimensional characteristics, the inter-chain domain wall energy density is low, leading to loosely-coupled ferroelectric chains. This is potentially beneficial for high density ferroelectric memories: we estimate that the upper-limit of memory density in these compounds could reach hundreds of terabytes per square inch.

Determination of perpendicular magnetic anisotropy based on the magnetic droplet nucleation

We propose an alternative method of determining the magnetic anisotropy field μ0HK in ferro-/ferrimagnets. On the basis of the droplet nucleation model, there exists linearity between domain-wall (DW) energy density and in-plane magnetic field. We find that the slope is simply represented by μ0HK and Dzyaloshinskii–Moriya interaction (DMI). By measuring the in-plane magnetic field dependence of the coercivity field, closely corresponding to the DW energy density, a robust value for μ0HK can be quantified. This robust value can be used to determine μ0HK over a wide range of values, overcoming the limitations caused by the small strength of the external magnetic field typically used in experiments.

Magnetic force microscopy studies in bulk polycrystalline iron

The paper presents magnetic force microscopy (MFM) studies on the effect of crystallographic orientation and external magnetic field on magnetic microstructure in a bulk polycrystalline iron specimen. The magneto crystalline anisotropic effect on the domain structure is characterized with the support of electron backscatter diffraction study. The distinct variations in magnetic domain structure are observed based on the crystallographic orientation of the grain surface normal with respect to the cube axis i.e. the easy axis of magnetization. Further, the local magnetization behavior is studied in-situ by MFM in presence of external magnetic field in the range of −2000 to 2000Oe. Various micro-magnetization phenomena such as reversible and irreversible domain wall movements, expansion and contraction of domains, Barkhausen jump, bowing of a pinned domain wall and nucleation of a spike domain are visualized. The respective changes in the magnetic microstructure are compared with the bulk magnetization obtained using vibrating sample magnetometer. Bowing of a domain wall, pinned at two points, upon application of magnetic field is used to estimate the domain wall energy density. The MFM studies in presence of external field applied in two perpendicular directions are used to reveal the influence of the crystalline anisotropy on the local micro-magnetization.

Inflation expels runaways

We argue that moduli stabilization generically restricts the evolution following transitions between weakly coupled de Sitter vacua and can induce a strong selection bias towards inflationary cosmologies. The energy density of domain walls between vacua typically destabilizes Kahler moduli and triggers a runaway towards large volume. This decompactification phase can collapse the new de Sitter region unless a minimum amount of inflation occurs after the transition. A stable vacuum transition is guaranteed only if the inflationary expansion generates overlapping past light cones for all observable modes originating from the reheating surface, which leads to an approximately flat and isotropic universe. High scale inflation is vastly favored. Our results point towards a framework for studying parameter fine-tuning and inflationary initial conditions in flux compactifications.

Intrinsic asymmetry in chiral domain walls due to the Dzyaloshinskii–Moriya interaction

We present an analytical description of the energy density of chiral magnetic domain walls (DWs) that considers variations in DW width. Surprisingly, under the application of a longitudinal in-plane magnetic field, the DW width varies abnormally, resulting in an asymmetric variation of the DW energy density. Such asymmetry is attributable to the nonlinear contribution to the effective magnetic field from the Dzyaloshinskii–Moriya interaction. The formation of such asymmetric DWs is confirmed by a micromagnetic simulation. The present prediction proposes a possible origin of the experimental asymmetry related to chiral damping.

Topological properties of a Valence-Bond-Solid

We present a projector quantum Monte Carlo study of the topological properties of the valence-bond-solid ground state in the J-Q3 spin model on the square lattice. The winding number is a topological number counting the number of domain walls in the system and is a good quantum number in the thermodynamic limit. We study the finite-size behavior and obtain the domain wall energy density for a topological nontrivial valence-bond-solid state.

Asymmetric magnetic bubble expansion under in-plane field in Pt/Co/Pt: Effect of interface engineering

We analyze the impact of growth conditions on the asymmetric magnetic bubble expansion under an in-plane field in ultrathin Pt/Co/Pt films. Specifically, using sputter deposition, we vary the Ar pressure during the growth of the top Pt layer. This induces a large change in the interfacial structure as evidenced by a factor three change in the effective perpendicular magnetic anisotropy. Strikingly, a discrepancy between the current theory for domain-wall propagation based on a simple domain-wall energy density and our experimental results is found. This calls for further theoretical development of domain-wall creep under in-plane fields and varying structural asymmetry.

Magnetic domain wall energy in Ni/Co superlattices

The magnetic domain wall energy density σW of a Ni/Co superlattice possessing perpendicular magnetic anisotropy was determined using the magnetic domain theory derived by Kooy and Enz (1960). To determine σW, we obtained the saturation magnetization, magnetic domain period, and perpendicular magnetic anisotropy energy by individual measurements. Using the magnetic domain period and the ferromagnetic layer thickness, we first determined the dipolar length. The estimated dipolar length was about 15–25nm, which is in good agreement with the change in the magnetization curve with the ferromagnetic layer thickness. By using the dipolar length and saturation magnetization, the σW was calculated to be 4–7erg/cm2.