Domain Wall Energy Density Research Articles

Influence of structural disorder on magnetic domain formation in perpendicular anisotropy thin films

Using a combination of resonant soft x-ray scattering, magnetometry, x-ray reflectivity and microscopy techniques we have investigated the magnetic properties and microstructure of a series of perpendicular anisotropy Co/Pt multilayer films with respect to structural disorder tuned by varying the sputtering deposition pressure. The observed magnetic changes in domain size, shape and correlation length originate from structural and chemical variations in the samples, such as chemical segregation and grain formation as well as roughness at the surface and interfaces, which are all impacted by the deposition pressure. For low pressure samples we find evidence of a random "gas-like" distribution of magnetic domains, while in the higher pressure samples the domain structure exhibits only short range "liquid-like" positional ordering. The structural and chemical disorder induced by the higher deposition pressure first leads to an increase in the number of magnetic point defects that limit free domain wall propagation. Then, as the sputtering pressure is further increased, the domain wall energy density is lowered due to the formation of local regions with reduced magnetic moment, and finally magnetically void regions appear that confine the magnetic domains and clusters, similar to segregated granular magnetic recording media.

Structural reasons for the perpendicular anisotropy in ferrospinel single-crystal films

Results of investigations into the perpendicular anisotropy of ferrospinel single crystal films are analyzed. The exchange interaction constants and the contribution of the exchange energy, energy of crystallographic anisotropy, and perpendicular anisotropy to the domain wall energy density are estimated. It is demonstrated that the parameters characterizing the perpendicular anisotropy depend on the chemical composition, degree of structure imperfection, and technological conditions of synthesis. The conclusion is drawn that the perpendicular anisotropy is caused by the magnetic constants of the material, macro- and microstresses, and anisotropy of the crystal shapes.

Intrinsic stress-induced adaptive ferroelectric domain rearrangement in the monoclinic Pb(Mg 1/3Nb 2/3)O 3–PbTiO 3 single crystal

Response of sub-microdomains in an adaptive ferroelectric Pb(Mg 1/3Nb 2/3)O 3–34%PbTiO 3 single crystal to the temperature-induced stress field was investigated by scanning electron acoustic microscopy and piezoresponse force microscopy. Formation of different types of domain configurations (wave-like, “W”-like and lattice-like) closely related to nanodomain cooperative response after the sample subjected to frozen treatment was presented. In the adaptive ferroelectric state lattice-like domain structures demonstrated more stable behavior compared to other types of domains (wave-like and “W”-like) due to their minimum domain wall energy density, and provided a type of effective structure to remove domain topological change under the stress field.

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.

Phase field simulations of ferroelectric nanoparticles with different long-range-electrostatic and -elastic interactions

Two-dimensional phase field simulations of ferroelectric nanoparticles with different long-range (LR)-electrostatic and -elastic interactions and different domain wall energy densities are conducted based on the time-dependent Ginzburg–Landau equation. The phase field simulations exhibit vortex patterns of polarizations, which have purely toroidal moments of polarizations and macroscopically negligible averaged polarizations, in nanoparticles without or with weak LR-elastic interactions when LR-electrostatic interactions are fully taken into account. However, a single-domain structure without any toroidal moment of polarizations is formed in small nanoparticles if LR-electrostatic interactions are completely ignored or LR-elastic interactions are fully taken into account. The polarization gradient energy or domain wall energy density plays also an important role in the formation of polarization structure. The vortex structure transits from a multivortex structure to a single-vortex structure as the domain wall energy density increases.

Magnetic domain configurations of epitaxial chromium dioxide (CrO2) nanostructures

Magnetic domain structures of submicrometric epitaxial CrO2 fabricated using selective-area growth technique were studied by magnetic force microscopy. In-plane, lamellar domain structure with fragmented walls aligned along the magnetic easy axis direction is observed, indicating the existence of a large magnetocrystalline anisotropy. A classical model for ferromagnetic materials with a uniaxial anisotropy was used to explain this domain configuration. Estimates of the domain wall energy density and exchange stiffness constant for CrO2 were obtained.

Plane symmetric bulk viscous domain wall in Lyra geometry

In this paper general solutions are found for domain walls in Lyra geometry in the plane symmetric spacetime metric given by Taub. Expressions for the energy density and pressure of domain walls are derived in both cases of uniform and time varying displacement field beta. Some physical consequences of the models are also given. Finally, the geodesic equations and acceleration of the test particle are discussed.

Isolated Domain Structure and Its Polar–Surface Asymmetry of Ferroelectric BaMgF4 Single Crystals

The isolated, six-side polygonal domain structures are observed in the orthorhombic as-grown BaMgF4 single crystal by optical microscope and atomic force microscope. The domain configurations demonstrate highly domain wall anisotropy along one principal crystal axis and polar–surface inhomogeneity. The anisotropic behaviour is due to the anisotropy of domain wall energy density in the thermodynamic equilibrium process, and the asymmetric domain surface phenomena is ascribed to the combined contribution from the local electric fields and structure defects-induced mechanical stress during the domain evolution process.

Late-time entropy production due to the decay of domain walls

It is shown that late-time decay of domain walls can dilute unwanted relics such as moduli, if the universe was dominated by frustrated domain walls with tension σ=(1–100TeV)3. Since energy density of the frustrated domain walls decreases as slow as the inverse of the scale factor, an overclosure limit on the axion decay constant fa is also considerably relaxed. In fact fa can be as large as the Planck scale, which may enable us to naturally implement the QCD axion in the string scheme. Furthermore, in contrast to thermal inflation models, the Affleck–Dine baryogenesis can generate enough asymmetry to explain the present baryon abundance, even in the presence of late-time entropy production.

The correlation of damping capacity with grain-boundary precipitates in Fe–Cr-based damping alloys annealed at high temperature

We report the damping capacity measurements and grain-boundary (GB) precipitates observations on a set of four Fe–Cr-based ferromagnetic damping alloys annealed at 1473 K. The alloys were prepared by vacuum induction melt furnace of which each cast ingot weighed 15 kg. The technique of inverted torsion pendulum was employed to measure the damping capacity, and a field emission scanning electron microscope (FESEM) with a X-ray energy dispersive spectrometer (EDS) attachment was used to observe the grain-boundary precipitates. The results indicate the damping capacity of the alloys is definitely correlated with the amount of the grain-boundary precipitates as well as with the chromium concentration in the precipitates. Among the alloys investigated, Fe–Cr–2Al–Si exhibits the highest damping capacity but the least amount of grain-boundary precipitates with the lowest chromium concentration, and vice versa to that Fe–Cr–Al–Si(L) does. Though chromium concentration in the grain-boundary precipitates are very close, the amount of grain-boundary precipitates in Fe–Cr–Al is obviously less than that in Fe–Cr–Si, and the damping capacity of the former is apparently higher than that of the latter. Further discussion pointed out such correlation stems from the effects of alloying on the diffusion behavior of solute atoms as well as on the chemical potential of Cr in the matrix, with which correlates the magnetic properties especially the energy density of domain walls (DWs) which has a significant impact on the damping capacity of Fe–Cr-based damping alloys annealed at high temperature.

Conformal miniaturization of domains with low domain-wall energy: monoclinic ferroelectric states near the morphotropic phase boundaries.

A theory is developed for intermediate monoclinic (FE(m)) phases near morphotropic phase boundaries in ferroelectrics of complex oxides. It is based on the conformal miniaturization of stress-accommodating tetragonal domains under the condition of low domain-wall energy density. The microdomain-averaged lattice parameters are determined and attributed to the parameters of an adaptive monoclinic phase. The theory is applied to the temperature, electric field, and compositional dependent FE(m) lattice parameters. The predictions of the theory are rigidly obeyed over the entire FE(m) stability range.

The local internal stress in ferromagnetic alloys. Dislocation–solute interaction model for local internal stress source

In order to elucidate the Raleigh and Left Shift phenomena encountered in the investigations into damping capacity (internal friction) of ferromagnetic alloys (Acta Metall Sin 34 (1998) 1039; Trans Jpn Inst Met 25 (1984) 891; Trans Jpn Inst Met 20 (1979) 409; Mater Sci Forum 119–121 (1993) 415; Metall Mater Trans A 25 (1994) 111), the solute atom model (Mater Design (in press)) for the local internal stress source is modified and replaced by the dislocation–solute interaction model proposed by the authors. The coercive force as well as crystal lattice parameter of FeCrAl and FeCrAlSi alloys was measured and the local internal stress of these alloys was discussed. It is pointed out that only when the alloy is fully re-crystallized, the potential of damping capacity could be fully developed, and at the pre-requisite of which do not lower the energy density of domain walls (Mater Design 21 (2000) 541), to choose those alloying element that distort crystal lattice slightly is benefit to improve the damping capacity of ferromagnetic alloys.

Temperature dependence of the exchange parameter and domain-wall properties

The A exchange parameter and its temperature dependence were determined for epitaxially grown magnetic thin garnet films. The method is based on the measurement of saturation magnetization, uniaxial anisotropy field, and zero-field stripe domain period. The temperature dependence of domain-wall energy density and domain-wall width was also determined. A correlation was found between domain-wall pinning field and domain-wall parameters, which can be useful for the experimental verification of theories that describe the coercivity on the basis of domain-wall parameters.

Magnetohistory effect of Pr 2Fe 17− xMn x compounds

In this paper, the magnetohistory effect of Pr 2Fe 17− x Mn x ( x=1–9) compounds was studied. The zero-field cooling thermomagnetic curves M ZF( T) of the compounds show a strong decrease below T C with decreasing temperature. The peak temperature T P decreases nearly linearly with increasing Mn substitution. Considerable magnetic hardness is also present at low temperature, which can be attributed to the presence of narrow Bloch walls. The coercivity mechanism is due to domain wall pinning effect, which is demonstrated through the initial magnetization curves. The temperature dependence of H c is represented quite satisfactorily by a formula derived by Egami. The deduced domain wall energy density γ and domain wall width δ are 19.2×10 −3 J/m 2 and 14.4 Å, respectively.

Plane Symmetric Domain Wall in Lyra Geometry

In this paper general solutions are found for domain walls in Lyra geometry in the plane symmetric spacetime metric given by Taub. Expressions for the energy density and pressure of domain walls are derived in both cases of uniform and time varying displacement field $\beta$. It is also shown that the results obtained by Rahaman et al [IJMPD, {\bf 10}, 735 (2001)] are particular case of our solutions. Finally, the geodesic equations and acceleration of the test particle are discussed.

Analysis of Magnetic Domain Sizes in Ultrathin Ferromagnetic Films

Ultrathin magnetic films are considered where the thickness-induced second order phase transition occurs due to surface magnetic anisotropy changes. By increasing the thickness, the easy magnetization axis state passes through the easy cone state (for film thickness t: t1 < t < t2) into the easy magnetization plane state. The characteristic material length lc (defined as the ratio of the domain wall energy density to the demagnetization energy) was calculated up to thickness t2. The exact determination of stripe domain period, p, was proposed, applying the transcendent Lerch functions to the classical Kooy-Enz model. Near t2 where lc vanishes, the critical period, pc, was also discussed. Considering real sets of material parameters taken for ultrathin cobalt films, it was found that by increasing the thickness, the equilibrium domain period drastically decreases from practically infinity (many kilometers for t = 0.5 nm) into the nanometer scale near t2.

Anomalous temperature dependence of coercivity in rare earth cobalt magnets

We report on the anomalous nonmonotonic temperature dependence of coercivity H c( T) which has been observed in bulk-hardened 2:17 magnets. This anomalous effect appears to be universal for all R(Co,Fe,Cu,Zr) z magnets (R=Sm and Y) with different amount of Cu having a cellular (or cellular-like) microstructure consisting of R 2Co 17 cells surrounded by the RCo 5 cell boundary phase. Cu substitutes mostly in the RCo 5 cell boundary phase leading to dilution of its intrinsic magnetic properties including the anisotropy field and Curie temperature. The anomalous behavior in H c( T) is explained by both the domain wall pinning and nucleation models. Domain wall pinning explains the anomalous behavior as a temperature-induced transition at a critical temperature T cr from a low H c repulsive DW pinning ( γ 1:5⪢ γ 2:17, γ is domain wall energy density) to a high H c attractive pinning ( γ 2:17⪢ γ 1:5). The nucleation model can be used in the case of complete magnetic isolation of the 2:17 cells. This condition is expected to be fulfilled at any temperature above RT in the Cu-rich magnets (nonmagnetic R(Co, Cu) 5 cell boundaries), and only above the T c of the Cu substituted 1:5 phase in the magnets with lower Cu content ( T c(1:5)< T c(2:17)).

Honeycomb domain structures in amorphous TbFe thin films

The magnetic properties and domain structure of amorphous TbFe thin films were studied by magnetic measurement and magnetic force microscope. Honeycomb domain structures were found in the as-deposited amorphous film. The domain structures were composed of many small white round dots embedded in the black matrix, which formed an irregular hexagonal pattern with some deformation. The average dot size was about 450 nm, with an average separation of 610 nm. The derived domain wall energy density γ and the exchange constant A were 0.95×10−2 and 1.79×10−11 J/m, respectively.

Magneto-elastic interchange in ferromagnetic alloys

The internal friction δ, exchange integral A, magnetocrystalline anisotropic constant K I and saturation magnetization M s of Fe–Cr–Al and Fe–Cr–Al–Si alloys annealed at 1373 and 1473 K are measured. The energy density and volume fraction of domain walls (DWs) of these alloys are calculated based on the theories of ferromagnetism and the magnetic parameters measured. The physical process of irreversible movement of 90° DWs is suggested. The results indicate the dissipated elastic energy per unit volume due to the irreversible movements of 90° DWs is equal in value to the energy density of DWs, that is γ w /δ w =λ s E/ 2. It is an effect of magneto-elastic interchange in ferromagnetic alloys.

Magnetic Domain Structure and Intrinsic Magnetic Material Parameters of Ternary Intermetallic RMn2Ge2 Compounds (R ? La, Ce, Pr and Nd)

Applying a powder pattern method the magnetic domain structures of polycrystalline intermetallic RMn2Ge2 (where R ≡ La, Ce, Pr, Nd) compounds were studied. The domain structures observed are typical for uniaxial materials. The domain wall energy density γ was determined from analysis of domain structure patterns, using different models of the domain structure. The obtained values are used to determine the intrinsic magnetic material parameters: domain wall width δB, critical diameters of single domain particles Dc and exchange constants A.