Domain Wall Relaxation Research Articles

Dynamic phase transitions in ferroic systems with pinned domain walls

The creep and relaxation of domain walls under an ac electric field that are observed in an ideal model system, periodically poled superionic KTiOPO4 (KTP), appear to occur in different regimes that are separated by a dynamic phase transition at a well-defined frequency, f m = 0.003 Hz, at temperature T = 233 K. The power-law dispersion of the creep susceptibility, χ ∝ 1 + (iωτ)− β (with β ≈ 0.4), and the large nonlinearity encountered for f<f m is contrasted with the Cole–Cole-type relaxational dispersion, χ ∝ [1 + (iωτ)1− α −1 (with α ≈ 0.3), for f > f m. Similar creep-to-relaxation transitions are observed at low frequencies in other ferroic systems with weak disorder: the multidomained uniaxial relaxor Sr0.69Ba0.31Nb2O6 (SBN), the quantum ferroelectric domain state of SrTi18O3 (STO18) and the superferromagnetic nanoparticle system [(Co80Fe20(1.4 nm)/Al2O3(3 nm)]10, which appear to belong to the same dynamical universality class.

Creep and Relaxation Dynamics of Domain Walls in Periodically PoledKTiOPO4

Creep and relaxation of domain walls under ac electric fields are observed in an ideal model system, periodically poled KTiOPO4, to occur in different regimes, which are separated by dynamic phase transitions at frequencies f(m)(T)=f(m0)exp((-DeltaE/k(B)T), with f(m0)=3 x 10(9) Hz and DeltaE=0.6 eV. Power law dispersion of the creep susceptibility, chi proportional to 1+(iomegatau)(-beta), with beta approximately equal to 0.4, and large nonlinearity encountered at f < f(m), is contrasted with Cole-Cole-type relaxational dispersion, chi proportional to (1+[iomegatau](1-alpha))(-1), with alpha approximately 0.3, at f > f(m).

Collective magnetic states of ferromagnetic nanoparticles in the superspin limit

Soft ferromagnetic Co80Fe20 nanoparticles embedded discontinuously in [Co80Fe20(tn)/Al2O3]m multilayers are treated as superspins with random size, position and anisotropy. Freezing into collective states rather than single particle blocking is encountered at low temperatures. At low particle density, tn 1.2 nm, superferromagnetic (SFM) domain wall relaxation is, e.g., evidenced by polarized neutron reflectivity. Thermoremanent logarithmic decay rates reveal a universal power law with exponents changing from n 1 for SFM in agreement with recent Monte Carlo simulations. At intermediate densities, a crossover occurs from n 1 as T Tc. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Ferroelectric domain wall relaxation in Ba0.25Sr0.75TiO3 films displaying Curie-Weiss behavior

Ferroelectric films may be used in integrated circuits for high frequency and memory applications. Losses and interfaces between films and electrodes are problematic. This work concerns the temperature and electric field response of the complex dielectric permittivity and the relaxation of domain walls in a ferroelectric layer that is of sufficient quality to show a Curie-Weiss behavior. Laser ablation was used to deposit 1200 nm thick Ba0.25Sr0.75TiO3 layers between metallic oxide, (100 nm) SrRuO3 and (120 nm) La0.67Ca0.33MnO3, films in epitaxial heterostructures. The electric field response (E⩽80kV∕cm) of the real ϵ′ and imaginary ϵ″ parts of the complex permittivity of the intermediate Ba0.25Sr0.75TiO3 layer in these parallel plane film capacitors was studied at temperatures above and below the phase transition point TCurie. The latter was determined from the temperature dependence of the inverse dielectric permittivity and its value, TCurie=145K, agrees well with that of bulk single crystal. ϵ′ of the Ba0.25Sr0.75TiO3 layer could be suppressed about 80% by a field E=80kV∕cm at temperatures close to TCurieϵ′(T,E) and ϵ″(T,E) curves were used to gain insight into the relaxation dynamics of ferroelectric domain walls (DW) in the Ba0.25Sr0.75TiO3 layer. Their influence on ϵ′ was noticed up to T=230K, well above TCurie. The most probable relaxation time τ of the DW in Ba0.25Sr0.75TiO3 follows a relation τ=τ0exp[(ϕ−βE)∕kT], where τ0=1.2×10−10sϕ=75–105meV, and β=4.7×10−24Jm1∕2V−1∕2.

Interaction between free boundaries and domain walls in ferroelastics

We study the relaxation of ferroelastic domain walls in the vicinity of a free surface, by means of a nonlinear continuum elastic model treated with finite elements on an adaptive grid. Domain walls bend towards the free surface, as a consequence of the interplay of the energy per unit length of the domain wall and the long-range elastic strains which are generated by deviations from the prescribed compatible orientation. We also analyze the order parameter on the free surface. For walls orthogonal to the free surface we find, in accordance with previous studies, a double-peak structure. For different angles the picture is more complex, and in some cases only one small peak survives.

Size-dependent effects on the magnetization dynamics of Condon domains

The existence of magnetic domains in nonferromagnetic metals at quantizing magnetic fields is examined under conditions of de Haas\char21{}van Alphen oscillations in the range of strong magnetic fields in thin slabs in a three-dimensional electron gas. Dynamics of Condon domain walls are studied in bulk metals and films at time-varying and time-independent applied magnetic fields. The temperature, magnetic field, purity, and sample size-dependent effects on the width, velocity and mobility of domain walls are calculated. Domain wall resonance and relaxation effects are considered in the three-dimensional electron gas.

Dielectric behaviour of strontium tartrate single crystals

Strontium tartrate trihydrate (STT) crystals have been grown in silica hydrogel. Various polarization mechanisms such as atomic polarization of lattice, orientational polarization of dipoles and space charge polarization in the grown crystals have been understood using results of the measurements of dielectric constant (έ′) and dielectric loss (tan δ) as functions of frequency and temperature. Ion core type polarization is seen in the temperature range 75–180°C, and above 180°C, there is interfacial polarization for relatively lower frequency range. One observes dielectric dispersion at lower frequency presumably due to domain wall relaxation.

90° domain wall relaxation and frequency dependence of the coercive field in the ferroelectric switching process

The mechanisms involved in the polarization switching process in soft and hard Pb(Zr53,Ti47)O3 (PZT) bulk ceramics were investigated through the dependency of the hysteresis loop on the frequency. In order to determine the influence of the defects on the domain switching dynamics, the samples were characterized in the virgin state and after a fatigue or a depinning process. The frequency dependence of the polarization revealed a strong relaxation of the 90° domain walls at ∼100 Hz. The results also revealed a strong influence of the kind of defect and their distribution in the ferroelectric matrix on the domain switching dynamics, which were reflected in the frequency dependence of the coercive field and the percentage of the backswitching. Initially, it was observed that the frequency dependence of the coercive field for the soft and the hard PZT in the virgin state had just one rate of change per decade in the entire frequency range investigated, which is the standard behavior found in the literature. However, after the fatigue or the depinning process, two rates of changes were noticed. Consequently, evidence of an upper-frequency limit for the coercive field changes was found. The percentage of the backswitching and its behavior for the soft PZT was almost independent of the fatigue state in the entire frequency range investigated. Nevertheless, for the hard PZT, an opposite behavior was verified. The reorientation of the domains was modeled as occurring in a viscous medium where several forces, such as viscous and restoring forces, act on them.

Domain wall relaxation frequency and magnetocrystalline anisotropy in Co- and Fe-based nanostructured alloys

The magnetic behaviour and the frequency dependence of the initial complex permeability are analysed in very soft ferromagnetic Co- and Fe-based nanostructured alloys obtained by thermal treatments of amorphous ribbons. The spectra of the real and imaginary parts of the permeability show the typical features of domain wall relaxation and are characterized by a continuous distribution of relaxation times. In the framework of the random anisotropy model, the spread in the values of the relaxation frequency reflects a dispersion of the effective anisotropy constants and, in turn, a nonuniform distribution of the grain diameters. The results well agree with those deduced by the distribution function of the anisotropy fields and by the scanning and/or transmission electron microscopy analysis.

Electromagnetic Wave Absorbing Properties of High-Permittivity Ferroelectrics Coated with ITO Thin Films of 377 Ω

For the aim of thin electromagnetic wave absorbers used in quasi-microwave frequency band, this study proposes the high-permittivity ferroelectrics of quarter wavelength thickness (λ/4 spacer) coated with ITO thin film of 377 Ω/sq (impedance transformer). For high-permittivity dielectrics, BaTiO3 (BT), 0.9Pb(Mg1/3Nb2/3)O3-0.1PbTiO3 (PMN-PT) and 0.8Pb(Mg1/3Nb2/3)O3-0.2Pb(Zn1/3Nb2/3)O3 (PMN-PZN) are prepared by conventional ceramic processing technique. The ferroelectric materials show high dielectric constant and dielectric loss in microwave frequency range and their dominant loss mechanism is considered to be domain wall relaxation or dynamics of polar clusters. The microwave absorbance (determined at 2 GHz) of BT, PMN-PT and PMN-PZN are found to be 65% (at a λ/4 thickness of 3.5 mm), 20% (2.5 mm) and 37% (2.5 mm), respectively. By coating ITO thin films on the ferroelectric substrates with a thickness of λ/4, the microwave absorbance is greatly improved. Particularly, when the sheet resistance of ITO films is closed to 377 Ω/sq, the reflection loss is reduced to −20 dB (99% power absorption). This is attributed to the wave impedance matching led by ITO thin film combined with a λ/4 thickness of high-permittivity dielectric spacer. It is, therefore, successfully proposed that the ITO/ferroelectrics structure with controlled electrical properties and thickness can be useful as thin microwave absorbers used in quasi-microwave frequency band.

Domain Wall Relaxation, Creep, Sliding, and Switching in Superferromagnetic DiscontinuousCo80Fe20/Al2O3Multilayers

The ac susceptibility of a superferromagnetic discontinuous multilayer [Co(80)Fe20(1.4 nm)/Al(2)O3(3 nm)](10) is measured as a function of temperature, frequency, and field amplitude and compared to static and dynamic hysteresis loops. Its properties are successfully mapped onto the predicted [T. Nattermann, V. Pokrovsky, and V. M. Vinokur, Phys. Rev. Lett. 87, 197005 (2001)]] dynamical phase transitions, which link the relaxation, creep, sliding, and switching regimes of pinned domain walls.

Crystallization and soft magnetic behavior of Fe85.6−xMoxZr3.3Nb3.3B6.8Cu1 alloys

The influence of the partial substitution of Fe by Mo on the magnetic behavior and the frequency dependencies of the complex magnetic permeability are studied in Fe85.6−xMoxZr3.3Nb3.3B6.8Cu1 alloys. With the increase of the Mo content, the crystallization temperature will increase. The spectra of real and imaginary parts of the complex permeability were measured in the frequency of 0.1 kHz to 1 MHz, the obtained permeability spectra shows typical features of domain wall relaxation dispersion. With the increase of the Mo content, the core loss will decrease and the relaxation frequency will increase obviously.

Fabrication and Properties of Thin Microwave Absorbers of Ferroelectric Materials Used in Mobile Telecommunication Frequency Bands

High-frequency dielectric and microwave absorbing properties have been investigated in ferroelectric materials (BaTiO(BT), (1-x)Pb)O-xPbTiO(PMN-PT), (1-x)PbO-xPb(Zn_{\frac{1}{3}}Nb_{\frac{2}{3}}$)O(PMN-PZN) for the aim of thin microwave absorbers in the frequency range of mobile telecommunication. The specimenns are prepared by conventional ceramic processing and complex permittivity has been measured by transmission/reflection method. The ferroelectric materials show high dielectric constant and dielectric loss in the microwave range and their domiant loss mechanism is considered to be domain wall relaxation. The microwave absorbance of BT 0.9PMN-0.1PT, and 0.8PMN-0.2PZN specimen (determined at 2) are found to be 99.5% (at a thickness of 4.5 mm), 50% (2.5 mm), and 30% (2.5 mm), respectively. It is suggested that PMN-PT or PMN-PZN ferroelectrics are good candidate materials for the spacer of λ/4 absorber. The use of ferroelectric materials is effective in reducing the thickness of absorber with their advantage of high dielectric constant.

Temperature Dependence of Complex Permeability and Domain Wall Relaxation in Polycrystalline Perovskite La0.7Sr0.3MnO3

The magnetic spectra of the polycrystalline perovskite La 0.7 Sr 0.3 MnO 3 have been measured at various temperatures and in the frequency range 10 Hz-100 MHz using an impedance analyzer. The complex permeability and the relaxation of magnetic domain walls have been investigated. A pronounced dispersion of the relaxation in the spectra has been observed. The relaxation frequency reduces from 1.47 MHz to 772 kHz with decreasing temperature from 296 to 77 K. Meanwhile, the static permeability becomes smaller from 42 to 26. The relaxation is ascribed to the displacements of domain walls, and the damping mainly originates from the eddy currents associated with wall motions.

Temperature Dependence of Complex Permeability and Domain Wall Relaxation in Polycrystalline Perovskite La0.7Sr0.3MnO3

Temperature Dependence of Complex Permeability and Domain Wall Relaxation in Polycrystalline Perovskite La0.7Sr0.3MnO3

Soft magnetic behaviour and permeability spectra in amorphous and nanocrystalline Fe 80.5Nb 7B 12.5 alloys

The magnetic behaviour and the frequency dependencies of the complex magnetic permeability are studied in a series of heat-treated amorphous and nanocrystalline Fe 80.5Nb 7B 12.5 samples with different volume fractions of the crystalline phase. The magnetic behaviour has been studied by vibrating sample magnetometry (VSM) and by room-temperature hysteresis loop measurements. The spectra of real and imaginary parts of the complex permeability, μ( f)= μ′( f)−j μ′′( f) , were measured using an impedance analyzer in the frequency range from 0.01 to 10 MHz. The obtained permeability spectra for the investigated nanocrystalline alloys show typical features of a domain wall relaxation dispersion. A marked deterioration of the soft magnetic behaviour takes place in the partially crystallized samples after annealing for 1 h at 803 K. This is reflected by a drastic reduction of permeability and a strong increase of relaxation frequency. An improvement of soft magnetic behaviour characterized by low values of coercivity and relaxation frequency as well as by high permeability is observed after annealing for 1 h at 883 K which resulted in an advanced degree of nanocrystallization in the samples.

Study of microwave absorptions in M-hexaferrites for anti-radar applications

Microwave absorption of sintered M-type hexaferrites (BaFe12−2xRuxZnxO19) is investigated as a function of the substitution ratio x. The substitution with Ru and Zn has been shown to reduce the axial anisotropy of the BaM-hexaferrite which becomes in-plane for x ≈ 0.4. Large saturation magnetization and in-plane magnetic anisotropy allow to obtain high permeability values at microwave frequencies. To study the behavior of the ferrites at these frequencies, the complex constitutive parameters ε and μ (respectively permittivity and permeability) are simultaneously measured from 0.5 up to 18 GHz using a coaxial technique. Two absorption phenomena are observed: the ferrimagnetic resonance and the domain wall relaxation; the latter is studied with the Globus' model. Anti-radar applications are also mentioned.

Effect of proton irradiation on magnetic relaxation in amorphous material

The frequency spectra of the susceptibility in the amorphous Fe 81B 13.5Si 3.5C 2 of as-quenched and proton-irradiated samples show a typical Debye-type relaxation of domain walls. The susceptibility decreases with proton dose, while the relaxation frequency increases. The results are discussed in terms of the domain size and internal stress at the induced defects after proton irradiation.

Frequency behaviour of Zn–Mn ferrites nanoparticles obtained by high-energy ball milling

Zinc–manganese spinel ferrites have been obtained by high-energy ball milling from precursors (1) oxides and carbonates and (2) acid oxides and hydroxides. Results reveal that the use of one or another precursor leads to final products with different structural and magnetic characteristics. Measurements of the domain wall relaxation frequency exhibited differences depending on the type of precursor. These results are interpreted in terms of the variations in the magnetocrystalline anisotropy between the samples.

Surface Magnetoimpedance Measurements in Soft-Ferromagnetic Materials

We present an investigation of the surface magnetoimpedance (Z s ) in ribbons of the amorphous alloy Co 70.4 Fe 4.6 Si 15 B 10 for a broad range of frequencies (2× 10 3 Hz≤f≤2 × 10 8 Hz) and magnitudes of the ac electrical current (2 mA ≤ I ac ≤ 75 mA). The experimental data are interpreted in terms of a theoretical model valid for any value of the skin depth δ, which is based on a modification of the currently used semi-infinite sample geometry model, in order to account for a broad range of δ, The shape of the Z S versus applied field (H) curve is mainly determined by the variation of δ with H. which can attain several orders of magnitude in the field range of the experiments (-3.2 × 10 3 A/m ≤ H ≤ 3.2 × 10 3 A/m). The results of the model fit very well the Z S versus f data using three adjustable parameters: the domain-wall relaxation time τ (= 250 ns for all values of I ac used in the experiments), the transversal magnetic permeability X T (I ac ) and a resonance linewidth ΔH which depend on the value of H.