Hysteresis Scaling Research Articles

Effect of sintering parameters on the dynamic hysteresis scaling behavior of Ba0.85Sr0.15Zr0.1Ti0.9O3 ceramics

ABSTRACTThis article presents the effect of processing parameters on the ferroelectric hysteresis behavior of Ba0.85Sr0.15Zr0.1Ti0.9O3 (BSZT) ceramics. The ferroelectric hysteresis scaling relations for coercive field (Ec) and remnant polarization (Pr) as a function of temperature have been proposed. The power law temperature exponents based on scaling were systematically established for all the hysteresis parameters. The temperature dependent scaling of Ec and Pr at sintering temperature of 1400, 1425, 1450 and 1475°C yields EcαT0.43, EcαT0.84, EcαT0.50, EcαT0.37 and PrαT−1.73, PrαT−1.55, PrαT−1.73, PrαT−1.69 respectively. Additionally, the scaling relations for the samples sintered at 1450°C at different time intervals of 3, 4, 5 and 6 hrs were also established. Finally, to understand the domain dynamics, back switching polarization (Pbc) as a function of temperature (T) was also estimated by Arrhenius law and the average activation energy was evaluated.

Enhanced thermal energy conversion and dynamic hysteresis behavior of Sr-added Ba0.85Ca0.15Ti0.9Zr0.1O3 ferroelectric ceramics

This paper deals with a study of Ba0.85Ca0.15−xSrxTi0.9Zr0.1O3 (BCT-BZT-Sr) (x = 0%, 5%, 10% and 15%) polycrystalline ceramics for thermal energy conversion applications using the Olsen cycle. A maximum energy conversion density of 108 kJ/m3 was observed in pristine BCT-BZT for cycle operating at 30–90 °C and 0–20 kV/cm. Moreover, the samples with Sr contents (x) of 5%, 10% and 15% display an energy conversion density of 179 kJ/m3, 149 kJ/m3 and 200 kJ/m3, respectively. The Sr addition almost double the energy conversion over the pristine sample under the similar conditions. Also, the temperature (T)-dependent dynamic hysteresis scaling relations for coercive field (EC) and remnant polarization (Pr) were systematically investigated. The power-law scaling exponents are obtained for EC versus T as EC ∝ T−0.65, EC ∝ T−0.61, EC ∝ T−0.56 and EC ∝ T−0.63 for the samples with Sr contents of 0%, 5%, 10% and 15%, respectively. Similarly, the scaling relations for Pr are Pr ∝ T−1.59, Pr ∝ T−1.59, Pr ∝ T−1.36 and Pr ∝ T−1.32 for the samples with Sr contents of 0%, 5%, 10% and 15%, respectively.

Temperature‐Dependent Scaling Behavior of Dynamic Hysteresis in Pb(Zr,Ti)O3 Ceramics

The dynamic hysteresis scaling behaviors of Nb‐doped Pb(Zr0.52Ti0.48)O3 ceramics have been investigated as a function of electric field amplitude (E0) and frequency (f) at different temperatures (T). The loop area <A> of saturated loops is found to follow various power laws as <A> ∝ E00.3065 at fixed f and <A> ∝ f 0.0120 at fixed E0. Furthermore, the linear scaling relation <A> = k3 fαE0β + b3 is estimated under various temperatures. The exponents α (=0.01) and β (=0.10) are T‐independent, whereas the slopes k3 and y‐intercepts b3 are T‐dependent because the increasing temperature in the same phase range only decreases the threshold field of the reversal rather than change the dynamic reversal process.

Electrocaloric Behavior and Temperature‐Dependent Scaling of Dynamic Hysteresis of Ba0.85Ca0.15Ti0.9Zr0.1O3 Ceramics

This article presents electrocaloric effect in Ba0.85Ca0.15Ti0.9Zr0.1O3 (BCTZO) using an indirect approach based on Maxwell's relations. The peak electrocaloric performance is found to be an adiabatic temperature change of 0.41 K with electrocaloric strength of 19 mK cm/kV and a heat carrying capacity of ~0.17 J/g under an electric field of 0–21.5 kV/cm. The ferroelectric hysteresis scaling relations for coercive field (EC), remnant polarization (Pr), and hysteresis area (<A>) as a function of temperature (T) are also systematically investigated. The power‐law temperature exponents are obtained for all the hysteresis parameters. The scaling relations are established as Ec ∝ T−0.6584, Pr ∝ T−1.59, and <A> ∝ T−1.01623. The presented scaling relations are compared with those reported in the literature for other ferroelectric materials.

Angular dependence of hysteresis scaling and coercivity for anisotropically distributed ferromagnetic nanoparticles in paramagnetic matrix

We have investigated anisotropy behavior of coercivity and scaling law for nano-scale ferromagnetic phases embedded in a paramagnetic matrix of an austenitic stainless steel. Small ferromagnetic martensites are induced by uniaxial tensile deformation. A scaling-law relationship between the hysteresis loss and remanence, with a power law exponent of 1.47 ± 0.09, has been found, irrespective of stress, martensite volume fraction, and angle between the magnetization and tensile directions. A coefficient of the scaling law decreases with volume fraction, whereas it increases with increasing the angle and maximizes when the magnetization direction is perpendicular to that of the tensile. This trend is opposite to that of coercivity. The behavior of the coefficient and the coercivity was discussed from the viewpoint of morphology of martensite particles.

Ultra-Thin, High Quality HfO2 on Strained-Ge MOS Capacitors with Low Leakage Current

Ultra-thin HfO2 MOS capacitors on strained-Ge (s-Ge) have been fabricated with an extracted effective oxide thickness (EOT) of 4.9 Å and leakage current less than 0.2 A/cm2. The CV measurements show no hysteresis and areal capacitance scaling for device sizes of 50×50 to 200×200 µm2. A high series resistance is observed, likely due to a 500 meV valence band offset between the s-Ge and relaxed Si0.55Ge0.45 virtual substrate. The capacitance results suggest an extremely-scaled, high quality dielectric on s-Ge suitable for deeply scaled CMOS.

Study of Ferroelectric Hysteresis Scaling Exponents in Aged Polycrystalline BaTiO3

The evolution of electric field dependent dynamic ferroelectric hysteresis area of aged and de-aged un-doped polycrystalline BaTiO3 (BTO) is studied. It is observed that the field exponent of aged sample is significantly different as compared to de-aged BTO at low strengths of applied electric field. The observations are discussed in terms of orientation of defect dipoles and it is suggested that the relation between hysteresis area (A) and the electric fields in aged samples is of the form⟨A⟩∝(E±EI ) n , where E is the applied electric field; EI is the internal bias field generated due to defect diploes and n is the scaling exponent.

Magnetic hysteresis scaling in thulium: Implication of irreversibility-related scaling for soliton wall motion in an Ising system

We report low-field magnetic hysteresis scaling in thulium with strong uniaxial anisotropy. A power-law hysteresis scaling with an exponent of 1.13±0.02 is found between hysteresis loss and remanent flux density of minor loops in the low-temperature ferrimagnetic phase. This exponent value is slightly lower than 1.25–1.4 observed previously for ferromagnets and helimagnets. Unlike spiral and/or Bloch walls with a finite transition width, typical for Dy, Tb, and Ho with planar anisotropy, a soliton wall with a sudden phase shift between neighboring domains may dominate in Tm due to its Ising-like character. The observations imply the presence of universality class of hysteresis scaling that depends on the type of magnetic anisotropy.

Hysteresis Scaling Behavior in a Remanent Magnetization State

Scaling laws of minor hysteresis loops have been examined in cold rolled low carbon steels with varying initial magnetic states, field sweep rate, and temperature. Minor B-H loops, obtained in a remanent initial state are non-symmetrical in shape and their center largely deviates from the origin of the B-H space, which is in contrast to symmetrical loops obtained in a demagnetized initial state. However, it was found that a relation between maximum flux density and hysteresis loss of both the symmetrical and non-symmetrical loops exhibits the same curves in the wide field region and has a power law with the same exponent of 1.59 ± 0.02, irrespective of initial magnetic state, rolling reduction ratio, and temperature. The coefficient of the power law, which is sensitive indicators of internal stress, increases with rolling reduction or decreasing temperature and was obtained with a standard deviation of 2%. These observations demonstrate that the scaling analysis of minor B-H loops is advantageous for on-site evaluation of materials degradation in ferromagnetic structural steels where a demagnetized initial state is difficult to obtain.

Magnetic hysteresis scaling behavior in terbium and holmium

Hysteresis scaling for magnetic minor loops has been examined in the heavy rare-earth metals Tb and Ho, varying the temperature and magnetic-field amplitudes. In addition to the low-temperature ferromagnetic phase below ${T}_{\mathrm{c}}$, the scaling law between the hysteresis loss and remanent flux density with an exponent of $\ensuremath{\sim}$1.3 was observed in the higher-temperature helical antiferromagnetic phase for both metals. The coefficient which reflects the pinning fields of the domain walls decreases with increasing temperature below ${T}_{\mathrm{c}}$, but it exhibits a sharp increase after the onset of the helical antiferromagnetic phase. The observations above ${T}_{\mathrm{c}}$ were explained as due to the irreversible motion of spiral domain walls, unlike the 180${}^{\ensuremath{\circ}}$ Bloch walls that are typical in the ferromagnetic phase.

Universal Hysteresis Scaling for Incommensurate Magnetic Order in Dysprosium

We study the scaling properties of magnetic minor hysteresis loops in a polycrystalline dysprosium metal, varying temperature and magnetic-field amplitudes. We observe irreversibility-related hysteresis loss in the helical antiferromagnetic phase, which is related with remanent flux density as a power law with the same scaling exponent of 1.25±0.05 as that in ferromagnetic materials. In contrast to hysteresis scalings in ferromagnets associated with 180° Bloch walls, the observed law is governed by spiral walls which separate helical domains with oppositely rotating spins.

Hysteresis scaling relations in polycrystalline BaTiO 3 bulk ceramics

The scaling behaviors of the dynamic ferroelectric hysteresis of polycrystalline BaTiO 3 bulk ceramics were investigated. To enhance the accuracy of prediction, not only sets of the scaling relation of hysteresis area 〈 A〉 against frequency f and field amplitude E 0 were established, but also were sets of scaling relation of remnant polarization ( P r ) and coercive field ( E C ) against frequency f and field amplitude E 0. All scaling relations of hysteresis parameters, 〈 A〉, P r , and E C , displayed obviously the inter-correlation between f- and E 0-exponents in both sub-coercive field and above coercive field conditions. By first approximation, the scaling relations took a form of A ∝ f − 0.39 E 0 1.06 , P r ∝ f − 0.18 E 0 0.47 , and E C ∝ f − 0.33 E 0 0.46 above the coercive field condition; whereas the scaling relations in the form of A ∝ f − 0.55 E 0 3.40 , P r ∝ f − 0.43 E 0 1.73 , and E C ∝ f − 0.27 E 0 1.35 were obtained under a sub-coercive field condition. The frequency observation range affected directly the scaling exponents. Over the same frequency range, the scaling relations obtained in this study are generally comparable to previously reported scaling behavior in BaTiO 3 single crystals, as well as in other polycrystalline bulk ceramics, suggesting that materials (both single and polycrystalline) with similar domain switching mechanisms should have comparable dynamic hysteresis and scaling behavior.

Dynamic ferroelectric hysteresis scaling of BaTiO3 single crystals

The scaling behavior of the dynamic hysteresis of ferroelectric BaTiO3 single crystals was investigated. Two sets of the scaling relation of hysteresis area ⟨A⟩ against frequency f and field amplitude E0 were clearly established. Above the coercive field, the scaling took a form of ⟨A⟩∝f−0.195E00.950. On the other hand, the scaling in the form of ⟨A⟩∝f1.667E0−2.804E04.157 was obtained under subcoercive field condition. While these scaling relations were generally comparable to previously reported ones, it was found that the f and E0 exponents depended on E0 and f, respectively, which was in contrast to the prior theoretical prediction and experimental investigations.

Scaling of hysteresis loops at phase transitions into a quasiabsorbing state

Models undergoing a phase transition to an absorbing state weakly broken by the addition of a very low spontaneous nucleation rate are shown to exhibit hysteresis loops whose width Deltalambda depends algebraically on the ramp rate r . Analytical arguments and numerical simulations show that Deltalambda approximately r(kappa) with kappa=1(beta'+1) , where beta' is the critical exponent governing the survival probability of a seed near threshold. These results explain similar hysteresis scaling observed before in liquid crystal convection experiments. This phenomenon is conjectured to occur in a variety of other experimental systems.

Hysteresis scaling of uniaxially anisotropic Heisenberg model

We simulate by the Monte Carlo method the dynamic hysteresis and hysteresis scaling of two-dimensional uniaxially anisotropic Heisenberg model submitted to a time-oscillating magnetic field h of frequency f and amplitude h0. It is revealed that the hysteresis area as a function of f and h0 exhibits well-defined power law behaviors over the low-f and high-f regimes as long as h0 is high enough. The power law exponents for the low-f regime depend on the uniaxially anisotropic factor K, but the exponents for the high-f regime are universal. The single-peaked hysteresis dispersions at different h0 follow both the empirical scaling approach and the single-variable scaling hypothesis, respectively, demonstrating the existence of a single characteristic time for spin reversal mode given the amplitude h0. However, the scaling may be broken when h0 is low, due to the coexistence of spin reversal and spin tilting resonances.

Dynamic hysteresis scaling of first-order phase transition ferroelectrics near the phase transition pointin the (η2)3 model

The dynamic hysteresis of the first-order phase transition around the transition pointTc in ferroelectrics is studied by investigating the dynamic response of the Landau–Devonshire(η2)3 model to a time-varying external field of frequencyf andamplitude E0. It is revealed that the single-loop hysteresis as obtained above the upper critical pointT+ and below the absoluteinstability point T0 shows dynamic behaviours very different from the double-loop hysteresis obtained betweenTc and T+. An extensive calculation reveals a power-law scaling for hysteresis area as a function ofE0, while no reliable power-law scaling for the area as a function off is availablein the low-f regime. The scaling for the double-loop hysteresis seems not to fall into the same class assingle-loop hysteresis. Furthermore, the power-law exponents, if any, are somewhattemperature-dependent, but this dependence is very weak in the regime of lowE0 andhigh f.

Thickness-dependent dynamic hysteresis scaling behavior in epitaxial Fe/GaAs(001) and Fe/InAs(001) ultrathin films

The dynamic hysteresis scaling behavior in epitaxial Fe/GaAs(001) and Fe/InAs(001) thin films (thickness range 7.3–150 Å) has been investigated as a function of Fe film thickness in the field sweep rate range 0.005–1000 kOe/s using the magneto-optic Kerr effect. The hysteresis loop area A follows the scaling relation A∝(dH/dt)α. We find two distinct dynamic regimes: the low dynamic regime in the sweep rate range 0.005–250 kOe/s, and the high dynamic regime beyond 250 kOe/s. There is a marked increase in α between the low and high dynamic regimes which we attribute to the dominant reversal mechanism changing from domain wall motion to nucleation. In the low dynamic regime α is a decreasing function of Fe film thickness, and this behavior is attributed to the effect of interface-induced pinning.

Dynamic hysteresis behavior in epitaxial spin-valve structures

We report the dynamic hysteresis behavior of epitaxial single ferromagnetic fcc NiFe(001), fcc Co(001) layers, and fcc NiFe/Cu/Co(001) spin-valve structures investigated as a function of field sweep rate in the range of 0.01–270 kOe/s using the magneto-optic Kerr effect. The hysteresis loop area A is found to follow the scaling relation A∝Ḣα with α∼0.13 and ∼0.02 at low sweep rates and ∼0.70 and ∼0.30 at high sweep rates for 60 Å NiFe and 40 Å Co single magnetic layer structures, respectively. For the single and double spin valves, the “double-switching” behavior which occurs at low sweep rates transforms to “single switching” at ∼154 and ∼192 kOe/s, respectively. Our results provide direct experimental evidence that the magnetic anisotropy strength affects dynamic hysteresis scaling in ultrathin magnetic films.

Magnetization reversal dynamics in epitaxial spin-valve structures

We report the dynamic hysteresis behavior of epitaxial single ferromagnetic NiFe, Co layers, and NiFe/Cu/Co spin-valve structures investigated as a function of field sweep rate $\mathrm{H\ifmmode \dot{}\else \.{}\fi{}}(dH/dt)$ in the range 0.01--270 kOe/sec using the magneto-optic Kerr effect. In situ reflection high-energy electron-diffraction images confirmed that the NiFe, Cu, and Co layers grew epitaxially in the (100) orientation where the fcc NiFe, Co〈110〉 in-plane directions correspond to the Si〈100〉 directions. For $\mathrm{Cu}/60\AA{}\mathbf{NiFe}/\mathrm{C}\mathrm{u}/\mathrm{S}\mathrm{i}{(H}_{c}=5\mathrm{Oe})$ and $\mathrm{Cu}/40\AA{}\mathbf{Co}/\mathrm{C}\mathrm{u}/\mathrm{S}\mathrm{i}{(H}_{c}=104\mathrm{Oe})$ single magnetic layer structures, the hysteresis loop area A is found to follow the scaling relation $A\ensuremath{\propto}{H}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\sim}0.13$ and \ensuremath{\sim}0.02 at low sweep rates and \ensuremath{\sim}0.70 and \ensuremath{\sim}0.30 at high sweep rates, respectively. This result indicates that the NiFe and Co layers in the spin-valve structures can be expected to show distinct scaling behavior at high sweep rate. We found that the ``double-switching'' behavior which occurs at low sweep rates transforms to ``single switching'' at \ensuremath{\sim}154 kOe/sec and \ensuremath{\sim}192 kOe/sec, respectively, for the single and double spin valves due to the different dynamic response of the NiFe and Co layers. Our results provide direct experimental evidence that the magnetic anisotropy strength affects dynamic hysteresis scaling in ultrathin magnetic films, in contrast with the predictions of current theoretical models.

Hysteresis scaling for Ising systems on fractal structures

Dynamical phase transitions in Ising systems on Sierpinski Carpets and bond-percolation lattices at percolation threshold are studied by means of standard Monte Carlo simulations. We find that the area of hysteresis loop A can be scaled with respect to the sweep rate h of a linear driving field. However, the exponent in the scaling expression, A∼ h b , is universal only for Ising systems on Sierpinski carpets. We conclude that the hysteresis scaling is universal for the field-driven first-order phase transitions in Ising systems on fractal structures. Based on scaling hypothesis, we derive the expression of finite-size effect on the hysteresis. The exponent b is obtained by this method in some Sierpinski carpets.