Frequency dependence of the coercive field and the internal bias field in ferroelectric thin films

The dependences of the coercive field and the internal bias field on the switching field frequency for lead zirconate titanate and lead titanate thin films are experimentally studied over a wide temperature range. It is shown that, as the frequency increases, the coercive field and the bias field in these films increase at the rate dependent on the temperature and the substrate used.     

On the dependence of the coercive field of BaTiO3 single crystals on their thickness

The paper gives the results of measuring the coercive field of single-domain single crystals of BaTiO₃, the thickness of which was lowered by successive etching. The initial decrease in the thicknessd is accompanied by a sudden increase in the coercive fieldE _c (E _c /d –1·5 × × 10⁵ V/cm²); after etching off layers larger than 10^–3 ÷ 2×10^–3cm the coercive field grows much more slowly (E _c /d –7×10³ V/cm²). The high initial growth ofE _c is interpreted by means of Schottky exhaustion layers with non-zero gradient of the electric potential.In conclusion, the authors would like to thank H. Arend, P. Coufová and J. Jarý for providing high-quality single crystals and for much valuable advice during the work and V. Dvoák and K. Pátek for remarks on this paper.     

In-plane magnetic anisotropy and coercive field dependence upon thickness of CoFeB

The structural and magnetic properties of as-grown 5–50 nm thin ion-beam sputter deposited transition metal–metalloid Co₂₀Fe₆₀B₂₀ (CFB) films are reported in this communication. A broad peak observed at 2θ∼45° in the glancing angle X-ray diffraction pattern revealed the formation of very fine nano-sized grains embedded in majority amorphous CFB matrix. Although no magnetic field is applied during deposition, the longitudinal magneto-optic Kerr effect measurements performed at 300 K in these as-grown films clearly established the presence of in-plane uniaxial magnetic anisotropy (K_u). It is argued that this observed anisotropy is strain-induced. This is supported by the observed dependence of direction of K_u on the angle between applied magnetic field and crystallographic orientation of the underlying Si(100) substrate, and increase in the coercivity with the increase of the film thickness.     

Frequency dependence of coercive properties

Significant frequency dependence of domain wall coercive field, due to the widening of the hysteresis loops, was observed based on AC hysteresis curve measurements in epitaxial magnetic garnet films. Domain wall oscillation measurements did not reveal any frequency dependence. The different results of the two measurement methods were analyzed, and the observed frequency dependence was attributed to the inertia of the moving domain walls. It was shown that the real value of the domain wall pinning field cannot be determined by AC hysteresis measurements, even in non-conducting materials.     

On the interpretation of the thickness dependence of the coercive field of BaTiO3 single crystals

It is shown in the paper that the thickness dependence of the coercive field of unetched and of successively etched BaTiO₃ single crystals can be explained by the presence of a ferroelectric surface layer with decreased permittivity. In contrast to the Merz model [1], which considered a homogeneous layer, the authors assume that the permittivity inside the layer gradually decreases in the direction to the surface. By using experimental results it has been found for the constant, characterizing (according to [1]) the thickness dependence of the coercive field of unetched crystals, that=1.6 V, which is in satisfactory agreement with experiment.The authors thank V. Dvoák C.Sc, J. Fousek C.Sc, and Z. Málek C.Sc. for stimulating discussions.     

Angular dependence of the coercive field in sintered Fe77Nd15B8 magnets

The intrinsic nucleation and instability fields of uniaxial single domain particles are determined including the effects of the second anistropy constant and of oblique applied magnetic fields. The theoretical results for the angular dependences of the nucleation and pinning fields are compared with the angular dependence of the coercive field as measured for oriented sinter magnets of composition Fe₇₇Nd₁₅B₈. The experimental results are compatible with the assumption that at room temperature the coercive field in Fe₇₇Nd₁₅B₈ is determined by a nucleation mechanism.     

General features of the intrinsic ferroelectric coercive field

The value of the intrinsic ferroelectric coercive field is obtained independently, from general energy considerations and from the predictions of several models of the ferroelectric state. All predictions yield a value of the order of the depolarization field, which is equal to the spontaneous polarization divided by the dielectric permittivity, and are consistent with the recent measurements of the intrinsic ferroelectric coercive field in ultrathin Langmuir-Blodgett films of copolymers of polyvinylidene fluoride with trifluoroethylene. Prior studies succeeded only in measuring the much smaller extrinsic coercive fields, which are limited by nucleation processes and domain motion.     

Temperature dependence of the coercive force of deformed silicon iron crystals

The temperature dependence of the coercive force of deformed silicon iron (Fe-3.15 Si) crystals was studied. It was shown that the current theories relating coercive force to dislocation density do not explain changes observed in H_c. The latter were attributed to changes in the domain structure whose necessity was proved thermodynamically.     

Theory of the coercive field in amorphous ferromagnetic alloys

The coercive field of amorphous ferromagnetic alloys is determined by defect structures, surface irregularities, relaxation phenomena and intrinsic fluctuations of the material properties. Within the framework of micromagnetism these different contributions are determined quantitatively. It is shown that in magnetostrictive alloys defect structures are dominant whereas in non-magnetostrictive materials surface irregularities and relaxation effects become important.     

Scaling of the coercive field in ferroelectrics at the nanoscale

The scaling of the coercive field in ferroelectric films at the nanoscale is investigated experimentally. The scaling in the films of copolymer vinylidene fluoride and BaTiO₃ with thickness equal by the order of value to the critical domain nucleus size 1–10 nm reveals deviation from the well-known Kay-Dunn law. At this thickness region coercive field does not depend on thickness and coincides with Landau-Ginzburg-Devonshire value.     

Out-of-plane coercive field of Ni80Fe20 antidot arrays

The out-of-plane magnetic anisotropy and out-of-plane magnetization reversal process of nanoscale Ni₈₀Fe₂₀ antidot arrays deposited by magnetron sputtering technique on an anodic aluminum oxide (AAO) membrane are investigated. The angular dependence of out-of-plane remanent magnetization of Ni₈₀Fe₂₀ antidot arrays shows that the maximum remanence is in-plane and the squareness of the out-of-plane hysteresis loop follow a |cos θ| dependence. The angular dependence of out-of-plane coercivity of Ni₈₀Fe₂₀ antidot arrays shows that the maximum coercivity lies on the surface of a cone with its symmetric axis normal to the sample plane, which indicates a transition of magnetic reversal from curling to coherent rotation when changing the angle between the applied magnetic field and the sample plane.     

Angular dependence of the coercive force of textured rare earth permanent magnets

On the basis of model calculations experimental results on the angular dependence of the coercivity H_c and the remanence coercivity H_R of hard magnetic materials of the type SmCo₅, Sm₂(Co, Fe, Cu, Zr)₁₅ and Nd₂Fe₁₄B are discussed. In the model coherent rotation as well as incoherent magnetization jumps (e.g. 180°-Bloch walls) are included. The texture is described by an axial symmetric distribution of the easy axes with only oneparameter. For Sm₂(Co, Fe, Cu, Zr)₁₅ the model explains irreversible (H_R (θ)-curves) as well as reversible (H_R(θ)−H_c(θ)) magnetization processesin good agreement with the experiments, whereas stronger deviations exist for SmCo₅ and Nd₂Fe₁₄B, especially in the H_c(θ)-curves. These deviations should be caused by other reversible magnetization processes     

Investigation of ferroelectric coercive field in LiNbO3

3 using the pulse-field method was performed. It was found that the coercive field varies with time after domain reversal. The possible origins of this phenomenon are discussed. Received: 27 January 1997/Accepted: 7 April 1997     

The influence of planar defects on the coercive field of hard magnetic materials

Planar defects are found to act as strong pinning centres in hard magnetic materials. The interaction of the domain wall with planar defects is assumed to originate in a local perturbation of exchange coupling and crystalline anisotropy. The coercive field is calculated within the framework of micromagnetic continuum theory as well as with a discrete lattice theory which accounts for the interaction between the individual atomic spins. The theory has been applied to discuss the influence of grain boundaries and antiphase boundaries in the intermetallic compound Co₅Sm.     

The coercive field of sintered and melt-spun NdFeB magnets

The magnetic hysteresis loops have been investigated in the temperature range between 4.2 and 575 K for aligned sintered permanent magnets of nominal composition Nd₁₅Fe₇₇B₈ and for isotropic melt-spun ribbons of composition Nd₁₅Fe₇₆B₉. The measured temperature and field dependence of the coercive field is analysed within the framework of theoretical results for nucleation fields of the ideal Nd₂Fe₁₄B matrix and, of disturbed surface regions of Nd₂Fe₁₄B grains. Furthermore the pinning of domain walls at thin soft magnetic grain boundary phases is considered for the high temperature range. It is concluded that for both types of NdFeB magnets the relevant magnetic hardening mechanisms at lower temperatures are nucleation processes in magnetically inhomogeneous regions whereas at higher temperatures the pinning of domain walls at grain boundaries predominates. The critical temperature where the change of nucleation hardening to pinning hardening occurs depends sensitivity on the crystal anisotropy, the grain boundary microstructure and the macroscopic grain- and multi phase arrangements.     

Electron emission in ferroelectrics for different values of the coercive field

Results are presented of experimental studies of electron emission from single crystals of triglycine sulfate, nominally pure and doped with Cr³⁺. The relation between the parameters of the processes of switching and electron emission from ferroelectrics by a coercive field and the threshold field for the onset of emission is investigated. It is shown that the temperature and concentration dependences of the threshold field can be explained by the corresponding dependences of the coercive field. Fiz. Tverd. Tela (St. Petersburg) 41, 1675–1678 (September 1999)     

The influence of size on coercive field of ultra soft magnetic materials

We report here a size dependence of the coercive field in the millimeter–centimeter range length scale of ribbon like samples prepared from ultra soft amorphous and nanocrystalline alloys. A model is proposed where surface pinned domain walls are considered having an effective stiffness constant linearly increasing with the demagnetization factor.