Showing papers in "Journal of Applied Physics in 1968"
TL;DR: In this article, an experimental technique using powders is described which permits the rapid classification of materials according to the magnitude of nonlinear optical coefficients relative to a crystalline quartz standard and the existence or absence of phase matching direction(s) for second-harmonic generation.
Abstract: An experimental technique using powders is described which permits the rapid classification of materials according to(a) magnitude of nonlinear optical coefficients relative to a crystalline quartz standard and(b) existence or absence of phase matching direction(s) for second‐harmonic generation.Results are presented for a large number of inorganic and organic substances including single‐crystal data on phase‐matched second‐harmonic generation in HIO3, KNbO3, PbTiO3, LiClO4·3H2O, and CO(NH2)2. Iodic acid (HIO3) has a nonlinear coefficient d14∼1.5×d31 LiNbO3. Since it is readily grown from water solution and does not exhibit optical damage effects, this material should be useful for nonlinear device applications.
5,070 citations
TL;DR: In this article, a theoretical study on the optimization of second harmonic generation (SHG) and parametric generation (PG) by a laser beam in a uniaxial nonlinear crystal is presented.
Abstract: A theoretical study is presented on the optimization of second harmonic generation (SHG) and parametric generation (PG) by a laser beam in a uniaxial nonlinear crystal. Numerically computed curves show the dependence of the SHG power, and the reciprocal of the PG threshold power, on the parameter l/b, where l is the optical path length in the crystal and b is the confocal parameter (determined by the focal length of the focusing lens and the minimum radius of the laser beam, assumed to be in the TEM00 mode of an optical resonator). The calculations take full account of diffraction and double refraction. In the absence of double refraction, the optimum focusing condition is found to be l/b=2.84. For PG the optimization of the crystal length l is also discussed, and curves are given showing the dependence of the threshold on l for the case in which signal and idler have the same losses. It is shown that the computed functions are also relevant to the mixing of two Gaussian beams and to parametric amplificat...
1,700 citations
TL;DR: In this paper, the effect of the Josephson pair current in a weak-link superconductor junction is considered and two special cases which illustrate the basic principles involved are worked out.
Abstract: Because the Josephson pair current in a weak‐link superconductor junction is a nonlinear parametric function of junction voltage, the ac impedance seen by the junction influences both the response time to changes in bias and the dc voltage‐current characteristics. The first effect is obvious; the second, considered here, has not been generally recognized. Both are relevant to device design. Two special cases which illustrate the basic principles involved are worked out in detail; they correspond, respectively, to ac capacitive and inductive loading. The results partly explain differences in the dc voltage‐current characteristics of plane‐parallel and point‐contact junctions.
1,153 citations
TL;DR: In this paper, the axially symmetric eddy-current problems are solved in two configurations of wide applicability. But the solutions are in the form of integrals of first-order Bessel functions giving the vector potential, from which other electromagnetic quantities of interest can be obtained.
Abstract: Solutions have been obtained for axially symmetric eddy‐current problems in two configurations of wide applicability. In both cases, the eddy currents are assumed to be produced by a circular coil of rectangular cross section, driven by a constant amplitude alternating current. One solution is for a coil above a semi‐infinite conducting slab with a plane surface, covered with a uniform layer of another conductor. This solution includes the special cases of a coil above a single infinite plane conductor or above a sheet of finite thickness, as well as the case of one metal clad on another. The other solution is for a coil surrounding an infinitely long circular conducting rod with a uniformly thick coating of another conductor. This includes the special cases of a coil around a conducting tube or rod, as well as one metal clad on a rod of another metal. The solutions are in the form of integrals of first‐order Bessel functions giving the vector potential, from which the other electromagnetic quantities of interest can be obtained. The coil impedance has been calculated for the case of a coil above a two‐conductor plane. The agreement between the calculated and experimental values is excellent.
1,027 citations
TL;DR: In this article, the spontaneous polarization of ferroelectric Bi4Ti3O12 was shown to be monoclinic point group m at 25°C, where m is the number of points in the a−c plane.
Abstract: The symmetry of ferroelectric Bi4Ti3O12 is shown to be monoclinic point group m. The spontaneous polarization PS is approx 50 μC/cm2 at 25°C and lies in the monoclinic a‐c plane at an angle of less than 5 deg from the plane of the crystal sheets. A complete determination of the optical indicatrix as a function of temperature is given. Switching for fields along the c axis occurs by a unique ``rocking'' of the large PS vector and leads to interesting electrical‐optical behavior. The domain structure is quite complex, and observed wall orientations are compared with those predicted theoretically.
760 citations
TL;DR: In this article, the authors developed a simple phenomenological model capable of describing the present experimental situation from the standpoint of yield, variance, and bandgap dependence, based on the premise that e, the average amount of radiation energy consumed per pair, can be accounted for by a sum of three contributions: the intrinsic bandgap (EG), optical phonon losses r(ℏωR), and the residual kinetic energy (9/5) EG.
Abstract: The problems dealt with concern the production of electron‐hole pairs in a semiconductor exposed to high‐energy radiation. The goal is to develop a simple phenomenological model capable of describing the present experimental situation from the standpoint of yield, variance, and bandgap dependence. We proceed on the premise that e, the average amount of radiation energy consumed per pair, can be accounted for by a sum of three contributions: the intrinsic bandgap (EG), optical phonon losses r(ℏωR), and the residual kinetic energy (9/5) EG. The approach differs from prior treatments in the sense that the residual kinetic energy relates to a threshold for impact ionization taken to be 32EG in accordance with indications stemming from studies of avalanching in p‐n junctions. This model is subjected to three quantitative tests: (a) Fano‐factor variations are found to reflect the relative weight of phonon losses [K=r(ℏωR)/EG], but residual energy fluctuations govern the statistical behavior for K2 ≲0.3. An appl...
702 citations
623 citations
TL;DR: In this paper, the energy spectra of Auger electrons emitted from many elements and alloys have been observed, and differentiation of the secondary electron energy distribution by perturbation and synchronous detection techniques, and suppression of the effects of low-energy secondaries, were used to obtain well-defined spectra.
Abstract: The energy spectra of Auger electrons emitted from many elements and alloys have been observed. Differentiation of the secondary electron‐energy distribution by perturbation and synchronous detection techniques, and suppression of the effects of low‐energy secondaries, were used to obtain well‐defined spectra. The Auger lines afford a sensitive indicator for light elements, though spectra for elements as heavy as gold have been obtained. Because the method examines only a superficial layer of the sample, it is useful for detecting contamination, surface migration, or segregation, and for diffusion studies. Cleaning of the surfaces is critical for useful analysis. Quantitative analysis is hindered by noise and the lack of known surface conditions for calibration.
391 citations
389 citations
TL;DR: In this article, the energy spectra of Auger electrons from clean Au, Ag, Cu, Pd, and Ni surfaces have been determined, and the mean escape depth for Ag (without significant loss of energy) varies between 4 and 8 A for energies of 72 and 362 eV, respectively.
Abstract: The energy spectra of Auger electrons from clean Au, Ag, Cu, Pd, and Ni surfaces have been determined. Uniform deposition of a second metal onto clean metal surfaces has made it possible to assess the depth of the surface region which contributes to the Auger peaks in the secondary electron energy distribution characteristic. These results indicate that the mean escape depth for Auger electrons in Ag (without significant loss of energy) varies between 4 and 8 A for energies of 72 and 362 eV, respectively. It has been shown (using Auger electron spectroscopy for detection of surface imuprities and low‐energy electron diffraction for determining surface structure) that a clean Au (100) surface is reconstructed into a (1×5) structure, while clean Ag (100), Cu (100), and Pd (100) surfaces are characterized by bulk atomic arrangement. The combination of these two techniques has also been effectively applied to the interpretation of the structure and composition of CuAu surface alloys.
386 citations
TL;DR: Poole-Frenkel model for internal field assisted thermal emission with compensation for relative densities of donor and acceptor sites was proposed in this paper, where the model was applied to thermal emission.
Abstract: Poole-Frenkel model for internal field assisted thermal emission with compensation for relative densities of donor and acceptor sites
TL;DR: In this paper, the average size of acicular γ-Fe2O3 particles of the type used in magnetic recording tapes was determined from x-ray line broadening, and all magnetic properties showed a strong dependence on average crystallite size.
Abstract: Magnetic properties have been measured for a number of samples of acicular γ‐Fe2O3 particles of the type used in magnetic recording tapes. The average particle size and shape were approximately the same for all samples. However, the average crystallite sizes of the samples, as determined from x‐ray line broadening, ranged from 50 to 700 A. All magnetic properties measured showed a strong dependence on average crystallite size. Saturation magnetization at room temperature, σ, decreased sharply with decreasing crystallite size. An excellent fit to the σ vs crystallite size data was made by assuming that the crystallites were separated by a nonmagnetic grain boundary on the order of 6 A wide. Room‐temperature coercive force decreased with decreasing crystallite size, and the ratio Hc(83°K)/Hc(293°K) increased sharply with decreasing crystallite size.The data support a particle model in which the constituent crystallites interact magnetostatically across nonmagnetic grain boundaries. A critical crystallite diameter of order 400 A may be inferred. Below this crystallite size, superparamagnetic behavior is observed; above this size, noncoherent magnetization reversals in the crystallites are suggested. This model is quite consistent with the ``fanning'' mode of reversal based on a ``chain‐of‐spheres'' model which has been considered by several authors to be most compatible with their data on γ‐Fe2O3 particle assemblies.
TL;DR: In this paper, carbon was deposited on virgin, natural diamond powder from methane gas at 1050°C and 0.3 Torr. The deposits were identified as new diamond by chemical analysis, chemical etching, density measurements, x-ray and electron diffraction, microwave absorption, electron spin resonance, and visual observations.
Abstract: Carbon was deposited on virgin, natural diamond powder from methane gas at 1050°C and 0.3 Torr. The deposits were identified as new diamond by chemical analysis, chemical etching, density measurements, x‐ray and electron diffraction, microwave absorption, electron spin resonance, and visual observations. The crystalline quality of the new diamond layers has not been established; it cound range from polycrystalline material with a large number of defects to true epitaxial layers.
TL;DR: In this paper, the magnetic moments of the slowly cooled and quenched material are 3.4 and 3.9 μB per unit chemical formula, respectively, and the Neel temperatures are 798°K and 792°K, respectively.
Abstract: Mossbauer spectra of CoFe2O4 show that this spinel is not completely inverse and that the degree of inversion depends on the heat treatment of the material. The magnetic moments of the slowly cooled and the quenched material are 3.4 and 3.9 μB per unit chemical formula, respectively, and the Neel temperatures are 798°K and 792°K, respectively. From the width and the shape of the absorption lines of the Mossbauer spectra several magnetic hyperfine fields have been identified with different B sites and the temperature dependences of these fields have been determined. The different hyperfine fields have been attributed to 57Fe nuclei in B sites with different ratios of iron and cobalt ions in the six nearest‐neighbor A sites.
TL;DR: In this article, it was shown that both compounds represent spontaneous collective-electron magnetism and that the reduced moment of SrRuO3 is due to holes in both the up-spin and down-spin bands.
Abstract: Magnetization measurements of SrRuO3 and CaRuO3 confirm that SrRuO3 is ferromagnetic with TC = (160±5) °K and that CaRuO3 has antiferromagnetic exchange interactions dominant. They further identify in CaRuO3 a Neel temperature TN = (110±10) °K and parasitic ferromagnetism below TN having a σ0 = (3.2±0.4) × 10−2 emu/g at 4.2°K. High‐field (to 125 kOe) magnetization and neutron‐diffraction data for SrRuO3 are consistent with a reduced spontaneous ferromagnetic moment μ0 = (1.4±0.4) μB and no ordered antiferromagnetic component. Resistivity measurements confirm a low resistivity (ρ<10−3Ω·cm) at room temperature having a metallic temperature coefficient. It is concluded that both compounds represent spontaneous collective‐electron magnetism and that the reduced moment of SrRuO3 is due to holes in both the up‐spin and down‐spin bands. Antiferromagnetic CaRuO3 is predicted to have narrower ``4d'' bands.
TL;DR: In this paper, the origin of pulse formation in laser is investigated in terms of a homogeneously broadened, two-level ring laser model, and a simple approximate equation is derived, by which most of the features of the final pulse are given analytically.
Abstract: The origin of pulse formation in lasers is investigated. The main features of this phonomenon are explained in terms of a homogeneously broadened, two‐level ring laser model. First, it is found that a stationary (cw) solution cannot exist for certain choices of laser parameters. By a numerical integration of the laser equations, it is shown next that a buildup of a pulse occurs for these parameters. The final (steady‐state) pulse shape and its velocity are determined. Furthermore, it is found that a multistable operation is possible. A simple approximate equation is derived, by which most of the features of the final pulse are given analytically.
TL;DR: In this article, the absolute saturation of Fe and Ni was determined by considering all contributions in the change of magnetization in high magnetic fields, i.e., internal demagnetizing fields, homogeneous rotations, and paramagnetic terms.
Abstract: Numerous measurements of saturation magnetization of Fe and Ni are reported. Saturation magnetization is determined by consideration of all contributions in the change of magnetization in high magnetic fields, i.e., internal demagnetizing fields, homogeneous rotations, and paramagnetic terms. The value found for the absolute saturation of iron is σ0,∞ = 221.71±0.08 emu/g, corresponding to M = 2.216 μB, in good agreement with previously accepted values. For Ni, the absolute saturation value obtained is σ0,∞ = 58.57±0.03 emu/g, corresponding to M = 0.616 μB, in good agreement with other previous data but 1.6% larger than the Weiss and Forrer's value of M = 0.606 μB.
TL;DR: In this paper, a pressure-induced phase transformation in NaCl which occurs rapidly and reversibly at approx 300 kbar and room temperature has been observed in a diamond-anvil high-pressure cell.
Abstract: A pressure‐induced phase transformation in NaCl which occurs rapidly and reversibly at approx 300 kbar and room temperature has been observed in a diamond‐anvil high‐pressure cell. X‐ray diffraction data indicate that the high‐pressure polymorph has the cesium chloride (B2) structure. The lattice parameters of the low‐ (B1) and high‐ (B2) pressure phases at the transformation pressure are, respectively, 4.872±0.004 A and 2.997±0.004 A, and the volume change for the transformation is − 1.00±0.05 cm3 mole−1. The entropy change for the phase transformation has been calculated from the volume change and from the high‐temperature‐pressure data obtained by the shock experiments of Fritz et al. and found to be 1.5±0.3 cal deg−1 mole−1. Comparison with other alkali chlorides indicates that a linear relationship exists between the entropy change and the volume change for the B1‐B2 phase transformation. A thermodynamic equation accounting for this relationship has been derived under the assumption that the Gruneisen parameter is proportional to the Ath power of the volume. An equation which relates this factor A to the adiabatic bulk modulus and its pressure and temperature derivatives has also been derived.
TL;DR: In this article, a schematic band model for the ferromagnetic phase is presented, where localized ''3d'' electrons occur at thermally excited highspin Co3+ ions, from strontium-rich regions, where the ''3D'' electrons are collective and give ferromagnetism at low temperatures.
Abstract: Crystallographic, magnetic, and electrical studies of the system La1−xSrxCoO3.00±0.01 for 0≤x≤0.5 give indirect evidence for the presence of chemical inhomogeneities separating strontium‐free regions, where localized ``3d'' electrons occur at thermally excited high‐spin Co3+ ions, from strontium‐rich regions, where the ``3d'' electrons are collective and give ferromagnetism at low temperatures. These different regions occur within the same rhombohedral perovskite crystal and appear to represent two different electronic phases within the same crystallographic phase. A schematic band model for the ferromagnetic phase is presented.
TL;DR: In this article, the dielectric constants of the materials were determined at a frequency of 0.53 GHz and at temperatures up to 800°C, and the results leave little doubt that BiFeO3 is ferroelectric or antiferroelectric.
Abstract: Solid solutions of BiFeO3 with PbTiO3, PbTi0.5Zr0.5O3, and PbZrO3 were prepared. The crystallographic data on these solutions, which are basically perovskitic, are given. The dielectric constants of the materials were determined at a frequency of 0.53 GHz and at temperatures up to 800°C. Dielectric Curie points were found in solutions containing up to 90 mole % BiFeO3. These results leave little doubt that BiFeO3 is ferroelectric or antiferroelectric. The extrapolated Curie point for BiFeO3 is above 850°C. BiFeO3 appears more likely to be ferroelectric than antiferroelectric, but the distinction between the two classifications may not be sharp.
TL;DR: A simple scanning transmission electron microscope has been built using a field-emission electron source, a new electron gun, and one lens to produce a high-contrast picture with 30 A resolution.
Abstract: A simple scanning transmission electron microscope has been built using a field‐emission electron source, a new electron gun, and one lens to produce a high‐contrast picture with 30 A resolution. The final spot size is limited by the properties of the lens, in the same manner as a conventional transmission microscope. The field‐emission tip requires a pressure below 10−9 Torr for stable operation and can have a lifetime of several months. The intensity of the source is such that high‐quality pictures can be obtained in 10 sec. Specimen contamination or damage is small, as would be expected in view of the good vacuum conditions. The theory and design of the instrument are discussed, and experimental results are shown.
TL;DR: In this article, a very fine stylus is pressed against the surface of a metal crystal with a load which can be as small as 10−4 g, and the deformation observed simultaneously by performing the experiment in a scanning electron microscope.
Abstract: A technique is described for observing and measuring the deformation of solids on a very small scale. A very fine stylus (approx 1000 A in diameter) is pressed against the surface of a metal crystal with a load which can be as small as 10−4 g, and the deformation observed simultaneously by performing the experiment in a scanning electron microscope. Measurements were made on crystals of gold, copper, and aluminium. The behavior under these conditions of microdeformation was unusual in that no penetration occured until a critical load was reached. This critical load was frequently very high and corresponded to a shear strength which approached the theoretical shear strength of metals. Microfriction experiments could also be performed by allowing the stylus to slide over the crystal and the nature of the surface deformation could be examined during the sliding process.
TL;DR: In this paper, the dilatations are explained as compaction of the silica structure resulting from oxygens moving into some of the ''free volume'' where they may be locked-in on reco...
Abstract: The dilatations (negative) caused by neutrons, 40–600 keV electrons, 140 keV H+, D+, He+, and gamma rays are given as a function of dose and are compared. The presaturation dependence is linear for neutrons, He+, and D+, and depends on the 0.5–0.7 power of dose for H+, electrons, and gamma rays. The dilatations are not temperature dependent from about 0°–100°C, hence are not thermally activated. The dilatations are explained as compaction of the silica structure resulting from oxygens moving into some of the ``free volume,'' the structural change being similar to that occurring on pressure, shock, or thermal compaction of vitreous silica. The mechanism given for the neutron‐induced compaction involves the state of high vibrational excitation developed in the slowing down of scattered atoms. The compaction by gamma rays, electrons, protons, or deuterons is explained as caused by transient ionization relaxing Si–O binding to permit oxygens to move into the ``free volume'' where they may be locked‐in on reco...
TL;DR: In this article, the authors consider the effects of heating when the applied field is changed suddenly and magnetic flux enters adiabatically into the bulk of a semi-infinite slab of superconductor.
Abstract: The isothermal critical‐state model of hard superconductors is extended to include the effects of heating when the applied field is changed suddenly and magnetic flux enters adiabatically into the bulk. We consider the following specific situation. A semi‐infinite slab of superconductor is cooled in a magnetic field lying in its surface plane. Next, the external field is raised isothermally by an amount Hs. This excess field decreases linearly to a depth δ= 10Hs/4πJc from the surface. Finally, the field is raised by an infinitesimal amount ΔH in a time short compared to the thermal diffusion time and long compared to the electromagnetic diffusion time. Each element of volume exposed to the changing field receives a thermal impulse proportional to the local‐flux‐change times Jc. This thermal impulse, in turn, lowers the critical current and allows more flux to penetrate. We find that if Hs exceeds some critical value Hfj, then the isothermal critical state is not the only allowed state of the superconductor. This instability field is given in terms of the critical current density Jc, derivative of the critical current density with temperature, ∂Jc/∂T, and the volume specific heat C by the formula Hfj= [−π3CJc/(∂Jc/∂T)]1/2. The application of the incremental field ΔH can initiate an avalanching process, or a flux jump, that terminates in an adiabatic critical state. Immediately following the flux jump the internal field, the induced supercurrent, and the temperature rise at each position are associated in a self‐consistent way with the avalanche of flux that has entered the superconductor. In this framework a flux jump is viewed as a switching from the isothermal critical state to an adiabatic critical state. The magnitude of the jump is related to Js and is calculated.
TL;DR: In this article, the phase boundaries at approximately 825, 675, and 525 mole × NaNbO3 at 25°C, in addition to one very near the NaNBO3 end member.
Abstract: Thermal and x‐ray diffraction measurements on compositions from the system NaxK1−xNbO3 have revealed the presence of phase boundaries at approximately 825, 675, and 525 mole × NaNbO3 at 25°C, in addition to one very near the NaNbO3 end member The optimum piezoelectric properties in this system are apparently associated with compositions near the latter boundary Calorimetric determinations of the enthalpy and entropy changes associated with the ferroelectric→ferroelectric and ferroelectric→paraelectric transformations in the system clearly revealed the presence of the phase boundaries while measurements of the transformation temperatures alone did not readily reveal the boundaries Two different superlattice perovskite phases were observed in the system, one existing in the region ∼098≥x≥0825 and another in the region 0825≥x≥0675 No multiple‐cell structures were observed in the system at NaNbO3 concentrations below about 70 mole%
TL;DR: In this paper, the electrocaloric effect, antiferroelectric to ferroelectric transitions, and hysteresis loss heating have been recorded together with the hystresis loops for four different ceramic ferroelectrics near room temperature.
Abstract: Variations of sample temperature arising from the electrocaloric effect, antiferroelectric to ferroelectric transitions, and hysteresis‐loss heating have been recorded together with the hysteresis loops for four different ceramic ferroelectrics near room temperature. Both the electric‐field dependence and the temperature dependence of the electrocaloric effect were accurately predicted by the usual thermodynamic expression for the effect. Values for the heat capacity and the pyroelectric constant were also obtained from the data. The sample temperature of one composition which becomes antiferroelectric under zero applied field near 40°C was monitored at various temperatures as antiferroelectric to ferroelectric transitions were forced by an electric field. Above 55°C, the temperature change at the transition could be fitted with a theory originally developed for the field‐enforced antiferroelectric to ferroelectric transition in PbZrO3.
TL;DR: In this paper, the authors considered the itinerant electron model in the limit of very low exchange splitting energies and derived the magnetic isotherms giving M(H, T) to cover a wide range of fields and temperatures.
Abstract: The itinerant electron model is considered in the limit of very low exchange splitting energies. Magnetic isotherms giving M(H, T) are derived to cover a wide range of fields and temperatures. The isotherms are transformed so as to show that plots of M 2 vs H/M at different temperatures give parallel straight lines. The differential susceptibility below and above the Curie temperature is derived as a function of T. The free energy corresponding to this model is calculated and several results concerning the specific heat of very weak itinerant ferromagnets are deduced. Some properties related to spin wave excitations are also considered. New experimental data on the material ZrZn2 are considered on the basis of the theory and shown to be in reasonable agreement with it. Several characteristic parameters of this material are deduced, for example a value of the exchange splitting energy 0.040 eV, and of the effective interation between the itinerant electrons 0.35 eV. The occurrence of very weak itinerant ferromagnetism in other substances is also discussed.
TL;DR: The Hall mobility of holes in silicon p-type inversion layers has been measured as a function of gate voltage (perpendicular electric field), inversion layer orientation (100, (110), and (111) surfaces), direction of current flow within an inversion, and temperature as discussed by the authors.
Abstract: The Hall mobility of holes in silicon p‐type inversion layers has been measured as a function of gate voltage (perpendicular electric field), inversion layer orientation [(100), (110), and (111) surfaces], direction of current flow within an inversion layer, and temperature. It has been shown that hole mobility in silicon inversion layers depends not only on the crystalline orientation of the inverted surface, but also on the azimuthal direction of current flow within the inversion layer. Thus, on the (110) silicon surface at room temperature, the inversion‐layer hole mobility is 40% higher in the[l10] direction than in the [001] direction. Room‐temperature piezoresistance tensors have been experimentally determined for inversion layers on the (100), (110), and (111) surfaces of silicon. It is found that, in general, the piezoresistance coefficients are not the same as those for the same directions in bulk silicon and that they depend on the orientation of the surface. The existence of these anomalous effects can be understood in terms of quantization of the carrier wavefunction in the surface channel, which is narrow compared with the carrier wavelength in bulk silicon. This quantization tends to depopulate that part of the Brillouin zone within which k⊥, the component of wavevector perpendicular to the surface, is small. If the dependence of energy on k is not quadratic, as is true for the valence band of silicon, the effective masses for conduction in the plane of the surface can be complicated functions of k⊥. The mass anisotropies estimated from the cyclotron resonance parameters for the valence band of bulk silicon are in qualitative agreement with the experimental mobility values.
TL;DR: The theory of fine-particle magnets is based on the theorem that the state of lowest free energy of a ferromagnetic particle is one of uniform magnetization for particles of less than a certain critical size.
Abstract: The theory of fine‐particle magnets is based on the theorem that the state of lowest free energy of a ferromagnetic particle is one of uniform magnetization for particles of less than a certain critical size and one of nonuniform magnetization for larger particles. The theorem is inferred from several approximate calculations and has not been proved rigorously. Rigorous statements can be made if one is content to replace equalities by inequalities and exact values of critical radii by upper and lower bounds. For a sphere of radius a with uniaxial anisotropy, it can be shown that the lowest‐free‐energy state is one of uniform magnetization if a ac1 (for low anisotropy) or ac2 (for high anisotropy), where ac0, ac1 (>ac0), and ac2(>ac0) are determined by the exchange and anisotropy constants and the spontaneous magnetization. These bounds locate the critical radius to within about 12% at low anisotropy but only to within an order of magnitude or more at high.