Single-ion Model Research Articles

Numerical Simulation of Carbon Impurities In JT‐60U Experiment

AbstractNumerical simulation of the behavior of carbon impurity for the JT‐60U divertor experiment has been carried out. Two approaches are examined for the impurity model: (1) a full charge state model and (2) a single average ion model. The full model simulates fairly well the power loss due to the impurities. The amount of power loss obtained by the single average ion model disagrees with that of the full model.

Stress induced anisotropy and temperature dependence of the magnetostriction in Fe73.5Cu1Nb3Si13.5B9 amorphous alloy

The magnetic anisotropy, Kσ, induced by heating under applied tensile stress has been studied for the Fe73.5Cu1Nb3Si13.5B9 amorphous alloy as a function of the annealing temperature. The induction process was carried out by means of current annealing in samples as-quenched and preannealed (TP.A.=400 °C during 2 min). It is found that the easy axis of this anisotropy is transverse to the tensile stress. The dependence of the stress induced anisotropy on annealing temperature is, in both cases, similar to that reported in other different metallic glasses when annealing at temperature below Tc=350 °C, while Kσ is practically constant (≊500 J m−3) in the annealing temperature range from 350 to 525 °C. On the other hand, the magnetostriction constant, λs, was determined as a function of the measuring temperature within the range from 4.2 K up to 600 K. The results can be well accounted for by the single-ion model up to 350 K, while above this temperature the contribution of two-ion mechnism is also inferred.

Analysis of the magnetic properties of R2Co17 (R=Pr, Nd, Sm, Gd, Tb, Dy, Ho, and Er).

High-field isotherms at low and high temperatures and other magnetic properties of ${\mathit{R}}_{2}$${\mathrm{Co}}_{17}$ (R=Pr, Nd, Sm, Gd, Tb, Dy, Ho, and Er) measured on single crystals are analyzed on the basis of the single-ion model. The fitted crystalline electric-field parameter ${\mathit{A}}_{20}$ for the Pr ion is several times smaller in absolute value than those for all the other rare-earth ions. The result is similar to that observed in the R${\mathrm{Co}}_{5}$ series, and it is suggested that the Pr ion in ${\mathrm{Pr}}_{2}$${\mathrm{Co}}_{17}$, as in ${\mathrm{PrCo}}_{5}$, is valence fluctuated.

Anomalous magnetic properties of Pr ions in PrxR1-xCo5 (R identical to Y,Sm)

The magnetic hyperfine fields of Pr ions in PrCo5 are measured by spin-echo NMR at 4.2 K. The magnetic properties for the PrxY1-xCo5, PrxSm1-xCo5 and DyxSm1-xCo5+0.2x compounds are analysed on the basis of the single-ion model under the assumption that rare-earth ions are triply ionized. The magnetic moment and the hyperfine fields for Pr ions in PrCo5 are calculated to be much larger than those observed in experiments, while good agreement is observed for Sm and Dy ions in SmCo5 and DyCo5.2, respectively.

Crystalline electric field at the rare-earth sites in R xY 1 - xCo 5 + y compounds (R = Dy and Tb)

The magnetic properties of R x Y 1 - x Co 5 + y compounds are reproduced well by a calculation based on the single-ion model. The values of the exchange field H cx and crystalline-electric-field parameters A m n at the rare-earth ion sites in R x Y 1 - x Co 5 + y (R = Dy and Tb) are evaluated by fitting the calculations to the experiments. The experiments include the temperature dependence of the spontaneous magnetization, the temperature dependence of the normalized magnetic moments of the rare-earth ions, the temperature dependence of the cone angle, the magnetization curves along the crystal axes at 4.2 K, and the hyperfine field at the Dy ion site.

Perpendicular anisotropy in magnetic multilayer films

A single-ion model approximated by point charge interaction is proposed to account for the perpendicular anisotropy K u in Tb/Fe, Pt/Co multilayer films. For the former, a quasi-self-consistent method of determining the crystal field coefficient D and the average orientation of the moments in the interface is developed during the fitting process of K u. For the latter, spin-orbit coupling under the control of a trigonal crystal field is proposed to be the origin of the observed perpendicular anisotropy. Furthermore, the criterion for the appearance of the perpendicular anisotropy in the two kinds of multilayer films is discussed.

Abnormal magnetic properties of the Nd ion in Nd xY 1−xCo 5 compounds

It reveals that the calculation based on the single-ion model fails in reproducing a series of experiments for Nd xY 1−xCo 5 compounds. The experiments include the temperature dependence of the spontaneous magnetization, the temperature dependence of the cone angle, and the magnitization curves along the crystal axes at 4.2 K. In the calculation, it was assumed that the rare-earth ions are triply ionized. If, for a satisfactory reproduction of the experiments, it is allowed that the main crystalline-electric-field parameter A 20 varies with temperature, decrease of A 20 with increase of temperature becomes unreasonably fast. The values of the magnetic moment of the Nd ion and the hyperfine field at the nucleous of the Nd ion were calculated, by using the fitted parameters, to be much higher than those observed in experiments. The abnormal results suggest that the Nd ion is valence fluctuated.

Magnetostriction of (Fe-Co)3 Tb Compounds and Amorphous Fe3 Tb Alloys

The magnetostriction of (Fe 1-x Co x ) Tb (0?×?1.0) compounds and amorphous Fe 3 Tb alloys were measured at room temperature and at 77K. The value of ? ? -? ? at 77K and 20 kOe of (Fe 1-x Co x ) 3 Tb compounds increases drastically from 1500×10?6 to 3000×10?6 as x is increased from 0 to 1.0. The value of ? ? -? ? for amorphous Fe 3 Tb is about 30 to 40% smaller than the value for the crystalline material. The effect of Co substitution on the magnetostriction of (Fe 1-x Co x )Tb compounds is discussed on the basis of the single ion model. The magnetic field dependence of magnetostriction in Fe 3 Tb amorphous alloy is also discussed in connection with the magnetization process.

Low lying energy levels of CsFeCl3

Submillimeter wave ESR has been performed to investigate the singlet ground state and the first excited doublet of the quasi-1D hexagonal magnet CsFeCl3 at 4.2 K. Using backward travelling wave tubes of 220 GHz and 370 GHz bands combined with pulsed magnetic fields up to 10 T, we succeeded in observing all five possible transitions for H//c and HIc for the first time. The results suggest that the single ion model is not applicable to this system in order to interpret all the absorption lines observed in our experiment.

Spin reorientation transition in mixed (Dy, Gd)Fe 11Ti alloys

The spin reorientation temperature of (Dy 1− x Gd x )Fe 11Ti alloys was determined from ac susceptibility measurements in the 80–300 K temperature range. The reorientation was theoretically analyzed with the help of a single-ion model for the rare-earth crystal-field and exchange interactions. The T SR vs x dependence was calculated by using the CEF parameters of Hu et al. (ref. [10]) as a starting point. With a slight adjustment an excellent agreement with our data was obtained.

Magnetization and perpendicular anisotropy in Tb/Fe multilayer films.

A single-ion model approximated by point-charge interactions is proposed to account for the perpendicular anisotropy K(u) in Tb/Fe multilayer films with variant modulation periods. In multilayers, K(u) depends not only on the crystal field, but also on the orientation of the magnetic moments along the z direction in the period. A quasi-self-consistent method of determining the crystal-field coefficient D and the average orientation of the moments in the interface was developed during the fitting process of K(u). The crystal-field coefficient D = 2.4 X 10(-17) erg is determined. The best-fit values of K(u) and M(s) are in good agreement with experiment.

Self-consistent approximation for spin-1/2 quantum Heisenberg antiferromagnets.

A single-ion model approximated by point-charge interactions is proposed to account for the perpendicular anisotropy K(u) in Tb/Fe multilayer films with variant modulation periods. In multilayers, K(u) depends not only on the crystal field, but also on the orientation of the magnetic moments along the z direction in the period. A quasi-self-consistent method of determining the crystal-field coefficient D and the average orientation of the moments in the interface was developed during the fitting process of K(u). The crystal-field coefficient D = 2.4 X 10(-17) erg is determined. The best-fit values of K(u) and M(s) are in good agreement with experiment.

（Ｆｅ‐Ｃｏ）３Ｔｂ化合物並びに非晶質Ｆｅ３Ｔｂの磁歪

Magnetostriction of (Fe1-xCox)3Tb (0≤x≤1.0) compounds and amorphous Fe3Tb alloy were measured at room temperature and 77K. The value of λ//λ⊥ at 20 kOe of (Fe1-xCox)3Tb compounds increases drastically from 1500×10-6 to 3000×10-6 with increases in x from 0 to 1.0 at 77K. The value of λ//λ⊥ for amorphous Fe3Tb is about 30-40% smaller than that for the crystalline one. The effect of Co substitution on magnetostriction of (Fe1-xCox)3Tb compound is discussed based on the single ion model. The magnetic field dependence of magnetostriction in Fe3Tb amorphous alloy is also discussed in connection with magnetization process.

Properties of photorefractive nonstoichiometric bismuth silicon oxide, BixSiO_15x_+2

Single crystals of bismuth silicon oxide (BSO) were Czochralski grown nonstoichiometrically from high-purity starting materials. Several series of three crystals were grown from nonstoichiometric melts starting with a bismuth oxide–rich melt. The intrinsic absorption shoulder of BSO was modified in amplitude with growth from nonstoichiometric melts. Two-beam coupling was used to determine photorefractive material parameters of the nonstoichiometric crystals. The data were analyzed with the two-beam coupling, two-carrier single multivalent ion model of the photorefractive effect. Parameters determined include the effective trap density, the hole–electron competition parameter, and the ratio of hole-to-electron absorption. Higher absorption correspond to a higher effective trap density and gain coefficient. The two-beam coupling gains, measured in the diffusion regime, are believed to be the largest reported for BSO, 0.70 cm−1, and are correlated to nonstoichiometric-growth-induced changes in the native defect concentrations.

Measurement of pre-sheath flow velocities by laser-induced fluorescence

For the first time, the pre-sheath ion flow velocity has been measured using the Doppler shift of laser-induced fluorescence in singly-ionized argon ions. The velocity shows a monotonic increase, from a value of about 0.15 of the sound speed V S far from the target to 0.5 of V s at a distance of 5 mm from the surface. The temperature, the floating potential and the density are calculated from cylindrical probe measurements taken in the same region under identical conditions. These experimental results are compared with those from a 1D isothermal single-ion fluid model of the pre-sheath and a kinetic electron/fluid ion model. Both models agree well with the density profile, but underestimate the potential change and overestimate the velocity. In addition, the bulk flow velocity has been independently determined from “Mach probe” measurements, using various candidate theories to relate the Mach number to the ratio of the upstream to downstream saturation currents. Comparison with the optical measurements indicate that the probe models which include viscosity provide reasonable agreement with our Mach probe data.

The magnetic anisotropy of R2Fe14B (R = Nd, Pr) and error analysis

The anisotropy constants K 1, K 2 of R 2Fe 1B (R = Nd, Pr) are calculated on the basis of the single ion model, and the truncation error of the free energy expansion is analysed. At low temperature, we found that the truncation error cannot be neglected but also need to be considered carefully.

A simple model for multi-ion permeation. Single-vacancy conduction in a simple pore model

Recent experimental evidence suggests that certain membrane channels operate in a nearly ion-saturated state. We therefore consider a "single-vacancy" model of ion permeation: if a channel has n conducting sites, it will contain either n or n-1 ions. Simple analytical expressions for the current, conductance, and reversal potential under bi-ionic conditions are derived. The results are compared with those of single ion models and recent experiments on Ca2(+)-activated K+ channels.

Magnetostriction of Amorphous Pr0.2(Fe1-xCox)0.8 Alloys

The magnetostriction of amorphous Pr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.2</sub> (Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> ) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.8</sub> alloys (0 ≤ x ≤ 0.6) and Pr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</sub> (Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.8</sub> Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.2</sub> ) × (Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.43</sub> B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.57</sub> ) × (0.7 ≤ x ≤ 0.85, 0.15 ≤ y ≤ 0.3, 0 ≤ z ≤ 0.3) alloys was measured in the temperature range from 77 to 400°K. The value of the magnetostriction λ (λ=(2/3) [Δ1/1) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">″</sub> -(Δl/l) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⊥</sub> ]) for Pr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.2</sub> (Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> ) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.8</sub> exhibits a maximum at x=0.2; it is about 760 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> at 77°K and 260 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> at room temperature. The temperature dependence of the magnetostriction is discussed in terms of the single-ion model.

HIGH-FIELD MAGNETIZATION PROCESS OF Ho2Fe14B COMPOUND

The magnetization processes of the Ho and Fe sublattices in Ho2Fe14 compound along the [100] , [110] and [001] axes at 0 K are analysed in detail by the calculation based on the single-ion model. The high-field magnetization processes of Ho2Fe14 at 0 K along the principal crystal axes in a field up to 2000 kOe are predicted by the calculation.

Magnetisation processes of the R ions in R2Fe14B (R=Er and Tm) in a field up to 1000 kOe at 78 K

The experiment magnetisation curves M(H) of Er2Fe14B and Tm2Fe14B along the (100), (110) and (001) axes up to 550 kOe measured at 78 K are reproduced well by a calculation based on the single-ion model. The calculations shows that during the magnetisation process in such a high field both the magnetic moment and magnetic anisotropy of the R ion vary strikingly. When the field is applied along the (100) and (110) axes, both the magnetic moment and magnetic anisotropy quench at about 740 and 570 kOe for the Er and Tm ions, respectively. But when the field is applied along the (001) axis, they quench at about 570 kOe for the Tm ion while no quenching occurs for the Er ion.