Higher-harmonic Susceptibilities Research Articles

Inter-grain superconductivity of polycrystalline FeSr2YCu2O6+y

The fundamental and higher-harmonic susceptibilities χn=χn′−iχn′′ (n=1, 2, 3, 5 and 7) were measured to study the inter-grain superconducting properties of polycrystalline FeSr2YCu2O6+y. The real part χ1′ and imaginary part χ1″ appeared below Tc1=56K and Tc2=45K, respectively. Tc1 and Tc2 correspond to the onset temperatures of the superconductivity in individual grains and the superconductivity across grain boundaries, respectively. The higher-harmonic susceptibilities χn (n=2, 3, 5 and 7) appeared below Tc2. The results suggest that the higher-harmonic susceptibilities were generated by the non-linear magnetization caused by the magnetic flux penetration through grain boundaries. The inter-grain magnetization curves were obtained by substituting measured χn in Fourier series. The temperature dependence of χn (n=1, 2, 3, 5 and 7) calculated by the Kim–Anderson critical-state model were approximately fitted with the observed those of χn. The inter-grain critical-current density at 0K under zero magnetic field was estimated at about 2×104A/m2 from the fitting parameters of the Kim–Anderson critical-state model. The magnetization curves and these parameters imply that the inter-grain critical-current density hardly depends on a weak magnetic field below 0.1mT.

Study of magnetization processes using higher harmonic ac‐susceptibility

AbstractThe ac‐susceptibility of a La0.7Sr0.3MnO3 epitaxial film was measured up to the 11th harmonic as a function of ac‐field amplitude, superimposed dc‐field and temperature. The experimental data reflect the magnetization hysteresis‐loop shape in a very precise and detailed way. This is further elucidated by numerical simulations of the ac‐susceptibility within a Preisach model with Gaussian distribution function. Using parameters from magnetization measurements the simulated ac‐susceptibility curves were found to be in good agreement with the experimental results. This shows that measurements of higher harmonic susceptibilities are a powerful tool for the precise study of magnetization processes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

MAGNETIC FIELD RESPONSES OF HARMONIC SUSCEPTIBILITIES OF HIGH TC SUPERCONDUCTOR YBCO

The temperature dependence of the harmonic susceptibilities has been measured on a melt textured YBCO for different amplitudes of the AC magnetic field with combination of a DC magnetic field. The model calculations have been performed on the basis of a model which incorporates the effects of the collective creep concept in a critical-state equation. The temperature dependencies of the activation energy and the critical current density chosen as U = [U0(1 - (T/Tc)4)/μ)][(Jc/J)μ - 1] and Jc = J0[(1 + (T/Tc)2)]-1/2[(1 - (T/Tc)2)]5/2 respectively have been used to explain the DC bias field and temperature dependencies of the harmonic susceptibilities. The predictions of the model for fundamental and higher harmonic susceptibilities were consistent with the experimental data.

Higher harmonics of theacsusceptibility: Analysis of hysteresis effects in ultrathin ferromagnets

The initial ac susceptibility is used to monitor the higher harmonic susceptibilities ${\ensuremath{\chi}}_{n}(T,{\ensuremath{\omega}}_{0})$ as a function of temperature. To our knowledge, for the first time we present ${\ensuremath{\chi}}_{n}(T,{\ensuremath{\omega}}_{0})$ up to $n=11$ for a $({\mathrm{Fe}}_{2}/{\mathrm{V}}_{5}{)}_{50}$ superlattice in the ultrathin-film limit. A detailed analysis of ${\ensuremath{\chi}}_{n}(T,{\ensuremath{\omega}}_{0})$ yields the full temperature-dependent hysteresis loops, including the coercive field ${H}_{C}(T)$ and the saturation magnetization ${M}_{S}(T),$ with high accuracy close to the Curie temperature ${T}_{C}.$ We show that this type of analysis allows for an independent determination of ${T}_{C}.$ In addition, the ${\ensuremath{\chi}}_{n}(T,{\ensuremath{\omega}}_{0})$ are calculated in the framework of a mean-field theory which compares well with the experimental data.

The non-linear susceptibility at metamagnetic transition in TbNiSn

The linear and non-linear AC-susceptibility of TbNiSn single crystals for b-axis has been measured under DC magnetic field at 4.2 and 1.8 K , below Neel temperature. The divergence of the third higher-harmonic susceptibility was observed at the critical fields of metamagnetic transitions. This result suggests the spin relaxation time extremely increase around the critical field.

Vortex dynamics of (Bi,Pb) 2Sr 2Ca 2Cu 3O y silver-sheathed tape by ac susceptibility measurements

The complex ac susceptibility ( χ n = χ ′ n −i χ ′′ n ) measurements were performed on a (Bi,Pb) 2Sr 2Ca 2Cu 3O y silver-sheathed tape to study the vortex dynamics in a time window of 10 −4–10 −2 s . The fundamental ac susceptibility of the tape as a function of temperature, ac field amplitudes and frequencies were obtained. The current dependent activation energy was derived as U( j)∝ j −0.42, characteristic of the vortex glass/collective pinning model. By using such U( j) relation, higher harmonic susceptibilities χ n ( n=2–7) were obtained based on the numerical resolution of the flux diffusion equation. We found that theoretical results agree well with experimental data.

Application of the method of moments for calculating the dynamic response of periodically driven nonlinear stochastic systems

It is shown that the method of moments allows one to calculate the first- and higher-harmonic susceptibilities of nonlinear stochastic systems with high accuracy. The dependence of the spectral amplification at the first three harmonics on the noise intensity is studied. It is shown that stochastic resonance at the third harmonic occurs at two separate values of the noise intensity for not too large a bias. Also, it is demonstrated that even when the bias is so large that the bistable system turns into a monostable one, the stochastic resonant enhancement of the system's sensitivity to the external driving field is still observed at some optimal non-zero value of the noise intensity.

Angular dependence of harmonic ac responses in textured(Bi, Pb)2Sr2Ca2Cu3Oy/Ag tapes

A silver-sheathed (Bi, Pb)2Sr2Ca2Cu3Oy tape isstudied in terms of harmonic ac susceptibilitiesχn = χn'-iχn'' (n = 3, 5, 7) to reveal the angular dependence of its physicalproperties. When the screening method is used, the higher harmonicresponses are directly related to the nonlinear E(J) relationof the sample. Therefore, the effect of the silver sheath on the higherharmonic susceptibilities can be neglected. We perform measurements of theharmonic susceptibilities as a function of applied magnetic field or theangle between the magnetic field and the tape plane at varioustemperatures. The measured data are scaled onto a single curve by using thethree-dimensional scaling relation. The derived anisotropic parameterγ ranges from 5.1 to 5.6 at the measured temperature region, whichis consistent with the values obtained from transport measurements of thesame tape. Such a small γ-value is attributed to the misalignment ofthe grains in the tape.

Increasing of superconducting pinning potential U p and critical current J c due to the hydrogen loading in sintered YBCO

YBCO sintered samples have been hydrogenated using chemical absorption. Experimental measurements of the ac higher harmonic susceptibility versus frequency of applied magnetic field have been performed. Increasing of pinning potential U p and critical current J c due to the adsorbed hydrogen has been found. An increasing of 5% in J c and U p has been quantitatively measured using the non-linear magnetic diffusion equation.

酸化物超伝導体の合成と評価 アモルファス金属錯体法で合成した（Ｌａ１−ｘＣａｘ）（Ｂａ１．７５−ｘＬａ０．２５＋ｘ）Ｃｕ３Ｏ７＋δの高調波複素帯磁率

We measured the temperature dependence of the 2nd, 3rd and 5th higher-harmonic susceptibilities of(La1-xCax)(Ba1.75-xLa0.25+x)Cu3O7+δ, x=0.2, 0.4, 0.5, prepared by the amorphous metal-complex method. We attempted to fit the calculations based on the Kim-Anderson critical-state model to the experimental results of χn. The analysis shows that the pinning force density is enhanced with increasingχ.

酸化物超伝導体の合成と特性 ＭＢＥ法で作成したＹＢａ２Ｃｕ３Ｏ７−ｄ単結晶薄膜の高調波複素帯磁率

酸化物超伝導体の合成と特性 ＭＢＥ法で作成したＹＢａ２Ｃｕ３Ｏ７−ｄ単結晶薄膜の高調波複素帯磁率

Homogeneity of Superconductivity in YBa2Cu3Ox Single Crystals

We investigated the homogeneity of high-purity YBa2Cu3Ox (123) single crystals at different oxygen concentrations by means of the higher-harmonic susceptibility. The superconductivity of the onset temperature at 93.8 K was observed in the samples of the hypostoichiometric composition (x=6.87). Also, we succeeded in obtaining the 123 single crystals of the optimum stoichiometry (x=7.00) which showed a sharp single transition at 92.5 K corresponding to occurrence of the homogeneous superconductivity.

Ｈｏ系セラミック超伝導体の高調波複素帯磁率

For the study of magnetic properties of sintered high-Tc ceramic superconductors, we measured harmonic ac susceptibilities Xn = Xn' - ixn of Bi1.6Pb0.4Sr2Ca2Cu3Oy immersed in an external field H(t) = H'dc + Haccos(ωt), where Hdc (≥ 0) is a dc bias field and Hac (> 0) is an ac field amplitude. Measurements of Xn were carried out for n = 1, 2, 3, 5, 7, 9 and μOHac = 0.01-0.1 mT. The fundamental frequency used was 132 Hz. The observed results were analyzed within the construct of the Kim-Anderson model for critical-current density. Similar to our previous work for an YBa2Cu3Oy sample with Fe impurities, generation of the higherharmonic susceptibilities seems to arise from the supercurrent according to the same model. Details of the measurement and the analysis are presented.

Harmonic susceptibilities of a sintered oxide superconductor.

The superconducting transition of a sintered ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathrm{y}}$ pellet with Fe impurities was measured in terms of harmonic susceptibilities ${\mathrm{\ensuremath{\chi}}}_{\mathrm{n}}$=${\mathrm{\ensuremath{\chi}}}_{\mathrm{n}}^{\ensuremath{'}}$-i${\mathrm{\ensuremath{\chi}}}_{\mathrm{n}}^{\mathrm{\ensuremath{''}}}$ (n=1, 2, 3, 5, and 7). The results were analyzed in the framework of the critical-state model and the weak-link model. Generation of the higher-harmonic susceptibilities seems to arise from the supercurrent according to the Kim-Anderson critical-state model, while the Ishida-Mazaki weak-link model, based on the assumption that the intergrain network behaves like a single loop as a whole due to its coherent nature, fails to describe the data. However, phenomenological considerations suggest that the extended weak-link model, in which a number of coaxial weak-link loops are assumed in the specimen, would be more practical for analyses of the magnetic response of oxide ceramic superconductors prepared by sintering.

Harmonic Susceptibilities of a Single-Crystal YBa2Cu3Oy Bulk Superconductor

The magnetic response of a single-crystal YBa2Cu3Oy bulk specimen in a weak magnetic field was measured in terms of harmonic susceptibilities χn=χn′-iχn′′ (n=1, 2, 3). From the fundamental susceptibility χ1 measured in an ac field parallel and perpendicular to the c axis, we found an apparent anisotropic nature of the sample. χ2 and χ3 were analyzed within the framework of the Kim-Anderson model for critical current density. Comparison of the observed and calculated χn suggests that generation of the higher-harmonic susceptibilities arises from the supercurrent according to the critical-state (Kim-Anderson) model, although the absolute values of calculated χn are several times larger than the observed ones. Details of the experiment are presented together with the analyses of the data.

Ｂｉ系セラミック超伝導体の高調波複素帯磁率

For the study of magnetic properties of sintered high-Tc ceramic superconductors, we measured harmonic ac susceptibilities Xn = Xn' - ixn" of Bi1.6Pb0.4Sr2Ca2Cu3Oy immersed in an external field H(t) = H'dc + Haccos(ωt), where Hdc (≥ 0) is a dc bias field and Hac (> 0) is an ac field amplitude. Measurements of Xn were carried out for n = 1, 2, 3, 5, 7, 9 and μOHac = 0.01-0.1 mT. The fundamental frequency used was 132 Hz. The observed results were analyzed within the construct of the Kim-Anderson model for critical-current density. Similar to our previous work for an YBa2Cu3Oy sample with Fe impurities, generation of the higherharmonic susceptibilities seems to arise from the supercurrent according to the same model. Details of the measurement and the analysis are presented.

超伝導体の交流磁場応答

The measurement of complex susceptibilities Xn = Xn' - ixn in a weak ac magnetic field is one of the useful probes for the study of the magnetic response of type-II superconductors. The fundamental susceptibility X1 provides two different physical natures of the material. Namely, the real component is caused by the magnetic shielding, indicating the phase transition between the superconducting and the normal states. Meanwhile, the imaginary component is proportional to the energy dissipation in the specimen. Higher-harmonic susceptibilities Xn (n ≥ 2) give information on the magnetization which is closely related to the shielding current induced in the sample. We review in this article Xn observed for ceramic high-Tc superconductors and the theoretical analysis of the results within the construct of the critical-state model.

Higher-harmonic susceptibilities of a multiconnected Josephson network in a superconducting transition

We have measured higher-harmonic susceptibilities ∣χ n∣=(χ′ n 2 +χ″ n 2 ) 1 2 (n⩽ 11) of a multiconnected Josephson network in the course of superconducting transition. Results are in good agreement with predictions derived from our phenomenological model.