Scaling of ac susceptibility and the nonlinear response function of high-temperature superconductors

The amplitude-dependent ac susceptibility of high-temperature superconductors is shown to obey some empirical scaling relations. We try to analyze this behavior by extending a dc nonlinear response function of mixed state to the ac cases. The derived equations for critical current and ac susceptibility X(T) agree with the scaling relations of experimental data.     

Scaling of vortex transport properties and nonlinear ac response of high-temperature superconductors

The macroscopic behavior of high-temperature superconductors is described by a nonlinear response function in combinations with Maxwell equations. This function is compatible with the suggested different model pinning barriers U(J). A comparison of this function to the scaling behavior of the isothermal current-voltage characteristics measured in twinned YBa₂Cu₃O (YBCO) samples shows fair agreement. We also compare the amplitude dependence of ac susceptibility derived from this function with several experimental results of high-temperature superconductors and find a general power law in the out-of-phase peak shift. Received 4 August 1999 and Received in final form 30 November 1999     

Critical slowing down in the single crystalline relaxor SBN75

The dielectric susceptibility of strontium-barium niobate, Sr_0.75Ba_0.25Nb₂O₆, reveals strong relaxor behaviour. It is shown that the relationship between the frequency of the ac probing field and the temperature, at which the real part of the susceptibility passes through a maximum, satisfactorily follows the activated dynamic scaling law predicted for the random-field Ising model. Applicability of a power law as suggested by the dynamic scaling theory is discussed.     

Crossover effects induced by lattice compressibility in random magnets

Crossover behaviour induced by lattice compressibility in a random magnet is studied using solutions of the renormalization group recursion relations to leading order in =4–d. An effective exponent of the magnetic susceptibility is introduced and the size of the crossover region is estimated. Crossover scaling functions for the free energy, specific heat, and magnetic susceptibility are also obtained.     

Critical behaviour of a one-dimensional crystal at the displacive limit

The partition function of a one-dimensional, one-component model is calculated exactly by means of a transfer-operator method, and the critical behaviour at the displacive limit is evaluated analytically. We prove a generalized scaling hypothesis and discuss the scaling behaviour in the critical region. We find critical exponents for the specific heat,=2/3 for the susceptibility, and a crossover exponent = 2/3. The results satisfy the scaling relations which do not involve the dimensionality but violate those which contain the dimensionality. Scaling functions for the susceptibility and the order parameter are calculated.Supported by Schweizerischer Nationalfonds.     

Critical behaviour of an amorphous ferromagnet close to the percolation threshold

A detailed study of the magnetisation, electrical resistivity and ac magnetic susceptibility of the amorphous Fe₃Ni₇₇B₁₈Si₂ alloy has been performed. This alloy is ferromagnetic with the Curie temperature T_c = 19,5 K. Critical exponents δ = 4,9 and α = ?0,51 were obtained from the experiment while γ = 1,66 and β = 0,43 were calculated from the scaling relations. However the effective critical exponent γ ¹ deduced from the initial magnetic susceptibility exhibits a non-monotonic variation with temperature reaching a maximum of about 1.8 around 43 K. The results are discussed in terms of recent theoretical predictions.     

Magnetization scaling in the ruthenate-cuprate RuSr2Eu1.4Ce 0.6Cu2O10-δ (Ru-1222)

The magnetic properties of the superconducting ruthenate-cuprate RuSr₂Eu _1.4Ce_0.6Cu₂O_10-δ (Ru-1222) have been studied by a scaling analysis of the dc magnetization and ac susceptibility measurements. Non-linear M(H) curves reveal the presence of nano-size clusters with a net magnetic moment of ∼10² μ_B at 180 K, near the deviation from a Curie-Weiss behavior. On cooling, no scaling was observed down to 90 K, discarding the possibility of magnetic phase separation of collinear ferromagnetic particles. We explain this result in terms of a variable number of contributing particles, with a temperature dependent net magnetic moment. For 70 K ≤T≤ 90 K the scaling plots evidence the emergence of a system of non-interacting particles, which couple on further cooling. The observed cluster-glass features are preserved down to the lowest measured temperature (10 K); no signature of long-range order was detected. The frequency shift of the peak in the real part of the ac susceptibility does not follow the Vogel-Fulcher type dependence, as previously reported. The puzzling temperature dependence of the coercive field, H_C(T), is correlated with the changes in the scaling factors.     

Critical behavior of a spherical model with a free surface

Critical phenomena ind-dimensional ferromagnetic spherical models on hypercubic lattices with free surfaces are studied. The surface specific heat and surface susceptibilities are obtained. The exponents characterizing the divergence of these surface quantities at the bulk critical temperature are found to satisfy recently proposed scaling relations. The variation of the susceptibility with distance from the surface is also discussed. The author's recent scaling theory for surface properties is investigated in detail, and found to give an exact representation for the free energy of a three-dimensional spherical model of finite thickness in finite bulk and surface magnetic fields. A scaling form for the surface free energy is derived.     

Magnetic phases of amorphous transition metal-metalloid alloys

Hysteresis loop and ac susceptibility measurements were performed on three series of amorphous alloys: (A_wB_1-w)₇₅P₁₆B₆Al₃, where (A, B) are (Fe, Ni), (Co, Ni) and (Fe, Mn). Upon cooling, low w alloys undergo paramagne t to spin glass transitions. Alloys with higher w first experience a Curie transition to a ferromagnetic state, and then a spin freezing transition to a spin glass state. the T dependence of the width of the ac hysteresis loop is used to determine the spin freezing transition temperature. A magnetic phase diagram is presented for each alloy series and the value of w required for ferromagnetism, w_C, is determined. When measured in the presence of small constant fields, the ac susceptibility of alloys with w just above w_C has maxima near both transition temperatures. The field and temperature dependences of the peaks are explained by scaling arguments, used to determine the critical exponent δ for the Curie transition, and suggest that a similar scaling law holds for the ferromagnet to spin glass transition.     

Evidence of spin glass dynamics in dilute LiHoxY1-xF4

ac susceptibility measurements are presented on the dilute, dipolar coupled, Ising magnet LiHoxY1-xF4 for a concentration x=0.045. The frequency and temperature dependences of the susceptibility show characteristic glassy relaxation. The absorption spectrum is found to broaden with decreasing temperature suggesting that the material is behaving as a spin glass and not as an exotic spin liquid as was previously observed. A dynamical scaling analysis suggests a spin glass transition temperature of 43+/-2 mK with an exponent znu=7.8+/-0.2.     

Perpendicular susceptibility of completely shielded elliptical and rectangular superconducting films

The perpendicular susceptibility -χ₀$-{\chi }_0$ of completely shielded elliptical and rectangular superconducting films with different aspect ratios has been calculated accurately. The obtained χ₀${\chi }_0$ may be compared with the measured low-field limit of ac susceptibility to check the quality of superconducting films, and used as a scaling parameter to obtain field amplitude dependent complex critical-state ac susceptibility.     

Dynamic regimes in films with a periodic array of antidots

We have studied the dynamic response of Pb thin films with a square array of antidots by means of ac susceptibility measurements. At low enough ac drive amplitudes h, vortices moving inside the pinning potential give rise to a frequency- and h-independent response together with a scarce dissipation. For higher amplitudes, the average distance travelled by vortices surpasses the pinning range and a critical state develops. We found that the boundary h^*(H,T) between these regimes smoothly decreases as T increases whereas a step-like behavior is observed as a function of field. We demonstrate that these steps in h^*(H) arise from sharp changes in the pinning strength corresponding to different vortex configurations. For a wide set of data at several fields and temperatures in the critical state regime, we show that the scaling laws based on the simple Bean model are satisfied.Received: 13 October 2003, Published online: 19 February 2004PACS: 74.78.Na Mesoscopic and nanoscale systems - 74.25.Sv Critical currents - 74.78.Db Low-T_c films     

Viscous behavior in a quasi-1D fractal cluster glass

The spin glass transition of a quasi-1D organic-based magnet ([MnTPP][TCNE]) is explored using both ac and dc measurements. A scaling analysis of the ac susceptibility shows a spin glass transition near 4 K, with a viscous decay of the thermoremanent magnetization recorded above 4 K. We propose an extension to a fractal cluster model of spin glasses that determines the dimension of the spin clusters (D) ranging from approximately 0.8 to over 1.5 as the glass transition is approached. Long-range dipolar interactions are suggested as the origin of this low value for the apparent lower critical dimension.     

A method for distinguishing power-law and approximate power-law behavior in glassy relaxation: Ionic conducting glasses

The question of whether an apparent power-law behavior in the ac conductivity of glasses is a real power-law, or is the product of a factor linear in the frequency and logarithmic corrections is important for the interpretation of the data. The former behavior is predicted by theories which invoke scaling relations a priori and attribute the frequency dependence to hierarchical scaling, multifractal scaling, or anomalous diffusion on fractal structures. The latter behavior is a natural result of a pair approximation. A simple procedure is suggested for the purpose of distinguishing the two possibilities. The procedure involves plots of the locus of ordered pairs of frequency and temperature for which the imaginary part of the dielectric constant is a constant.     

A new mean field theory on critical scaling in spin-glasses

The critical exponents γ, δ in the non-linear susceptibility are given by making use of the free energy simply consisting of order parameter, magnetization and what was previously named an internal field parameter. The crossover exponent ø also is obtained. It is found that they satisfy the scaling relations proposed independently by Suzuki et al.     

The influence of impurities on the quasiparticle tunneling current between weakly coupled quasi-one-dimensional charge density waves

The dc and ac conductivity of a tunneling junction between two impure quasi-one-dimensional charge density wave (CDW) systems is calculated. The non-magnetic impurities are considered in the self-consistent Born approximation (SCBA). Impurities modify the density of states (DOS) of the pure CDW system for quasiparticles inside the energy region of the gap 2(T). As in the pure case, the theory predicts in addition to a tunneling current which is proportional to the product of the DOS a term proportional to the cosine of the order parameter phase difference. In the case of a normal state/CDW junction, analytical expressions are obtained forT=0 showing deviations from the pure case. The linear ac conductivity is obtained by the scaling relation between the dc and the ac response.     

Phase transitions far from thermal equilibrium in spin systems

The nonlinear effects in the spin resonance due to the negative differential r.f. magnetic susceptibility are considered. The r.f. magnetization is shown to exhibite a kind of first order phase transition. A set of scaling relations, valid near the appropriate critical point, is obtained.     

Spin-glass behaviour of novel ternary uranium aluminide U3Co4+ x Al12− x (x = 0.55)

Experimental results on dc and ac susceptibility, magnetization and magnetic relaxation, specific heat, electrical resistivity and magnetoresistivity up to 8?T are reported for the novel ternary uranium aluminide U₃Co_4.55Al_11.45. The temperature dependence of the dc susceptibility shows a cusp at a characteristic temperature T _f?=?8–10?K that depends weakly on the applied magnetic field. The observed pronounced difference between the ZFC and FC magnetizations, as well as the decay in the remanent, both give evidence that a highly irreversible, frozen state is formed below T _f which is reminiscent of spin-glass behaviour. The real and imaginary parts of the ac susceptibility show that the corresponding T _f peaks are only slightly dependent on frequency. Electrical resistivity measured at zero and in fields up to 8?T indicates that the Kondo-like state becomes dominant at temperatures above T _f.     

Universal non-monotonic smectic fluctuations of liquid crystal films in a magnetic field

Free-standing liquid crystal films with positive diamagnetic susceptibility can have the smectic ordering enhanced by an external field applied perpendicular to the plane layers. Within a quadratic functional integral approach, we investigate the interplay between the smectic order induced by an external field H and that due to the surface tension γ between the film and the surrounding gas. We find that the average smectic fluctuation is a non-monotonic function of film thickness, with a characteristic thickness scale ξ _H delimiting the predominance of surface tension and magnetic field effects. This characteristic thickness obeys simple asymptotic power-law relations as a function of the ordering terms which allows us to represent the average smectic fluctuations in a universal scaling form. Received 7 January 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: marcelo@ising.fis.ufal.br