Universal Scaling Hypothesis Research Articles

Critical behavior near the paramagnetic-ferromagnetic phase transition in polycrystalline La0.6Ca0.2Ba0.15□0.05MnO3

In this paper, we present a detailed study on the structural and critical behavior around paramagnetic (PM)-ferromagnetic (FM) phase transition in La0.6Ca0.2Ba0.15□0.05MnO3 (LCBMO). Our powder specimen was synthesized using the conventional solid-state reaction method and was analyzed by X-ray diffraction and magnetic measurements. X-ray diffraction analysis, at room temperature, shows that LCBMO adopts an orthorhombic structure with Pbnm space group. Detailed analyses of magnetic-field dependences of magnetization in the vicinity of the paramagnetic-ferromagnetic transition, M(H,T), reveal that LCBMO undergoes a second-order magnetic phase transition. Critical behavior has been studied through various techniques such as modified Arrott plot (MAP), Kouvel-Fisher method (KF) and critical isotherm (CI) analysis. The estimated Critical exponents are close to those expected for the mean-field model (β=0.5, γ=1 and δ=3). The reliability of the critical exponent values was confirmed by the Widom scaling relation, as well as the universal scaling hypothesis.

Magnetocaloric effect and its correlation with critical behavior in La0.5Ca0.4Te0.1MnO3 manganese oxide

The critical behavior of La0.5Ca0.4Te0.1MnO3 compound is investigated based on the data of static magnetic measurements in the vicinity of its critical temperature TC. The estimated critical exponents for La0.5Ca0.4 Te0.1MnO3 are found to be 3D-Ising model (β = 0.343 and γ = 1.261 at an average TC = 260 K through various techniques such as modified Arrott plot (MAP), Kouvel–Fisher (KF) method and critical isotherm analysis (CIA). The reliability of the critical exponents’ values was confirmed by the Widom scaling relation (WSR) and the universal scaling hypothesis. We noted that the critical exponents γ are almost similar to the value of the mean-field theory which can be explained by the existence of a long-range dipole–dipole interaction. Following the Harris criterion, we deduced that the disorder in our case is relevant, which could be the cause of the change in the universality class.The magnetic phase transition and the magnetic entropy change (−ΔSm) in the La0.5Ca0.4 Te0.1MnO3 manganite is investigated by measuring the magnetization as a function of temperature. By investigating the field dependence of RCP and (−ΔSm), it was possible to evaluate the critical exponents of the magnetic phase transitions. Their values are in good agreement with those obtained from the critical exponents by Widom scaling relation (WSR) using the modified Arrott and Kouvel–Fisher methods.

Critical analysis of the paramagnetic to ferromagnetic phase transition in Pr0.55K0.05Sr0.4MnO3

The critical properties of monovalent doped manganite Pr0.55K0.05Sr0.4MnO3 around the paramagnetic to ferromagnetic phase transition were investigated through various methods: the modified Arrott plots (MAP), the Kouvel–Fisher method and the critical isotherm analysis. Data obtained near Tc were examined in the framework of the mean field theory, the 3D-Heisenberg model, the 3D-Ising model, and tricritical mean field. The deduced critical exponents values obtained using MAP method were found to be β=0.44(4) with TC≈303K and γ=1.04(1) with TC≈302K. Kouvel–Fisher method supplies the critical values to be β=0.41(2) with TC≈302K and γ=1.09(1) with TC≈302K. The obtained critical parameters show a tendency towards the mean-field behavior, suggesting the existence of long-range ferromagnetic order in the compound studied. The exponent δ deduced separately from isotherm analysis at T=303K was found to obey to the Widom scaling relation δ=1+γ/β. The reliability of obtained exponents was confirmed by using the universal scaling hypothesis. The itinerant character of ferromagnetism in the present system was also tested by using Rhodes–Wohlfarth's criterion.

Critical parameters near the phase transition temperature in La0.67–xDyxPb0.33MnO3

La0.67–xDyxPb0.33MnO3 (x=0.00 and x=0.10) were elaborated by the solid state method and checked by X-ray diffraction. Close to magnetic temperature transition, the order transition and the critical behavior were investigated by dc magnetization measurements versus x composition. The critical properties were investigated through various techniques such as modified Arrott plot (MAP), Kouvel-Fisher (KF) method and critical isotherm (CI) analysis based on the data of static magnetic measurements recorded around the Curie temperature TC. The values of critical exponents (β and γ) estimated were found to lie between those predicted for a 3D-Ising model for x=0.00 and those of 3D-Heisenberg model for x=0.10. The reliability of the critical exponent's values was confirmed by the Widom scaling relation and the universal scaling hypothesis. The change in the universality class should be due to the increase of the Dy content.

Influence of Pr-doped manganite on critical behavior of La0.7−xPrxBa0.3MnO3 (x=0.00, 0.1, 0.2)

The La0.7−xPrxBa0.3MnO3 (x=0.00, 0.1, 0.2) polycrystalline samples were prepared by solid-state reaction and their crystallographic structure was achieved by XRD patterns analysis. Magnetization measurements were performed versus temperature and applied magnetic field to investigate magnetic properties such as critical behavior near Tc. Analysis in the vicinity of the ferromagnetic (FM)–paramagnetic phase-transition temperature evidences a second-order phase transition. Saturation magnetization and the initial susceptibility versus temperature are found to obey asymptotic relations. Using modified Arrott plot, Kouvel–Fisher method and critical isotherm analysis, the critical parameters (TC, β, γ, and δ) are determined in the two characteristic regions of low- and high-magnetic fields. The estimated critical exponents are close to both 3D-Heisenberg and mean field model values. The reliability of the critical exponent values was confirmed by the Widom scaling relation and the universal scaling hypothesis. The change in the universality class should be due to the increase of Pr content.

Critical behavior in Sr-doped manganites La0.6Ca0.4−xSrxMnO3

The critical behavior of La0.6Ca0.4−xSrxMnO3 (x=0, 0.2 and 0.4) compounds has been investigated based on the data of static magnetic measurements in the vicinity of its critical temperature TC. Through various techniques such as modified Arrott plot, Kouvel–Fisher method and critical isotherm analysis, the estimated critical exponents are found to be (β=0.267, γ=0.992, δ=4.896 at TC=268.12), (β=0.501, γ=1.045, δ=2.992 at TC=344.37) and (β=0.386, γ=1.293, δ=4.88 at TC=371.02), for x=0, 0.2 and 0.4; close to tricritical mean field, mean field and 3D-Heisenberg model values, respectively. The reliability of the critical exponents values was confirmed by the Widom scaling relation and the universal scaling hypothesis. Following the Harris criterion, we deduced that the disorder in our case is relevant, which can be the cause of the change in the universality class. Moreover, the local exponent n was studied in terms of the field dependence of the magnetic entropy change. It has been noted that n evolves with field in the entire studied temperature range for all samples. The invalidity of the mean field model for x=0 and 0.4 contents was confirmed at the peak temperature. Far above the transition temperature, the Curie–Weiss law is well satisfied. The differences observed in the n values below the transition are mentioned. Furthermore, unlike the modified Arrott or Kouvel–Fischer methods, the performed analysis is shown to be useful to examine critical exponents and their effects in mixed phases materials.

Critical Behavior of Ferromagnetic Transition in SnO2-Based Diluted Magnetic Semiconductor

Isothermal magnetization data in the critical region of the ferromagnetic transition for Co-doped SnO2-based diluted magnetic semiconductor were measured and analyzed in terms of the modified Arrott plot method and, independently by the Kouvel–Fisher method. The critical exponents β,γ, and δ, corresponding to spontaneous magnetization, initial susceptibility and isothermal magnetization, respectively, were determined and the values are found to be comparable to the mean-field model. The critical exponent values are found to be consistent with the Widom scaling relation and the universal scaling hypothesis. The temperature variation of the effective critical exponent is found to show the characteristic behavior of a disordered system.

Critical behavior studies in ferromagnetic (Nd, K)–Mn–O compounds

The critical scaling behavior of K-doped Nd–Mn–O based double-exchange ferromagnetic compounds was studied by measuring isothermal magnetization of Nd 0.84K 0.16MnO 3 and Nd 0.77K 0.23MnO 3 samples. The critical exponents β, γ and δ corresponding to the spontaneous magnetization, initial susceptibility and isothermal magnetization, respectively, were determined by analyzing the magnetization data in terms of the modified Arrott plot method. The critical exponent values of both samples are found to be comparable to values predicted by a mean field model. The role of ferromagnetic clusters on the scaling behavior is discussed. The critical exponent values are found to be consistent with the Widom scaling relation and the universal scaling hypothesis.

Breakdown of One-Parameter Scaling in Quantum Critical Scenarios for High-Temperature Copper-Oxide Superconductors

We show that if the excitations which become gapless at a quantum critical point also carry the electrical current, then a resistivity linear in temperature, as is observed in the copper-oxide high-temperature superconductors, obtains only if the dynamical exponent z satisfies the unphysical constraint, z < 0. At fault here is the universal scaling hypothesis that, at a continuous phase transition, the only relevant length scale is the correlation length. Consequently, either the electrical current in the normal state of the cuprates is carried by degrees of freedom which do not undergo a quantum phase transition, or quantum critical scenarios must forgo this basic scaling hypothesis and demand that more than a single-correlation length scale is necessary to model transport in the cuprates.

Dynamic scaling of phase separation in CuCo alloys

The Langer-Bar-Miller (LBM) theory and the non-linear Cahn theory on phase separation dynamics in alloys have been reviewed briefly and applied to calculate dynamics of phase separation of homogenized CuCo alloys. The three-parameter technique of the LBM theory for evaluating compositional fluctuations is applicable only in a narrow range of alloy composition. In this narrow range, the as-calculated equal time structure function S(k,t), where k is the wave vector and t is time, does not follow the universal scaling hypothesis in the late stage of phase separation: km3S(k/km) = f(k/km), where f is a scaling function and km is the peak position of S(k,t). The kinetic growth exponent, defined by km as a power function of time, does not agree with prediction of the scaling analysis. The non-linear Cahn approach has been applied to evaluate the profile and amplitude spectra of the compositional fluctuations during phase separation in both meta-stable and non-stable regions. Overall range of alloy composition, the structure function S(k,t) in the late stage of phase separation shows scaling behaviours quite well consistent with the universal scaling hypothesis. The kinetic growth exponent equals to 0.22 in the non-stable region, well consistent with prediction of the scaling analysis. In the meta-stable region, this exponent increases up to 0.28 as the alloy composition decreases down to 0.01, exhibiting good agreement with theory of coarsening kinetics.