Universal Scaling Hypothesis Research Articles

Universal scaling hypothesis of quantum spatial search in complex networks

Since quantum spatial searches on networks have a strong network dependence, the question arises whether the universal perspective exists in this quantum algorithm for various networks. Here, we propose a universal scaling hypothesis of the quantum spatial search on complex networks such as small-world and scale-free networks. The average path length, a key quantity in the complex network science, is useful to expose this universal feature, where the collapse plot can be generated for the optimal time, the maximal finding probability, and the optimal hopping parameter. Based on the path integral method, we also clarify that the probability amplitude in the continuous-time quantum walk can be determined by the path length distribution. Published by the American Physical Society 2024

Sm substitution effect on the critical behaviour of Laves phase Gd1−xSmxCo2 intermetallic nearby the ferromagnetic-paramagnetic phase transition

In this work, we present a comparative and detailed study of the critical behavior near ferromagnetic-paramagnetic phase transition in the intermetallic Laves phase compounds Gd1−xSmxCo2, x = 0.5, 0.6 and 0.7. The investigated samples exhibit a second-order phase transition at Curie temperature TC. The critical exponents β, γ, and δ have been estimated through diverse techniques: the Modified Arrott plot, the Kouvel-Fisher plot, the critical isotherm technique, and the magnetocaloric effect method. The critical exponents values that were determined have been validated using the universal scaling hypothesis, wherein the isotherm magnetization curves M(H) converge into two distinct universal branches below and above TC. The substitution of Gd by Sm changes the universality class in the (Gd,Sm)Co2 compounds. For the sample Gd0.5Sm0.5Co2, the critical exponents obtained are closely consistent with the predictions of the 3D-Heisenberg model featuring a magnetic system with a short-range exchange interaction. While, for both samples Gd0.4Sm0.6Co2 and Gd0.3Sm0.7Co2, the values deviate from known theoretical models and might belong to an unconventional universality class with an intermediate-range exchange interaction.

Thermomagnetic properties and critical behaviour studies in the ferromagnetic – Paramagnetic phase transition in Pr0.6Sr0.35Ag0.05MnO3 and Pr0.6Sr0.3Ag0.1MnO3 ceramics

Abstract Magnetic ordering and critical exponents of Pr0.6Sr0.35Ag0.05MnO3 (x = 0.05) and Pr0.6Sr0.3Ag0.1MnO3 (x = 0.1) ceramics are identified by magnetic measurements. Banerjee criterion and field dependences of the ΔSMmax disclose that both samples exhibit a second-order phase transition. The values obtained for the magnetic performances make these samples promising candidates for magnetic refrigeration. The determined exponents obey the mean-field model with a long-range ferromagnetic interaction. The reliability of the obtained critical exponents is examined by using the universal scaling hypothesis. Temperature variation in effective exponents βeff and γeff resemble with those for disordered ferromagnet. Using critical exponents universal curves for the ΔSM(T) are constructed.

Magnetocaloric properties and critical behavior in double perovskite RE2CrMnO6 (RE = La, Pr, and Nd) compounds

Magnetocaloric effect (MCE) is a thermodynamic response of the coupling effect between the magnetic sub-lattice(s) with applied magnetic fields, which is strongly correlated with the corresponding magnetic transition. In this work, the magnetic properties, magnetic phase transition, MCE and critical behavior of the paramagnetic (PM) to ferromagnetic (FM) transition in double perovskite RE2CrMnO6 (RE = La, Pr, and Nd) compounds are investigated. The double perovskite compounds reveal a second-ordered magnetic phase transition around TC of 112, 93, and 80 K for RE of La, Pr, and Nd, respectively. The corresponding values of peak magnetic entropy change (-ΔSMmax) around TC are 1.31, 1.86, and 2.23 J kg−1K−1 under the ΔH of 0–7 T. Moreover, the critical exponent study was conducted to probe the nature of critical behavior around the PM to FM transition by the modified Arrott plot (MAP), Kouvel-Fisher (K–F), ΔH dependence of -ΔSMmax, and universal scaling hypothesis methods. The evaluated reliable critical exponents (β, γ, and δ) data for RE2CrMnO6 (RE = La, Pr, and Nd) follows the mean-field theory model, proving the existence of long-range FM orders in these double-perovskite oxide compounds.

Assessment of structural, optical, magnetic, magnetocaloric properties and critical phenomena of La0.57Nd0.1Sr0.18Ag0.15MnO3 system at room temperature

In this research paper, our central focus is upon structural, optic, magnetic, magnetocaloric, and critical phenomena of La0.57Nd0.1Sr0.18Ag0.15MnO3 (LNSMAO) compound. This compound is crystallized in the rhombohedric system, with a $$R\mathop 3\limits^{ - } c$$ space group. The band gap energy of this powder was 2.5 eV. Therefore, the LNSAMO sample proved to be not only a photocatalysis material but also a photovoltaic application. The FTIR spectra confirmed the formation of the structure of orthorhombic perovskite. The second-order transition of the magnetic phase in the LNSMAO sample was also reported by the positive slopes of the Arrott plot. Beneath 5 T, the values of magnetic entropy change and relative cooling power, respectively, amounted to about 5.08 J kg−1 K−1 and 146.7 J/Kg. In perspective, this sample stands for an agreeable candidate for magnetic refrigeration. By analyzing the dependence on the field of the magnetic entropy change (ΔSM) data as well as the relative cooling power (RCP), it was possible to assess the values of the critical exponents. Moreover, the critical exponents of LNSMAO compound were estimated based on multiple techniques like Kouvel-Fisher (KF), modified Arrott plot (MAP) method, and critical isotherm analysis (CIA). The reliability of these critical behaviors was verified by the Widom scaling relation and the universal scaling hypothesis. Our results demonstrate an excellent correlation between magnetocaloric effect (MCE) properties in manganese systems and critical behavior.

Long-range ferromagnetic ordering in La0.7Sr0.3Mn0.9Cu0.1O3 manganite

Nanosized La0.7Sr0.3Mn0.9Cu0.1O3 manganite was synthesized via the sol–gel procedures. The structural, morphological, magnetic and magnetocaloric properties as well as the critical phenomena were investigated. The sample was described by X-ray diffraction (XRD) technique at room temperature which confirms the single phase with a rhombohedral structure belonging to the R$$\overline{3}$$c space group. The magnetic measurements indicated the presence of a second-order ferromagnetic–paramagnetic phase transition at 320 K. According to hysteresis cycles, at 10 K a typical soft FM behavior with a low coercive field was observed. The critical exponents values (β, γ, and δ) as well as the Curie temperature TC were determined using different approaches such as the extrapolation of Arrott plots, Kouvel–Fisher (KF) method and critical isotherm analysis. The critical parameters values (β = 0.489 ± 0.003 with TC = 323.41 K ± 0.23, γ = 1.014 ± 0.020 with TC = 324.32 K ± 0.48 and δ = 3.074) are located near those theoretically predicted by mean-field theory, indicating the long-range ferromagnetic coupling in this system. The reliability of these critical parameters was confirmed by both the universal scaling hypothesis and the Widom scaling relation. Additionally, to estimate the spontaneous magnetization MS (T), we used a process which depends on the analysis of the magnetic entropy change (− ΔSM). A satisfactory agreement was found between the values of the spontaneous magnetization determined from the entropy change ((− ΔSM) vs. M2) and those obtained from the extrapolation of the Arrott curves (μ0H/M vs. M2).

Critical behavior of [formula omitted] intermetallic compound

The critical behavior of a new ternary intermetallic compound Gd2Rh3Ge has been investigated around the second order ferromagnetic transition temperature (TC). The field dependence of magnetic entropy changes and isothermal magnetization at critical temperature were used to study critical behavior in Gd2Rh3Ge. The exponents β = 0.299(2) and γ = 1.042(1) were evaluated from the modified Arrott-plot method, while β = 0.308(1) and γ = 0.982(2) were estimated through the Kouvel-Fisher method. The reliability of the obtained critical exponents were examined by using the universal scaling hypothesis. These estimated values for the critical exponents indicate that the ferromagnetic compound Gd2Rh3Ge has long-range interactions between spins, which decays with distance (r) as J(r) ∼r-(σ+d) with σ = 1.91.

Critical Behavior and Magnetic Properties of Manganite-Derived Oxide La0.67Sr0.33MnO3: a Monte Carlo Study

Critical behavior and magnetic properties of La0.67Sr0.33MnO3 (symbolized as LS33MO) have been studied by means of Monte Carlo simulation (MCS). By using the heat-bath algorithm and the Ising model up to third nearest neighbor exchange interactions, we have computed the magnetic and magneto-caloric properties. The effects of the temperature (T) and the external magnetic field (h) on the magnetic behavior of LS33MO have been discussed. The results demonstrate that the Curie temperature (TC) is close to the experimental value. The magnetic entropy shows a maximum value around TC which increases linearly with the rise of the external field h. For h = 5T, the maximum entropy ($$ \Delta {S}_m^{\mathrm{max}} $$) is about 3.67 J K−1 kg−1 which is in good agreement with the experimental results. The relative cooling power (RCP) has been estimated and it has been found that it increases with respect to the external field. The predicted critical behavior has been studied by isothermal magnetization of LS33MO nanoparticle compound. The critical exponents (Crt.Exps) are determined by various approaches, such as the modified Arrott plot (AP) and critical isotherm ways. Therefore, the Crt.Exp values obtained by different techniques are β = 0.306, γ = 1.178, and δ = 4.025 respectively. The trustworthiness of the values of the Crt.Exp was approved by the Widom scaling equation and the universal scaling hypothesis.

Magnetic, Magnetocaloric and Correlation with Critical Behavior in Pr0.8Sr0.2MnO3 Compound Prepared via Solid-State Reaction

In this study, the critical behavior and magnetic and magnetocaloric properties in a polycrystalline Pr0.8Sr0.2MnO3 sample synthesized by solid-state technique were investigated in detail. By analyzing the temperature and the field dependence of magnetization, we have demonstrated that this compound exhibits a clear second-order magnetic phase transition around the Curie temperature estimated at TC = 161 K. Refined values of the critical exponents β, γ and δ determined by the modified Arrott plots, the critical isotherm and Kouvel–Fisher analysis show that our compound is described by the 3D Ising model. The reliability of these critical exponents was further confirmed using the universal scaling hypothesis. Under an applied magnetic field of 5 T, the calculated value of the maximum of the magnetic entropy change is estimated at 1.740 J K−1 kg−1 and the relative cooling power (RCP) turns out to be 134.46 J kg−1. Moreover, the critical exponents were evaluated from RCP results which confirm the correlation between the critical behavior and magnetocaloric results in the Pr0.8Sr0.2MnO3 compound.

Structural, magnetic, critical behavior and phenomenological investigation of magnetocaloric properties of La0.6Ca0.4−xSrxMnO3 perovskite

Structural, magnetic, critical behavior and magnetocaloric properties of La0.6Ca0.4−xSrxMnO3 (x = 0.0, 0.1 and 0.4) compounds have been investigated. Rietveld refinement of the X-ray diffraction patterns indicates that our samples are pure single phase adopting the rhombohedral structure (R-3c) for x = 0.0 and the orthorombic structure (Pbnm) for x = 0.1 and 0.4. Temperature dependence of magnetization curves exhibit a second order paramagnetic (PM)/ferromagnetic (FM) phase transition at Curie temperature Tc. The critical behavior has been determined through the isothermal magnetization measurements around the critical temperature Tc by means of various techniques such as modified Arrott plot (MAP), Kouvel-Fisher (KF) method and critical isotherm analysis (CIA). The results are fully satisfactory to the requirements of the Widom scaling relation and the universal scaling hypothesis confirming their accuracy. A phenomenological model is applied to describe the magnetocaloric effect (MCE) behavior of compounds under investigation. At $$ \mu_{0} H = 5T $$ , the obtained RCP values stand for about 98, 77 and 68% of that observed in pure Gd for x = 0.0, 0.1 and 0.4, respectively, making of these materials considered as promising candidates for magnetic refrigeration applications near room temperature. By analyzing the field dependence of the magnetic entropy change data as well as the relative cooling power, it was possible to evaluate the critical exponent values which were found not only agree with those deduced from (MAP), (KF) and (CIA) methods, but they also obey the scaling theory. Our findings confirm the good correlation between the critical behavior and the MCE properties in manganite systems.

Critical behavior and magnetocaloric effect in La0.7Ba0.25Nd0.05Mn1-xCuxO3

In this work, the magnetic and magnetocaloric properties of La0.7Ba0.25Nd0.05Mn1-xCuxO3 samples (x = 0 - 0.07) synthesized by the sol-gel method are presented. The compounds exhibited a second-order phase transition (SOPT) of ferromagnetic-paramagnetic (FM-PM) phase transition following Banerjee’s criterion. Curie temperature TC decreased with increasing doping concentration. The critical behavior analysis using modified Arrott plots (MAP) showed a short-range FM ordering. Significant entropy change of samples was observed near the TC, which decreased with Cu content. The SOPT nature of compounds was confirmed by both the universal curves and scaling hypothesis.

Critical Behavior Near the Ferromagnetic Transition in Phase-Separated $$\hbox {La}_{0.5}\hbox {Ca}_{0.2}\hbox {Sr}_{0.3}\hbox {MnO}_{3}$$ La 0.5 Ca 0.2 Sr 0.3 MnO 3 Manganite

The critical behavior of $$\hbox {La}_{0.5}\hbox {Ca}_{0.2}\hbox {Sr}_{0.3}\hbox {MnO}_{3}$$ manganite has been investigated by measuring the magnetization around the Curie temperature $$T_\mathrm{C}$$ . The experimental results indicate that this sample exhibits a second-order phase transition. The critical exponents ( $$\beta $$ , $$\gamma $$ and $$\delta $$ ) are estimated using the Kouvel–Fisher technique and critical isotherm analysis. The reliability of obtained exponents was confirmed by using the universal scaling hypothesis. The obtained $$\beta $$ value ( $$=0.47$$ ) is close to that expected for the mean-field model ( $$=0.5$$ ), while the $$\gamma $$ value ( $$=1.28$$ ) lies between the 3D Ising ( $$=1.24$$ ) and 3D Heisenberg ( $$=1.336$$ ) models. This reveals that the critical exponents of this half-doped manganite do not correspond to the conventional universality classes. In addition, the results show that the ferromagnetic interaction is of itinerant type.

Correlation between critical behavior and magnetocaloric effect for La0.8-x·xNa0.2-x·xMnO3 (x=0 and 0.1) compounds

The critical behavior of manganite perovskite type La0.8-x·xNa0.2-x·xMnO3 (with x = 0 and 0.1) was studied based on the experimental magnetic measurements in the paramagnetic ferromagnetic transition region using different techniques such as the modified Arrott plot, the Kouvel-Fisher method and critical isothermal analysis. Experimental results revealed that the two samples show a second-order magnetic phase transition. The deduced critical exponents are close to a 3D Ising model for La0.8Na0.2MnO3 and a 3D tricritical mean field model for La0.7·0.1Na0.1·0.1MnO3. The reliability of these critical exponents was confirmed by the Widom scaling relation and the universal scaling hypothesis. Moreover, an excellent agreement was found between the spontaneous magnetization determined from the entropy change and from the extrapolation of the modified Arrott plots, confirming the universal behavior of the magnetocaloric effect in these systems.

Ferromagnetic long-range ordering in nano-crystalline La0.7Ca0.3Mn1-xNixO3 (x = 0, 0.02) manganites

Abstract Nanosized La0.7Ca0.3Mn1-xNixO3 (x = 0, 0.02) manganites were synthesized via the auto-combustion method. The critical behavior of these samples was then carefully investigated by analyzing the results of static magnetic measurements near their critical temperatures. The samples exhibited second-order phase transition, and the effect of Ni doping was to lower the critical temperature. The analysis of the experimental data was carried out by means of various techniques, such as modified Arrott plots, the Kouvel-Fisher method, and critical isotherm analysis, which revealed that the values of the critical exponents β, γ, and δ are close to those theoretically predicted by mean-field theory. By using the Widom scaling relation and the universal scaling hypothesis, the dependability of the obtained values of the critical exponents was confirmed. Moreover, the temperature dependence of the spontaneous magnetization was estimated from the analysis of the variation of the magnetic entropy change with the magnetization within the framework of mean-field theory. Interestingly, the spontaneous magnetization determined from the entropy change and that obtained from classical extrapolation of the Arrott curves displayed high concordance. These results strongly suggested that the interactions among spins in the investigated compound are long-range.

Magnetocaloric Effect and Critical Behavior Investigations in La0.45Pr0.2Sr0.35MnO3 Manganite Oxide

Structural, magnetic, and magnetocaloric effect (MCE) properties and the critical behavior of the La0.45Pr0.2Sr0.35MnO3 sample prepared by the sol–gel method have been investigated. The X-ray diffraction characterization reveals that our sample crystallizes in the orthorhombic structure with Pnma space group. Magnetization versus temperature measurement shows that our compound exhibits a ferromagnetic–paramagnetic transition. The Curie temperature is found to be 348 K. Close to this temperature, the maximum values of the magnetic entropy change (ΔSM) and the relative cooling power (RCP) are found to be 2.84 J/kg/K and 230 J/K under µ0H = 5 T, respectively. The Arrott plots revealed that this compound exhibits a second-order magnetic phase transition at TC. The critical behavior has been investigated by several techniques which are the modified Arrott plot method, the Kouvel–Fisher method, and the critical isotherm analysis. The obtained critical exponents β, γ, and δ are consistent with those predictions of the mean-field model. Their reliability was confirmed by Widom’s scaling relation, as well as the universal scaling hypothesis.

Critical phenomena and estimation of the spontaneous magnetization from a mean field analysis of the magnetic entropy change in La0.7Ca0.1Pb0.2Mn0.95Al0.025Sn0.025O3.

In the present work, we have studied the universal critical behavior in the perovskite-manganite compound La0.7Ca0.1Pb0.2Mn0.95Al0.025Sn0.025O3. Experimental results revealed that all samples exhibit a second-order magnetic phase transition. To study the critical behavior of the paramagnetic–ferromagnetic transition, various techniques such as modified Arrott plots, the Kouvel–Fisher method and critical isotherm analysis were used to determine the values of the Curie temperature TC, as well as the critical exponents β (corresponding to the spontaneous magnetization), γ (corresponding to the initial susceptibility) and δ (corresponding to the critical magnetization isotherm). The critical exponent values for our sample are consistent with the prediction of the mean field model (β = 0.46, γ = 1.0, and δ = 2.94 at an average TC = 302.12 K), indicating that the magnetic interactions are long-range. The reliability of the critical exponent values was confirmed by the Widom scaling relation (WSR) and the universal scaling hypothesis. Moreover, to estimate the spontaneous magnetization of La0.7Ca0.1Pb0.2Mn0.95Al0.025Sn0.025O3 perovskite, we used the magnetic entropy change (ΔSM), obtained from isothermal magnetization. The results obtained through this approach are compared to those obtained from classical analysis using Arrott curves. An excellent agreement is found between this approach and the one obtained from the extrapolation of the Arrott curves.

Griffiths-like phase, critical behavior near the paramagnetic-ferromagnetic phase transition and magnetic entropy change of nanocrystalline La0.75Ca0.25MnO3

In this work, we report the structural and magnetic properties of La0.75Ca0.25MnO3 nanoparticles synthesized by the sol-gel route. Rietvield refinement of X-ray powder diffraction confirms that our sample is single phase and crystallizes in orthorhombic system with Pnma space group. The facts that effective magnetic moment is large and the inverse susceptibility deviates from the Curie Weiss lawn indicate the presence of Griffiths-like cluster phase. The critical exponents have been estimated using different techniques such as modified Arrott plot, Kouvel-Fisher plot and critical isotherm technique. The critical exponents values of La0.75Ca0.25MnO3 are very close to those found out by the mean-field model, and this can be explained by the existence of a long-range interactions between spins in this system. These results were in good agreement with those obtained using the critical exponents of magnetic entropy change. The self-consistency and reliability of the critical exponent was verified by the Widom scaling law and the universal scaling hypothesis. Using the Harris criterion, we deduced that the disorder is relevant in our case. The maximum magnetic entropy change (ΔSM) calculated from the M-H measurements is 3.47 J/kg K under an external field change of 5 T. The ΔSM-T curves collapsed onto a single master curve regardless of the composition and the applied field, confirming the magnetic ordering is of second order nature. The obtained result was compared to ones calculated based on the Arrott plot and a good concordance is observed. Moreover, the spontaneous magnetization obtained from the entropy change is in excellent agreement with that deduced by classically extrapolation the Arrott curves. This result confirms the validity of the estimation of the spontaneous magnetization using the magnetic entropy change.

Critical Behavior of La0.8Ca0.2Mn1−xCoxO3 Perovskite (0.1 ≤ x ≤ 0.3)

The critical properties of La0.8Ca0.2Mn1−xCoxO3 (x = 0, 0.1, 0.2 and 0.3) compounds were investigated by analysis of the magnetic measurements in the vicinity of their critical temperature. Arrott plots revealed that the paramagnetic PM-ferromagnetic (FM) phase transition for the sample with x = 0 is a first order transition, while it is a second order transition for all doped compounds. The critical exponents β, γ and δ were evaluated using modified Arrott plots (MAP) and the Kouvel-Fisher method (KF). The reliability of the evaluated critical exponents was confirmed by the Widom scaling relation and the universal scaling hypothesis. The values of the critical exponents for the doped compounds were consistent with the 3D-Heisenberg model for magnetic interactions. For x = 0.1, the estimated critical components are found inconsistent with any known universality class. In addition, the local exponent n was determined from the magnetic entropy change and found to be sensitive to the magnetic field in the entire studied temperature range.

Structural, magnetic, magnetocaloric and critical behavior investigations of La0.65Dy0.05Sr0.3MnO3 manganite

In the present work, we report a detailed study of the structural, magnetic, magnetocaloric properties as well as critical behavior in La0.65Dy0.05Sr0.3MnO3 ceramic synthetized by the conventional solid-state reaction. Rietveld refinement of the X-ray diffraction patterns indicates that our sample is pure single phase adopting the rhombohedral structure (R3¯c space group). Temperature dependence of magnetization exhibits a paramagnetic (PM) to ferromagnetic (FM) transition at Curie temperature TC = 265 K. Close to this transition, the magnetic entropy change reaches a maximum of about 2.19 J/kgK and the relative cooling power (RCP) value is of 241 J/kg, when a magnetic field of 5 T is applied. Additionally, Banerjee's criteria, Landau theory and the universal behavior of phase transitions were also studied to assess magnetic phase ordering in this material, such investigations indicate that the phase transition from the PM to FM states is of second order. Through various techniques such as modified Arrott plot (MAP), Kouvel–Fisher (KF) method and critical isotherm (CI) analysis, the critical parameters (TC, β, γ, and δ) have been determined. The estimated critical exponents (β = 0.515, γ = 1.082 and δ = 2.932 at TC = 264.85 K) are found to be close to the mean-field model. This proves the existence of long range ferromagnetic interactions in this system. The reliability of the critical exponent values was confirmed by the Widom scaling relation and the universal scaling hypothesis.

Critical behavior in the La0.6Ca0.4−xSrxMnO3 nano-particle compounds for x = 0, 0.05 and 0.4

The critical behavior associated with the magnetic phase transition has been investigated by magnetization isotherms in La0.6Ca0.4−xSrxMnO3 nano-particle compounds for x = 0 (S0C1), 0.05 (SC. 4-4) and 0.4 (S1C0). The critical exponents are estimated by various techniques, such as the Modified Arrott plot, Kouvel–Fisher plot and critical isotherm techniques. Thus, the average values of the critical exponent and the critical temperature obtained by the different methods are (βmoy=0.47;γmoy=1.02;δmoy=3.00;TC=230.6K) for S0C1, (βmoy=0.47;γmoy=1.00;δmoy=3.21;TC=361.9K) for S1C0, and (βmoy=0.26;γmoy=1.02;δmoy=4.92;TC=286.4K) for SC. 4-4. These values are in good agreement with those given by the theoretical models: Mean-Field model (β = 0.5, γ = 1 and δ = 3) for S0C1 and S1C0 compounds; and Tricritical mean-Field model (β = 0.25, γ = 1 and δ = 5) for SC. 4-4 one. The reliability of the critical exponent values was confirmed by the Widom scaling relation and the universal scaling hypothesis.