Analysis Of Critical Behavior Research Articles

Critical Behavior of the (111)‐Oriented LaCoO3/SrTiO3 Thin Film

Apart from the impact of different substrates on epitaxial thin films due to lattice constant mismatches, the properties of epitaxial thin films are also influenced by the same substrates with different crystal orientations. Herein, the (111)‐oriented SrTiO3 (STO) substrates are used to fabricate the LaCoO3 (LCO) epitaxial thin films rather than the more common (001)‐oriented STO substrates. It undergoes one paramagnetic–ferromagnetic phase transition around 50 K. This phase transition is similar to the previously observed for (001)‐LCO/STO, but the Curie temperature (T c) is significantly lower than the previously reported 80 K. To investigate the decrease of T c and gain further insight into the phase transition, the critical behavior analysis of thin film is performed. The critical exponents are determined to be β = 1.591(3) and γ = 0.937(1) by reconstructing a modified Arrott plot, and the reliability of these exponents is confirmed by the Widom scaling relation. Using the renormalization group theory approach, it is discovered that the film has a long‐range magnetic interaction with space dimensionality d = 2 and spin dimensionality n = 1, and the magnetic exchange interaction decays .

Structural and magnetic property analysis of bulk and nanocrystalline Ni1.8Mn1.2Sn Heusler alloy

The effect of nanocrystallite size on crystal structure and magnetic properties of off-stoichiometric Ni1.8Mn1.2Sn Heusler alloy has been investigated. XRD (X-Ray Diffraction) and HRTEM (High-Resolution Transmission Electron Microscopy) analysis revealed the presence of both the full Heusler (Ni2MnSn) L21 and inverse Heusler (Mn2NiSn) XA crystal symmetries. Hence, the sample can be treated as a natural composite of both phases. However, the magnetic analysis reveals that the magnetization does not follow a linear relationship with the volume fraction of the individual phases. Rather, the antiferromagnetic coupling between the two phases may be responsible for lowering the net magnetization. On the other hand, magnetization value further decreases for ball-milled sample (nanocrystallite size). Critical magnetic behavior analysis reveals that the magnetic ordering in bulk sample follows mean field theory, and for nanocrystalline sample, the magnetic ordering is a short-range type.

Higher-dimensional black hole solutions with scalar hair and dilaton field and toroidal horizons and interior solution

In this study, we investigate black hole solutions with toroidal horizons in scalar hair and dilaton gravity. First, we obtain the field equations in n-dimensions. Then, we propose different models (ansatz) and find the exact solutions for these types of ansatzs. These solutions are not asymptotically (anti) de Sitter or flat, except in one special case. We also show that the BTZand BTZ-like solutions emerge from some of these solutions as a special case. We also show that when the event horizon radius increases, the temperature will be the same in various dimensions. The only difference is noticeable near the origin (this statement is clear from the figures). For these solutions, we obtained a new version of the Smarr formula. In addition, we show that the presence of the scalar field makes the black holes more stable near the origin, except for the BTZ case. In general, the presence of a scalar field is an important factor in black hole stability investigations. In the critical behavior analysis, we find that there is no evidence to show the existence of P-V criticality. Here, we present a class of interior solutions corresponding to the solution in a scalar hair gravity exterior. The solution obtained in the linear case was regular and well-behaved at the stellar interior.

Strongly correlated electrons in the ferroelectric metal LiOsO3

The metallic $\mathrm{LiOs}{\mathrm{O}}_{3}$ undergoes a transition to a polar phase below ${T}_{s}\ensuremath{\approx}140\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. This unusual property provides a unique opportunity to study the interaction between free electrons and electric dipoles. We report a suite of measurements of physical properties in $\mathrm{LiOs}{\mathrm{O}}_{3}$ as a function of temperature, including resistivity and magnetoresistance down to 0.16 K, thermoelectric power, high-precision magnetization, specific heat, and thermal conductivity on textured single-crystal samples. Enhancements from the electron contribution to the specific heat and the paramagnetic susceptibility indicate that electrons in $\mathrm{LiOs}{\mathrm{O}}_{3}$ are highly correlated. An anomalously large Kadowaki-Woods ratio also supports the argument of strongly correlated electrons in $\mathrm{LiOs}{\mathrm{O}}_{3}$. In the nonpolar phase above ${T}_{s}$, electrons are coupled strongly to the lattice vibrations, which leads to the resistivity saturation at high temperatures and eventually a crossover to the hopping conduction. The data of thermal conductivity and specific heat are consistent with an order-disorder transition at ${T}_{s}$. The analysis of critical behavior in the resistivity, specific heat, and the thermal conductivity provides useful information for understanding the electron-dipole interaction in $\mathrm{LiOs}{\mathrm{O}}_{3}$.

Exact 2+1 dimensional rotating black hole solution in f(R)-gravity and its thermodynamical properties

In this work, we obtain the exact rotating black hole solution in f ( R ) -gravity model( R is not considered as a constant here) and investigate its thermodynamics, especially phase transition and critical behavior in the anti-de-Sitter (AdS) extended phase space. One particular characteristic of this solution is that when we set J = 0 , the Massive BTZ black hole solution recovers. We also obtain the exact form of the f ( R ) model for this solution. In the thermodynamical analysis, we calculate the thermodynamical quantities like the temperature and entropy for this solution and we compare them with the BTZ corresponding quantities. Also, We show the validity of the first law of thermodynamics. After that, we investigate the stability(local and global) of this obtained solution. In the critical behavior analysis, we find that there is no evidence to show the existence of P − V criticality like the ordinary BTZ case.

Manifestation of Nonconventional Magnetic Interaction in Electron-Doped Ca0.85Dy0.15MnO3 from Magnetic Properties and Critical Behavior Analysis

Manifestation of Nonconventional Magnetic Interaction in Electron-Doped Ca0.85Dy0.15MnO3 from Magnetic Properties and Critical Behavior Analysis

Critical behavior at high magnetic fields in LaPr(Ca,Sr)MnO manganites

In this work, we demonstrate that La0.225Pr0.4(Ca1−xSrx)0.375MnO3 manganites with 0≤x≤0.10, exhibit a discontinuous first order ferromagnetic-paramagnetic transition at temperatures ~ 230–240 K, which evolves to a continuous second order ferromagnetic-paramagnetic transition according to the intensity of the applied magnetic field. Under high magnetic fields and through a magnetization scaling analysis, we have determined the critical exponents of the sample with x = 0.05 - β = 0.15, γ = 0.77, and δ = 6.24, and x = 0.10 - β = 0.165, γ = 0.62, and δ = 4.69. The exponents values obey the scaling laws but do not belong to any existing universality class. This analysis of critical behavior can be used to predict the magnetic entropy change under high magnetic fields.

Ising critical behavior and room temperature magnetocaloric effect in itinerant ferromagnetic Mn5Ge2.9Fe0.1 compound

In this work, a novel polycrystalline Mn5Ge2.9Fe0.1 compound has been prepared and a detailed analysis on structural, physical and magnetocaloric properties is carried out. Mn5Ge2.9Fe0.1 compound is a second order-itinerant ferromagnet with enhanced Sommerfeld coefficient. The resistivity of this compound is found to show saturation at high temperatures due to spin fluctuations in the compound. Critical behavior analysis has been performed in near-Curie temperature regime and the exponents are estimated. The validity of these exponents is double checked by adopting several scaling hypothesis. The above study however revealed that the magnetic interactions in Mn5Ge2.9Fe0.1 compound is of short-range and comply well with 3D-Ising model. Nevertheless, a modest MCE around room temperature in concert with a substantial temperature width renders Mn5Ge2.9Fe0.1 compound as an appreciable magnetic refrigerant.

What happens for the BTZ black hole solution in dilaton f(R)-gravity?

In this work, we obtain the black hole solutions in the dilaton [Formula: see text]-gravity (R is not considered as a constant here) and investigate their thermodynamics especially phase transition and critical behavior in the anti-de Sitter (AdS) extended phase-space. We obtain the exact Banados, Teitelboim and Zanelli (BTZ) counterpart solutions in dilaton [Formula: see text]-gravity which is the basis of our work. We also obtain the exact form of [Formula: see text] model for some solutions. In the thermodynamical analysis, we calculate the thermodynamical quantities like the temperature and entropy for these solutions and we compare them with the BTZ corresponding quantities. After that, we investigate the stability (local and global) for these obtained solutions. In the critical behavior analysis, we find that there is no evidence to show the existence of P–V criticality (like the ordinary BTZ case) in this modified gravity model except some unusual P–V behavior in the corresponding diagrams.

Determination of Phase Transition and Critical Behavior of the As-Cast GdGeSi-(X) Type Alloys (Where X = Ni, Nd and Pr).

The aim of the paper is to present a study of the magnetocaloric effect and the nature of phase transition in the Gd80Ge15Si5 (S1), Gd75Ge15Si5Ni5 (S2), Gd75Ge15Si5Pr5 (S3) and Gd75Ge15Si5Nd5 (S4) alloys. The magnetic entropy changes determined for studied samples, under external magnetic field ~3T, were 11.91, 12.11, 5.08 and 4.71 J/(kg K) for S1, S2, S3 and S4, respectively. The values of refrigerant capacity (under ~3T) were 164, 140, 160 and 140 J/kg for S1, S2, S3 and S4, respectively. The first order phase transition was detected for samples S1 and S2, while specimens S3 and S4 manifested the second order phase transition at the Curie point (TC). The analysis of temperature evolution of the exponent n (ΔSM = C·(Bmax)n) showed the validity of this method in detecting either the first or the second order phase transition and the structural transition. The analysis of critical behavior was carried out for samples S3 and S4. The critical exponents and precise TC values were calculated. The ascertained critical exponents were used to determine the theoretical value of the exponent n, which corresponded well with experimental result.

Two-dimensional magnetic interplay in the tensile-strained LaCoO3 thin films.

High-quality epitaxial LaCoO3 (LCO) thin films have been deposited on SrTiO3 (STO) substrates with pulsed laser deposition (PLD). We find that the LCO films undergo a typical ferromagnetic-paramagnetic (FM-PM) phase transition at ∼80 K. To understand the nature of magnetic phase transition, various methods, including the modified Arrott plot and critical isotherm analysis, were used to determine the critical exponents, which are β = 0.754(1) with a Curie temperature TC = 79.8(8) K and γ = 1.52(2) with TC = 79.9(2) K. The reliability of these critical exponents was confirmed using the Widom scaling relation and the scaling hypothesis. Further analysis revealed that the spin coupling within the LCO films exhibits two-dimensional (2D) long-range magnetic interaction and the magnetic exchange distance decays as J(r) ∼r-(3.46). Our critical behavior analysis may shed new light on the further understanding of the origin of FM and the relatively fixed TC in LCO thin films.

Three-dimensional Ising ferrimagnetism of Cr-Fe-Cr trimers in FeCr2Te4

We carried out a comprehensive study of magnetic critical behavior in single crystals of ternary chalcogenide $\mathrm{Fe}{\mathrm{Cr}}_{2}{\mathrm{Te}}_{4}$ that undergoes a ferrimagnetic transition below ${T}_{c}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}$ 123 K. Detailed critical behavior analysis and scaled magnetic entropy change indicate a second-order ferrimagnetic transition. Critical exponents $\ensuremath{\beta}=0.30(1)$ with ${T}_{c}=122.4(5)\phantom{\rule{0.16em}{0ex}}\mathrm{K}, \ensuremath{\gamma}=1.22(1)$ with ${T}_{c}=122.8(1)\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, and $\ensuremath{\delta}=4.24(2)$ at ${T}_{c}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}123\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ suggest that the spins approach the three-dimensional Ising ($\ensuremath{\beta}=0.325, \ensuremath{\gamma}=1.24$, and $\ensuremath{\delta}=4.82$) model coupled with attractive long-range interactions between spins that decay as $J(r)\ensuremath{\approx}{r}^{\ensuremath{-}4.88}$. Our results suggest that the ferrimagnetism in $\mathrm{Fe}{\mathrm{Cr}}_{2}{\mathrm{Te}}_{4}$ is due to itinerant ferromagnetism among the antiferromagnetically coupled Cr-Fe-Cr trimers.

Towards a Universal Measure of Complexity.

Recently, it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and propose a universal measure of complexity that is based on Gell-Mann’s view of complexity. Our universal measure of complexity is based on a non-linear transformation of time-dependent entropy, where the system state with the highest complexity is the most distant from all the states of the system of lesser or no complexity. We have shown that the most complex is the optimally mixed state consisting of pure states, i.e., of the most regular and most disordered which the space of states of a given system allows. A parsimonious paradigmatic example of the simplest system with a small and a large number of degrees of freedom is shown to support this methodology. Several important features of this universal measure are pointed out, especially its flexibility (i.e., its openness to extensions), suitability to the analysis of system critical behaviour, and suitability to study the dynamic complexity.

Investigation of Magnetic Entropy Change and Critical Behavior Analysis of Cu- and Si-Doped Ni–Mn–Sn Heusler Alloys

We have studied the magnetic property as a function of temperature and magnetic field (μ0.H) and critical exponent on Ni–Mn-based Heusler alloys such as Ni46Mn41Sn13 (NMS), Ni46Mn41Sn10Si3 (NMSS), and Ni46Mn38Cu3Sn13 (NMCS). Magneto entropy change and the order of phase transition are estimated around the martensite and austenite phases of all these samples. Magnetic critical behavior of each sample is analyzed around second-order ferromagnetic (FM) austenite phase transition employing Arrott and Kouvel–Fisher plots. The reliability of estimated critical exponents is verified by Widom scaling relation and M3 vs H plot. Furthermore, one more local exponent n which depends on the magnetic state is also estimated through the isothermal magnetization of magnetic entropy change (∆SM) plots of all these samples. The obtained values for all these alloys are well close to the mean-field theoretical model and it is proposed that the existence of long-range magnetic interaction around austenite transition of these materials.

Anisotropic magnetocaloric effect and critical behavior in CrSbSe3

We report anisotropic magnetocaloric effect and critical behavior in quasi-one-dimensional ferromagnetic CrSbSe$_3$ single crystal. The maximum magnetic entropy change $-\Delta S_M^{max}$ is 2.16 J kg$^{-1}$ K$^{-1}$ for easy $a$ axis (2.03 J kg$^{-1}$ K$^{-1}$ for hard $b$ axis) and the relative cooling power $RCP$ is 163.1 J kg$^{-1}$ for easy $a$ axis (142.1 J kg$^{-1}$ for hard $b$ axis) near $T_c$ with a magnetic field change of 50 kOe. The magnetocrystalline anisotropy constant $K_u$ is estimated to be 148.5 kJ m$^{-3}$ at 10 K, decreasing to 39.4 kJ m$^{-3}$ at 70 K. The rescaled $\Delta S_M(T,H)$ curves along all three axes collapse onto a universal curve, respectively, confirming the second order ferromagnetic transition. Further critical behavior analysis around $T_c \sim$ 70 K gives that the critical exponents $\beta$ = 0.26(1), $\gamma$ = 1.32(2), and $\delta$ = 6.17(9) for $H\parallel a$, while $\beta$ = 0.28(2), $\gamma$ = 1.02(1), and $\delta$ = 4.14(16) for $H\parallel b$. The determined critical exponents suggest that the anisotropic magnetic coupling in CrSbSe$_3$ is strongly dependent on orientations of the applied magnetic field.

The analysis of magnetocaloric effect and magnetic critical behavior in Mn5Ge3−xAgx compounds

Structure, critical behavior and magnetic properties of Mn5Ge3−xAgx compounds with x = 0 and 0.1 have been investigated. With the substitution of Ge by Ag, the Curie temperature decreases from 299.8 to 295.1 K. Investigations for isothermal magnetization curves by Arrott curves, the Landau theory and phenomenological universal curves reveal that this system undergoes a second-order phase transition. To investigate the nature of magnetic transition, a detailed critical parameter study obtained by modified Arrott plots, Kouvel-Fisher method, and critical isothermal analysis has been performed. In comparison with the values given by standard models, these obtained critical parameters suggest a 3D long-range magnetic coupling with the exchange distance decaying as J(r) ≈ r−4.57 and J(r) ≈ r−4.67 for Mn5Ge3 and Mn5Ge2.9Ag0.1.

Critical Properties and Magnetocaloric Effect in La0.7Ba0.3Mn0.8Ti0.2O3 Ceramic

In this work, critical behavior, and magnetocaloric effect, as well as the relationship between these characteristics in polycrystalline sample La0.7Ba0.3Mn0.8Ti0.2O3 has been studied in detail. The positive value of the slope of Arrott plots exhibits that the magnetic phase transition of this sample is of a second order at Curie temperature of 96 K. The critical exponents β, γ, and δ have been determined using various ways including the modified Arrott plots, the Kouvel–Fisher plots, and the critical isotherm analysis. Interestingly, the experimental critical exponent values were β = 0.349 ± 0.002, γ = 1.350 ± 0.033, and δ = 4.868 ± 0.002, which are close to those deduced for the 3D-Heisenberg model below the Curie temperature and for the 3D-XY model above it. Additionally, the ferromagnetic interaction in La0.7Ba0.3Mn0.8Ti0.2O3 was found to be at the borderline of the long-range and short-range magnetic coupling, which was confirmed through the exchange distance decaying of $$ J\left( r \right)\sim r^{ - 4.9} $$. Moreover, the magnetocaloric characteristics of La0.7Ba0.3Mn0.8Ti0.2O3 were consistent with the analysis of critical behavior.

Understanding high ordering temperature in Gd6FeBi2 magnet: Critical behavior, electronic structure and crystal-field analysis

Gd6FeBi2 is reported as the only one room-temperature magnet among more than hundreds of compounds with its structural type, which makes it more attractive in potential applications. To reveal the origin of such high ordering temperature, critical behaviors, electronic structure and crystal-field effects of Gd6FeBi2 are investigated in this work. The short-range Gd-Fe ferrimagnetic interaction is supported by the crystal and electronic structure analyses. Unlike the strong Fe-Fe exchange interactions, the Gd-Fe exchange interaction shows limited influence on the critical exponents determined by long-range exchange interactions, which seems a common feature in rare earth – transition metal based alloys without exchange interactions between transition-metal atoms. However, the strong Gd-Fe hybridization reduces the influence of vibronic couplings on the short-range exchange interaction and thus allows a high Tc. The broadening or splitting mechanism of Gd 4f-electron bands is addressed based on crystal-field analysis and likely another factor for elevated Tc in Gd6FeBi2 and Gd-based compounds with non-magnetic elements. Different magnetic behaviors among isostructural compounds, and the relationship between the band splitting and crystal-field effects is also discussed.

Neutron diffraction and magnetic properties of Co2Cr1−xTixAl Heusler alloys

We report the structural, magnetic, and magnetocaloric properties of Co$_2$Cr$_{1-x}$Ti$_x$Al ($x=$ 0--0.5) Heusler alloys for spintronic and magnetic refrigerator applications. Room temperature X-ray diffraction and neutron diffraction patterns along with Rietveld refinements confirm that the samples are of single phase and possess a cubic structure. Interestingly, magnetic susceptibly measurements indicate a second order phase transition from paramagnetic to ferromagnetic where the Curie temperature (T$_{\rm C}$) of Co$_2$CrAl increases from 330~K to 445~K with Ti substitution. Neutron powder diffraction data of the $x=$ 0 sample across the magnetic phase transition taken in a large temperature range confirm the structural stability and exclude the possibility of antiferromagnetic ordering. The saturation magnetization of the $x=$ 0 sample is found to be 8000~emu/mol (1.45~$\mu_{\rm B}$/{\it f.u.}) at 5~K, which is in good agreement with the value (1.35$\pm$0.05~$\mu_{\rm B}$/{\it f.u.}) obtained from the Rietveld analysis of the neutron powder diffraction pattern measured at temperature of 4~K. By analysing the temperature dependence of the neutron data of the $x=$ 0 sample, we find that the change in the intensity of the most intense Bragg peak (220) is consistent with the magnetization behavior with temperature. Furthermore, an enhancement of change in the magnetic entropy and relative cooling power values has been observed for the $x=$ 0.25 sample. Interestingly, the critical behavior analysis across the second order magnetic phase transition and extracted exponents ($\beta\approx$ 0.496, $\gamma\approx$ 1.348, and $\delta\approx$ 3.71 for the $x=$ 0.25 sample) suggest the presence of long-range ordering, which deviates towards 3D Heisenberg type interactions above T$_{\rm C}$, consistent with the interaction range value $\sigma$.

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.