Critical Isotherm Analysis Research Articles

Magnetic field driven critical behavior in bulk Gd

Gadolinium (Gd) has been proven to be such a complex magnetic system that its static universality class varies as a function of the reduced temperature (|ɛ| = |T−TC|/TC). Though many works have been done, physical mechanisms of this phenomenon have not been fully elucidated. In this work, we analyzed the static magnetization data, M(H), around the ferromagnetic-paramagnetic phase transition temperature (TC) based on Banerjee's criteria, the modified Arrott plot and Kouvel–Fisher techniques, the critical isotherm analysis, and the scaling hypothesis to reconsider the phase transition, magnetic order, and isotropic and uniaxial behaviors of a polycrystalline Gd bulk. The M(H) data analyses with H variations up to 140 kOe indicated that Gd still keeps the nature of a second-order phase transition and short-range magnetic order. In the critical region of |ɛ| = 3.4 × 10−3–6.9 × 10−2, we observed the critical-behavior transition from a mixed isotropic and uniaxial ferromagnet for H = 3–10 kOe through an isotropic 3D Heisenberg ferromagnet for H = 10–100 kOe to a uniaxial 3D Ising ferromagnet for H = 100–140 kOe. The results demonstrate the possibility of using high fields to identify the universality class of Gd. The fluctuations and preferred reorientation of spins in the hexagonal close-packed lattice at temperatures T > 230 K are thought to cause these interesting phenomena.

Novel critical behavior of magnetization in URhSi: Similarities to the uranium ferromagnetic superconductors UGe2 and URhGe

We study the critical behavior of dc magnetization in the uranium ferromagnet URhSi around the paramagnetic to ferromagnetic phase transition at ${T}_{\mathrm{C}}\ensuremath{\sim}10$ K with a modified Arrott plot, a Kouvel-Fisher plot, the critical isotherm analysis, and the scaling analysis. URhSi is isostructural to uranium ferromagnetic superconductors URhGe and UCoGe. The critical exponent $\ensuremath{\beta}$ for the temperature dependence of the spontaneous magnetization below ${T}_{\mathrm{C}}$, $\ensuremath{\gamma}$ for the magnetic susceptibility, and $\ensuremath{\delta}$ for the magnetic isotherm at ${T}_{\mathrm{C}}$ in URhSi have been determined as $\ensuremath{\beta}=0.300\ifmmode\pm\else\textpm\fi{}0.002$, $\ensuremath{\gamma}=1.00\ifmmode\pm\else\textpm\fi{}0.02$, and $\ensuremath{\delta}=4.38\ifmmode\pm\else\textpm\fi{}0.04$ by the scaling analysis and the critical isotherm analysis. These critical exponents fulfill the Widom scaling law $\ensuremath{\delta}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}1+\phantom{\rule{0.16em}{0ex}}\ensuremath{\gamma}/\ensuremath{\beta}$. Magnetization has strong uniaxial magnetic anisotropy in the ferromagnetic state of URhSi. However, the universality class of the ferromagnetic transition does not belong to the three-dimensional Ising system with short-range exchange interactions between magnetic moments ($\ensuremath{\beta}=0.325$, $\ensuremath{\gamma}=1.241$, and $\ensuremath{\delta}=4.82$). The obtained exponents in URhSi are similar to those in the uranium ferromagnetic superconductors ${\mathrm{UGe}}_{2}$ and URhGe, and uranium ferromagnets UIr and $\mathrm{U}({\mathrm{Co}}_{0.98}{\mathrm{Os}}_{0.02}$)Al. We have previously reported the unconventional critical behavior of magnetization in the uranium ferromagnetic superconductors [N. Tateiwa et al., Phys. Rev. B 89, 064420 (2014)]. The universality class of the ferromagnetic transition in URhSi may belong to the same one in the uranium ferromagnetic superconductors and the uranium ferromagnets. The unconventional critical behavior of the magnetization in the uranium compounds cannot be understood with previous theoretical interpretations of critical phenomena. The absence of the superconductivity in URhSi is discussed from several viewpoints. The improvement of the sample quality in URhSi could provide a good opportunity to gain a deeper understanding of the ferromagnetic superconductivity in the uranium ferromagnets.

Magnetism and critical behavior of double perovskite RE2CoMnO6 (RE = La and Eu) compounds

Abstract The magnetic properties and critical behavior near the Curie temperature TC in the double perovskite RE2CoMnO6 (RE = La and Eu) were systematically investigated via the modified Arrott plots (MAP), the Kouvel-Fisher plot (K-F), and the critical isotherm analysis (CI). The reliable value of critical parameters (β, δ, and γ) obtained from K-F plot are to be 0.4704, 0.9978, and 3.12 with TC of 210.8 K for La2CoMnO6, and to be 0.6065, 0.9237, and 2.52 with TC of 130.3 K for Eu2CoMnO6, respectively. Moreover, the reliability of critical parameters of two samples was further verified by different methods including the Widom scaling relation and the magnetic equation. The obtained values of critical parameters are all close to the value of the mean-field theoretical model which manifested the presence of the long-range FM order for RE2CoMnO6 (RE = La and Eu) compounds.

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.

Three-dimensional Heisenberg critical behavior in amorphous Gd65Fe20Al15 and Gd71Fe3Al26 alloys

Amorphous Gd65Fe20Al15 and Gd71Fe3Al26 alloys have ever been reported to exhibit giant refrigerant capacity around their magnetic ferromagnetic-paramagnetic phase transition, which is desirable in magnetic refrigeration. In this paper, we have investigated the critical behavior of amorphous Gd65Fe20Al15 and Gd71Fe3Al26 alloys in order to better understand their magnetic phase transition. We compared the critical exponents estimated using modified Arrott plot and Kouvel-Fisher plot methods. The critical exponents obtained by Widom's law are in good agreement with those calculated from critical isotherm analysis. According to the obtained critical exponents, the magnetic properties of these two samples were re-scaled, indicating that the magnetic behavior of these alloys could be expressed by a universal and unified law. By analyzing the effective critical exponents and exchange interaction of the two alloys, we have determined that Gd65Fe20Al15 and Gd71Fe3Al26 exhibit isotropic short-range magnetic interaction and close to the 3D-Heisenberg model.

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.

Short and long range ordering in La1−xSrxCoO3 cobaltites

We have carefully studied the relation between the critical and electrical behavior of rhombohedral La1−xSrxCoO3 (x = 0.2–0.5) compounds prepared by solid-state reactions. The results obtained from analyzing M(T, H) data indicate that all compounds undergo a second-order phase transition and the ferromagnetic-paramagnetic (FM-PM) transition temperature increases from approximate 182 K for x = 0.2 to 253 K for x = 0.5. Basing on the modified Arrott and Kouvel-Fisher techniques, scaling hypothesis, and critical isotherm analysis, we have determined the critical exponent values characteristic of magnetic order of La1−xSrxCoO3, with β = 0.361–0.489, γ = 1.021–1.346, and δ = 2.99–4.72. Interestingly, though all compounds are metallic ferromagnets, we have found the phase segregation in magnetic order as x > 0.3, where magnetic interactions tend to change from long-to-short-range FM order together with the absence of the insulating-like behavior at temperatures below 100 K. These phenomena are related to the spatial coexistence of multiple electronic and magnetic phases due to the changes in concentration of cobalt ions, spin-state transitions, and the existence of poor-hole anti-FM and hole-rich FM regions.

Impression of magnetic clusters, critical behavior and magnetocaloric effect in Fe3Al alloys.

Herein, we report unusual magnetic behavior in arc melted bulk stoichiometric Fe3Al alloy with a D03 structure. The temperature variation in the magnetization measurements revealed two transitions, i.e. one at ∼763 K and another at ∼830 K. Below 763 K, it exhibits ferromagnetic ordering and the nature of the transition is second order. However, the second transition is more complex and detailed analysis of the magnetic data suggested the coexistence of ferromagnetic and paramagnetic phases (two-phase: α + D03/α + B2) and structural transitions triggered by temperature. We observed dual peaks in the magnetic entropy change curve, in accordance with the magnetization results, which corroborate the occurrence of a two-phase system. We believe that the concurrent magnetic ordering and the complex two-phase are associated with the evolution of short-range ordered magnetic clusters having a magnetic moment of ∼103μB in the host matrix. A cluster hypothesis is proposed to explain the observed intricate magnetic behavior of this alloy at high temperature. The estimated critical exponents using a modified Arrott plot, Kouvel-Fisher plot and critical isotherm analysis lie in between the 3D-Heisenberg and 3D-Ising model, indicating a short-range interaction and magnetic inhomogeneity, which again are consistent with the magnetization results. The obtained critical exponents follow the universal scaling behavior, which indicates the renormalization of interactions around the magnetic ordering transition (TC). Despite the obvious larger thermal entropy at very high temperature, our synthesized Fe3Al alloy showed enhanced magnetic entropy changes. The obtained magnetic entropy change for binary Fe3Al alloy shows twice the value of that of other binary/ternary Fe-based alloys.

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.

Appearance of Griffiths-Like Phase in a New Pyrochlore Compound La2Mn2O7−δ

The La2Mn2O7 − δ compound was prepared using ceramic method. The X-ray diffraction study revealed that this compound crystallized in pyrochlore oxide–type monoclinic structure with the P2/M space group. Concerning the magnetization measurements, they showed a paramagnetic (PM) behavior at high temperature and a ferromagnetic (FM) transition near 167 K. As for the magnetic measurements, they demonstrated the possible existence of a Griffiths-like phase, which was observed for the first time, to our knowledge, in a pyrochlore oxide-type A2B2O7. This originality can be due to the competition between the AFM and FM interactions of the Mn ions, induced by oxygen deficiency. The critical isotherm analyses indicated that the 3D-Heisenberg was the most acceptable model in the case of our compound.

Critical behavior and magnetocaloric effect in Mn3Si2Te6

The critical properties and magnetocaloric effect of semiconducting ferrimagnet Mn$_3$Si$_2$Te$_6$ single crystals have been investigated by bulk magnetization and heat capacity around $T_c$. Critical exponents $\beta = 0.41\pm0.01$ with a critical temperature $T_c = 74.18\pm0.08$ K and $\gamma = 1.21\pm0.02$ with $T_c = 74.35\pm0.05$ K are deduced by the Kouvel-Fisher plot, whereas $\delta = 4.29\pm0.05(3.40\pm0.02)$ is obtained by a critical isotherm analysis at $T = 74(75)$ K. The magnetic exchange distance is found to decay as $J(r)\approx r^{-4.79}$, which lies between the mean-field and 3D Heisenberg models. Moreover, the magnetic entropy change $-\Delta S_M$ features a maximum at $T_c$, i.e., $-\Delta S_M^{max} \sim$ 2.53(1.67) J kg$^{-1}$ K$^{-1}$ with in-plane(out-of-plane) field change of 5 T, confirming large magnetic anisotropy. The heat capacity measurement further gives $-\Delta S_M^{max}$ $\sim$ 2.94 J kg$^{-1}$ K$^{-1}$ and the corresponding adiabatic temperature change $\Delta T_{ad}$ $\sim$ 1.14 K with out-of-plane field change of 9 T.

Effects of Mn site substitution on magnetic ordering and critical behavior in Nd0.67Sr0.33MnO3 manganite

In this study, we investigated the structural, magnetic order, and critical exponent behaviors for substitutions of 3d transition elements (Cr, Fe, and Co) at the Mn site in Nd0.67Sr0.33MnO3. Rietveld refinement confirmed that all of the compounds had an orthorhombic crystal structure. X-ray absorption spectroscopic analysis confirmed minor variations in the Mn3+/Mn4+ ratio due to doping with transition metal elements at the Mn site. The parent and Cr-substituted compounds obeyed the Curie–Weiss law, whereas the other compounds did not, thereby indicating the presence of some ferromagnetic clusters within the paramagnetic matrix. The critical behavior of the system was analyzed using the modified Arrott plot method and critical isotherm analysis. The critical exponents β and γ calculated for the parent compound were consistent with the predictions based on the tricritical model, whereas the critical exponents determined for the substituted compounds were close to the mean field model. The critical exponents governing the magnetic phase transition calculated from the field dependence of the magnetic entropy change were in good agreement with those obtained from the modified Arrott plot and critical isotherm analysis.

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.

Structural, magnetic, magnetocaloric and critical properties of La0.9Ba0.1MnO3 manganite

Polycrystalline La0.9Ba0.1MnO3 (LBMO) manganite samples are synthesized by usual solid state reaction technique. X-ray powder diffraction at room temperature indicates that our samples crystallize in the rhombohedral structure with an R3¯c space group. Magnetocaloric and critical behavior of the sample is probed through temperature and magnetic field dependent magnetization measurements. The compound shows paramagnetic-ferromagnetic (PM-FM) transition at critical temperature (TC) of 280 K and the nature of this transition is of second order. The deviation in the inverse of susceptibility versus temperature plot from Curie–Weiss law near TC unveiled the presence of Griffiths phase (GP) at TG = 292 K with susceptibility exponent λ = 0.3. The presence of Griffiths phase (GP) proves the existence of ferromagnetic clusters in the paramagnetic domain. Having second order phase transition sample shows a maximum magnetic entropy change (ΔSMmax) of 0.665 J/kg K for the magnetic field change of 4 Tesla. The sample also exhibits high relative cooling power (RCP) of 28.83 J/kg against this field. The critical behavior of second order phase transition in this sample is analyzed using Modified Arrott plots (MAP), Kouvel Fisher (KF) and critical isotherm analysis method. The estimated critical exponents of the sample are β ≈ 0.3, γ ≈ 1.32 and δ ≈ 5.1. These values of the critical exponents are also verified by scaling equations of state. Further the change in magnetic entropy (ΔSM) versus applied field obeys the power law ΔSM = (μoH) n with exponent value n = 0.55 at TC = 280 K.

Effect of Gd substitution on the critical scaling of the ferromagnetic transition of La0.6-x Gdx Sr0.4 MnO3(x=0, 0.05, 0.1) manganite

This paper presents a detailed study on the critical properties of perovskite manganite La0.6-x Gdx Sr0.4 MnO3(x = 0, 0.05, 0.1) synthesized by Sol-gel method. The critical exponents near the PM-FM phase transition are determined through various methods such as modified Arrot plot, Kouvel-Fisher methods, and critical isothermal analysis based on the data of magnetic measurements recorded around the Curie temperature. These specimens are in agreement with their corresponding values proved by Widom scaling law, as well as the scaling theory. According to the values of critical exponents, the presence of the phase transition is found to be not relevant to the common transition classes but they can be attributed to some abnormal variations. It is suggested that the induced lattice disordering and magnetic disordering, as a result of Gadolinium incorporation, to be potential reasons for the presence of a large magnetocaloric effect, in addition to an anomalous ferromagnetic phase transition in the studied material.

Critical properties of the quasi-two-dimensional metallic ferromagnet Fe2.85GeTe2

We have investigated the critical behavior of Fe2.85GeTe2 single crystals near the paramagnetic-ferromagnetic transition by bulk dc magnetization measurements. The critical exponents β, γ and δ, obtained from modified Arrott plot, Kouvel–Fisher method, and critical isothermal magnetization analysis, could fulfill the Widom scaling law. The self-consistency and reliability of these exponents are further verified by the magnetic state equations below and above the Curie temperature at high magnetic field. In addition, the exchange distance deduced from the susceptibility exponent is shown to decay as . Based on the observations, we suggest that the competition between direct magnetic exchange and Coulombic and/or RKKY interactions should be responsible for the intrinsic magnetism in this system.

Universal curve and long-range ferromagnetic order in the intermetallic compound Mn0.92Sn0.08CoGe

In this work, the universal curve, critical behavior and magnetocaloric effect of the intermetallic compound Mn0.92Sn0.08CoGe around room temperature have been investigated. Magnetic data indicate that Mn0.92Sn0.08CoGe exhibits the characteristic of second-order transition around the room temperature 286 K. Moreover, the universal curve, well fitted by a Lorentz function, further proves second-order nature of the transition. The critical exponents obtained from various techniques such as modified Arrott plot (MAP), Kouvel-Fisher (KF) method, and critical isotherm analysis (M(TC)) are found to basically fulfill the Widom scaling relation: δ = 1 + γ/β and obey the scaling equation of M (H, ε) = εβf±(H/εβ+γ), revealing the extracted critical exponents are reliable. The obtained critical exponents are close to the prediction of the mean-field model, suggesting the existence of long-range magnetic interactions coupling with the exchange distance decaying as J (r) ≈ r−4.4.

Critical properties and field dependence of the magnetic entropy change in Pr0.8K0.2MnO3 ceramic: A comparison between solid-solid state and sol-gel process

We have performed a systematic study of the critical properties of Pr0.8K0.2MnO3 manganite synthesized using two various methods in the vicinity of the ferromagnetic–paramagnetic phase transition. Our compound was successfully prepared by using the solid state reaction at high temperatures and Pechini sol-gel method. The X-ray diffraction pattern shows that all our samples adopt an orthorhombic structure with Pnma space group. Moreover, the critical exponents β, γ and δ are estimated through various techniques such as the modified Arrott plot, the Kouvel–Fisher method and the critical isotherm analysis founded on the data of the magnetic measurements on record near the Curie temperature. Compared to standard models, the estimated critical exponents are close to the theoretical values of 3D-Heisenberg model for the sample elaborated by solid state reaction and tricritical mean-field model for the sample elaborated by the sol-gel method. These results indicate the presence of a ferromagnetic short-range order in our samples. The calculated values using the Widom scaling equation are proximate to those obtained values from critical isotherm M (TC, µ0H). The accuracy of the critical exponents values was confirmed with the scaling hypothesis, the magnetization curves fall onto two sides independents below and above TC. Interestingly, the change of the universality class is due to the relevant the diminution of grain size. These results imply that the critical behavior of our samples depended sorely on the synthesis technique.

Critical behaviors of ferromagnetic-paraferromagnetic transition in La0.5Sr0.5MnO3 nanowires bundles under low applied field

The critical behaviors of the perovskite La0.5Sr0.5MnO3 nanowires bundles around the ferromagnetic-paraferromagnetic (FM-PM) transition through modified Arrott plot and critical isothermal analysis is investigated. The obtained critical exponents are determined by modified Arrott Noakes equation (H/M)1/γ=(T−Tc)/Tc+(M/M1)1/β under a low external magnetic field of 0–0.8T, where β = 0.93 and γ = 2.25 were obtained at Tc ≈ 328 k. The availability of the parameters is proved by fulfilling the Widom scaling relation δ=1+γ/β which obeys the single scaling equation of M(H,|ε|)=εβf±(H/|ε|β+γ). The critical exponents determined in this system is unique and not following theories in any published literature. It may be attributed to the nano-size effect and surface magnetism of this system.

Critical behavior and magnetocaloric effect in the multiferroic double perovskite Lu2NiMnO6

A systematic investigation on the structure, magnetism, magnetocaloric effect, and critical behaviors of multiferroic Lu2NiMnO6 synthesized by sol-gel method are reported. This compound crystallizes in a monoclinic structure with the space group P21/n. Upon decreasing temperature, a single magnetic transition from paramagnetic to ferromagnetic phase has been observed, around which considerable magnetic entropy changes can be obtained. Besides, evaluation of the critical exponents are performed using various techniques, like the modified Arrott plot, Kouvel-Fisher method and critical isotherm analysis based on the magnetic data around magnetic transition temperature. The obtained critical exponent values are found to be coincided and comparable with those predicted by the mean-field model, which are also confirmed by the single scaling equation: m = f±(h), where m and h are the renormalized magnetization and field, respectively by observation of isotherm M(H) curves below and above the critical temperatures collapsing into two independent universal branches. The exponents determined in this study are in good agreement with those calculated from the renormalization group approach for a three-dimensional system coupled with the attractive long-range interactions between spins that decay as J(r)∼r−(3+σ) with σ = 1.325.