The critical properties of perovskite manganite La0.1Nd0.6Sr0.3MnO3 around the paramagnetic-ferromagnetic phase transition are investigated through various techniques such as modified Arrott plot, Kouvel-Fisher method, and critical isotherm analysis. The magnetic data analyzed in the critical region using the above methods yield the critical exponents of $\beta${}=0.257\ifmmode\pm\else\textpm\fi{}0.005 and $\gamma${}=1.12\ifmmode\pm\else\textpm\fi{}0.03 at TC=249.32\ifmmode\pm\else\textpm\fi{}0.03$\hskip0.3em${}K. The exponent $\delta${}=5.17\ifmmode\pm\else\textpm\fi{}0.02 independently obtained from the critical magnetization isotherm was found to basically fulfill the Widom scaling relation $\delta${}=1+$\gamma${}/$\beta${}. Moreover, the critical exponents also obey the single scaling equation of M(H,$\epsilon${})=$\epsilon${}$\beta${}f\ifmmode\pm\else\textpm\fi{}(H/$\epsilon${}$\beta${}+$\gamma${}). These results indicate that the obtained critical exponents are reliable. The values deduced for the critical exponents are closed to the theoretical prediction of tricritical mean-field model rather than the universal theory of three-dimensional Heisenberg model and mean-field model. These results suggest the present composition may be close to a tricritical point in the La0.7$-${}xNdxSr0.3MnO3 phase diagram.

Magnetic and electronic transport properties of perovskite manganite La_0.6Er_0.1Sr_0.3MnO₃ have been thoroughly examined through the measurements of magnetization, electron paramagnetic resonance(EPR), and resistivity. It was found that the substitution of Er³⁺ for La³⁺ ions introduced the chemical disorder and additional strain in this sample. An extra resonance signal occurred in EPR spectra at high temperatures well above T _C gives a strong evidence of electronic phase separation(EPS). The analysis of resistivity enable us to identify the polaronic transport mechanism in the paramagnetic region. At low temperature, a new ferromagnetic interaction generates in the microdomains of Er³⁺-disorder causing the second increase of magnetization. However, the new ferromagnetic interaction does not improve but decreases electronic transport due to the enhancement of interface resistance among neighboring domains. In view of a really wide temperature region for the EPS existence, this sample provides an ideal platform to uncover the evolution law of different magnetic structures in perovskite manganites.

One method of calculating critical exponents based on the field dependence on magnetic entropy change was applied to study critical behavior in ${\text{Pr}}_{0.55}{\text{Sr}}_{0.45}{\text{MnO}}_3$ . By using the obtained critical exponents, the modified Arrott plot [A. Arrott and J. E. Noakes, Phys. Rev. Lett. 19, 786 (1967)] is consistent with that by using conventional method. The calculated critical exponents not only obey the scaling theory, but also inosculate the deduced results from the Kouvel–Fisher method [J. S. Kouvel and M. E. Fisher, Phys. Rev. 136, A1626 (1964)]. It eliminates the drawback due to utilization of multistep nonlinear fitting in a conventional manner. Therefore, this means can be applied to investigate critical behavior.

The cubic B20 compound FeGe, which exhibits a near room temperature skyrmion phase, is of great importance not only for fundamental physics such as nonlinear magnetic ordering and solitons but also for future application of skyrmion states in spintronics. In this work, the critical behavior of the cubic FeGe is investigated by means of bulk dc-magnetization. We obtain the critical exponents (β = 0.336 ± 0.004, γ = 1.352 ± 0.003 and β = 5.276 ± 0.001), where the self-consistency and reliability are verified by the Widom scaling law and scaling equations. The magnetic exchange distance is found to decay as "Equation missing"r^−4.9, which is close to the theoretical prediction of 3D-Heisenberg model (r⁻⁵). The critical behavior of FeGe indicates a short-range magnetic interaction. Meanwhile, the critical exponents also imply an anisotropic magnetic coupling in this system.