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.

Layered ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ is a promising two-dimensional (2D) material for van der Waals bonded ferromagnetic devices since its ferromagnetism can be maintained upon exfoliating the bulk down to a few layers. However, the magnetic interaction properties and phase-transition type of this system remain controversial. In this work, we systematically study the magnetic properties and critical behavior of ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ single crystal. The angle dependence of magnetization indicates that ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ has a weak magnetic anisotropy along the $c$ axis but no magnetic anisotropy in the $ab$ plane. Based on the field-dependent magnetic entropy change $\left[\mathrm{\Delta }{S}_M(T,H)\right]$, the critical exponents of $\beta =0.177\left(9\right)$, $\gamma =1.746\left(8\right)$, and $\delta =10.869\left(5\right)$ are obtained around $T_C=66.4\left(3\right)$ K. With these critical exponents, the $M(T,H)$ and $\mathrm{\Delta }{S}_M(T,H)$ curves follow the universality scaling laws, implying their high reliability and self consistency. The determined critical exponents are close to the 2D-Ising model with spatial dimensionality $d=2$ and spin dimensionality $n=1$. These results suggest that for 2D-Ising-like ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$, the weak magnetic anisotropy is crucial for the stabilization of the long-range ferromagnetic ordering, which is also consistent with the prediction of renormalized spin wave theory.