Nontrivial critical behavior at magnetic transitions: A case study of Sm 7 Pd 3

We present a comprehensive analysis of the critical behavior of ${\mathrm{Sm}}₇{\mathrm{Pd}}₃$ in the vicinity of its second-order magnetoelastic transition at ${T}_{\mathrm{c}}=173\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The critical exponents (CEs) $\ensuremath{\beta}$ and $\ensuremath{\gamma}$, determined using both the standard convergence procedure and the average normalized slope (ANS) method, diverge at ${T}_{\mathrm{c}}$---a characteristic typically associated with first-order transitions. Notably, none of the established universality classes satisfactorily describe the critical behavior of ${\mathrm{Sm}}₇{\mathrm{Pd}}₃$, and we discuss the possible origins of this deviation in the context of the strong spin-lattice coupling intrinsic to the sample. We emphasize the importance of accurately selecting the critical temperature and magnetic field ranges to ensure robust critical behavior analysis, and propose a quantitative approach to assess the reliability of the extracted CEs. Additionally, we demonstrate that in the ANS method, the critical exponents $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ should be calculated separately using data for $T\ensuremath{\leqslant}{T}_{\mathrm{c}}$ and $T\ensuremath{\geqslant}{T}_{\mathrm{c}}$, respectively. Our findings underscore the need for a revised theoretical framework to accurately describe second-order magnetoelastic transitions.