New Methods for Critical Analysis: Revealing the Simultaneous Existence of Universality Classes in Nontrivial Magnetic Systems

Abstract

In magnetic systems, the microscopic constituents exhibit power law behavior near the paramagnetic transition temperature, $T_C$. The critical exponents (CEs) associated with the physical quantities that demonstrate singular behavior at $T_C$ illustrate the critical behavior, specifically the range and type of exchange interactions emerging in magnetic systems. However, it is realized that the developed methodologies may not yield accurate values of CEs, especially for magnetic systems with competing interactions, referred to as nontrivial magnetic systems. Currently, no comprehensive method effectively addresses the competing effects of the range of magnetic interactions among the constituent entities emerging in such systems. Additionally, there is no definitive explanation for CE values that do not belong to any single universality class. Here, we present new methodologies for critical analysis aimed at determining both the range of exchange interaction(s) and appropriate values of CEs. Using computational and experimental investigations, we analyze the magnetic behavior of trivial Ni and nontrivial Gd. Our findings demonstrate that (i) the critical behavior remains the same on either side of $T_C$, (ii) the critical behavior associated with local electron moments remains unaffected by the magnetic field, and (iii) in Gd, the critical role of competing interactions becomes evident: local electron moments follow a three-dimensional Ising-type short-range interaction, while itinerant electron moments exhibit a mean-field-type long-range Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which weakens under an external magnetic field due to the localization effect on itinerant electrons.