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.

References in corpus (14)

• Critical Phenomena and Renormalization-Group Theory
• Atomistic spin model simulations of magnetic nanomaterials
• Exchange interaction between single magnetic adatoms
• Quantitative simulation of temperature dependent magnetization dynamics and equilibrium properties of elemental ferromagnets
• Evidence of long-range ferromagnetic order and spin frustration effects in the double perovskite $L{a}_{2}CoMn{O}_6$
• Critical behavior of the van der Waals bonded ferromagnet Fe${}_{3-x}$GeTe${}_2$
• Critical exponents can be different on the two sides of a transition: A generic mechanism
• Indirect exchange interaction between magnetic adatoms in a monolayer MoS2
• Magnetically-driven electronic phase separation in the semimetallic ferromagnet EuB${}_6$
• Magnetism of gadolinium: a first-principles perspective
• Multiple phases with tricritical point and Lifshitz point in skyrmion host Cu${}_2$OSeO${}_3$
• Spin exchange Hamiltonian and topological degeneracies in elemental gadolinium
• Magnetic interactions and magnetocaloric effect in (La0.5Pr0.5)0.6Ba0.4MnO3: Effect of A-site co-doping
• Suppression of f-Electron Itinerancy in CeRu2Si2 by a Strong Magnetic Field