Correlação entre spins localizados e itinerantes com interações de troca Kondo e magnéticas em um cluster hexagonal (tipo Grafeno)

Abstract

The study of magnetic properties in many-body systems remains a fundamental challenge in Condensed Matter Physics, mainly due to the competition between strong electronic correlations, collective quantum effects, and constraints imposed by spatial geometry. Simplified models, particularly finite spin arrangements, are widely used to investigate essential phenomena such as antiferromagnetic interactions, magnetic frustration, singlet formation, and the Kondo coupling between localized and itinerant moments. In this dissertation, we analyze a hexagonal cluster similar to that found in graphene composed of six sites, a structure that preserves relevant symmetries and enables a controlled examination of the influence of itinerant electrons on the behavior of localized spins. Each site hosts a fixed magnetic moment, while itinerant electrons move through the lattice, allowing a direct investigation of the competition between electronic obility and exchange interactions. The theoretical description is based on the Ising–Kondo and Heisenberg–Kondo Hamiltonians, which incorporate kinetic-energy terms, magnetic interactions between localized spins, and local Kondo coupling. The quantum basis of the model is constructed using a binary representation of states, and the numerical solution is obtained through exact diagonalization and the Lanczos method. These matrices are large and grow rapidly with the number of itinerant electrons, which motivates the use of high-performance computational resources such as CENAPAD (the National High-Performance Computing Center) at UNICAMP, allowing the calculation of the relevant magnetic correlations. The analysis focuses on the quantities D, F and S², which characterize, respectively, the correlation between localized spins, the correlation between localized and itinerant spins, and the total spin of the system. The results show that the hexagonal geometry plays a crucial role in shaping the distribution of correlations. Strong Kondo interactions promote the screening of localized spins, while increasing temperature tends to suppress magnetic correlations. Thus, the hexagonal cluster proves to be an effective platform for understanding, in a controlled manner, the competition between different magnetic mechanisms in correlated systems, providing a solid foundation for future studies involving other geometries and interaction regimes.