Magnetic Properties of the frustrated J1-J2 square lattice with Kondo interactions

Abstract

The magnetic and electronic properties of materials are governed by the complex interplay between localized exchange interactions and coupling with itinerant electrons. This work investigates the competition between magnetic frustration and the Kondo effect in a J1 − J2 square lattice. Magnetic frustration is introduced through competing nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions. The Kondo effect, governed by the coupling JK, introduces a nonmagnetic screening mechanism via the formation of Kondo inglets. To solve the resulting Hamiltonian, we employ a rigorous Cluster Mean-Field (CMF) approximation coupled with exact diagonalization on a 4-site cluster. The methodology is validated by reproducing the known J1 − J2 phase diagram, which shows the suppression of the N´eel temperature (TN ) at the point of maximum frustration (J2/J1 ≈ 0.5). The results demonstrate that the introduction of JK further suppresses long-range magnetic order, promoting the formation of a Kondo singlet state, particularly in the highly frustrated regime. These findings characterize the quantum boundaries between magnetic and non-magnetic phases and provide a crucial foundation for mapping the full phase diagram across varying coupling strengths and electron densities.