Correlated electron systems with competing interactions provide a valuable platform for examining exotic magnetic phases. Theoretical models often focus on nearest-neighbor interactions, although long-range interactions can have a considerable impact on the behavior of the system, creating distinct and complicated magnetic phases. We investigate the consequences of competing interactions in a half-filled one-band Hubbard model on a simple cubic lattice, incorporating hopping processes up to third-nearest-neighbors, to explore the underlying magnetotransport properties. Our magnetic phase diagrams at low temperatures, obtained using semiclassical Monte Carlo analysis, reveal that the long-range interactions can disrupt one form of magnetic phase while creating a new type of magnetic order. For the nonperturbative regime (on-site Hubbard repulsive strength $U\sim$ bandwidth), the C-type antiferromagnetic ground state is preferred over the G-type antiferromagnetic phase when the interaction between second-nearest-neighbor sites becomes significant relative to the nearest-neighbor interactions. However, interactions beyond the second-nearest-neighbors are required to stabilize the A-type antiferromagnetic ground state. Remarkably, at low temperatures, a highly correlated paramagnetic insulating phase develops at the intersection between the antiferromagnetic phases, which might promote a three-dimensional spin-liquid state.

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• Frustrated magnetism
• Magnetic coupling
• Magnetic interactions
• Magnetic order
• Magnetic phase transitions
• Magnetism
• Magnetotransport
• Magnetic insulators
• Magnetic systems
• Monte Carlo methods