Magnetic Quantum Phenomena in a Three-sublattice Graphene-like Superlattice with Linear Spin-wave Theory

This study employs the linear spin-wave theory with the Holstein-Primakoff transformation and the retarded Green's function method to analyze energy gaps, frequencies in middle of energy gaps, spinwave resonance (SWR) frequency, and quantum fluctuations in a three-sublattice bilayer graphenelike superlattice. There exist three spin-wave spectra along the k x -direction and two distinct energy gaps in the system. Key findings show that under certain conditions, intralayer and interlayer exchange coupling and anisotropy can modulate the width and position of the energy gap, SWR frequency, and quantum fluctuations. At ground state, sublattice magnetic moments are below classical values due to quantum fluctuations. Notably, intralayer ferrimagnetic interactions amplify quantum fluctuations more significantly than ferromagnetic interactions.