  We present a comprehensive investigation of the magnetic ordering in
biphenylene network (BPN) layers, employing density functional theory (DFT)
calculations under external perturbations, including uniaxial strains and hole
doping. We compute fully relaxed structures, energy bands, and magnetic states
by performing DFT calculations augmented with extended Hubbard interactions,
encompassing both on-site and inter-site interactions, to accurately capture
electron correlations. We emphasize the importance of the extended Hubbard
forces by contrasting BPN layers with and without the forces. Our results
reveal that in their fully relaxed structures, both BPN monolayer and bilayer
are non-magnetic. We exploit external perturbations to induce magnetic
ordering. The application of uniaxial strains induces magnetic phase
transitions, leading to ferrimagnetic and antiferromagnetic states in BPN
monolayer and bilayer, respectively. Additionally, we investigate hole doping
as an alternative mechanism for inducing magnetic transitions. Our findings
shed light on the tunability of magnetic properties in BPN layers through
external perturbations, demonstrating the promise of low-dimensional materials
in future spintronics and nanoelectronic applications.
