Fermions in a (2+1)-dimensional magnetized spacetime with a cosmological constant: Domain walls and spinning magnetic vortices

In this study, we investigate the relativistic dynamics of fermions in a (2+1)-dimensional sector of the Bonnor-Melvin magnetic (BMM) spacetime background, which features a homogeneous magnetic field aligned with the symmetry axis and a nonzero cosmological constant while maintaining Lorentz invariance under boosts along the z-direction. We analyze the (2+1)-dimensional solution in gravity coupled with nonlinear electrodynamics, excluding the presence of a brane, and derive the radial wave equation governing relativistic fermions in this background. By transforming the problem into a one-dimensional Schrödinger-like equation, we obtain exact eigenvalue solutions, demonstrating that the system supports impenetrable magnetic domain walls that confine fermionic states. In the process, it is unavoidable to extend our analysis to massless fermions, where we establish the generality (as a byproduct and a side effect of the current study, so to speak) of our findings and show that the stationary states of Dirac-Weyl fermions can give rise to rotating ring-like modes, supporting the presence of spinning magnetic vortices in, for example, magnetized monolayer Dirac materials.