Emergent geometric phase effects on the stochastic dynamics of superparamagnetic nanoparticles in curved spacetime

We investigate the influence of geometric phase effects, specifically the Berry phase, on the magnetization dynamics of superparamagnetic nanoparticles embedded in a weakly curved spacetime. Extending the classical Néel–Brown stochastic framework, we incorporate curvature-induced corrections into the Fokker–Planck–Brown (FPB) formalism to capture the interplay between quantum geometric phases and relativistic background geometry. Our study combines analytical approximations with numerical simulations implemented via advanced Python codes, enabling precise characterization of relaxation, nutation spectra, and nonlinear susceptibility under varying gravitational fields and magnetic anisotropies. The results reveal significant modifications to magnetization dynamics attributable to spacetime curvature, suggesting novel relativistic mechanisms for spin control at the nanoscale. This work bridges nanomagnetism, geometric quantum phases, and general relativity, opening new perspectives for the design of gravitation-enhanced magnetic sensors and quantum devices operating in curved geometries.