Testing the chaos bound in the spinor field of Einstein-Euler-Heisenberg-Anti-de Sitter spacetime

Violations of the chaos bound have been observed in scalar fields. In this work, we investigate the Lyapunov exponents of chaotic particles in the spinor field of an Einstein-Euler-Heisenberg-Anti-de Sitter spacetime, and test the validity of the chaos bound in this field. The influences of the black hole charge, the Euler-Heisenberg constant, cosmological constant, particle charge and total angular momentum on the exponents are analyzed. With other parameters fixed, chaos bound violations occur only within specific ranges of black hole charge, particle spin, or total angular momentum-unlike in Reissner-Nordstr\"om spacetimes, where violations intensify with larger parameter values. Notably, anti-alignment of particle spin with the $z$-axis can trigger violations even for small cosmological constants, while no violations arise for the spin aligned with the $z$-axis regardless of the cosmological constant. Our results show that the cosmological constant drastically reshapes chaos bound violation conditions compared to Reissner-Nordstr\"om spacetimes, highlighting the spin's pivotal role in chaos onset.