Tuning Magnetic Stability in Lanthanide Single-Atom Magnets on Defective Boron Nitride: From Intrinsic Protection to Field-Induced Spin-Lifetime Engineering

The pursuit of atomic-scale magnetic storage has driven intense research into lanthanide-based single-atom magnets (SAMs), where magnetic bistability and long magnetic relaxation times are essential for practical applications. However, a fundamental challenge is to achieve strong uniaxial magnetic anisotropy while simultaneously suppressing quantum tunneling of magnetization (QTM), since the former stabilizes the magnetization whereas the latter enables rapid relaxation and undermines magnetic memory. Here, we systematically investigate the magnetic stability and relaxation dynamics of Ho (4f10, J = 8) and Tb (4f8, J = 6) adatoms adsorbed on defective hexagonal boron nitride (Dh-BN) with C3v symmetry, using an integrated approach combining density functional theory (DFT+U+SOC) and model Hamiltonian analysis. Our results reveal that the interplay between total angular momentum J and crystal field symmetry dictates the intrinsic magnetic stability. For Ho@Dh-BN, C3v symmetry protects the degenerate |J = 8, mJ ≈ ±8⟩ ground states from QTM, as transverse crystal field terms (ΔmJ = ±3) cannot mix the |±8⟩ states. This yields a substantial effective reversal barrier of Urev = 28.72 meV and an Arrhenius magnetic lifetime of 1150 s at 12 K, demonstrating robust zero-field stability. In stark contrast, Tb@Dh-BN exhibits strong mixing of its |J = 6, mJ ≈ ±6⟩ ground states via QTM channels, resulting in a vanishing reversal barrier and no magnetic stability at zero field. Remarkably, applying an external magnetic field (B = 8 T) along the easy axis can restore the stability in the Tb system: the magnetic field lifts the ground-state degeneracy to suppress QTM by purifying the wave functions and forces magnetization reversal to proceed via multistep spin-flip pathways. This raises an effective barrier to Urev = 42.10 meV and extends the Arrhenius magnetic lifetime to 791 s at 18 K. Our work establishes two complementary design principles for achieving long spin lifetimes in lanthanide SAMs: intrinsic protection through favorable combinations of J and crystal field symmetry that inherently forbid QTM, and active field-induced stabilization that dynamically suppresses QTM in otherwise unstable systems. The findings provide a comprehensive microscopic understanding of magnetic relaxation in surface-supported lanthanide atoms and offer a clear theoretical roadmap for engineering electrically or magnetically addressable atomic-scale memory devices.