Electric-field writing of out-of-plane bistable single-atom states on monolayer MoS₂

Single adatoms units supported by two-dimensional materials offer an appealing platform for atomic scale state control, but any memory-related interpretation requires distinguishable metastable states, a realistic retention assessment, and a clear readout mechanism. Here, based on first-principles calculations, we systematically screen 29 transition-metal adatoms on monolayer MoS₂ and identify seven elements that exhibit intrinsic out-of-plane conformational bistability. Fe is selected as a prototype because it possesses two well-defined adsorption states with distinct vertical heights separated by a finite zero-field barrier. The operative bistable coordinate is the adsorption height of the Fe atom rather than a magnetic order parameter of the MoS₂ substrate. The two structural branches also exhibit different localized spin-polarization responses: the low adsorption state shows an opposite induced spin-polarization on the nearest Mo/S environment, whereas the high adsorption state shows a predominantly parallel local response. Electronic-structure analysis reveals that this behavior originates from adsorption-height-dependent Fe-substrate interaction: the low state is characterized by stronger Fe-3d-S-3p/Mo-4d hybridization and bonding stabilization, whereas the high state is accompanied by weakened p-d hybridization and the occupation of an Fe-4s-related antibonding state. Additional field-dependent NEB calculations show that an out-of-plane electric field reshapes the double-well energy landscape and lowers the vertical switching barrier, while lateral migration remains less favorable for the pristine model considered here. Local harmonic vibrational analysis and HTST estimates further show that the bistable states can be kinetically stable at low temperature, but the present barriers are insufficient for long-term room-temperature nonvolatile retention. These results establish Fe@MoS₂ as a local-field-controllable conformationally bistable single-atom system with an adsorption-height-dependent local magnetic response.