Theoretical analyses of actinide single-atom magnetic behavior: Spin-vibration coupling and spin relaxation dynamics of single uranium atom on MgO/Ag(100)

Single-atom magnet (SAM) represents the single bit with ultimate atomic-scale limit in the field of magnetic storage and spintronics. Large magnetic reversal barrier and long magnetic lifetime of SAM are vitally important for its application to single-atom magnetic memory, which is intensely related to the spin dynamics induced by spin-vibration coupling (SVC) between magnetic adatom and substrate. In this work, we investigated the static magnetic energy level, relaxation pathway, SVC interaction, spin dynamics, and magnetization relaxation rate combined with the density functional theory method and crystal field model Hamiltonian analysis as well as ab initio calculations. The static relaxation pathway reveals an effective magnetization reversal barrier (${U}_{\mathrm{eff}}$) of 92.1 meV, much higher than the experimental excitation energy of 7.7 meV, which is due to the abundant intermediate SVC-induced spin-vibration states between the ground and first excited magnetic states, especially the state caused by vibrational mode $\ensuremath{\hbar}\ensuremath{\omega}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}7.56\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$, opening a fast relaxation channel for magnetization reversal. The quantum tunneling of magnetization (QTM) event is the primary cause of magnetization reversal in the temperature of $1--6\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, with an estimated QTM relaxation time ($\ensuremath{\tau}$) of 0.02 s. The spin dynamics demonstrates that the Raman regime is the dominant relaxation mechanism at $6--50\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, and the relaxation rates in $6--10\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ almost completely contribute from the two-mode Raman transitions involving vibrational modes of 4.71 and 7.56 meV. The predicted magnetic blocking temperature (${T}_{\mathrm{B}}$) of $1.5--17\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ indicates that the U@MgO system exists a loop hysteresis in this temperature, exhibiting a characteristic SAM behavior. Our SVC calculations suggest that the fast relaxation in U@MgO system can be suppressed by weakening or quenching the SVC interaction for the low-energy vibrational modes. The quantitative predictions of relaxation rate and magnetic blocking temperature provide a guidance on the future magnetic measurements.