Symmetry effects on the spin switching of adatoms

Abstract

Highly symmetric magnetic environments have been suggested to stabilize the magnetic information stored in magnetic adatoms on a surface. Utilized as memory devices such systems are subjected to electron tunneling and external magnetic fields. We analyze theoretically how such perturbations affect the switching probability of a single quantum spin for two characteristic symmetries encountered in recent experiments and suggest a third one that exhibits robust protection against surface-induced spin flips. Further we illuminate how the switching of an adatom spin exhibits characteristic behavior with respect to low energy excitations from which the symmetry of the system can be inferred. Recently, single magnetic atoms on surfaces, or so-called magnetic adatoms, have gained a lot of interest for spin-based information storage and processing [1][2][3]. These concepts are mostly based on strong magnetic anisotropy energy [4,5], which reduces spin degeneracy at zero magnetic field, thereby defining preferential spatial orientations of the spin. While magnetic anisotropy introduces an energy cost for magnetization reversal, countless studies have illustrated that in the presence of strong magnetic anisotropy, individual magnetic adatoms still exhibit rather short lifetimes [6][7][8] owing to the interplay of the hybridization of the moment bearing orbitals and the underlying substrate. Such observations question the role of both tunneling electrons as well as substrate electrons in dynamical processes of the atomic spin [5,[9][10][11][12][13]. In order to enhance the dynamic stability of such adatoms, strong magnetic coupling between individual spins can be utilized to protect the total spin from fluctuations [2,14].A different approach, that stabilizes a single magnetic moment of an adatom, was utilized by a particular choice of both spin and underlying substrate symmetry [3]. In particular for a threefold symmetric system with the net magnetic moment S = 8 of a holmium adatom, it is possible to protect the spin, in the absence of perturbations, from single-electroninduced spin reversal. It is yet unknown how perturbations, like current-based read out or static magnetic fields which break the symmetry of the system, effect the symmetry caused stability of the spin in such quantum systems.Here we approach this question with a focus on the prospects of using a specific symmetry to protect a spin from switching. We extract the effective switching rate between the high-spin ground states via all possible spin paths, as experimentally manifested in two-state telegraph noise, utilizing a master equation approach. With comparative analysis we show how a single spin on two-, three-and fourfold symmetric substrates [15] responds to temperature, external magnetic field, as well as inelastic tunneling electrons. Higher symmetries are not part of our discussion since they are difficult to realize experimentally. We find that the threeand fourfold symmetric systems are both protected against single-electron-induced ground state s...

Superlattice of Single Atom Magnets on Graphene

“…This crossing allows QTM mediated by first-order electron or phonon scattering in the C 6v CF. 20 Figure 3c illustrates these three different mechanisms. The observed magnetic hysteresis up to B = ±5.6 T outperforms the best Dy-based single-ion molecular magnets.…”

“…In addition, in the C 6v symmetry first-order scattering (ΔJ z = ±1) with conduction electrons and phonons cannot induce direct transition between states with J z = 7 and J z = −7. 19,20 Even considering coupling with nuclear spins, i.e., hyperfine interactions, the Dy atoms are protected from QTM for the following reasons: first, more than half of the isotopes of Dy (56.2% natural abundance) have no nuclear spin (I = 0). Second, all the other isotopes have a nuclear spin I = 5/2 and its coupling to the integer total electron moment leads to a half integer spin, for which QTM is forbidden due to Kramers' theorem.…”

“…First, from a general point of view, the higher the CF symmetry, the lower the number of channels for QTM. 20 In the limit of perpendicular anisotropy and C ∞v symmetry, QTM is forbidden and the magnetization of the atom has to overcome the entire MAE barrier to reverse its direction. In this respect, graphene, with its C 6v symmetry, represents an ideal substrate to minimize the possibility of direct QTM.…”

General scheme for stable single and multiatom nanomagnets according to symmetry selection rules

“…For this purpose, we solve the master equation (see Refs. [4,19]) for a sixfold rotational symmetric system with small transversal anisotropy, H , and several different spin magnitudes. As already mentioned before, we neglect the small energy renormalization of the atomic levels due to the coupling with the tip.…”

“…With time the scientific community has started to recognize the role played by the symmetries of the system [3,17,19]. Their implications are extremely relevant not only in determining whether the two low-energy atomic states are magnetized but also in constraining their stochastic dynamics.…”