An orbitally derived single-atom magnetic memory

A single magnetic atom on a surface epitomizes the scaling limit for magnetic information storage. Indeed, recent work has shown that individual atomic spins can exhibit magnetic remanence and be read out with spin-based methods, demonstrating the fundamental requirements for magnetic memory. However, atomic spin memory has been only realized on thin insulating surfaces to date, removing potential tunability via electronic gating or distance-dependent exchange-driven magnetic coupling. Here, we show a novel mechanism for single-atom magnetic information storage based on bistability in the orbital population, or so-called valency, of an individual Co atom on semiconducting black phosphorus (BP). Distance-dependent screening from the BP surface stabilizes the two distinct valencies and enables us to electronically manipulate the relative orbital population, total magnetic moment and spatial charge density of an individual magnetic atom without a spin-dependent readout mechanism. Furthermore, we show that the strongly anisotropic wavefunction can be used to locally tailor the switching dynamics between the two valencies. This orbital memory derives stability from the energetic barrier to atomic relaxation and demonstrates the potential for high-temperature single-atom information storage.

It is well known that hydrogen can have a significant impact on the properties of atoms [1][2][3] . For two procedures were used: (1) the cryostat was regularly warmed to T > 40 K and the system pumped with a turbomolecular pump to remove adsorbed hydrogen from the cryostat, and (2) samples were generally studied for less than 10 days to minimize hydrogen contamination.
Control spectra were routinely taken on the BP to ensure no spurious features were observed. In Supplementary Table 1, we list the spin-resolved 3d-subshell occupancies of the Co adatom on BP calculated for the two orbital configurations. From the projections, it is clear a major orbital redistribution takes place within the 3d xz and 3d yz subshells upon vertical relaxation (Δn≈0.4 e -). Additionally, the reduced ligand interactions make the 3d z2 subshell more favorable as the atom relaxes away from the BP surface. One can see that in the J H,low state the magnetic moment originates predominantly from the 3d x2-y2 orbital with some contribution from the 3d z2 orbital. On the contrary, the magnetization in the J H,high state is distributed almost equally over all orbitals of the 3d symmetry except 3d z2 , whose contribution is negligible. down, and total) and magnetic moment projected onto the cubic harmonics for JH,low and JH,high. Due to differences in orthogonality between the original d-orbital hybrid functions and the cubic harmonics, the total d-orbital occupancy is slightly overestimated with respect to the populations given in figure 2.

JH,low JH,high
To gain insight into the charge redistribution around the Co adatom on the BP surface, we calculate the in-plane averaged charge density difference (Δn) along the z-direction. Here, Δn is defined as Δn = n Co+BP -n BP -n Co , where n Co+BP is the charge density of BP with the Co adatom, n BP is the charge density of BP without the adatom, and n Co is the charge density of the free Co atom in a S = 3/2 state. The corresponding quantity (Δn) is shown in Supplementary

Supplementary Note 3: Comparison of dI/dV spectroscopy with density of states calculations
Representative dI/dV spectra for the J T site (Fig. 2j), J H,low (Fig. 2k), and J H,high (Fig. 2l) all show strong deviation from the bulk BP 5 . Comparing these spectra to calculations for Co on single layer BP, sharp peaks in the dI/dV spectra can be attributed to Co-related impurity states or ionization events, similar to previous observations in bulk semiconductors 6 . The two peaks observed in the J T spectrum (Fig. 2j) can be assigned to ionization events, as they shift strongly (>100 mV) with varying tip height (Supplementary Figure 9a,d). The primary features in the J H,low spectrum, peaks at -580 mV and 280 mV (Fig. 2k), do not shift significantly with tip height (Supplementary Figure 9b,e). The predicted DOS for J H,low shows Co hybrid d-bands at both of these energies, which can tentatively be assigned to the origin of the dI/dV peaks. The measured dI/dV spectrum for J H,high is given in Fig. 2l. The spectrum is characterized by its diminished intensity and single sharp peak at approximately 420 mV. As seen in Supplementary

Supplementary Note 4: Tip-induced ionization
Tip-induced band-bending (TIBB) locally influences the energy of semiconductor bands due to insufficient screening from charge carriers; it has been observed that if a defect level, shifted with the material bands, passes through E F , it will undergo an ionization event. The instantaneous change in charge state is observable as a step in the tunneling current (peak in dI/dV) because the local potential landscape is modified via an effective Coulomb potential at the atom [6][7][8][9] . Using dI/dV spectral mapping, we map out the spatial location of such a charging  (Fig. 4e); at Vs < 0 V, electrons tunnel from filled sample states into empty tip states, when a filled electronic state is depopulated, the tunneling current decreases. Such an explanation successfully accounts for the isotropic character of the charging event and the spatial evolution of the charging state with decreasing bias magnitude. (g) Evolution of charging ring radii (reff) with bias voltage for JH,low (dark blue) and JH,high (light blue). (h) Qualitative level structure in the flat band condition showing primary JH,low (solid dark blue line) and JH,high (solid light blue line) energy levels responsible for ionization in the regime 200 mV < Vs < 700 mV. Significantly, these are the two states that are ionized during the telegraph switching. An additional JH,high state (dashed light blue line) is depicted, which is responsible for the charging event at -300 mV < Vs < -100 mV.
Supplementary Figure 11 demonstrates the methods used to calculate the uncertainty when estimating the charging ring radii shown in Fig. 3c. First, the ring radius was approximated via r eff =L/2π, where L is defined at the circumference of the ring. This effective definition was used to accommodate deviations from ideal circular behavior. The error bars were then determined by one of two methods, shown in Supplementary Figure 11. The first method fit the largest and smallest possible ellipsoids to the data, calculating r min and r max as with r eff . The second method directly measured the smallest and largest radius for each ring. The larger of the two error values was then displayed using error bars in Fig. 3c.
Supplementary Figure 11. Charging ring uncertainty. Image of charging ring observed in dI/dV signal with two sources of experimental uncertainty shown. One source of uncertainty comes from determining the ring circumference. To estimate the possible error, the minimum and maximum possible circumferences were determined, labeled Lmin and Lmax in the figure, and used to correspondingly calculate rmin and rmax for a given charging ring. The second source of experimental uncertainty was introduced due to a non-spherical tip shape corresponding to a non-circular charging ring. Here, the rmin and rmax values were directly measured. The larger of the values from the two methods was used for error estimates.