Cobalt deposition and manipulation

The result of Co deposition on a BP surface cleaved in situ is shown in Fig. 1a, where the surface illustrates the expected buckled rhombohedral structure. Individual clean Co atoms are identified as bi-lobed butterfly-like shapes due to the anisotropic extension of their charge density upon adsorption onto BP (see Supplementary Figure 1 for larger area images before and after deposition and Supplementary Figure 2 for analysis on the presence and influence of hydrogen). As seen in Fig. 1a, two types of bi-lobed Co species are observed (boxed atoms Fig. 1a), related through mirror symmetry along the zig-zag [010] direction, similar to single vacancies in BP29. High-resolution analysis of the STM data (Supplementary Figure 3) reveals that the bi-lobed species reside on top sites. These species account for approximately ~98% of the as-deposited atoms, indicating favorability toward top-site adsorption during low-temperature (T ≈ 5 K) deposition; here, the areal density (Fig. 1a) is approximately 0.022 ± 0.003 nm−2 (see Supplementary Figure 1).

Fig. 1 Adsorption and switching of Co on BP. a Six Co species on BP as deposited at T < 5 K (V s = −400 mV, I t = 20 pA, scale bar = 1 nm). Boxed atoms show species related through mirror plane along [010]. b Four atoms from a have been switched into J H,low (V s = −400 mV, I t = 20 pA, scale bar = 1 nm). c Two atoms from b have been switched into J H,high (V s = −400 mV, I t = 20 pA, scale bar = 1 nm). d Switching characteristics from J H,low to J H,high with V s = 420 mV and e J H,high to J H,low with V s = −680 mV. Approximate threshold biases for switching (V th ) are noted. Orange circles indicate the tip position during the switching sequence. The inset images showing before and after configurations are 4 nm × 4 nm in size. f Schematic representation of adsorption energy curves for Co species on BP Full size image

Upon current injection with the STM tip above a voltage threshold (Fig. 1d), individual Co atoms can be manipulated from the top site to a hollow site (Fig. 1b and Supplementary Figure 4), as confirmed by atomic resolution imaging (Supplementary Figure 3). This shift of binding site involves a clear modification to the spatial charge density distribution. Surprisingly, we find that there are two unique and stable shapes of the Co atom within the same hollow site (Figs. 1c, d and 2), as exhibited by the variation in the charge density. We denote these two states as J H,low and J H,high (index H denotes the atomic site and high/low refers to the size of the magnetic moment shown in Fig. 2e, f). In addition to their unique spatially distributed charge density, J H,high can also be distinguished by its larger apparent height in STM constant-current images (J H,high = 176 ± 8 pm, J H,low = 132 ± 4 pm at V s = −400 mV). Switching between J H,low and J H,high was achieved via location-dependent current injection (Fig. 1d, e), with J H,high to J H,low at |V s | ≳ 320 mV and J H,low to J H,high at V s ≳ 320 mV. Notably, the switching between different hollow-site states is fully reversible, as shown in Supplementary Figure 4. However, once a Co atom is manipulated into the hollow site, we were not able to relocate it back into a top site (denoted J T , cf. Fig. 1f). Each of the three atomic configurations remained stable (as probed for measurement times up to 17 h) until intentionally perturbed. Furthermore, unlike charge switching in single dopants on semiconductors, the atomic state remains fixed after removing the applied bias16 and the charging lifetime is expected to be very short due to the strong native p-doping of the BP crystal29.

Fig. 2 Ground states of Co atoms. High-resolution image of Co in a J T (V s = −400 mV, I t = 200 pA, scale bar = 1 nm), b J H,low (V s = −60 mV, I t = 200 pA, scale bar = 1 nm), and c J H,high (V s = −60 mV, I t = 200 pA, scale bar = 1 nm) configurations with same color scale as Fig. 1. DFT calculations of charge density distributions, including magnetic moment (m), n d , and n s , for d Co on a top site, e Co in a hollow site, and f Co in a hollow site with U = 4 eV. g–i Schematics of relaxed atomic adsorption geometries with out-of-plane distance (d) noted. j–l dI/dV spectra taken on each atom Full size image

Ab initio calculations and state identification

To elucidate the origin of each experimentally observed Co state, we performed density functional theory (DFT) calculations for a Co atom residing on a top (Fig. 2d) and hollow site (Fig. 2e, f) to compare with experimental data (Fig. 2a–c). The calculations were carried out for monolayer BP under the generalized gradient approximation (GGA); to include the effects of local Coulomb interactions in the Co 3d orbital, calculations involving a Hubbard-U correction (GGA + U method) were also performed. Varying the Hubbard-U parameter (Supplementary Figure 5) reveals the mutually exclusive stability of two unique states with a critical value at approximately U = 3.5 eV, where the state favorability between J H,low and J H,high is inverted. Plotting the spatial distribution of the total charge density from the DFT calculations (Fig. 2d–f), we were able to directly associate each calculation to a corresponding constant-current STM image. The qualitative agreement is excellent and enables us to confirm the experimental binding-site analysis and to roughly approximate the effective screening parameter (U = 0–3 eV for J T and J H,low , U = 4–6 eV for J H,high —see Supplementary Figure 5) for the Coulomb repulsion of the Co 3d orbital. When including relaxation into the hollow-site calculations, we find that the atomic positions in the surface plane are identical (although out-of-plane distances are different—see Fig. 2h, i, and the schematic potential diagrams in Fig. 1f); namely, the experimental switching from J H,low to J H,high can neither be attributed to a change in binding site nor to different charge configurations.

The use of the Hubbard-U correction allows us to assess distance-dependent screening from the surface within the 3d shell of the Co atom. As substrate separation (d) is reduced, the more extended 4s orbital becomes energetically less favorable due to Pauli repulsion with the BP ligand field, while the increased screening of the 3d orbital increases its energetic favorability by decreasing Coulomb repulsion in the system. The resulting occupation of the Co 4s (n s ) and 3d (n d ) orbitals is given in Fig. 2 for each of the states (resolved into the 3d subshells in Supplementary Table 1). We find from these calculations that the relaxation (Δd) from J H,low to J H,high (Fig. 2h, i) is accompanied by a redistribution of the 4s-orbital and 3d-orbital populations (for further detail, see Supplementary Figures 6, 7, and 8). As expected, when modifying metal 3d-orbital occupancy, the total magnetic moment also changes between 1.00μ B for J H,low and 2.34μ B for J H,high . Furthermore, calculations of the magnetic anisotropy indicate that the easy axis also changes from in-plane (J H,low ) to out-of-plane (J H,high ) (Supplementary Table 2). This suggests that the magnetic anisotropy of Co can be controlled electrically in this system. We note that similar orbital behavior has been predicted for transition-metal atoms on graphene30,31,32, where multiple states (different d) were analogously predicted due to the reorganization of the orbital occupancies. Quantum chemistry calculations for Co on graphene further indicated that the energy barrier between states could reach nearly 300 mV30, which might explain the remarkable stability of the states observed here. This also indicates that using the orbital degree of freedom may be much more robust compared to using solely the bistability of the spin ground states.

Tip-induced local gating

In order to elucidate the valency switching mechanism, we studied the influence of tip-induced band bending (TIBB) on the Co states. Due to insufficient screening from charge carriers, the applied potential between tip and sample locally influences the energy of semiconductor bands; if an impurity level, shifted with the material bands, passes through the Fermi level (E F ), it will undergo an observable charging/discharging event in STM and scanning tunneling spectroscopy (STS)33. Such charging events resulting from TIBB can be distinguished by peaks in dI/dV whose location and intensity are strongly sensitive to the stabilization parameters (Supplementary Figure 9) and tip location (Supplementary Figure 10)33,34. While all states demonstrate ionization events, we limit our focus in this work to the J H,low and J H,high states. A representative dI/dV spectrum for J H,low (Fig. 2k) clearly shows a strong peak at approximately 280 mV, while the primary peak for J H,high (Fig. 2l) is seen at 420 mV. In conjunction with the spectroscopic mapping (see below), the shaded regions (labeled q+) are identified as bias ranges where the Co species have been ionized. At biases greater than these thresholds, the atoms are non-locally ionized via the tip-induced potential along the BP surface.

To gain a more complete picture of this local surface potential, we used constant height imaging to map out the spatial dependence of the ionization as a function of bias voltage (Fig. 3a, b)34. The size of the isotropic disk (stepwise increase in current around the Co, or the so-called charging ring when imaged in dI/dV maps—Supplementary Figures 10 and 11) scales similarly for both states with bias according to hyperbolic contours of constant TIBB (Fig. 3c). This indicates equivalent screening from the BP for each Co configuration. Furthermore, the trend of the effective ring radii (r eff = L/2π, where L is the ring circumference) with applied bias (see also Supplementary Figure 10) indicates a flat-band condition of V FB < −300 mV (Fig. 3d). Such a condition is achievable with a tip work function of 4.0–4.1 eV. Identifying the flat-band condition and the ring-radius dependence on bias indicates that the ionization events are caused by the upward bending of states below E F (see Fig. 3d). Theoretical calculations for both configurations reveal non-zero density of states below E F ; however, J H,low clearly has a strong 3d-orbital peak in the DOS between E F and the valence band edge (E v ). Consistently smaller radii for J H,high compared to J H,low indicate that larger TIBB is needed to ionize J H,high (near 400 mV); thus, this state must lie farther from E F than the ionized state of J H,low (Supplementary Figure 10h).

Fig. 3 Ionization of Co. a Constant-height current map of J H,low (setpoint conditions: V s = 500 mV, I t = 40 pA), showing isotropic charging state (highlighted with dashed blue ring) as a disk in the current map (logarithmic color scale, scale bar = 1 nm). Charged (q+) and uncharged (q0) regions are denoted. b Constant height map of same Co atom initialized into J H,high state (setpoint conditions: V s = 500 mV, I t = 40 pA, scale bar = 1 nm, logarithmic color scale). The atom switches into J H,low for a small section in the middle of the image. c Charging ring effective radius (r eff = L/2π) as a function of bias for J H,low (dark blue) and J H,high (light blue). Red lines show threshold bias (V*) determined from switching data and corresponding critical radius (r*) for J H,low and J H,high . Error bars are derived from experimental uncertainty in the measured disk radius, further explained in Supplementary Figure 11. d Schematics of proposed flat-band condition (V FB ≈ −0.4 eV) and band bending at selected bias near a, b Full size image

Switching dynamics and mechanism

Upon gating the Co into the charged regimes (q+ regions in Fig. 2k, l) with the STM tip, a discrete, bistable conductance signal, or the so-called telegraph noise, is measured on the Co atoms (Fig. 4a). The bistable states are correlated to the J H,low (dark blue) and J H,high (light blue) configurations of Co via independent constant-current measurements at lower negative biases (−400 mV < V s < −200 mV), which do not perturb the respective states. The ability to read and write both Co orbital configurations confirms its utility as a binary memory; thus, we denote J H,low as state 0 and J H,high as state 1. To further probe the stability and favorability of these states, we studied the bias and spatial dependencies of the telegraph noise. We define τ as the residence time for the given state, as derived in ref 35. Figure 4b illustrates the effect of bias at constant height. Maintaining a constant tip-sample separation, while smoothly varying the bias, results in a proportional change in the TIBB at the surface. In this manner, the influence of TIBB on the state stability can be directly measured without artifacts introduced by changing the tip-sample distance. As seen in the top panel of Fig. 4b, at lower biases τ H,low and τ H,high are nearly equivalent and strongly decay with increasing TIBB, resulting from the increased energy and flux of the tunneling electrons. However, above a threshold voltage V s = V* ≈ 540 mV, the state-dependent lifetimes diverge from each other, leading to a large state favorability or what we define as asymmetry \(\left( {A = \left( {\frac{{\tau _{{\mathrm{H}},{\mathrm{high}}} - \tau _{{\mathrm{H}},{\mathrm{low}}}}}{{\tau _{{\mathrm{H}},{\mathrm{high}}} + \tau _{{\mathrm{H}},{\mathrm{low}}}}}} \right)} \right)\) (lower panel Fig. 4b), whereby τ H,high is strongly diminished. This divergence indicates that given sufficient gating (above the critical bias threshold V*), there is a strong energetic favorability in the decay mechanism from J H,high to J H,low (Fig. 4c). Reexamining the charging ring data from Fig. 3c, we see that this critical bias corresponds to a J H,high critical charging ring radius (r*) of approximately 2 nm. We also note here that the onset of telegraph switching occurs after the ring radius for J H,low exceeds r*. These observations suggest that a minimum gate potential (measured as a ring radius r*) is required to achieve efficient switching for both states. This threshold is likely related to the extension of the ionized Co charge density, which can span 2–4 nm (see Fig. 5a), as the screening for both states is nearly identical. Based on these observations, we sketch the qualitative energy diagram for the subcritical (r eff < r*, Fig. 4c left panel) and supercritical (r eff > r*, right panel) regimes; significantly, the only observed barrier modification is the one between ionized species (E*).

Fig. 4 Orbital memory. a Two-state conductance signal with J H,high (light blue) showing high conductance and J H,low (dark blue) showing low conductance. b State lifetime and asymmetry as a function of tip bias with tip height held constant. Linewidth of lifetime curves indicates measurement error. V* highlights critical threshold where TIBB causes lifetime depression for J H,high . c Energy schematics illustrating excitation/ionization (E0 to E*) and switching mechanism for orbital memory. (Left) Sub-threshold behavior with nearly equivalent lifetimes (symmetric upper well structure) and (right) supercritical behavior with strongly diminished J H,high lifetime (imbalanced upper well structure) Full size image