As an initial rough guide in our search for interesting magnetic metals to contact the C60
, and to select relevant bonding sites, we first performed calculations of the binding energy of a single adatom from the first row transition metals (from vanadium to copper) with C60
. This will clearly overestimate the binding of the C60
to a higher coordinated tip-atom but we are here focussing on the trends in binding energy depending on tip-atom species. Based on the simple adatom calculations we seek high magnetization and a high binding energy to get a stable contact. The results are summarized in for different sites on the C60
molecule. It can be seen that nickel has the strongest binding energy but with zero total magnetization (M
), and thus, is probably not interesting for investigations of spin transport. On the other hand, chromium enjoys the largest M
, due to its largest unpaired electronic configuration [Ar]3d5
but with the least binding energy strength. It has already been shown that copper STM tips can pick up C60
]. Noting that the maximum of binding energy for copper to C60
is ≈0.8 eV, we conclude that the same action should be possible with vanadium while enjoying a decent M
Table 1 Binding energy and total magnetization M
T = ∫v(n
up − n
3 per unit cell. The distance between the adatom and C60 has been optimized.
Based on the data of the simple guiding calculations we chose vanadium in the full C60-contact simulations on the system depicted in . In the following we demonstrate that this choice for contact material in an STM setup is successful in achieving a good spin-filter- and spin-valve performance. Here, ferromagnetic (FM) and anti-ferromagnetic (AFM) spin alignment between atoms of tip and adatom, have been considered. The site on the C60 with the highest binding energy for a V adatom is η5, which is roughly over the center of a pentagon of a C60, and due to the symmetric structure of the C60, this site is contacted by both the tip and the adatom. We find that the binding energy of the C60 to the V-tip (upper part in ) is 1.3 eV, while binding of C60 to the adatom on the Cu substrate (lower part in ) is 1.1 eV. The spin-resolved transmissions for the FM and AFM cases are shown in . We first focus on the highly conducting contact configuration where the atomic structure of the C60 along with vanadium atoms and first copper layers of both sides have been relaxed to the force threshold of 0.05 eV/Å. We also show the transmission spin polarization (TSP), defined as
Figure 2 Transmission spectra for FM and AFM arrangements. The first row shows spin-resolved transmission spectra for each arrangement. The second row demonstrates the corresponding transmission spin polarization as defined in the text. The third and forth rows (more ...)
and channel decomposed transmission values in . Here, we first point out a remarkable spin-filtering effect in the FM arrangement, whereby two almost open channels conduct in the vicinity of the Fermi level for the majority spin component, while the minority channels are almost closed. For the minority spin component the resonance peaks at ≈0.2 and 0.4 eV produce dips in the corresponding TSP curve, however, these will only be of importance for a voltage bias comparable to these energies. Transmission eigenvalues of the first three dominant channels are shown in the third and forth panels, that clearly show two distinct channels for the FM-majority spin channels. Furthermore, it is striking that the channels in the AFM configuration are almost closed, except for small resonance peaks at ≈0.35 eV, which again only will come into play for higher voltages.
To better understand the nature of spin transport in the system, we have calculated the spatially-resolved scattering states in the contact region [32
]. The results are shown in . Here, we consider the conducting FM arrangement and focus on the two eigenchannel scattering states with highest transmission at E
(moving in the direction up-to-down), which both are almost fully transmitting. For the majority spins, we notice the d
orbital nature of wavefunctions on the V adatoms contacting C60
chosen perpendicular to the surface). This is in accordance with the Mulliken population analysis of the majority spin states of the V tip and adatoms, where the d
each appears half-filled. On the other hand, the d
are closer to being filled, while the s
is closer to being empty. This points to a charge transfer from the V atoms to the C60
leaving the d
orbital energies closest to E
. Since the d
orbitals match the symmetry with angular momentum m
= 1 for rotation around the V–C60
–V axis of the pentagon-prone 3-fold degenerate LUMO states (t1
]), we can expect the observed orbitals in the transport channels. For minority spins d
orbitals are almost empty and shifted away from E
, resulting in a vanishing transmission. The rotational symmetric m
= 0 channels appear as resonances in the channel transmissions above E
and thus play a minor role.
Scattering states at E = E
F of first two dominant eigenchannels for (a,b) majority and (c,d) minority spin components in FM arrangement. Blue and red indicate the positive and negative sign of the real part of the wavefunction.
In typical STM experiments the conductance is probed from the tunnel-regime to contact. We have performed transport calculations as the tip is approaching the surface adatom until the tip–molecule distance (d shown in ) approximately reaches the equilibrium distance discussed above. In we display the conductance along with the corresponding TSP as a function of the tip distance. As can be seen, there is a trend of an increasing conductance of the majority spins and thus TSP, in the FM case, while in the AFM case, the conductance values are considerably smaller all the way to the equilibrium contact distance.
Spin-resolved conductance and transmission spin polarization (TSP) vs C60-adatom separation.
The difference between the FM and AFM conductance properties indicates how it is possible to probe the spin coupling mediated by the C60 between the magnetic tip and substrate. The calculated magnetic interaction between the tip and adatom, the magnetic exchange energy defined as E
FM − E
AFM, is shown in when the tip molecule is approaching the adatom. This shows that the FM arrangement becomes favorable as the molecule reaches the equilibrium distance to the surface adatom. To be sure about the fidelity of the values obtained here, we have performed the same study using the PW method. We found that the trend is the same and that the values are even more pronounced in favor of FM arrangement, though of the same order of magnitude.
(a) Magnetic exchange energy, (b) conductance for FM and AFM configurations (inset in log-scale) and (c) Fano factor of transmission as a function of C60-adatom separation for the FM and AFM configurations.
A graph of the total conductance versus C60-adatom distance is shown in . The conductance behavior demonstrates a magnetic valve, being closed for FM and open for AFM, if we imagine an external control over the magnetization of tip/substrate. In a typical experiment with a bulk magnetic tip the magnetization of the tip will be determined by the intrinsic magnetic anisotropy of the crystalline magnetization, which fixes the magnetization axes. As the tip molecule approaches the adatom on the non-magnetic surface, its magnetization will be determined by the interaction with the tip mediated by the molecule. In this case the adatom magnetization will align according to the thermal occupations.
The absolute distance is typically not known in an actual STM experiment. In principle, a particular conductance could be realized with both FM or AFM spin configurations – a conductance of e
2/h could result from a single spin-channel with perfect transmission or two half-transmitting channels. In combination with measurements of the conductance, measurements of current shot-noise as characterized by the Fano factor,
can provide further insights into the distribution of transmissions in the conductance channels as demonstrated for molecular contacts [35
]. In , we observe how the noise is significantly smaller for the FM configuration and drops already well before contact (d
≈ 1.5 Å) is established. Since the shot noise in the FM case is low in contact, while the conductance is close to 2G
, it can be inferred from this that the transport is carried by two almost perfectly transmitting channels in the FM contact configuration.