Atomic-scale magnetometry with a single-molecule spin sensor at the apex of a scanning tunneling microscope

Atomic-scale magnetometry with a single-molecule spin sensor at the apex of a scanning tunneling microscope

B. Verlhac    N. Bachellier    L. Garnier    M. Ormaza Université de Strasbourg, CNRS, IPCMS, UMR 7504, F-67000 Strasbourg, France    P. Abufager Instituto de Física de Rosario, Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) and Universidad Nacional de Rosario, Av. Pellegrini 250 (2000) Rosario, Argentina    R. Robles Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain    M.-L. Bocquet PASTEUR, Département de Chimie, Ecole Normale Supérieure, PSL Research University, Sorbonne Universités, UPMC Univ. Paris 06, CNRS, 75005 Paris, France    M. Ternes Institute of Physics II B, RWTH Aachen University, 52074 Aachen, Germany Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425 Jülich, Germany    N. Lorente Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastián, Spain Centro de Física de Materiales (CFM), 20018 Donostia-San Sebastián, Spain    L. Limot limot@ipcms.unistra.fr Université de Strasbourg, CNRS, IPCMS, UMR 7504, F-67000 Strasbourg, France
July 20, 2019
Abstract

Recent advances in scanning probe techniques rely on the chemical passivation of the probe-tip termination with single molecules weakly connected to the metallic apex. Information, otherwise unaccessible with a metallic tip, can be gathered in this way Gross et al. (2009); Weiss et al. (2010); Chiang et al. (2014); Wagner et al. (2015); Guo et al. (2016); Mönig et al. (2018). The success of this approach opens the tantalizing prospect of introducing spin sensitivity through the probe-tip termination by a magnetic molecule. Here, we use a nickelocene-terminated tip (Nc-tip), which offers the possibility of producing spin excitations on the tip apex of a scanning tunneling microscope (STM) Ormaza et al. (2017a). We show that when the Nc-tip is a hundred pm away from a surface-supported object, magnetic effects may be probed through changes in the spin excitation spectrum Heinrich et al. (2004) of nickelocene. We use this detection scheme to determine the exchange field and the spin polarization of the sample with atomic-scale resolution. Our findings demonstrate that the Nc-tip provides a novel approach for investigating surface magnetism with STM, from single magnetic atoms to surfaces, as we exemplify for a single Fe atom on Cu(100) and for surface atoms within a cobalt island grown on Cu(111).

In a conventional STM setup the magnetic ground state of an isolated object —atom or molecule—is inferred by collecting spin-related fingerprints in the conductance measured with a metallic tip. These isolated objects may also serve as spin sensors when they are controllably moved on the surface with the help of the tip within their local magnetic environment. The magnetic ground state is in fact prone to change in the presence of a magnetic coupling. Exchange and surface-mediated Ruderman-Kittel-Kasuya-Yosida interactions have been spatially mapped in this way by monitoring the zero-bias peak in the differential conductance () associated to the Kondo effect Otte et al. (2009); Tsukahara et al. (2011); Néel et al. (2011); Fu et al. (2012), the tunneling magnetoresistance Meier et al. (2008); Khajetoorians et al. (2011a, b), the spin excitation spectra and spin relaxation times Hirjibehedin et al. (2006); Chen et al. (2008); Loth et al. (2010); Yan et al. (2017). Recently, also dipolar and hyperfine interactions have been observed via electrically-driven spin resonances Natterer et al. (2017); Willke et al. (2018).

Having a well-calibrated sensor attached to the tip apex would provide a more advantageous setup since the tip can be freely positioned above a target object on the surface. This detection scheme eliminates surface-mediated interactions and benefits from the vertical-displacement sensitivity of the STM as the sensor-object distance is no longer imposed by the surface corrugation. Probing a magnetic exchange interaction across a vacuum gap is however experimentally demanding Kaiser et al. (2007); Bork et al. (2011); Schmidt et al. (2011); Yan et al. (2014); Choi et al. (2016); Muenks et al. (2017); Schmidt et al. (2011) as scanning probe techniques suffer, unfortunately, from the poor structural and magnetic knowledge of the tip apex. To overcome this limitation and accurately capture the junction geometry through comparison to first-principles calculations, we use a tip decorated by a spin nickelocene molecule (Fig. 1a) Ormaza et al. (2017a, b), which comprises a Ni atom sandwiched between two CH cyclopentadienyl rings.

Figure 1: Spin excitation spectra above the Cu surface and a single Fe atom. (a) Schematic view of the tunnel junction. Atom colors: Cu (orange), C (grey), H (white), Ni (green), Fe (red). (b) spectra acquired above a surface atom of Cu(100) at a distance between pm and  pm. The solid red line is a fit based on a dynamical scattering model Ternes (2015), and yields an axial magnetic anisotropy of  meV, a coupling between the localized Nc spin and the tip electrons of , and a spin-conserving potential scattering of . Inset: Image of Nc on Cu(100) acquired with a copper-coated tip apex ( mV,  pA, size:  nm). (c) Image of Fe atoms on Cu(100), i.e. counter-image ( mV,  pA, size:  n), and corresponding line profile of one atom (Inset) revealing the presence of a tilted Nc at the tip apex. The tilt angle is estimated via the height difference between the left an right protrusion of the line profile. (d) spectra acquired with the tip positioned above the high-intensity side of the ring-shaped Fe atom. For clarity, the spectra in (b) and (d) are shifted vertically from one another by /mV (: quantum of conductance). Shorter tip distances than  pm result in the transfer of Nc atop the Fe atom (Figs. S1b and S1c).

We prepare the Nc-tip with atomic control. We first perform soft tip-surface indentations into our pristine working surfaces, either Cu(100) or Cu(111) (Supplemental Sec. I), to ensure a mono-atomically sharp Cu apex. Nickelocene is then imaged as a ring (inset in Fig. 1b), since the molecule adsorbs on copper with one cyclopentadienyl bound to the surface while the other is exposed to vacuum Bachellier et al. (2016). After transferring the Nc molecule from the surface to the tip —details of the molecule transfer to the tip can be found in Ormaza et al. (2017b), the Nc-tip is characterized through a counter-image (see below) and by spectral features found in the second derivative, , of the current with respect to the bias measured at a constant distance between tip and the pristine surface. Figure 1b presents a set of spectra recorded a different heights above Cu(100). We calibrate by performing controlled tip contacts to the surface tracking the current and defining as the distance where the transition from the tunneling to contact regime occurs (Supplemental Sec. II and Fig. S1a). The spectra vary with only in amplitude and are dominated by a peak at positive and a dip at negative at energies symmetric to zero. These peaks and dips correspond to inelastic tunneling events in which tunneling electrons excite the Nc from its magnetic ground state of , with as the magnetic quantum number projected onto the axis perpendicular to the rings of the molecule, to one of the two degenerate excited states . These states are at a higher energy  meV relative to the ground state Ormaza et al. (2017a), where is the axial magnetic anisotropy [see Eq. (1)]. The inelastic conductance is nearly one order of magnitude higher than the elastic conductance (Fig. S2), highlighting that the spin of nickelocene is well preserved from scattering events with itinerant electrons of the metal Ormaza et al. (2017a); Rubio-Verdú et al. (2018). This behavior is remarkable, differentiating Nc from other single objects, which instead require a thin insulating spacer between them and the metal surface Heinrich et al. (2004); Hirjibehedin et al. (2006); Rau et al. (2014) or a superconductor Heinrich et al. (2013) to preserve their quantum nature.

We use the Nc-tip to probe surface magnetism through changes in the spin excitation spectrum as we first demonstrate by approaching a single magnetic Fe atom adsorbed on Cu(100) (Fig. 1a). Iron atoms on the surface (Supplemental Sec. I) protrude by  pm and are imaged with the Nc-tip as rings with an asymmetric apparent height (Fig. 1c). The structure observed in this so-called counter-image reflects the presence of Nc on the tip apex and is a consequence of the tilted adsorption geometry of the molecule. Indeed, density functional theory (DFT) calculations show that Nc bonds to the the tip-apex atom through two C atoms of the cyclopentadienyl ring Ormaza et al. (2017b). The tilt angle can be estimated through the line profile of the Fe atom (Inset of Fig. 1c) revealing for the tips used typically angles relative to the surface normal. Figure 1d presents a set of spectra recorded at different heights above the Fe atom. At  pm, the spectrum is indistinguishable from the one acquired above the bare Cu(100) (Fig. 1b), which indicates that in this low-energy range Fe is spectroscopically dark, i.e. its contribution to the spin excitation spectrum is negligible. However, for smaller heights we observe a splitting of the peak and the dip which becomes increasingly stronger as the tip-Fe distance decreases (Fig. 1d). So far we tested several Nc-tips and all showed similar behavior —the distances for a given splitting changing only by  pm. Apart from the splitting we also observe a striking intensity asymmetry of the split spectral features. While the amplitude of the positive peak and negative dip are identical for the Nc-tip probed against the bare surface (Fig. 1b), here we find that at positive bias the energetically lower excitation has higher peak amplitude than the energetically higher excitation, while at negative bias the dips show opposite behavior compared to the peaks.

Figure 2: Spin torque and magnetic coupling measured above a Fe atom. Panels (a) and (b) sketch the mechanism leading to the bias asymmetry in the spectra acquired above Fe. (a) At negative bias, inelastic electrons tunnel from the spin-up DOS at the Fe atom ( to the spin-down DOS of the copper surface leading to a dip. At positive bias, instead, the junction polarity is reversed and inelastic electrons tunnel from to leading to a peak. During the tunneling process, the electrons excite Nc from its ground to its first excited state. The weaker amplitude for the dip compared to the peak reflects the difference in the iron majority and minority DOS at the Fermi level () since copper is non-magnetic (). (b) Same mechanism as (a) but for inelastic tunnel electrons exciting Nc from its ground state to its second excited state. (c) Exchange field and (d) spin-polarization extracted from the spectra of Fig. 1d using Eq. (1). (e) DFT calculated configuration of the tunnel junction for a distance of pm with isosurface of the spin density (antiferromagnetic coupling).

The splitting and asymmetry of the line shape observed above Fe have magnetic origin. To rationalize these observations, we employ a spin Hamiltonian that includes the magnetic anisotropy of the Nc molecule and an effective Zeeman term which consists of the gyromagnetic factor (), the Bohr magnetron (), and the exchange field () produced by the Fe atom and acting along the -axis, i.e. the anisotropy axis, of the Nc molecule:

(1)

Within mean-field theory , where is the Fe-Nc exchange coupling and is the effective spin of Fe on the copper surface. This spin Hamiltonian successfully explains all the features observed in the spectra. Within this framework, the exchange field lifts the degeneracy between the two excited states and of nickelocene and causes the line shape to split apart. The bias asymmetry in the peaks and dips reflects instead the spin-transfer torque exerted on Nc Loth et al. (2010); Delgado et al. (2010); Novaes et al. (2010). This mechanism is sketched in Figs. 2a and 2b where we consider an antiferromagnetic coupling () between Nc and Fe. It is qualitatively similar to conventional spin-polarized STM Meier et al. (2008) and, more generally, to spintronic devices Sanvito (2011) where the spin-dependent density of states (DOS) in both electrodes determines the junction conductance. Here, however, the two excited spin states of Nc are spin-polarized, with the remarkable consequence that the junction spin-polarization reflects that of the object under investigation, i.e. the spin-polarization of the Fe atom. This mechanism recalls the one unveiled for Kondo systems coupled to magnetic electrodes Pasupathy et al. (2004); Fu et al. (2012); von Bergmann et al. (2015); Choi et al. (2016).

As illustrated in Fig. 2a, the excitation of Nc from the ground to its first excited state , requires a change in spin angular momentum of . Since the total angular momentum has to be conserved it can only be induced by electrons that compensate for this moment by flipping their spin direction during the tunneling process from to . Similarly, the excitation of Nc from the ground state to its second excited state requires electrons starting in a state and ending in a state (Fig. 2b). The sign of the bias, i.e. the tunneling direction, determines which of the minority () or majority () spin-dependent DOS of the Fe atom are source and sink for the inelastic tunneling electrons. Assuming the same transmission for each spin, the relative height of the dip at low negative voltage () compared to the peak at low positive voltage () yields a quantitative measure of the spin polarization , with and . The spin-polarization associated to the second excited state yields .

Figure 3: Spin excitation spectra above a cobalt surface. (a) Cobalt island on Cu(111) decorated with Nc molecules ( mV,  pA, size:  nm). The white lines highlight the presence of nickelocene. The white square corresponds to the area investigated in panels (b) and (f). Inset: Schematic view of a Nc-tip above a cobalt island. The arrow indicates the out-of-plane magnetization of the island. (b) Constant-height image acquired in the center of the island at  pm with  mV (size:  nm). We converted the recorded current into the corresponding effective . (c) spectra acquired with the tip positioned above a Co atom of the island. The tip was moved from pm to  pm. For clarity, the spectra are displaced vertically from one another by /mV. (d) Exchange field extracted from the spectra of panel (c) using Eq. (1). (e) spectra acquired at  pm above a top site [red dot in panel (b)] and above a hollow site [blue dot in panel (b)]. The image corrugation in panel (b) is calibrated using the exchange coupling of the two spectra in panel (e). (f) Constant-height image of the same area as in (b) also acquired at  pm, but with lower tunnel bias ( mV).

The fit to the line shape using Eq. (1) and a dynamical scattering model (solid red line in Fig. 1d) Loth et al. (2010); Ternes (2015) is highly satisfactory and provides quantitative values of the spin-polarization and the exchange field exerted by the Fe atom onto the Nc molecule assuming a gyromagnetic factor of . We find that the exchange field is an exponential function of (Fig. 2c), allowing us to exclude a magnetic dipolar interaction. Using our DFT-computed effective spin of (Supplemental Sec. III), the exchange coupling is  meV at the shortest probed Fe-Nc distances. Note that the magnetic anisotropy , which corresponds to the average position of the spin-split peaks and dips in Fig. 1d remains constant with distance. This indicates that the intramolecular structure of Nc is preserved on the tip apex Heinrich et al. (2015); Ormaza et al. (2017a). For the data presented in Fig. 1d, we find a spin-polarization of at all exchange fields (Fig. 2d), the data collected on an ensemble of different Nc-tips on different Fe atoms yielding a lower average value of . The positive value of observed experimentally is assigned to dominant majority spins of Fe (). This spin population is tentatively assigned to spin-down and electrons of Fe that, based on our DFT calculations, control the elastic electron transmission of the tunnel junction at the Fermi level (Supplemental Sec. IV, Fig. S3).

The sign of the exchange interaction between a magnetic atom and a magnetic tip apex is determined by the competition of direct and indirect interactions and may vary with tip-atom distance Tao et al. (2009). To gain insight into the exchange coupling between the Nc-tip and Fe atom, we computed with DFT the exchange energy defined as at various Nc-Fe distances by fully relaxing the junction geometry (Supplemental Sec. III); () is the total energy of the junction with the spin directions of Nc and Fe in parallel (antiparallel) alignment. The exchange interaction favors an antiparallel alignment of the two spins (Fig. 2e)—the junction geometry remaining constant up to pm where a chemical bond then starts to form between Fe and Nc (Fig. S1c). The energy difference between antiparallel and parallel alignment is meV at pm, while no difference could be evidenced above  pm. The antiferromagnetic coupling is attributed to the direct hybridization of the Fe -orbitals with the frontier molecular orbitals of nickelocene.

In the following, we extend the proof-of-concept for the Nc-tip to a collection of atoms. In particular, we investigate a prototypical ferromagnetic surface consisting of a nanoscale cobalt island grown on Cu(111) (Fig. 3a) Diekhöner et al. (2003); Pietzsch et al. (2004); Rastei et al. (2007); Heinrich et al. (2009). The islands are triangular-like and two-layers high with typical lateral extensions  nm for the cobalt-coverage used (Supplemental Sec. I). They possess, at low temperature, an out-of-plane magnetization perpendicular to the copper surface (Inset of Fig. 3a)  Pietzsch et al. (2006); Oka et al. (2010). Nickelocene adsorbs preferentially on cobalt, either on top of the nanoislands or on the bottom edge of the island as remarked for other molecules Iacovita et al. (2008). Nc-tips were routinely prepared by transferring a molecule from the edge of the island to the Cu-tip apex. Given the low molecular coverage, large pristine areas of cobalt may be found on the sample.

In Fig. 3b, we present a typical constant-height image acquired in a small area located in the center of a cobalt island (white square in Fig. 3a) at a bias  mV, very close to . The cobalt atoms of the island can be readily visualized with the Nc-tip. Remarkably, this atomic-scale contrast has magnetic origin. We may first note in fact that above non-magnetic Cu(111) this resolution is lost under the same tunneling conditions. More insight may be gathered through the vertical dependence of the spin excitation spectra acquired with the Nc-tip (Fig. 3c). At distances  pm above the cobalt surface, the spin excitation spectrum is similar to the spectra of Fig. 1b, which indicates that also the island is spectroscopically dark. Interestingly, upon vertically approaching a Co atom in the cobalt island, the peak and dip in the spectrum progressively split apart. The spectra show weak bias asymmetry (), suggesting that —in stark contrast to the single Fe adatom —the Co island does not have a significant different DOS for the majority and minority spin direction at . Using the spin Hamiltonian of Eq. (1) and , we find that the exchange field varies also here exponentially reaching values as high as T at the shortest distances explored ( pm, Fig. 3d). This corresponds to an exchange coupling of  meV taking our DFT-computed value of for the effective spin of a cobalt atom. This result surprises because a field created by the magnetized Co island should change only very little considering the small range of probed and the comparatively large island size. This indicates that the observed exchange field originates mostly by direct orbital overlap.

Figure 4: Computed exchange interaction between nickelocene and cobalt. (a) Isosurface of the spin density for a cobalt bilayer. Majority spins () and minority spins () are plotted in red and blue, respectively. Minority -electrons are mainly located on the Co atoms, while majority electrons are dispersive in nature Diekhöner et al. (2003); Pietzsch et al. (2006); Heinrich et al. (2009); Oka et al. (2010). The cobalt atoms have a magnetic moment of  , which is mainly carried by the orbitals (:  , :  , :  ). The spatial confinement of electrons within the island Diekhöner et al. (2003); Pietzsch et al. (2006); Oka et al. (2010) is not accounted for. (b) Difference in exchange energy () between the top position and the hollow/bridge positions. The energy difference was computed as a function of tip distance to the cobalt surface. The filled red area indicates the contact regime where the Nc molecule is covalently bond to the surface. Inset: Junction geometry used in the DFT calculations defining the top, hollow, and bridge site.

To clarify the observed atomic resolution on constant-height images taken at bias voltages close to , we compare in Fig. 3e two spectra, one with the Nc-tip positioned above a Co atom (designated hereafter as a top site of the surface; red dot in Fig. 3b) and the other with the Nc-tip above an hollow site of the surface (blue dot in Fig. 3b). As shown, the exchange field varies among the two sites and with it the position of the low-energy excitation peaks and dips. As these shift with the applied bias voltage , the tunneling current changes due to the dominant contribution of the inelastic channels. In particular at  mV and  pm, we have a situation where the inelastic excitation to the first excited state is possible only when the Nc-tip is placed above the top site, while above the hollow site this channel is closed. This yields then a contrast among the two sites in the constant-height images. At increased absolute bias ( mV), a loss of contrast in the constant-height image is observed because both inelastic excitations contribute to (Fig. 3f). To first approximation, the low-bias image shown in Fig. 3b therefore reflects the spatial dependence of the exchange field at the atomic scale.

To confirm the magnetic origin of the contrast, we computed with DFT the exchange energy by varying the distance between the Nc-tip and the cobalt surface (Fig. 4a and Supplemental Sec. III). Three locations were investigated, corresponding to a Nc-tip laterally positioned above the surface with its nickel atom centered above a top, hollow and bridge site of the surface (Inset of Fig. 4b). Just prior to the contact formation between Nc and the surface, which is the distance interval explored in the experiment, the exchange energy is markedly different between these sites (Fig. 4b), because the local character of the -electrons starts imprinting a lateral corrugation to the interaction. The exchange field can then be expected to change when moving the Nc-tip above the surface, in qualitative agreement with our experimental findings of Fig. 3b. We stress that for a quantitative comparison, which is beyond the scope of the present study, the non-collinearity among magnetic moments of Co and Nc should be taken into account.

In summary, we have shown that the spin excitations produced in a nickelocene molecule attached to the apex of a STM tip can be used to quantify at the atomic-scale the magnetic exchange interaction of Nc to surface-supported objects, as well as the spin-polarization of these objects. This is particularly dramatic for the case of a dense-packed magnetic layer, where our magnetic contrast shows a lateral resolution better than  pm, permitting us to image the single atomic magnetic moments of a cobalt surface. Present work can be extended to a large variety of magnetic systems relevant to molecular spintronics, either model systems such as single atoms or organometallic molecules. The visualization of complex spin textures should also be possible with an external magnetic field as in pioneering magnetic exchange force microscopy experiments Kaiser et al. (2007); Grenz et al. (2017).

Acknowledgements.
This work was supported by the Agence Nationale de la Recherche (Grant No. ANR-13-BS10-0016, ANR-15-CE09-0017, ANR-11-LABX-0058 NIE, ANR-10-LABX-0026 CSC). MT acknowledges support by the Heisenberg Program (Grant No. TE 833/2-1) of the German Science Foundation. NL acknowledges support by the Spanish MINECO (Grant No. MAT2015-66888-C3-2-R).

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