Spin-flip scattering selection in a controlled molecular junction

TL;DR

This study investigates how spin-flip scattering in a nickelocene molecular junction affects conductance, revealing a transition from inelastic scattering to a Kondo state as the tunneling barrier changes.

Contribution

It demonstrates the reversible spin state switching of nickelocene and the impact of tunneling barrier thickness on spin-flip scattering in molecular junctions.

Findings

Conductance is governed by spin-flip scattering near the Fermi energy.

A transition from inelastic spin-flip scattering to a Kondo ground state occurs.

Nickelocene switches from spin 1 to 1/2 between regimes.

Abstract

A simple double-decker molecule with magnetic anisotropy, nickelocene, is attached to the metallic tip of a low-temperature scanning tunneling microscope. In the presence of a Cu(100) surface, the conductance around the Fermi energy is governed by spin-flip scattering, the nature of which is determined by the tunneling barrier thickness. The molecular tip exhibits inelastic spin-flip scattering in the tunneling regime, while in the contact regime a Kondo ground state is stabilized causing an order of magnitude change in the zero-bias conductance. First principle calculations show that nickelocene reversibly switches from a spin 1 to 1/2 between the two transport regimes.

Full text

The magnetic anisotropy of surface-supported objects —atoms or molecules—has been attracting a growing interest in relation to ultra-dense storage technology Gambardella et al. (2003); Donati et al. (2016) and quantum computing Leuenberger and Loss (2001); Gatteschi et al. (2006). From a practical viewpoint, a uniaxial magnetic anisotropy energy of the form $DS_{z}^{2}$ provides stable magnetic states into which information can be encoded and may, moreover, be externally controlled Hirjibehedin et al. (2006); Zyazin et al. (2010); Parks et al. (2010); Bryant et al. (2013); Oberg et al. (2014); Heinrich et al. (2015); Dubout et al. (2015); Khajetoorians et al. (2015); Jacobson et al. (2015); Ormaza et al. (2017). Long-lived magnetic states are obviously desirable for data storage, but are keen to decoherence in surface-supported objects due to the effect of the environment Gauyacq and Lorente (2015); Delgado et al. (2015); Delgado and Fernández-Rossier (2017). One of the most common effects, which involves the spin-flip elastic scattering of conduction electrons, is the Kondo screening occurring below a critical temperature $T_{\text{K}}$ Hewson (1997). The general picture to address is that single objects have the potential for both magnetic anisotropy and the Kondo effect Otte et al. (2008), the outcome of their interplay depending on the object’s spin Žitko et al. (2009); Hurley et al. (2011); Korytár et al. (2012); Ternes (2015) and on the relative weight of $k_{\text{B}}T_{\text{K}}$ versus $D$ Žitko et al. (2008); Misiorny et al. (2012).

For several years now scanning tunneling microscopy (STM) has proven to be well suited for exploring the spin-flip scattering occurring in surface-supported single objects Gauyacq et al. (2012); Ternes (2015). Elastic and inelastic tunneling spectra can be used to probe the above mentioned interplay in an environment that can be characterized with atomic-scale precision. In recent experiments Oberg et al. (2014); Khajetoorians et al. (2015); Jacobson et al. (2015); Dubout et al. (2015), different surface topologies were used to tune the Kondo exchange interaction between the spin and the underlying metal, while spin control was possible through hydrogen doping of transition metal atoms. Here, we show that spin control can be achieved in a molecular junction using a functionalized STM tip. Up to now organic molecules have been used in scanning probe techniques to functionalize tips with the purpose of improving image resolution Gross et al. (2009); Weiss et al. (2010); Schull et al. (2011); Gross (2011) and, eventually, spectroscopic sensitivity Chiang et al. (2014); Guo et al. (2016). In this work, we attach a $S=1$ molecule with an easy-axis magnetic anisotropy ($D>0$), nickelocene [Ni(C5H5)2, noted Nc hereafter], to the tip apex of a STM and form a precise contact with a Cu(100) surface. We show that by moving Nc in and out of contact, we can control its spin and, concomitantly, the nature of the spin-flip scattering that governs the conductance around the Fermi energy of the junction. Our findings are corroborated by density functional theory (DFT) calculations.

The experiments were performed in an ultra-high vacuum STM operated at $2.5$ K. A clean Cu(100) surface was prepared by repeated cycles of Ar+ sputtering and annealing up to $800$ K at a base pressure of $2\times 10^{-10}$ mbar. Nickelocene molecules were deposited from a crucible onto the cold copper surface (below 80 K) at a rate of $0.025$ ML/min resulting in a sub-monolayer coverage. Directly after molecular deposition, the sample was inserted in the STM. An image of the Cu(100) surface after a molecular deposition is shown in Fig. 1(a), in which isolated Nc decorate the surface terraces. The molecules show a ring-shaped pattern, indicating that one cyclopentadienyl ring (C5H5, noted Cp hereafter) is exposed to vacuum, i.e., the long molecular axis of Nc is perpendicular to the Cu(100) surface Bachellier et al. (2016).

We found that in order to contact nickelocene between both electrodes, surface and tip, it is more stable to first transfer the molecule from the metallic surface to the tip —details of the molecule transfer to the metallic tip can be found in Ormaza et al. (2017). Prior to molecular transfer, care was taken to select a monoatomically sharp tip apex Limot et al. (2005). Information may be gathered on the status of Nc at the tip apex by acquiring counter-images  Heinrich et al. (2011), which consist in imaging single atoms on the surface with the molecular tip. The typical molecular pattern observed in the counter images of Cu adatoms is presented in Fig. 1(b) and differs from the feature-less protrusion observed with a metallic tip [encircled in Fig. 1(a)]. The pattern reveals that the tip is terminated by a Cp ring of a tilted Nc molecule, the tilt angle exhibiting some tip dependency. To confirm this assignment, we mimicked the molecular tip through DFT calculations by considering a Nc molecule adsorbed on a Cu atom on Cu(100) [inset of Fig. 1(c), see Supplementary Material]. The molecule is undeformed, tilted by $13^{\circ}$ with respect to the surface normal and linked through two C atoms to the Cu atom n (1). The corresponding simulated image in Fig. 1(c) is in good agreement with the experimental counter-image of Fig. 1(b).

The top panel of Fig. 1(d) presents the $dI/dV$ spectrum acquired with a Nc-tip above Cu(100). For comparison, we have included the $dI/dV$ spectrum acquired with a metallic tip above a Nc molecule on Cu(100). Both spectra were acquired with a lock-in amplifier using a frequency of 716 Hz and an amplitude of 150 $\mu$V rms; the metallic tip was verified to have a flat electronic structure in the bias range presented. The steps, symmetric with respect to zero bias, that are visible in the $dI/dV$ correspond to the manifestation of efficient spin-flip excitations within the molecule Ormaza et al. (2017). These occur between the ground state $\ket{S=1,M=0}$ and the doubly degenerate $\ket{S=1,M=\pm 1}$ excited states of the molecule, the threshold energy observed corresponding to the longitudinal magnetic anisotropy energy, $D$. The bottom panel shows the numerical derivative of the $dI/dV$ spectra in order to facilitate the identification of the threshold values. For Nc on the surface we find $D=(3.2\pm 0.1)$ meV, while for Nc on the tip the magnetic anisotropy grows to $D=(3.7\pm 0.3)$ meV. This reflects changes in the local ligand field induced by the different adsorption configuration Bryant et al. (2013); Heinrich et al. (2015); Ormaza et al. (2017).

We then engineered a molecular junction by bringing the Nc-tip into contact with Cu(100). For an increased control over the molecular junction, the contact was always performed atop a copper surface atom thanks to the use of atomically-resolved images [Inset of Fig. 2 (b)]. These images were routinely acquired by scanning the molecular tip while in contact with the surface Schull et al. (2011); Zhang et al. (2011), which may be taken as an indication of the robustness of a Nc-tip to external strain. The right panel of Fig. 2 (a) presents the conductance ($G$) versus tip displacement ($z$) curve acquired at a fixed bias of $-2$ mV with a Nc-tip vertically displaced towards the surface. The tip is here moved from its initial tunneling position $z=-2.1$ Å($G=2\times 10^{-4}$ in units $2e^{2}/h$) up to $z=0$ ($G=0.04$) where an abrupt increase of $G$ by more than a factor $10$ ($G=0.7$) reveals the transition between the tunneling and the contact regime (indicated by a dashed line). Notice that the exact values of the conductance as well as of the contact position under the same conditions present some tip dependancy. As we show below, the sudden change in $G$ is exclusively driven by a spin switch of nickelocene.

To elucidate this finding, we present in the left panel of Fig. 2 (a) a two-dimensionnal intensity plot of a series of $dI/dV$ spectra acquired at varying $z$. For completeness, Fig. 2 (b) presents the spectra for decreasing tip-surface distances. The spectra reveal the presence of spin-flip scattering events, whose nature may be reversibly controlled via $z$. Within the tunneling regime, the spectra exhibit inelastic spin-flip excitations as anticipated in Fig. 1(d). We note an enhancement of the differential conductance at voltages corresponding to the excitation threshold, which is increasingly pronounced as the contact point is approached ($z>-0.5$ Å). Recent studies have pointed out that this enhancement could reflect many-body effects including Kondo-like phenomena Hurley et al. (2011); Korytár et al. (2012); Ternes (2015). However, this scenario also requires a sizable reduction of the magnetic anisotropy energy, and therefore of the excitation threshold Oberg et al. (2014); Jacobson et al. (2015), at variance with our experimental observations. The enhancement here rather reflects a stationary population of excited states Loth et al. (2010); Delgado et al. (2010); Novaes et al. (2010); Ternes (2015) due to the increasingly large currents flowing through the junction when approaching contact. This so-called spin pumping can be expected to be significant due to the efficiency of the spin-flip excitations in Nc produced by tunneling electrons Ormaza et al. (2017), or more generally, in molecules Chen et al. (2008); Tsukahara et al. (2009); Gauyacq et al. (2010).

The most striking result is found once the molecular contact to the surface is established ($z>0$). As we anticipated above, a sudden increase in the conductance occurs at zero bias [Fig. 2 (a)], which we ascribe to the presence of a Kondo resonance. As shown in Fig. 2 (a), a sharp peak appears in the $dI/dV$, while the inelastic excitation thresholds are lost. The emergence of a spin-1 Kondo effect in the presence or in the absence of positive magnetic anisotropy is in principle possible Žitko et al. (2008); Misiorny et al. (2012) —the former case being unlikely here as the resonance does not split apart Parks et al. (2010). However, we find that the system actually behaves as a spin $1/2$-system. The peak is perfectly fitted by a Frota function (see Supplementary Material), which is close to the exact line shape expected for a spin-$1/2$ Kondo system  Frota (1992). From the fit, we find that the peak is centered at $\epsilon_{\text{K}}=(0.0\pm 0.1)$ meV for all studied tips up to the highest tip excursion explored (0.8 Å). The line width, therefore $T_{\text{K}}$, increases nearly exponentially with $z$ [Fig. 2(c)], similarly to other junctions comprising a single Kondo impurity Choi et al. (2012, 2016, 2017). To further confirm the spin-1/2 nature of the Kondo effect, we recall that the resonance amplitude (noted $\sigma$) should be a universal function of the normalized temperature $T/T_{\text{K}}$. For a quantitative analysis we therefore fit the curve in Fig. 2 (d) to the function $\sigma=[1+(T/T_{\text{K}})^{2}(2^{1/s}-1)]^{-s}$ (in units of $2e^{2}/h$) Goldhaber-Gordon et al. (1998) and extract $s=(0.29\pm 0.02)$, in remarkable agreement with the spin-1/2 Kondo effect of semiconductor quantum dots van der Wiel et al. (2000). The amplitude of the resonance is close to the unitary limit and indicates a complete Kondo screening n (2). Our findings therefore strongly support the emergence of a spin-1/2 Kondo effect where there is no magnetic anisotropy. To elucidate its origin, here below, we show through DFT calculations that Nc switches its spin from $1$ to $1/2$ upon contact with the surface.

The DFT calculations were performed by modeling the molecular tip by a Nc atop a Cu atom adsorbed on a Cu(100) plane [Fig. 3 (a)]. The molecular tip was placed at different distances from a Cu(100) surface and the junction was fully relaxed. Figures 3 (c)-(e) show the resulting molecular junctions for the three most representative configurations. In Fig 3 (c), the distance between the two Cu atomic planes (noted $d$) is $12.17$ Å and corresponds to the tunneling regime [see Fig. 1(c)] described previously. Figure 3 (d) shows the molecular junction at $d=11.14$ Å and corresponds to the transition between the tunneling and contact regimes. The transition point has been assigned to the point in which a change in the behavior of structural parameters is observed, and has been confirmed by the theoretical transmission probabilities [Fig. 3 (f)]. The molecule is distorted at the transition, but still bonded to the Cu atom through two C atoms. Finally, Fig. 3 (e) corresponds to $d=9.66$ Å and is representative of the molecular junction in the contact regime. The molecule exhibits Cp rings that are parallel to both metallic planes and the Cu atom is coordinated to five C atoms. Figure 3 (b) quantifies the structural changes with $d$. As shown, at the transition point the distances between the Cu and Ni atom with respect to the tip electrode, noted $d_{1}$ and $d_{1}+d_{2}$ respectively, is maximum, as well as the tilt difference between the Cp rings, noted $\Delta\Theta$. The distance between the Ni atom and the surface-electrode (noted $d_{3}$) instead decreases continuously with $d$. Experimentally, we have seen that in the tunneling regime despite the slightly different initial orientations that the molecule might have on the tip, similar results are obtained in the $dI/dV$ spectra for different molecular tips when going to contact. This indicates that the Nc molecule tends to adopt always the same configuration, with parallel Cp rings, when contacted between the tip and the surface.

From Fig. 3 (f) we can obtain the ratio between the transmission probabilities for the different spin channels (spin-up $T_{\uparrow}$, spin-down $T_{\downarrow}$), which is related to the spin polarization efficiency of the molecular junction. We find a -74$\%$ spin polarization for the junction in the tunneling regime and -55$\%$ in contact, where the spin polarization is $\frac{T_{\uparrow}-T_{\downarrow}}{T_{\downarrow}+T_{\uparrow}}$. The decreased value at contact is in agreement with the trend found in a previous theoretical study Yi et al. (2010).

Figure 3 (g) presents how the magnetization of the Nc molecule, the Ni atom and the Cu atom change with $d$. In the tunneling regime, the calculated magnetic moment for Nc is $1.7\mu_{\text{B}}$, the Ni atom carrying $1\mu_{\text{B}}$. At the transition, these values decrease to $1\mu_{\text{B}}$ and $0.7\mu_{\text{B}}$, respectively, and afterwards, at contact, stabilize around $0.75\mu_{\text{B}}$ for Nc and $0.5\mu_{\text{B}}$ for the Ni atom. The Cu atom remains non-magnetic during the contact process. The initial magnetic moment of the molecule is halved when contacted between the two electrodes, meaning that the molecular spin changes from $S=1$ to $S=1/2$. Such a spin switch is in agreement with the spectroscopic fingerprints highlighted experimentally.

The change on the molecular charge with respect to the gas phase from tunneling ($-0.12e^{-}$) to contact ($+0.07e^{-}$) is not enough to explain such a change on the magnetization. To scrutinize the effect of the deformation of the molecule on the molecular magnetization, the magnetization of the isolated Nc molecule in the same geometrical configuration as it shows in tunnel, at the transition and in contact was computed. No relevant difference was observed for the different configurations, indicating that the magnetization change is neither driven by the molecule-sustrate charge transfer nor the deformation suffered by the molecule.

Fig.4 (a) presents the spin-resolved transmission for the tunnel (thick line) and contact (thin line) regimes. The transmission of Fig. 4 (a) implies that the transport is mainly due to the hybridization of surface electronic states with the frontier molecular orbitals, which are $d_{xz}-$ and $d_{yz}-$based molecular orbitals Ormaza et al. (2017). To get a deeper understanding of the different features observed in the transmission function, the density of states projected (PDOS) onto the C($2p$) and Ni($3d$) atomic orbitals are shown in Fig. 4 (b). The clear correspondence between spin up and spin down peaks on the transmission function and the PDOS [Fig. 4 (b)] makes it possible to assign both peaks to the transmission through the spin-polarized degenerate frontier orbitals. The comparison between contact and tunnel results shows that the peaks associated to the frontier-orbital in both spin up and spin down channels shift towards the Fermi level in the contact regime, reducing the exchange splitting energy due to the screening of the intra-orbital Coulomb repulsion ($U$). This is due to the enhancement of the molecule-electrode interaction that also induces a more pronounced broadening of the molecular levels. Such increase of the hybridization ($\Gamma$) reduces the charge in the majority spin and increases the minority spin occupation. Our analysis then shows that both effects, namely, the increase of $\Gamma$ and the reduction of $U$ contribute to halve the magnetic moment of the molecule in the contact regime. Therefore, the spin transition can be explained by the coupling to the substrate of the frontier orbitals located close to the Fermi level.

In summary, we have shown how the spin of a Nc molecule and, associated, spin-flip scattering from Nc can be reversibly modified via a controlled contact to a copper electrode. The spin transition takes place due to the enhanced electronic screening following the Nc-surface contact. On a more general note, the portability of the Nc molecule or eventually of other metallocenes Ormaza et al. (2016) via the STM tip offers novel opportunities for testing how surface-supported objects modify the molecular magnetism of these molecules.