Probing spin-dependent charge transport at single-nanometer length scales

TL;DR

This paper introduces a novel method combining spin-polarized STM and molecular probes to visualize and analyze spin-dependent charge transport at nanometer scales, crucial for quantum device development.

Contribution

It presents a new experimental approach for real-space detection of spin transport properties with nanometer resolution using SP-STM and MONA techniques.

Findings

Reversal of current direction with tip magnetization in BiAg₂ surface state

Single Gd cluster affects spin-dependent charge transport

Proof-of-principle demonstration of the method's effectiveness

Abstract

The coherent transport of charge and spin is one key requirement of future devices for quantum computing and communication. Scattering at defects or impurities may seriously reduce the coherence of quantum-mechanical states, thereby affecting device functionality. While numerous methods exist to experimentally assess charge transport, the real-space detection of a material's spin transport properties with nanometer resolution remains a challenge. Here we report on a novel approach which utilizes a combination of spin-polarized scanning tunneling microscopy (SP-STM) and the recently introduced molecular nanoprobe (MONA) technique. It relies on the local injection of spin-polarized charge carriers from a magnetic STM tip and their detection by a single surface-deposited phthalocyanine molecule via reversible electron-induced tautomerization events. Based on the particular electronic structure of the Rashba alloy BiAg$_2$ which is governed by a spin-momentum-locked surface state, we proof that the current direction inverses as the tip magnetization is reversed by an external field. In a proof-of-principle experiment we apply SP-MONA to investigate how a single Gd cluster influences the spin-dependent charge transport of the Rashba surface alloy.

Full text

Introduction

The progressing miniaturization of electronics components in integrated circuits has reached a point where single defects Miroshnichenko2010 ; Waltl2020 and the coherent superposition of quantum-mechanical states Makhlin2001 ; Gabelli2006 ; Miroshnichenko2010 have to be considered. In fact, future technologies may fundamentally rely on nonlocal phase-coherent charge transfer processes, thereby enabling novel device concepts which materialize the enormous gain promised by quantum computation and communication, e.g., by utilizing Josephson tunneling junctions Makhlin2001 or zero-energy Majorana bound states Fu2010 .

Particularly fascinating are strategies where the conventional manipulation of charge is replaced by the manipulation of the electron spin. For a long time, the concept of spintronics relied on the combination of non-magnetic semiconductors with magnetic polarizers Wolf2001 ; Dieny2020 . However, the injection of spin-polarized charge carriers across material interfaces remained a serious challenge Ohno1999 . In this context, the spin–momentum-locking Hasan2010 ; Kohda2019 ; Moore2010 ; Fu2007 ; Zhang2009 ; Hsieh2009 of Rashba-split surface or interface states Bychkov1984 ; Koo2020 or topologically protected boundary states Konig2007 ; Sessi2016 ; Jung2021 represents a formidable opportunity to overcome these limitations. In fact, the discovery of Aharonov-Bohm oscillations in topological insulators Peng2010 or the observation of Datta-Das oscillation in the ballistic intrinsic spin Hall effect Choi2015 clearly demonstrate that the coherent propagation of quantum-mechanical electronic states is a viable approach towards future spintronic devices.

In spite of the high expectations in the combination of spin–momentum-locking and spintronics our capabilities in detecting the spatial distribution of spin currents are quite limited. The existence of the edge channels has been demonstrated by imaging the current-induced magnetic fields in HgTe quantum wells by means of SQUID microscopy with $\mu$m resolution Nowack2013 , but these data lack intrinsic spin sensitivity. Optical Kerr imaging methods are able to visualize the spin transport in lateral ferromagnet/semiconductor structures Crooker2005 , but their lateral resolution is limited by the wave length of light. Shorter transport distances can be probed by lithographically prepared Hall bars, but the pre-defined electrode configuration cannot be changed any more and material damage may occur during processing Matsuo2012 . Multi-probe scanning tunneling microscopy (STM) setups offer a much higher spatial resolution with inter-tip distances down to about 30 nm KHM2005 ; Miccoli2015 ; Yang2016 ; Leis2020 ; Leis2021 ; Leis2022 , but have not yet been successfully applied with spin-sensitive magnetic tips.

Recently, we developed the molecular nanoprobe (MONA) technique which is capable of detecting ballistic charge transport on length scales down to a few nanometers. In this technique, charge carriers locally injected by an STM tip propagate across the surface and are detected by a single molecule via a reversible electron-induced switching process, such as a tautomerization Kuegel2017a . Charge transport in surface states Kuegel2017 ; Christ2022 ; Leisegang2023 , anisotropic transport on fcc(110) surfaces Leisegang2021 , and the damping and amplification by coherent superposition of quantum-mechanical waves in engineered atomic-scale structures has been experimentally demonstrated Leisegang2018 .

In this study, we report on the development and application of spin-polarized (SP)-MONA. The capability of investigating ballistic transport properties of spin-polarized charge carriers in real-space on length scales of a few nanometers is demonstrated by utilizing spin–momentum-locked Rashba-split bands of the BiAg2 surface alloy. As shown in Fig. 1(a), BiAg2 features two downwards dispersing surface states within the $L$-projected bulk band gap, an occupied $s,p_{z}$-like band and a partially unoccupied $p_{x},p_{y}$-derived band. Both bands exhibit a giant Rashba splitting of $E_{0}-E_{\text{R}}\approx 200$ meV Ast2007 ; Ast2007a ; Bihlmayer2007 ; Bentmann2009 . The tunneling spectrum of the BiAg2 surface presented in Fig. 1(b) shows two peaks which indicate the onset energies $E_{0}$ of the Rashba-split surface states. Throughout the entire study, experiments will be performed at an energy $E=E_{\rm exc}=650$ meV, marked by a purple dashed line in Fig. 1(a) between $E_{0}$ and $E_{\rm R}$.

The unoccupied $p_{x},p_{y}$-derived band exhibits an unconventional spin polarization ElKareh2014 , characterized by a reversal at the upper onset of the band, $E_{0}$, as schematically represented by a transition from red to blue color in Fig. 1(a). This unusual Rashba splitting leads to a spin-dependent propagation of charge carriers injected in the unoccupied bands, which will be discussed for states with $k_{y}=0$ without limiting the generality of our considerations. While the electrons carrying a blue-colored spin ($\otimes$) move with a negative group velocity $v_{\otimes}^{\rm g}=\nabla_{k}E<0$, electrons with a red-colored spin ($\odot$) propagate in the opposite direction, $v_{\odot}^{\rm g}=\nabla_{k}E>0$. As a consequence, we expect a striking asymmetry of the charge carrier propagation in real space, with $\otimes$-electrons propagating to the left and $\odot$-electrons moving to the right.

To analyze this asymmetric propagation with the MONA technique, we manipulated a single phthalocyanine (H2Pc) to a defect-free area and subsequently deprotonated it to a detector molecule HPc, see Fig. 1(d). Yellow stars mark the locations where charge carriers are injected from the STM tip directly into the substrate. (see Methods for details). The charge carrier-induced tautomerization of HPc serves as a measure for transport, presented as normalized electron yield $\eta$ in the following.

As sketched in Fig. 1(c), the constant-energy cut at $E_{\rm exc}$ is governed by spin–momentum-locking, i.e., spins which are oriented perpendicular to the respective wave vector. Charge carriers with such an in-plane spin can be induced from a magnetically coated STM tip in the Rashba bands. The resulting asymmetry is expected to be strongest in the direction where the tip magnetization is colinear with the spin of the Rashba bands Meservey1994 ; Bode2003 . For electrons with $k_{y}=0$ this is the case for a tip magnetized along the in-plane $[01\bar{1}]$ direction of BiAg2. As sketched in Fig. 1(e,f), this should lead to the injection of blue $\otimes$-electrons with a negative group velocity, resulting in a high (low) transport towards the molecule at $\alpha=270^{\circ}$ ($\alpha=90^{\circ}$), i.e. an electron yield $\eta_{270}^{\text{blue}}>\eta_{90}^{\text{blue}}$. Inverting the in-plane tip magnetization along the $\left[0\bar{1}1\right]$ direction, see Fig. 1(f), would result in the injection of $\odot$-electrons with a positive group velocity. As a consequence, the preferred direction of charge transport would also invert, i.e. we expect $\eta_{90}^{\text{red}}>\eta_{270}^{\text{red}}$. To quantify the spin polarization of charge transport when reversing the tip magnetization, the asymmetry $A_{\alpha}$ of the electron yields $\eta$ at a given angle $\alpha$ can be calculated as $A_{\alpha}=\left(\eta_{\alpha}^{+2\,\text{T}}-\eta_{\alpha}^{-2\,\text{T}}\right)/\left(\eta_{\alpha}^{+2\,\text{T}}+\eta_{\alpha}^{-2\,\text{T}}\right)$. In contrast to a SP tip, the spin-averaged signal of a non-magnetic tip should result in a vanishing asymmetry $A_{\alpha}$.

Results

In Fig. 2 the results of measurements performed (a) with a non-magnetic W tip and (b) a Gd-coated magnetic tip are presented in polar coordinates. Each tip was treated in an external magnetic field of $\pm 2$ T (red stars and blue circles, respectively) before the data were acquired in remanence ([math] T). Charge carriers were injected with MONA parameters of $E_{\text{exc}}=650$ meV, $t_{\text{exc}}=2.0$ s, $I_{\text{exc}}=1.0$ nA at a distance of $d=4.0$ nm from the molecule under four different angles. The data for a non-magnetic W tip, Fig. 2(a), show an electron yield $\eta$ which, within error bars, is independent of the magnetic history of the tip. This can be quantified by an asymmetry $A_{\alpha}^{\text{NM}}<(2\pm 3)$%. The small anisotropy of $\eta$ between $0^{\circ}$/$180^{\circ}$ and $90^{\circ}$/$270^{\circ}$ results from the anisotropic coupling of the molecule to the substrate, as discussed in detail recently Leisegang2023 and quantified in the Suppl. Sects. 2 and 3.

In contrast, the data presented in Fig. 2(b) for charge carriers injected from a magnetically coated Gd tip reveal a striking difference between the $\pm 2$ T sweeps. While the red and blue data points at $0^{\circ}$ and $180^{\circ}$ coincide within the error bars ($A_{0}^{\text{FM}}=(4\pm 3)$%, $A_{180}^{\text{FM}}=(3\pm 3)$%), a significant deviation can be observed at $90^{\circ}$ and $270^{\circ}$. The tip treatment at $-2$ T results in a high (low) electron yield at $90^{\circ}$ ($270^{\circ}$), which inverts upon a treatment at $+2$ T. Quantitative analysis results in $A_{90}^{\text{FM}}=(27\pm 3)$% and $A_{270}^{\text{FM}}=(17\pm 3)$%.

These data are in line with our hypothesis of Fig. 1(e,f). Indeed, post-characterization of the specific Gd-coated tip used for the experiments of Fig. 2(b) on a test sample with Fe/W(110) monolayer islands confirms a significant in-plane polarization along the $0^{\circ}$–$180^{\circ}$ direction which can be inverted upon a field sweep at $\pm 2$ T, see Suppl. Sect. 6. Already at this point we can conclude, that the absence of a significant asymmetry for a non-magnetic tip in combination with the strong asymmetry observed for the magnetically Gd-coated tip proves that SP-MONA allows to detect spin-dependent transport in the spin–momentum-locked Rashba-split surface state of the BiAg2 alloy.

To further substantiate this claim, we conducted MONA measurements at eight different angles ($\Delta\alpha=45^{\circ}$) with a macroscopically different Gd-coated tip. Charge carriers were injected at a distance $d=4.5$ nm from the detector molecule. In Fig.  2(c) the results measured in remanence after a tip treatment at $\pm 2$ T are shown in a polar plot. Along the $135^{\circ}$–$315^{\circ}$ direction, the data points for $+2$ T and $-2$ T coincide within the error bars, whereas a significant difference can be observed for the other six angles. The quantitative analysis reveals a cosine-like behavior of the asymmetry $A$, as presented in Fig. 2(d), which can be fitted by $A(\alpha)=O+b\cos(\alpha-\alpha_{0})$. Hereby, $\alpha_{0}=(34.6\pm 0.1)^{\circ}$ represents the direction with the largest asymmetry, $A_{0}=(-14.2\pm 0.1)$%. We speculate that the offset $O=(-2.8\pm 0.2)$% is caused by an imperfect inversion of the tip magnetization during the field sweep, resulting in slightly different in-plane projections in remanence.

The experimental data presented so far were obtained on perfect surfaces to utilize the well-known spin–momentum-locked electronic structure of the Rashba surface alloy BiAg2. The strength of SP-MONA, however, lies in the analysis of imperfect surfaces where charge and spin transport is affected by, e.g., the presence of vacancies, interstitials, domain boundaries, or adatoms. To demonstrate the capability of SP-MONA, we conducted transport measurements across a magnetic cluster deposited on the BiAg2 surface. The carefully designed setup is presented in the topographic STM image of Fig. 3(a). It consists of two HPc molecule which are placed at a distance of about 30 nm on a defect-free region of the BiAg2 surface alloy. A Gd cluster was deliberately deposited from the STM tip at a distance of $\approx 4$ nm from the left molecule. This molecule will allow for the spin-dependent detection of charge carrier transport injected at the four surrounding injection points (yellow stars, $d=6.5$ nm) under the influence of the Gd cluster. In contrast, the right pristine HPc molecule is far from any defect or impurity and serves as a reference system.

Figure 3(b,c) depicts the averaged and normalized electron yields at remanence for the two MONA setups in (a). While the plot in Fig. 3(c) with its pronounced asymmetry along the $90^{\circ}$–$270^{\circ}$ direction is in perfect agreement with the observation of spin-dependent charge carrier transport in a Rashba-split surface state reported in Fig. 2(b), a strong influence of the cluster can be observed in Fig. 3(b). The overall electron yield across the cluster (data point at $90^{\circ}$) is significantly reduced, in-line with inelastic scattering events which would result in reduced ballistic transport between the injection point and the detector molecule. In contrast, the electron yield $\eta$ measured for the other directions are either equivalent or reveal a higher $\eta$ as compared to the right setup. This may be caused by the constructive superposition of quantum-mechanical states, as previously observed in similar experiments Leisegang2018 .

The calculated asymmetries allow for a discussion of the spin-dependent effects. Indeed, the data of the right reference setup, see Fig. 3(e), are consistent with expected cosine-like behavior. In contrast, an overall positive and partially reduced asymmetry is observed under the influence of the Gd cluster, see Fig. 3(d). Since both measurements were conducted with the very same tip, the changes clearly result from the presence of the Gd cluster, possibly caused by spin-flip scattering events. Especially the reversal at $\alpha=90^{\circ}$ from $A_{90}=(-14\pm 3)$% for the clean surface to $A_{90}=(7\pm 4)$% across the Gd cluster is quite surprising. Since the cluster exhibits an apparent height $h_{\rm Gd}=(173\pm 5)$ pm and a diameter $d_{\rm Gd}=(1.16\pm 0.13)$ nm only, and since Gd with its rather spherical charge distribution usually exhibits a relatively low magneto-crystalline anisotropy, we would expect that the cluster is superparamagnetic even at the measurement temperature of about 5 K. The frequent thermally induced magnetization reversals should reduce rather than invert the spin polarization of the ballistic current across the cluster. We speculate that the interaction of the cluster with the strongly spin–orbit-coupled substrate induces a strong anisotropy which—in combination with the magnetic field applied for tip magnetization reversal—is sufficient to induce a remanent magnetization. However, due to the unknown geometric and magnetic properties of the cluster, precludes a profound analysis.

Conclusions

Our study shows that SP-MONA is unique experimental method which allows to probe ballistic charge transport properties at previously inaccessible length scales. As a STM-derived technique the transport data can directly be correlated to topographic data, thereby allowing an assessment how crystallographic imperfections at surface or interfaces affect spin transport. While the Rashba-split surface state of the BiAg2 surface provided an ideal testbed to demonstrate the general capabilities of SP-MONA, topological insulators (TIs) Peng2010 or two-dimensional (2D) materials like graphene Berger2006 or transition metal chalcogenides Shen2022 will be highly interesting materials for future experiments.

Acknowledgments

This work was supported by the DFG through SFB 1170 (project A02). We also acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy through Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter – ct.qmat (EXC 2147, project-id 390858490).

Contributions

P.H. and M.L. performed the experiments and analyzed the resulting data with input from M.B. The experiments were conceived and designed by all authors. Experimental procedures and analysis tools were established by J.K. and M.L. and conducted by P.H. and M.L. P.H., M.L. and M.B. wrote the manuscript with input from J.K.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

Methods

Experimental setup

The results were obtained in a two-chamber ultra-high vacuum (UHV) system (base pressure ${p\leq 5\times 10^{-11}}$ mbar). STM measurements were carried out in the constant-current mode with a home-built low-temperature system with a base temperature of ${T_{\text{STM}}\approx 4.5}$ K, with the bias voltage applied to the sample. A magnetic field oriented perpendicular to the surface plane with ${\lvert\mu_{0}H\rvert\leq 3}$ T can be generated by a superconducting split-coil magnet.

Sample preparation

Clean Ag(111) was prepared by cycles that consisted of 30 min Ar-ion sputtering at an energy of ${E_{\text{Ar}}=500}$ eV and consecutive annealing at ${T_{\text{ann}}\approx 700}$ K for 20 min. In order to achieve the well-ordered BiAg2 alloy with the $(\sqrt{3}\times\sqrt{3})$Bi/Ag(111)$R30^{\circ}$ reconstruction, $1/3$ of a pseudomorphic monolayer Bi was deposited onto the clean Ag(111) surface from a home-built Knudsen cell evaporator. During the deposition of Bi, the sample was held at elevated temperatures of ${T_{\text{sample}}\approx 550}$ K. To reduce the defect density, the sample was afterwards held at ${T_{\text{sample}}\approx 500}$ K for one more minute Ast2007 ; ElKareh2013 ; ElKareh2014 ; Leisegang2023 . H2Pc molecules (Sigma-Aldrich) were deposited from a four-pocket Knudsen cell evaporator (Dodecon) onto the sample held at room temperature Leisegang2023 .

Molecule manipulation

As reported previously Leisegang2023 , H2Pc molecules tend to adsorb at step edges or defects rather than on flat terraces of the BiAg2 surfaces. Therefore, single molecules had to be moved to a defect-free surface area by means of STM manipulation. The manipulation was performed while scanning over the molecule and thereby dragging it. Typical tunneling parameters for this process were ${U_{\text{bias}}\leq 20}$ mV and ${I_{\text{set}}>5}$ nA. Eventually, the excitation barrier of the detector molecule was reduced by deprotonation of H2Pc to HPc with a voltage pulse ${U_{\text{bias}}\geq 2.5}$ V.

Tip preparation

In order to obtain magnetically sensitive tips we used the procedure described previously Haertl2022 . In short, the freshly etched W tips was flash-heated under UHV conditions and then dipped several nanometers into a $200$ AL thick Gd film on a W(110) substrate. Occasionally, a gentle voltage pulse of ${U_{\text{bias}}\geq\pm 4}$ V was applied between the Gd surface and the tip. A more detailed explanation on this tip preparation is given in Suppl. Sect. 5.

Tip characterization

To prepare unpolarized tips, a W tip was flash-heated under UHV conditions to remove any possible contamination with magnetic material. Each magnetically sensitive Gd-coated tip was characterized before and after utilizing them for MONA. Before the transport measurements, the magnetic sensitivity of the STM tip was verified by imaging the magnetic domain structure of $200$ AL thick Gd films on W(110) Haertl2022 , also see Supplementary Section 5. To unambiguously prove the existence of an in-plane component of the tip magnetization during MONA measurements, subsequent experiments were performed with the very same tip on Fe monolayer (ML) islands on W(110). This sample system is an ideal candidate for the post characterization since the Fe islands exhibit an in-plane magnetization pointing along the substrate’s $\left[1\bar{1}0\right]$ direction Krause2007 . It was made sure that the in-plane contrast inverted upon a field sweep between $\pm 2$ T, as confirmed by d$I$/d$U$ maps and spectroscopic data. For a detailed description and spin-polarized data on both substrates, see Suppl. Sect. 6.

The MONA technique

With the novel molecular nanoprobe technique (MONA) it is possible to investigate ballistic transport on the nanometer scale. Leisegang2021 ; Kuegel2017 ; Leisegang2018 ; Leisegang2018a ; Kuegel2018 ; Kuegel2019 ; Leisegang2020 ; Leisegang2023 . Hereby, reversible switching events of a single molecule (rotation and/or tautomerization) serve as a measure for transport of remotely induced hot charge carriers. In order to inject charge carriers and detect the state of the molecule by the very same STM tip, the following measurement protocol is used: (i) The initial state of the molecule is determined by a scan at non-invasive parameters ($U_{\text{scan}}=100\dots 200$ mV, $I_{\text{scan}}=30\dots 40$ pA); (ii) The STM tip is moved to the injection point at a distance $d$ away from the molecule where charge carriers are induced for a duration $t_{\text{exc}}$ with $U_{\text{exc}},I_{\text{exc}}$; (iii) Subsequently, the final state of the molecule is recorded by a topographic scan (see (i)). To account for the statistical nature of this process and to reduce the standard deviation, we repeated this procedure up to 4000 times for each data point. All data are presented as electron yield, which result from dividing the number of observed tautomerization events $S$ by the amount of injected charge carriers $\left(I_{\text{exc}}\cdot t_{\text{exc}}\right)$. The electron yield is normalized in the form that all three occurring rotations of the HPc molecule on the BiAg2 surface are considered equal and thus all three rotations are weighted by a factor of $1/3$ each to the total electron yield. A detailed rotation-resolved analysis can be found in the Supplementary for the respective measurements in sections 2-4. The error of the electron yield $\eta$ can be calculated by the standard deviation of the measured tautomerization events $\sigma_{S}$, since the uncertainties of the current $I$ and the injection time $t$ are negligible compared to the error of the tautomerization events. The error for the asymmetry $A$ is obtained by gaussian error propagation.

The overall measurement procedure

The overall measurement procedure contains eight steps: (i) In-situ preparation and pre-characterization of the magnetic tip on Gd(0001)/W(110) films; (ii) Sample exchange to H2Pc/BiAg2; (iii) Manipulation of H2Pc molecules from step edges into defect-free surface areas; (iv) Application of an out-of-plane magnetic field ($\pm 2$ T) to align the tip; (v) MONA measurements in remanent field; (vi) Apply magnetic field in the opposite field direction to invert the tip polarization; (vii) MONA measurements in remanent field; (viii) Post-characterization of the magnetic tip on Fe/W(110) monolayer islands to verify the in-plane polarization and the inversion of the tip magnetization at $\pm 2$ T.