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# Engineering the spin couplings in atomically crafted spin chains on an elemental superconductor

Nature Communicationsvolume 9, Article number: 3253 (2018) | Download Citation

## Abstract

Magnetic atoms on a superconductor give rise to Yu-Shiba-Rusinov (YSR) states within the superconducting energy gap. A spin chain of magnetic adatoms on an s-wave superconductor may lead to topological superconductivity accompanied by the emergence of Majorana modes at the chain ends. For their usage in quantum computation, it is a prerequisite to artificially assemble the chains and control the exchange couplings between the spins in the chain and in the substrate. Here, using a scanning tunneling microscope tip, we demonstrate engineering of the energy levels of the YSR states by placing interstitial Fe atoms in close proximity to adsorbed Fe atoms on an oxidized Ta surface. Based on this prototype platform, we show that the interaction within a long chain can be strengthened by linking the adsorbed Fe atoms with the interstitial ones. Our work adds an important step towards the controlled design and manipulation of Majorana end states.

## Introduction

Majorana particles1 have been proposed as key elements for topological quantum computation2,3,4,5 due to their unique statistical properties. One of the systems for realizing Majorana modes in condensed matter is a spin chain on a superconductor6,7,8,9. The recent investigation of self-assembled ferromagnetic Fe chains on superconducting Pb, featuring strong spin-orbit coupling, triggered enhanced interest in the possible realization of Majorana modes at the ends of such chains10,11,12,13,14,15. So far, this platform for Majorana physics has been tested almost exclusively for the substrate material Pb hampering the controlled assembly of magnetic atoms into chains or more complex networks, which are ultimately needed for braiding of Majorana modes and their usage in fault-tolerant quantum computation3,4,5. Moreover, the required Yu-Shiba-Rusinov (YSR)16,17,18 band formation crucially depends on the exchange couplings between the spins within the chain19,20,21 and between the spins and the conduction electrons of the host material22,23. Therefore, it is desirable to artificially construct such spin chains with full control over all the couplings in order to drive the system into desired topological phases24.

To this end, we explore the superconducting substrate of a (3 × 3) oxygen reconstructed Ta(100) surface (named Ta(100)-(3 × 3)O in the following) decorated with Fe atoms22. We first show that a spin chain constructed on the bare oxidized Ta(100) surface shows negligible interaction between nearest-neighbor Fe atoms. In the second step, we introduce Fe atoms in the interstitial sites in close proximity to the Fe adatoms using the tip of a scanning tunneling microscope (STM) and demonstrate the control over the energy levels of the YSR states. Finally we extend the method to build long chains of Fe adatoms that are interacting via interstitial Fe atoms and demonstrate spin coupling within the chain.

## Results

### Assembly and investigation of chains of Fe adatoms

As seen in the topographic STM image of the substrate (Fig. 1a), the regular network of oxygen atoms is imaged as a network of depression lines separating circular and cross-shaped plaquettes of (3 × 3) Ta atoms22. After low-temperature Fe deposition we see a statistical distribution of Fe adatoms with different apparent heights showing different spectroscopic features. In particular, one type of adatoms reveals a YSR state at a binding energy which varies for adsorption on a locally different substrate environment22. We were able to use vertical atom manipulation25,26 to construct arrays of Fe adatoms positioned on the centers of neighboring cross-shaped plaquettes (Fig. 1b–d, f; see Methods Section). Figure 1b–d show a single manipulated Fe adatom, a manipulated pair and a manipulated three-atom chain. Differential tunneling conductance (dI/dV) spectra taken with a superconducting tip on the manipulated atoms of the three structures (Fig. 1e) show a pair of peaks at energies close to the gap edge indicative of a YSR state with a relatively large binding energy (Eb ~ Δ)22. Note, that the YSR state neither does change with the number of atoms in the chain nor with the number of neighbors, indicating negligible interaction amongst the atoms on neighboring plaquettes16,21. This holds for a long chain built from 63 atoms (Fig. 1f, Supplementary Fig. 1) where we see similar spectroscopic features along the chain as well as at the ends.

In order to verify the negligible coupling between neighboring Fe atoms in the chains, we used the following procedure. Applying a small bias pulse (typically ±500 mV) to a manipulated Fe adatom, its electronic configuration can be switched between two states with strikingly different spectroscopic signature (Fig. 2a–d). For the original case discussed above (Fig. 2a), the spectrum shows the YSR states in the gap (Fig. 2c) and a resonance with a full width at half maximum on the order of 50 mV, indicating a partial Kondo screening of the magnetic moment of the Fe atom (Fig. 2d)23. In the following, we denominate this state of the Fe adatom as the “YSR-on” state. After applying a positive voltage pulse (Fig. 2b), the spectrum on the Fe adatom completely changed to the spectroscopic signature of a substrate spectrum (Fig. 2c, d). This most probably indicates that the Fe adatom has completely lost its magnetic moment. We refer to the corresponding state as the “YSR-off” state. Note, that the process is reversible by the application of a voltage pulse of reversed bias polarity. We suppose that the voltage-pulse induced switching of the electronic and magnetic properties of the Fe adatom is possibly due to a switching between two different metastable states of the Fe atom on the Ta(100)-(3 × 3) O reconstruction27,28. Using these two different spectroscopic signatures, we can also identify the state of the corresponding Fe adatom in a dI/dV image recorded at V = 50 mV (insets of Fig. 2a, b), revealing a lower dI/dV signal in the YSR-on state as compared to the YSR-off state. Below, we will investigate the effect of the controlled switching of an Fe adatom within the chains between the magnetic (YSR-on) state and the non-magnetic (YSR-off) state on the YSR states of the neighboring atoms, which will enable us to conclude on the magnetic coupling between the atoms in the chain16,21. This is demonstrated in a four-atom chain (Fig. 2e–g). When an atom within the chain is switched from the YSR-on state (Fig. 2e) to the YSR-off state (Fig. 2f shown exemplarily for the second atom from the top), the dI/dV spectra on all other atoms within the chain look almost identical (Fig. 2g). We, therefore, conclude that chains built from adatoms on neighboring plaquettes reveal negligible interatomic Fe interaction preventing the formation of a YSR band, as expected by the rather large interatomic distance (~ 1 nm) with a decoupling oxygen row in-between22.

## Discussion

In summary, we showed that the system of Fe adatoms on the Ta(100)-(3 × 3) O surface provides a promising playground for crafting magnetic chains of various length coupled to an s-wave superconductor, and tuning the different couplings within the system by IFAs. We demonstrated a strengthening of the magnetic interactions along the chain via the IFAs and a manipulation of the binding energy of the YSR state. This method can be extended to more complex systems as, e.g., networks of coupled chains38. Our work is thus an important step towards the controlled realization and manipulation of topological superconductivity and Majorana end modes.

## Methods

### Experimental methods

All STM and scanning tunneling spectroscopy measurements were carried out in a custom built SPECS STM under ultra-high vacuum conditions and at the base temperature of 1.1 K using an electrochemically etched bulk Cr-tip39 coated with tantalum22. Details of the surface cleaning as well as Fe atom deposition can be found elsewhere22.

Prior to the atom manipulation to create various arrays of magnetic adatoms, the surface was cleaned (Fig. 1a) by picking up all the adatoms using vertical manipulation. To this end, the tip was initially held on the atom with typical stabilization parameters of V = 50 mV and I = 50 pA. With feedback off, a typical bias voltage pulse of ~+1 V was applied in order to transfer the atom to the tip. For the transfer of Fe atoms from the tip to the center of the plaquettes or in-between two plaquettes the feedback was switched off and the tip was lowered by ~300–600 pm and a negative bias voltage pulse of 0.3–1 V was applied in discrete steps until an Fe atom dropped, as seen in both the z position of the tip and the image acquired afterwards. We did not observe YSR states on the Fe atoms adsorbed on the circular plaquettes. Therefore, we created all the atomic arrays by adatoms positioned on the cross-shaped plaquettes. Once the desired atomic arrays were created, the tip was mechanically dipped into the Ta surface in order to coat the tip apex with a superconducting Ta cluster.

Differential conductance spectra (dI/dV) were measured using a standard lock-in technique40 after stabilizing the tip at Vstab and Istab with a typical modulation voltage of Vmod = 20  μV (f = 827 Hz).

### Numerical deconvolution of the spectra

For the deconvolution of the spectra measured with a superconducting tip, initially the tip density of states Nt is obtained by numerically fitting the substrate spectrum to the expression for the lock-in detected tunneling spectrum of a superconductor-insulator-superconductor junction, given by40

$$\frac{{{\mathrm{d}}I}}{{{\mathrm{d}}V}}\left( V \right) \propto {\int}_{ - \pi /2}^{\pi /2} {\sin \alpha \cdot I\left( {V + \sqrt 2 V_{\bmod }\sin \alpha ,T} \right){\mathrm{d}}\alpha .}$$
(1)

Here, Vmod is the modulation voltage used for the lock-in measurements and

$$I\left( {V,T} \right) \propto {\int}_{ - \infty }^\infty {N_{\mathrm{t}}\left( E \right) \cdot N_{\mathrm{s}}\left( {E + V} \right) \cdot \left[ {f\left( E \right) - f\left( {E + V} \right)} \right] \cdot {\mathrm{d}}E,}$$
(2)

Where, f(E) is the Fermi function and Nt(s) is the BCS-Dynes density of states of the tip (sample) given by

$$N\left( {E,{\mathrm{\Gamma }}} \right) = N_{\mathrm{n}}\left( {E_{\mathrm{F}}} \right) \cdot \Re \left[ {\frac{{E + i{\mathrm{\Gamma }}}}{{\sqrt {\left( {E + i{\mathrm{\Gamma }}} \right)^2 - {\mathrm{\Delta }}^2} }}} \right].$$
(3)

We get the best fitting parameters for the tip with ∆t = 0.5 meV and Гt = 0.04 meV. Once the tip is characterized, we model the density of states for the YSR states as a sum of a gap and n Lorentzian peaks given by23,

$$N_{\mathrm{s}} = \frac{1}{{e^{\frac{{\Delta _{\mathrm{s}} - \left| E \right|}}{{\delta _{\mathrm{s}}}}} + 1}} + \mathop {\sum}\nolimits_{i = 1}^n {\frac{{A_i}}{{1 + \left( {\frac{{E - E_i}}{{\gamma _i}}} \right)^2}}}$$
(4)

Here, ∆s, δs, Ai, Ei and γi are the free parameters which are determined using nonlinear least square fitting.

### Data availability

The authors declare that all the relevant data are included in the paper and its Supplementary Information files. Additional data are available from the corresponding author upon request.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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## Acknowledgements

The authors thank Maria Valentyuk, Roberto Mozara, Alexander I. Lichtenstein, Saurabh Pradhan and Jonas Fransson for fruitful discussions, and Dörte Langemann for help with the manipulation. This work has primarily been supported by the ERC Advanced Grant ASTONISH (No. 338802). L.C. and J.W. acknowledge support through the DFG priority programme SPP1666 (grant no. WI 3097/2).

## Author information

### Affiliations

1. #### Department of Physics, University of Hamburg, Jungiusstrasse 9-11, D-20355, Hamburg, Germany

• A. Kamlapure
• , L. Cornils
• , J. Wiebe
•  & R. Wiesendanger

### Contributions

All authors conceived and designed the experiments. A.K. and L.C. performed the experiments. A.K. analyzed the data. A.K. and J.W. wrote the manuscript. All authors discussed the results and commented on the manuscript.

### Competing interests

The authors declare no competing interests.

### Corresponding author

Correspondence to A. Kamlapure.