- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access

Inelastic electron tunneling through adatoms and molecular nanomagnets

Daria Kývala and Jindřich Kolorenč*

  • *Contact author: kolorenc@fzu.cz
PDF

Phys. Rev. B 113, 035427 – Published 16 January, 2026

DOI: https://doi.org/10.1103/9sg1-j1bs

Abstract

We discuss a theoretical description of the inelastic electron tunneling spectra (IETS) of a magnetic nanosystem (an atom or a molecule) adsorbed on a solid surface measured in a scanning tunneling microscope (STM). We represent the nanosystem by means of a cluster Hubbard model, which allows us to study scenarios when the tunneling electrons sequentially interact with several magnetic centers inside the nanosystem or when the magnetic centers are made out of heavy atoms with a strong spin-orbit coupling and large orbital moments. The sequential tunneling through multiple centers is illustrated on an adatom probed by an STM tip with a nickelocene molecule attached to it. For atoms with large orbital moments, we find that the exchange interaction between the atom and the spin s of the tunneling electron is richer than the usually assumed Heisenberg form S·s or J·s, where S and J are the spin and total orbital moments of the atom. For atoms in axially symmetric environments, the J·s exchange would restrict the transitions accessible by IETS to those fulfilling |ΔJz|≤1, where Jz is the projection of the total angular momentum to the symmetry axis, whereas we arrive at a more permissive selection rule |ΔJz|≤2ℓ+1, where ℓ is the orbital momentum quantum number of the partially filled atomic shell carrying the magnetic moment.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (62)

  1. R. C. Jaklevic and J. Lambe, Molecular vibration spectra by electron tunneling, Phys. Rev. Lett. 17, 1139 (1966).
  2. P. K. Hansma, Inelastic electron tunneling, Phys. Rep. 30, 145 (1977).
  3. A. Léger, J. Klein, M. Belin, and D. Defourneau, Electronic transitions observed by inelastic electron tunneling spectroscopy, Solid State Commun. 11, 1331 (1972).
  4. A. Adane, A. Fauconnet, J. Klein, A. Leger, M. Belin, and D. Defourneau, Observation of electronic transitions in rare earth oxides by inelastic electron tunneling, Solid State Commun. 16, 1071 (1975).
  5. K. W. Hipps and U. Mazur, Inelastic electron tunneling: An alternative molecular spectroscopy, J. Phys. Chem. 97, 7803 (1993).
  6. G. Binnig, N. Garcia, and H. Rohrer, Conductivity sensitivity of inelastic scanning tunneling microscopy, Phys. Rev. B 32, 1336 (1985).
  7. B. C. Stipe, M. A. Rezaei, and W. Ho, Single-molecule vibrational spectroscopy and microscopy, Science 280, 1732 (1998).
  8. A. J. Heinrich, J. A. Gupta, C. P. Lutz, and D. M. Eigler, Single-atom spin-flip spectroscopy, Science 306, 466 (2004).
  9. 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).
  10. J. Fernández-Rossier, Theory of single-spin inelastic tunneling spectroscopy, Phys. Rev. Lett. 102, 256802 (2009).
  11. J. Fransson, Spin inelastic electron tunneling spectroscopy on local spin adsorbed on surface, Nano Lett. 9, 2414 (2009).
  12. M. Persson, Theory of inelastic electron tunneling from a localized spin in the impulsive approximation, Phys. Rev. Lett. 103, 050801 (2009).
  13. M. Ternes, Spin excitations and correlations in scanning tunneling spectroscopy, New J. Phys. 17, 063016 (2015).
  14. M. Ormaza, N. Bachellier, M. N. Faraggi, B. Verlhac, P. Abufager, P. Ohresser, L. Joly, M. Romeo, F. Scheurer, M.-L. Bocquet, N. Lorente, and L. Limot, Efficient spin-flip excitation of a nickelocene molecule, Nano Lett. 17, 1877 (2017).
  15. 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).
  16. C. Wäckerlin, A. Cahlík, J. Goikoetxea, O. Stetsovych, D. Medvedeva, J. Redondo, M. Švec, B. Delley, M. Ondráček, A. Pinar, M. Blanco-Rey, J. Kolorenč, A. Arnau, and P. Jelínek, Role of the magnetic anisotropy in atomic-spin sensing of 1D molecular chains, ACS Nano 16, 16402 (2022).
  17. A. Chiesa, S. Carretta, P. Santini, G. Amoretti, and E. Pavarini, Many-body models for molecular nanomagnets, Phys. Rev. Lett. 110, 157204 (2013).
  18. F. D. M. Haldane, New model for the mixed-valence phenomenon in rare-earth materials, Phys. Rev. B 15, 2477 (1977).
  19. A. Bringer and H. Lustfeld, Susceptibility of rare earth compounds in the intermediate valence state, Z. Physik B 28, 213 (1977).
  20. O. Gunnarsson, O. K. Andersen, O. Jepsen, and J. Zaanen, Density-functional calculation of the parameters in the Anderson model: Application to Mn in CdTe, Phys. Rev. B 39, 1708 (1989).
  21. D. V. Averin and Y. V. Nazarov, Virtual electron diffusion during quantum tunneling of the electric charge, Phys. Rev. Lett. 65, 2446 (1990).
  22. L. I. Glazman and M. Pustilnik, Low-temperature transport through a quantum dot, in Nanophysics: Coherence and Transport, Les Houches, edited by H. Bouchiat, Y. Gefen, S. Guéron, G. Montambaux, and J. Dalibard (Elsevier, Amsterdam, 2005), Vol. 81, pp. 427–478.
  23. H. A. Kramers and W. Heisenberg, Über die Streuung von Strahlung durch Atome, Z. Phys. 31, 681 (1925).
  24. J. W. Sakurai, Advanced Quantum Mechanics (Addison-Wesley, Reading, Massachusetts, 1967), pp. 47–50 and 53–57.
  25. A. Kotani and S. Shin, Resonant inelastic x-ray scattering spectra for electrons in solids, Rev. Mod. Phys. 73, 203 (2001).
  26. J.-P. Rueff and A. Shukla, Inelastic x-ray scattering by electronic excitations under high pressure, Rev. Mod. Phys. 82, 847 (2010).
  27. See Supplemental Material at http://link.aps.org/supplemental/10.1103/9sg1-j1bs for details on (i) derivation of the differential conductance, (ii) comparison with the theory formulated in Ref. [31], (iii) DFT calculations of Fe adatom on Cu(100) surface, and (iv) solution of the model of two exchange-coupled spins, Eq. (6), which includes Refs. [15, 31, 40, 58, 59, 60, 61, 62].
  28. R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users' Guide, Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM, Philadelphia, PA, 1998).
  29. A. Ruhe, Implementation aspects of band Lanczos algorithms for computation of eigenvalues of large sparse symmetric matrices, Math. Comp. 33, 680 (1979).
  30. H.-D. Meyer and S. Pal, A band-Lanczos method for computing matrix elements of a resolvent, J. Chem. Phys. 91, 6195 (1989).
  31. F. Delgado and J. Fernández-Rossier, Cotunneling theory of atomic spin inelastic electron tunneling spectroscopy, Phys. Rev. B 84, 045439 (2011).
  32. T. Miyake and F. Aryasetiawan, Screened Coulomb interaction in the maximally localized Wannier basis, Phys. Rev. B 77, 085122 (2008).
  33. R. Mozara, M. Valentyuk, I. Krivenko, E. Şaşıoğlu, J. Kolorenč, and A. I. Lichtenstein, Cobalt adatoms on graphene: Effects of anisotropies on the correlated electronic structure, Phys. Rev. B 97, 085133 (2018).
  34. E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, UK, 1935).
  35. M. Pivetta, F. Patthey, I. Di Marco, A. Subramonian, O. Eriksson, S. Rusponi, and H. Brune, Measuring the intra-atomic exchange energy in rare-earth adatoms, Phys. Rev. X 10, 031054 (2020).
  36. H. Ogasawara, A. Kotani, and B. T. Thole, Calculation of magnetic x-ray dichroism in 4d and 5d absorption spectra of actinides, Phys. Rev. B 44, 2169 (1991).
  37. M. Ormaza, P. Abufager, B. Verlhac, N. Bachellier, M.-L. Bocquet, N. Lorente, and L. Limot, Controlled spin switching in a metallocene molecular junction, Nat. Commun. 8, 1974 (2017).
  38. C. L. Degen, Scanning magnetic field microscope with a diamond single-spin sensor, Appl. Phys. Lett. 92, 243111 (2008).
  39. J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, High-sensitivity diamond magnetometer with nanoscale resolution, Nat. Phys. 4, 810 (2008).
  40. V. S. Stepanyuk, A. N. Baranov, W. Hergert, and P. Bruno, Ab initio study of interaction between magnetic adatoms on metal surfaces, Phys. Rev. B 68, 205422 (2003).
  41. S. Loth, C. P. Lutz, and A. J. Heinrich, Spin-polarized spin excitation spectroscopy, New J. Phys. 12, 125021 (2010).
  42. A. Ferrón, F. Delgado, and J. Fernández-Rossier, Derivation of the spin Hamiltonians for Fe in MgO, New J. Phys. 17, 033020 (2015).
  43. C. Wolf, F. Delgado, J. Reina, and N. Lorente, Efficient ab initio multiplet calculations for magnetic adatoms on MgO, J. Phys. Chem. A 124, 2318 (2020).
  44. R. D. Cowan, The Theory of Atomic Structure and Spectra (University of California Press, Berkeley, 1981).
  45. M. Swart, Metal–ligand bonding in metallocenes: Differentiation between spin state, electrostatic and covalent bonding, Inorg. Chim. Acta 360, 179 (2007).
  46. T. Schuh, T. Balashov, T. Miyamachi, S.-Y. Wu, C.-C. Kuo, A. Ernst, J. Henk, and W. Wulfhekel, Magnetic anisotropy and magnetic excitations in supported atoms, Phys. Rev. B 84, 104401 (2011).
  47. T. Miyamachi, T. Schuh, T. Märkl, C. Bresch, T. Balashov, A. Stöhr, C. Karlewski, S. Andre, M. Marthaler, M. Hoffmann, M. Geilhufe, S. Ostanin, W. Hergert, I. Mertig, G. Schön, A. Ernst, and W. Wulfhekel, Stabilizing the magnetic moment of single holmium atoms by symmetry, Nature (London) 503, 242 (2013).
  48. C. Karlewski, M. Marthaler, T. Märkl, T. Balashov, W. Wulfhekel, and G. Schön, Magnetic adatoms as memory bits: A quantum master equation analysis, Phys. Rev. B 91, 245430 (2015).
  49. T. Balashov, C. Karlewski, T. Märkl, G. Schön, and W. Wulfhekel, Electron-assisted magnetization tunneling in single spin systems, Phys. Rev. B 97, 024412 (2018).
  50. R. J. Elliott and M. F. Thorpe, Orbital effects on exchange interactions, J. Appl. Phys. 39, 802 (1968).
  51. L. L. Hirst, Theory of the coupling between conduction electrons and moments of 3d and 4f ions in metals, Adv. Phys. 27, 231 (1978).
  52. B. Coqblin and J. R. Schrieffer, Exchange interaction in alloys with cerium impurities, Phys. Rev. 185, 847 (1969).
  53. L. S. Wu, W. J. Gannon, I. A. Zaliznyak, A. M. Tsvelik, M. Brockmann, J.-S. Caux, M. S. Kim, Y. Qiu, J. R. D. Copley, G. Ehlers, A. Podlesnyak, and M. C. Aronson, Orbital-exchange and fractional quantum number excitations in an f-electron metal, Yb2Pt2Pb, Science 352, 1206 (2016).
  54. R. Rejali, D. Coffey, J. Gobeil, J. W. González, F. Delgado, and A. F. Otte, Complete reversal of the atomic unquenched orbital moment by a single electron, npj Quantum Mater. 5, 60 (2020).
  55. H. Ogasawara, A. Kotani, and B. T. Thole, Lifetime effect on the multiplet structure of 4d x-ray-photoemission spectra in heavy rare-earth elements, Phys. Rev. B 50, 12332 (1994).
  56. Such ground-state configuration is obtained by setting B20=−3.0eV and B40=−3.3eV, for instance.
  57. D. Kývala and J. Kolorenč, Dataset associated with publication “Inelastic electron tunneling through adatoms and molecular nanomagnets” [Data set], Zenodo (2025), https://doi.org/10.5281/zenodo.16732408.
  58. B. Lazarovits, L. Szunyogh, P. Weinberger, and B. Újfalussy, Magnetic properties of finite Fe chains at fcc Cu(001) and Cu(111) surfaces, Phys. Rev. B 68, 024433 (2003).
  59. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  60. K. Momma and F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Cryst. 44, 1272 (2011).
  61. S. H. Vosko, L. Wilk, and M. Nusair, Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis, Can. J. Phys. 58, 1200 (1980).
  62. P. Blaha, K. Schwarz, F. Tran, R. Laskowski, G. K. H. Madsen, and L. D. Marks, wien2k: An APW+lo program for calculating the properties of solids, J. Chem. Phys. 152, 074101 (2020).

Outline

Information

Phys. Rev. B 113, 035427– Published 16 January, 2026
  • Received 8 August 2025
  • Accepted 18 December 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation