- Editors' Suggestion
- Open Access
Disentangling bulk and surface electronic structure using targeted cleave planes in
Phys. Rev. B 114, 175125 – Published 17 September, 2026
DOI: https://doi.org/10.1103/sjrs-3fjz
Abstract
Rutile has attracted significant interest due to its putative unconventional electronic and magnetic properties and its proximity to superconductivity. However, the measurement and interpretation of its electronic structure have been complicated by a strongly three-dimensional crystal structure. Here, we demonstrate how the preparation of targeted (110) and (100) surfaces via focused-ion-beam-engineered cleaving allows the acquisition of high-quality measurements of the electronic structure using angle-resolved photoemission spectroscopy. Our results demonstrate that angle-resolved photoemission spectroscopy spectra of are, in fact, largely dominated by signatures of distinct surface electronic states. From comparison with density functional theory, we resolve a surface termination-dependent variation of these, and disentangle them from highly-three-dimensional bulk states and surface resonances. Moreover, we find a marked role of the substantial spin-orbit coupling of the Ru orbitals in the surface region, where a breaking of spatial inversion symmetry leads to significant Rashba-type spin splittings of the surface bands.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (42)
- H. Over, Surface chemistry of ruthenium dioxide in heterogeneous catalysis and electrocatalysis: From fundamental to applied research, Chem. Rev. 112, 3356 (2012).
- J. P. Ruf, H. Paik, N. J. Schreiber, H. P. Nair, L. Miao, J. K. Kawasaki, J. N. Nelson, B. D. Faeth, Y. Lee, B. H. Goodge, B. Pamuk, C. J. Fennie, L. F. Kourkoutis, D. G. Schlom, and K. M. Shen, Strain-stabilized superconductivity, Nat. Commun. 12, 59 (2021).
- N. Wadehra, B. Z. Gregory, S. Zhang, N. Schnitzer, Y. Iguchi, Y. E. Li, B. Pamuk, D. A. Muller, A. Singer, K. M. Shen, and D. G. Schlom, Strain-induced superconductivity in (100) thin-films, Commun. Mater. 6, 135 (2025).
- Y. Sun, Y. Zhang, C.-X. Liu, C. Felser, and B. Yan, Dirac nodal lines and induced spin Hall effect in metallic rutile oxides, Phys. Rev. B 95, 235104 (2017).
- L. Šmejkal, J. Sinova, and T. Jungwirth, Beyond conventional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X 12, 031042 (2022).
- T. Berlijn, P. C. Snijders, O. Delaire, H.-D. Zhou, T. A. Maier, H.-B. Cao, S.-X. Chi, M. Matsuda, Y. Wang, M. R. Koehler, P. R. C. Kent, and H. H. Weitering, Itinerant antiferromagnetism in , Phys. Rev. Lett. 118, 077201 (2017).
- Z. H. Zhu, J. Strempfer, R. R. Rao, C. A. Occhialini, J. Pelliciari, Y. Choi, T. Kawaguchi, H. You, J. F. Mitchell, Y. Shao-Horn, and R. Comin, Anomalous antiferromagnetism in metallic determined by resonant x-ray scattering, Phys. Rev. Lett. 122, 017202 (2019).
- P. Keßler, L. Garcia-Gassull, A. Suter, T. Prokscha, Z. Salman, D. Khalyavin, P. Manuel, F. Orlandi, I. I. Mazin, R. Valentí, and S. Moser, Absence of magnetic order in : Insights from spectroscopy and neutron diffraction, npj Spintron. 2, 50 (2024).
- L. Kiefer, F. Wirth, A. Bertin, P. Becker, L. Bohatý, K. Schmalzl, A. Stunault, J. A. Rodríguez-Velamazan, O. Fabelo, and M. Braden, Crystal structure and absence of magnetic order in single-crystalline , J. Phys.: Condens. Matter 37, 135801 (2025).
- M. Hiraishi, H. Okabe, A. Koda, R. Kadono, T. Muroi, D. Hirai, and Z. Hiroi, Nonmagnetic ground state in revealed by muon spin rotation, Phys. Rev. Lett. 132, 166702 (2024).
- A. Akashdeep, S. Krishnia, J.-H. Ha, S. An, M. Gaerner, T. Prokscha, A. Suter, G. Janka, G. Reiss, T. Kuschel, D.-S. Han, A. Di Bernardo, Z. Salman, G. Jakob, and M. Kläui, Surface-localized magnetic order in thin films revealed by low-energy muon probes, Appl. Phys. Lett. 128, 022406 (2026).
- R. González-Hernández, L. Šmejkal, K. Výborný, Y. Yahagi, J. Sinova, T. Jungwirth, and J. Železný, Efficient electrical spin splitter based on nonrelativistic collinear antiferromagnetism, Phys. Rev. Lett. 126, 127701 (2021).
- S. Karube, T. Tanaka, D. Sugawara, N. Kadoguchi, M. Kohda, and J. Nitta, Observation of spin-splitter torque in collinear antiferromagnetic , Phys. Rev. Lett. 129, 137201 (2022).
- H. Bai, Y. C. Zhang, Y. J. Zhou, P. Chen, C. H. Wan, L. Han, W. X. Zhu, S. X. Liang, Y. C. Su, X. F. Han, F. Pan, and C. Song, Efficient spin-to-charge conversion via altermagnetic spin splitting effect in antiferromagnet , Phys. Rev. Lett. 130, 216701 (2023).
- F. Pawula, A. Fakih, R. Daou, S. Hébert, N. Mordvinova, O. Lebedev, D. Pelloquin, and A. Maignan, Multiband transport in , Phys. Rev. B 110, 064432 (2024).
- X. Peng, Z. Liu, S. Zhang, Y. Zhou, Y. Sun, Y. Su, C. Wu, T. Zhou, L. Liu, Y. Li, H. Wang, J. Yang, B. Chen, Y. Li, C. Xi, J. Du, Z. Jiao, Q. Wu, and M. Fang, Universal scaling behavior of transport properties in non-magnetic , Commun. Mater. 6, 177 (2025).
- J. E. Graebner, E. S. Greiner, and W. D. Ryden, Magnetothermal oscillations in , and , Phys. Rev. B 13, 2426 (1976).
- Z. Wu, M. Long, H. Chen, S. Paul, H. Matsuki, O. Zheliuk, U. Zeitler, G. Li, R. Zhou, Z. Zhu, D. Graf, T. I. Weinberger, F. M. Grosche, Y. Maeno, and A. G. Eaton, Fermi surface of measured by quantum oscillations, Phys. Rev. X 15, 031044 (2025).
- V. Jovic, R. J. Koch, S. K. Panda, H. Berger, P. Bugnon, A. Magrez, K. E. Smith, S. Biermann, C. Jozwiak, A. Bostwick, E. Rotenberg, and S. Moser, Dirac nodal lines and flat-band surface state in the functional oxide , Phys. Rev. B 98, 241101(R) (2018).
- J. Liu, J. Zhan, T. Li, J. Liu, S. Cheng, Y. Shi, L. Deng, M. Zhang, C. Li, J. Ding, Q. Jiang, M. Ye, Z. Liu, Z. Jiang, S. Wang, Q. Li, Y. Xie, Y. Wang, S. Qiao, J. Wen, et al., Absence of altermagnetic spin splitting character in rutile oxide , Phys. Rev. Lett. 133, 176401 (2024).
- T. Osumi, K. Yamauchi, S. Souma, S. Paul, A. Honma, K. Nakayama, K. Ozawa, M. Kitamura, K. Horiba, H. Kumigashira, C. Bigi, F. Bertran, T. Oguchi, T. Takahashi, Y. Maeno, and T. Sato, Spin-degenerate bulk bands and topological surface states associated with Dirac nodal lines in , Phys. Rev. B 113, 085116 (2026).
- A. Smolyanyuk, I. I. Mazin, L. Garcia-Gassull, and R. Valentí, Fragility of the magnetic order in the prototypical altermagnet , Phys. Rev. B 109, 134424 (2024).
- S. Lee, S. G. Jeong, J.-P. Wang, B. Jalan, and T. Low, Strain-driven altermagnetic spin-splitting effect in , Nano Lett. 26, 8110 (2026).
- D. Q. Ho, D. Q. To, R. Hu, G. W. Bryant, and A. Janotti, Symmetry-breaking induced surface magnetization in nonmagnetic , Phys. Rev. Mater. 9, 094406 (2025).
- E. Torun, C. M. Fang, G. A. de Wijs, and R. A. de Groot, Role of magnetism in catalysis: (110) surface, J. Phys. Chem. C 117, 6353 (2013).
- V. Jovic, A. Consiglio, K. E. Smith, C. Jozwiak, A. Bostwick, E. Rotenberg, D. Di Sante, and S. Moser, Momentum for catalysis: How surface reactions shape the flat surface state, ACS Catal. 11, 1749 (2021).
- Z. Lin, D. Chen, W. Lu, X. Liang, S. Feng, K. Yamagami, J. Osiecki, M. Leandersson, B. Thiagarajan, J. Liu, C. Felser, and J. Ma, Bulk band structure of measured with soft x-ray angle-resolved photoemission spectroscopy, Phys. Rev. B 111, 134450 (2025).
- B. Yavorsky, O. Krasovska, E. Krasovskii, A. Yaresko, and V. Antonov, Ab initio calculation of the Fermi surface of , Phys. B 225, 243 (1996).
- A. Hunter, C. Putzke, I. Gaponenko, A. Tamai, F. Baumberger, and P. J. W. Moll, Controlling crystal cleavage in focused ion beam shaped specimens for surface spectroscopy, Rev. Sci. Instrum. 95, 033905 (2024).
- H. Oppermann and M. Ritschel, Zum chemischen transport der Übergangsmetalldioxide mit tellurhalogeniden, Krist. Tech. 10, 485 (1975).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/sjrs-3fjz for a schematic of the in-situ cleaver; additional DFT calculations of the electronic structure; and measurements performed at additional photon energies, including a photon-energy-dependent scan.
- P. D. C. King, B. Edwards, S. Mo, T. Antonelli, E. A. Morales, L. Hart, and L. Trzaska, Peaks: A Python package for analysis of angle-resolved photoemission and related spectroscopies, arXiv:2508.04803.
- P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, et al., QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
- P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. Buongiorno Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A. Dal Corso, S. de Gironcoli, P. Delugas, R. A. DiStasio, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, et al., Advanced capabilities for materials modelling with QUANTUM ESPRESSO, J. Phys.: Condens. Matter 29, 465901 (2017).
- D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Phys. Rev. B 88, 085117 (2013).
- Materials data on by Materials Project, 2020, doi: 10.17188/1307989.
- Y. Huang, J. Lai, J. Zhan, T. Yu, R. Chen, P. Liu, X.-Q. Chen, and Y. Sun, Ab initio study of quantum oscillations in altermagnetic and nonmagnetic phases of , Phys. Rev. B 110, 144410 (2024).
- G. Prandini, A. Marrazzo, I. E. Castelli, N. Mounet, and N. Marzari, Precision and efficiency in solid-state pseudopotential calculations, npj Comput. Mater. 4, 72 (2018).
- G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, J. Ibañez-Azpiroz, H. Lee, J.-M. Lihm, D. Marchand, A. Marrazzo, Y. Mokrousov, J. I. Mustafa, Y. Nohara, Y. Nomura, L. Paulatto, et al., Wannier90 as a community code: New features and applications, J. Phys.: Condens. Matter 32, 165902 (2020).
- Q. Wu, S. Zhang, H.-F. Song, M. Troyer, and A. A. Soluyanov, Wanniertools: An open-source software package for novel topological materials, Comput. Phys. Commun. 224, 405 (2018).
- H. Over, A. Seitsonen, E. Lundgren, M. Schmid, and P. Varga, Experimental and simulated STM images of stoichiometric and partially reduced (110) surfaces including adsorbates, Surf. Sci. 515, 143 (2002).
- M. Visscher et al., Disentangling bulk and surface electronic structure using targeted cleave planes in (dataset), University of St. Andrews Research Portal, 2026, https://doi.org/10.17630/1eca7dae-c35a-43fe-9521-d5873396bf99.