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Facet tomography of chromia's magnetoelectric multipole

Paul Lehmann1, Kai Wagner1, Pavlo Makushko2, Oleksandr V. Pylypovskyi2,3, Igor Veremchuk2, Sophie F. Weber4, Nicola A. Spaldin5, Denys Makarov2, and Patrick Maletinsky1

Phys. Rev. Research 8, 033135 – Published 4 August, 2026

DOI: https://doi.org/10.1103/4l6w-pgdj

Abstract

Roughness-insensitive surface magnetization is an intrinsic property of magnetoelectric antiferromagnets and is today understood as a manifestation of bulk magnetoelectric multipoles. Here, we provide an experimental quantification of the crystal-facet-dependent surface magnetization in the archetypical magnetoelectric antiferromagnet Cr2O3 and show that the data are consistent with a quadrupolar component of the bulk magnetoelectric multipolization. Using quantitative nanoscale magnetometry on lithographically defined rectangular mesas that expose 30 distinct crystallographic facets, we quantify mesa stray magnetic fields, which arise from differences between the mesa top and side-facet magnetizations. The resulting dataset supports a linear map from surface normal to surface magnetization, from which we directly infer the bulk quadrupolar component within the multipolization framework. Our work provides systematic, facet-resolved evidence of roughness-insensitive surface magnetization, including in-plane components, and delivers a quantitative route to constraining bulk multipoles from surface stray-field data. Beyond addressing the modern theory of magnetoelectric multipolization, our approach offers a generally applicable method to quantify surface magnetizations in antiferromagnetic compounds and informs the choice of crystal cuts for future spintronics devices.

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References (58)

  1. I. Dzyaloshinskii, On the magneto-electrical effect in antiferromagnets, J. Exp. Theor. Phys. 10, 628 (1960).
  2. D. N. Astrov, The magnetoelectric effect in antiferromagnets, J. Exp. Theor. Phys. 11, 708 (1960).
  3. D. N. Astrov, Magnetoelectric effect in chromium oxide, J. Exp. Theor. Phys. 13, 729 (1961).
  4. V. J. Folen, G. T. Rado, and E. W. Stalder, Anisotropy of the magnetoelectric effect in Cr2O3, Phys. Rev. Lett. 6, 607 (1961).
  5. G. T. Rado and V. J. Folen, Observation of the magnetically induced magnetoelectric effect and evidence for antiferromagnetic domains, Phys. Rev. Lett. 7, 310 (1961).
  6. T. Jungwirth, X. Marti, P. Wadley, and J. Wunderlich, Antiferromagnetic spintronics, Nat. Nanotechnol. 11, 231 (2016).
  7. K. Olejník, T. Seifert, Z. Kašpar, V. Novák, P. Wadley, R. P. Campion, M. Baumgartner, P. Gambardella, P. Němec, J. Wunderlich, J. Sinova, P. Kužel, M. Müller, T. Kampfrath, and T. Jungwirth, Terahertz electrical writing speed in an antiferromagnetic memory, Sci. Adv. 4, eaar3566 (2018).
  8. J. Li, C. B. Wilson, R. Cheng, M. Lohmann, M. Kavand, W. Yuan, M. Aldosary, N. Agladze, P. Wei, M. S. Sherwin, and J. Shi, Spin current from sub-terahertz-generated antiferromagnetic magnons, Nature (London) 578, 70 (2020).
  9. C. Binek and B. Doudin, Magnetoelectronics with magnetoelectrics, J. Phys.: Condens. Matter 17, L39 (2005).
  10. T. Kosub, M. Kopte, F. Radu, O. G. Schmidt, and D. Makarov, All-electric access to the magnetic-field-invariant magnetization of antiferromagnets, Phys. Rev. Lett. 115, 097201 (2015).
  11. T. Kosub, M. Kopte, R. Hühne, P. Appel, B. Shields, P. Maletinsky, R. Hübner, M. O. Liedke, J. Fassbender, O. G. Schmidt, and D. Makarov, Purely antiferromagnetic magnetoelectric random access memory, Nat. Commun. 8, 13985 (2017).
  12. S. Manipatruni, D. E. Nikonov, C.-C. Lin, T. A. Gosavi, H. Liu, B. Prasad, Y.-L. Huang, E. Bonturim, R. Ramesh, and I. A. Young, Scalable energy-efficient magnetoelectric spin–orbit logic, Nature (London) 565, 35 (2019).
  13. A. Mahmood, W. Echtenkamp, M. Street, J.-L. Wang, S. Cao, T. Komesu, P. A. Dowben, P. Buragohain, H. Lu, A. Gruverman, A. Parthasarathy, S. Rakheja, and C. Binek, Voltage controlled Néel vector rotation in zero magnetic field, Nat. Commun. 12, 1674 (2021).
  14. P. Rickhaus, O. V. Pylypovskyi, G. Seniutinas, V. Borras, P. Lehmann, K. Wagner, L. Zaper, P. J. Prusik, P. Makushko, I. Veremchuk, T. Kosub, R. Hübner, D. D. Sheka, P. Maletinsky, and D. Makarov, Antiferromagnetic nanoscale bit arrays of magnetoelectric Cr2O3 thin films, Nano Lett. 24, 13172 (2024).
  15. X. He, Y. Wang, N. Wu, A. N. Caruso, E. Vescovo, K. D. Belashchenko, P. A. Dowben, and C. Binek, Robust isothermal electric control of exchange bias at room temperature, Nat. Mater. 9, 579 (2010).
  16. K. D. Belashchenko, Equilibrium magnetization at the boundary of a magnetoelectric antiferromagnet, Phys. Rev. Lett. 105, 147204 (2010).
  17. N. A. Spaldin, Analogy between the magnetic dipole moment at the surface of a magnetoelectric and the electric charge at the surface of a ferroelectric, J. Exp. Theor. Phys. 132, 493 (2021).
  18. S. F. Weber, A. Urru, S. Bhowal, C. Ederer, and N. A. Spaldin, Surface magnetization in antiferromagnets: Classification, example materials, and relation to magnetoelectric responses, Phys. Rev. X 14, 021033 (2024).
  19. Although the ME-multipolization is a bulk quantity, the surface magnetization depends on the particular atomic termination at the surface.
  20. K. Du, X. Xu, C. Won, K. Wang, S. A. Crooker, S. Rangan, R. Bartynski, and S.-W. Cheong, Topological surface magnetism and Néel vector control in a magnetoelectric antiferromagnet, npj Quantum Mater. 8, 17 (2023).
  21. O. V. Pylypovskyi, S. F. Weber, P. Makushko, I. Veremchuk, N. A. Spaldin, and D. Makarov, Surface-symmetry-driven Dzyaloshinskii-Moriya interaction and canted ferrimagnetism in collinear magnetoelectric antiferromagnet Cr2O3, Phys. Rev. Lett. 132, 226702 (2024).
  22. P. Appel, B. J. Shields, T. Kosub, N. Hedrich, R. Hübner, J. Faßbender, D. Makarov, and P. Maletinsky, Nanomagnetism of magnetoelectric granular thin-film antiferromagnets, Nano Lett. 19, 1682 (2019).
  23. N. Hedrich, K. Wagner, O. V. Pylypovskyi, B. J. Shields, T. Kosub, D. D. Sheka, D. Makarov, and P. Maletinsky, Nanoscale mechanics of antiferromagnetic domain walls, Nat. Phys. 17, 574 (2021).
  24. M. S. Wörnle, P. Welter, M. Giraldo, T. Lottermoser, M. Fiebig, P. Gambardella, and C. L. Degen, Coexistence of Bloch and Néel walls in a collinear antiferromagnet, Phys. Rev. B 103, 094426 (2021).
  25. P. Schoenherr, L. M. Giraldo, M. Lilienblum, M. Trassin, D. Meier, and M. Fiebig, Magnetoelectric Force Microscopy on Antiferromagnetic 180° Domains in Cr2O3, Materials 10, 1051 (2017).
  26. B. B. Krichevtsov, V. V. Pavlov, R. V. Pisarev, and V. N. Gridnev, Spontaneous non-reciprocal reflection of light from antiferromagnetic Cr2O3, J. Phys.: Condens. Matter 5, 8233 (1993).
  27. P. Makushko, T. Kosub, O. V. Pylypovskyi, N. Hedrich, J. Li, A. Pashkin, S. Avdoshenko, R. Hübner, F. Ganss, D. Wolf et al., Flexomagnetism and vertically graded Néel temperature of antiferromagnetic Cr2O3 thin films, Nat. Commun. 13, 6745 (2022).
  28. L. Rondin, J.-P. Tetienne, T. Hingant, J.-F. Roch, P. Maletinsky, and V. Jacques, Magnetometry with nitrogen-vacancy defects in diamond, Rep. Prog. Phys. 77, 056503 (2014).
  29. A. Urru and N. A. Spaldin, Magnetic octupole tensor decomposition and second-order magnetoelectric effect, Ann. Phys. 447, 168964 (2022).
  30. J. M. D. Coey, Magnetism and Magnetic Materials (Cambridge University Press, Cambridge, 2010).
  31. A. F. Andreev, Macroscopic magnetic fields of antiferromagnets, J. Exp. Theor. Phys. Lett. 63, 758 (1996).
  32. Note that both the magnetic charge and current have units of amperes or Bohr magnetons per nanometer squared.
  33. Since we assume invariance along y, the my component does not contribute.
  34. D. N. Astrov, N. B. Ermakov, A. S. Borovik-Romanov, E. G. Kolevatov, and V. I. Nizhankovskii, External quadrupole magnetic field of antiferromagnetic Cr2O3, J. Exp. Theor. Phys. Lett. 63, 745 (1996).
  35. A. Borovik-Romanov and V. Nizhankovskii, Quadrupolar magnetic field outside antiferromagnetic Cr2O3, Acta Phys. Pol. A 92, 371 (1997).
  36. It is expected that for a particular bulk state, for different crystal facets, either of the AF's two sublattices can terminate the sample, which in turn would lead to magnetization jumps by “multipolization increments” [37]. A possible explanation for the observed smooth behavior of λM and IM as a function of φmesa, could be local averaging over these two surface termination scenarios.
  37. S. F. Weber and N. A. Spaldin, Characterizing and overcoming surface paramagnetism in magnetoelectric antiferromagnets, Phys. Rev. Lett. 130, 146701 (2023).
  38. O. L. de Lange and R. E. Raab, Electromagnetic boundary conditions in multipole theory, J. Math. Phys. 54, 093513 (2013).
  39. W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators, Phys. Rev. B 96, 245115 (2017).
  40. Due to the broken inversion and time-reversal symmetries, only terms odd in position are allowed for Cr2O3's multipole expansion.
  41. The actual fitting procedure, detailed in Appendix pp7, involves slightly more complicated expressions, since we also consider the NV orientation as free parameters.
  42. ME-annealing fields were applied along the [001] direction for the (001)-oriented sample and along [4¯01], which is normal to (104), for the (104)-oriented sample.
  43. Using literature data for the temperature dependence of Cr2O3's surface magnetization [20], we infer a room-temperature derivative of ∂msurf/∂T≈−0.08μBnm−2K−1. This implies that a temperature difference of roughly 4K would be required to account for the observed variation in qz2 between the two samples. Although sizable, such a temperature offset is plausible within our experimental setup.
  44. P. Lehmann, K. Wagner, P. Maletinsky, P. Makushko, D. Makarov, I. Veremchuk, O. Pylypovskyi, S. F. Weber, and N. Spaldin, Replication data for: Facet tomography of chromia's magnetoelectric multipole [Data set], Version 1, Zenodo, 2026, https://doi.org/10.5281/zenodo.20658751.
  45. I. Dzyaloshinskii, External magnetic fields of antiferromagnets, Solid State Commun. 82, 579 (1992).
  46. S. Shtrikman and D. Treves, Observation of the magnetoelectric effect in Cr2O3 powders, Phys. Rev. 130, 986 (1963).
  47. P. J. Brown, J. B. Forsyth, and F. Tasset, A study of magnetoelectric domain formation in Cr2O3, J. Phys.: Condens. Matter 10, 663 (1998).
  48. F. Casola, T. van der Sar, and A. Yacoby, Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond, Nat. Rev. Mater. 3, 17088 (2018).
  49. W. S. Huxter, M. F. Sarott, M. Trassin, and C. L. Degen, Imaging ferroelectric domains with a single-spin scanning quantum sensor, Nat. Phys. 19, 644 (2023).
  50. Z. Qiu, A. Hamo, U. Vool, T. X. Zhou, and A. Yacoby, Nanoscale electric field imaging with an ambient scanning quantum sensor microscope, npj Quantum Inf. 8, 107 (2022).
  51. A. Laraoui, H. Aycock-Rizzo, Y. Gao, X. Lu, E. Riedo, and C. A. Meriles, Imaging thermal conductivity with nanoscale resolution using a scanning spin probe, Nat. Commun. 6, 8954 (2015) 1.
  52. P. Maletinsky, S. Hong, M. S. Grinolds, B. Hausmann, M. D. Lukin, R. L. Walsworth, M. Loncar, and A. Yacoby, A robust scanning diamond sensor for nanoscale imaging with single nitrogen-vacancy centres, Nat. Nanotechnol. 7, 320 (2012).
  53. A. K. C. Tan, H. Jani, M. Högen, L. Stefan, C. Castelnovo, D. Braund, A. Geim, A. Mechnich, M. S. G. Feuer, H. S. Knowles, A. Ariando, P. G. Radaelli, and M. Atatüre, Revealing emergent magnetic charge in an antiferromagnet with diamond quantum magnetometry, Nat. Mater. 23, 205 (2024).
  54. A. Finco, A. Haykal, S. Fusil, P. Kumar, P. Dufour, A. Forget, D. Colson, J.-Y. Chauleau, M. Viret, N. Jaouen, V. Garcia, and V. Jacques, Imaging topological defects in a noncollinear antiferromagnet, Phys. Rev. Lett. 128, 187201 (2022).
  55. S. K. Treves, V. Ukleev, A. Apseros, J. R. Massey, K. Wagner, P. Lehmann, A. Kitaori, N. Kanazawa, J. A. Brock, S. Finizio, J. Reuteler, Y. Tokura, P. Maletinsky, and V. Scagnoli, Investigating skyrmion stability and core polarity reversal in NdMn2Ge2, Sci. Rep. 15, 461 (2025).
  56. I. Bertelli, B. G. Simon, T. Yu, J. Aarts, G. E. W. Bauer, Y. M. Blanter, and T. van der Sar, Imaging spin-wave damping underneath metals using electron spins in diamond, Adv. Quantum Technol. 4, 2100094 (2021).
  57. N. Hedrich, D. Rohner, M. Batzer, P. Maletinsky, and B. J. Shields, Parabolic diamond scanning probes for single-spin magnetic field imaging, Phys. Rev. Appl. 14, 064007 (2020).
  58. B. Krichevtsov, V. V. Pavlov, and R. V. Pisarev, Nonreciprocal optical effects in antiferromagnetic Cr2O3 subjected to electric and magnetic fields, J. Exp. Theor. Phys. 67, 378 (1988).

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