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  • Letter
  • Open Access

Influence of quantum fluctuations on the spin-flop transition in hematite

Tobias Dannegger1,*, Imre Hagymási2, Levente Rózsa2,3, and Ulrich Nowak1

  • *Contact author: tobias.dannegger@uni-konstanz.de

Phys. Rev. Research 8, L022029 – Published 15 May, 2026

DOI: https://doi.org/10.1103/31vr-79kp

Abstract

Magnetic phase transitions between ordered phases are often understood on the basis of semiclassical spin models. Deviations from the classical description due to the quantum nature of the atomic spins as well as quantum fluctuations are usually treated as negligible if long-range order is preserved, and are rarely quantified for actual materials. Here, we demonstrate that a fully quantum-mechanical framework is required for a quantitatively correct description of the spin-flop transition in the insulating altermagnet hematite between the collinear antiferromagnetic and the weakly ferromagnetic spin-flop phase at low temperature. By applying both exact diagonalization and density-matrix renormalization group theory to the quantum Heisenberg Hamiltonian, we show how a quantum-mechanical treatment of an ab initio parametrized spin model can significantly improve the predicted low-temperature spin-flop field over a classical description when compared to measurements. Our results imply that quantum fluctuations have a measurable influence on selecting the ground state of a system out of competing ordered magnetic phases at low temperature.

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References (41)

  1. V. P. Antropov, M. I. Katsnelson, B. N. Harmon, M. van Schilfgaarde, and D. Kusnezov, Spin dynamics in magnets: Equation of motion and finite temperature effects, Phys. Rev. B 54, 1019 (1996).
  2. A. Rohrbach, J. Hafner, and G. Kresse, Ab initio study of the (0001) surfaces of hematite and chromia: Influence of strong electronic correlations, Phys. Rev. B 70, 125426 (2004).
  3. V. V. Mazurenko and V. I. Anisimov, Weak ferromagnetism in antiferromagnets: α−Fe2O3 and La2CuO4, Phys. Rev. B 71, 184434 (2005).
  4. R. Logemann, A. N. Rudenko, M. I. Katsnelson, and A. Kirilyuk, Exchange interactions in transition metal oxides: The role of oxygen spin polarization, J. Phys.: Condens. Matter 29, 335801 (2017).
  5. Z. D. Pozun and G. Henkelman, Hybrid density functional theory band structure engineering in hematite, J. Chem. Phys. 134, 224706 (2011).
  6. T. Dannegger, A. Deák, L. Rózsa, E. Galindez-Ruales, S. Das, E. Baek, M. Kläui, L. Szunyogh, and U. Nowak, Magnetic properties of hematite revealed by an ab initio parameterized spin model, Phys. Rev. B 107, 184426 (2023).
  7. J. O. Artman, J. C. Murphy, and S. Foner, Magnetic anisotropy in antiferromagnetic corundum-type sesquioxides, Phys. Rev. 138, A912 (1965).
  8. B. R. Morrison, A. H. Morrish, and G. J. Troup, High-field antiferromagnetic resonance in α−Fe2O3, Phys. Status Solidi (B) 56, 183 (1973).
  9. E. J. Samuelsen and G. Shirane, Inelastic neutron scattering investigation of spin waves and magnetic interactions in α−Fe2O3, Phys. Status Solidi 42, 241 (1970).
  10. R. F. L. Evans, W. J. Fan, P. Chureemart, T. A. Ostler, M. O. A. Ellis, and R. W. Chantrell, Atomistic spin model simulations of magnetic nanomaterials, J. Phys.: Condens. Matter 26, 103202 (2014).
  11. U. Atxitia, D. Hinzke, and U. Nowak, Fundamentals and applications of the Landau-Lifshitz-Bloch equation, J. Phys. D: Appl. Phys. 50, 033003 (2017).
  12. J. Fidler and T. Schrefl, Micromagnetic modelling—The current state of the art, J. Phys. D: Appl. Phys. 33, R135 (2000).
  13. F. Bloch, Zur theorie des ferromagnetismus, Z. Phys. 61, 206 (1930).
  14. R. E. Watson, M. Blume, and G. H. Vineyard, Spin motions in a classical ferromagnet, Phys. Rev. 181, 811 (1969).
  15. P. W. Anderson, An approximate quantum theory of the antiferromagnetic ground state, Phys. Rev. 86, 694 (1952).
  16. T. Jolicoeur, E. Dagotto, E. Gagliano, and S. Bacci, Ground-state properties of the S=12 Heisenberg antiferromagnet on a triangular lattice, Phys. Rev. B 42, 4800 (1990).
  17. C. H. Woo, H. Wen, A. A. Semenov, S. L. Dudarev, and P.-W. Ma, Quantum heat bath for spin-lattice dynamics, Phys. Rev. B 91, 104306 (2015).
  18. J. Barker and G. E. W. Bauer, Semiquantum thermodynamics of complex ferrimagnets, Phys. Rev. B 100, 140401(R) (2019).
  19. R. F. L. Evans, U. Atxitia, and R. W. Chantrell, Quantitative simulation of temperature-dependent magnetization dynamics and equilibrium properties of elemental ferromagnets, Phys. Rev. B 91, 144425 (2015).
  20. R. Lebrun, A. Ross, O. Gomonay, S. A. Bender, L. Baldrati, F. Kronast, A. Qaiumzadeh, J. Sinova, A. Brataas, R. A. Duine, and M. Kläui, Anisotropies and magnetic phase transitions in insulating antiferromagnets determined by a spin-Hall magnetoresistance probe, Commun. Phys. 2, 50 (2019).
  21. I. Dzyaloshinsky, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J. Phys. Chem. Solids 4, 241 (1958).
  22. T. Moriya, New mechanism of anisotropic superexchange interaction, Phys. Rev. Lett. 4, 228 (1960).
  23. T. Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev. 120, 91 (1960).
  24. F. J. Morin, Magnetic susceptibility of αFe2O3 and αFe2O3 with added titanium, Phys. Rev. 78, 819 (1950).
  25. W. Yung-Li and H. B. Callen, Spin waves in the spin-flop phase of an antiferromagnet, and metastability of the spin-flop transition, J. Phys. Chem. Solids 25, 1459 (1964).
  26. F. B. Anderson and H. B. Callen, Statistical mechanics and field-induced phase transitions of the Heisenberg antiferromagnet, Phys. Rev. 136, A1068 (1964).
  27. J. Berger and R. M. Hornreich, Temperature dependence of the field induced magnetization reorientation in Dzialoshinsky-Moriya type weak ferromagnets, J. Phys. Chem. Solids 34, 2011 (1973).
  28. A. H. Hill, F. Jiao, P. G. Bruce, A. Harrison, W. Kockelmann, and C. Ritter, Neutron diffraction study of mesoporous and bulk hematite, α−Fe2O3, Chem. Mater. 20, 4891 (2008).
  29. R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users’ Guide (SIAM, Philadelphia, USA, 1998).
  30. J. Xu, S.-H. Tsai, D. P. Landau, and K. Binder, Finite-size scaling for a first-order transition where a continuous symmetry is broken: The spin-flop transition in the three-dimensional XXZ Heisenberg antiferromagnet, Phys. Rev. E 99, 023309 (2019).
  31. S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
  32. S. R. White, Density-matrix algorithms for quantum renormalization groups, Phys. Rev. B 48, 10345 (1993).
  33. U. Schollwöck, The density-matrix renormalization group, Rev. Mod. Phys. 77, 259 (2005).
  34. U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. (NY) 326, 96 (2011).
  35. K. A. Hallberg, New trends in density matrix renormalization, Adv. Phys. 55, 477 (2006).
  36. C. Hubig, I. P. McCulloch, U. Schollwöck, and F. A. Wolf, Strictly single-site DMRG algorithm with subspace expansion, Phys. Rev. B 91, 155115 (2015).
  37. T. Dannegger, I. Hagymási, L. Rózsa, and U. Nowak, Quantum spin Hamiltonian for hematite and its spin-flop transition, KonDATA (2026), doi:10.48606/5rj4ccwzf9sy7331.
  38. L. Engelhardt, M. Luban, and C. Schröder, Finite quantum Heisenberg spin models and their approach to the classical limit, Phys. Rev. B 74, 054413 (2006).
  39. C. Kittel, Introduction to Solid State Physics, 8th ed. (John Wiley & Sons, Hoboken, NJ, 2004).
  40. J. Oitmaa and W. Zheng, Curie and Néel temperatures of quantum magnets, J. Phys.: Condens. Matter 16, 8653 (2004).
  41. T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 (1940).

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