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Self-consistent versus non-self-consistent spin-spiral calculations of magnetic exchange interactions in VASP

Umit Daglum1,*, Maria Stamenova1, Ersoy Şaşıoğlu2, and Stefano Sanvito1

  • *Contact author: dalumm@tcd.ie
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Phys. Rev. B 113, 214401 – Published 1 June, 2026

DOI: https://doi.org/10.1103/pfn2-p6jb

Abstract

We present an ab initio investigation of magnetic exchange interactions using the spin-spiral method as implemented in the VASP code, comparing fully self-consistent (SC) total-energy calculations with non-self-consistent (NSC) band-energy evaluations within the same computational framework. Using representative 3d ferromagnets (Fe, Co, Ni) and Mn-based full Heusler compounds, we compute magnon dispersion relations and extract real-space Heisenberg exchange parameters from the Fourier transformation of spin-spiral energies. Curie temperatures are subsequently estimated within the mean-field and random-phase approximations. The SC approach yields exchange parameters and magnon spectra in excellent agreement with experimental and previous theoretical data, confirming its quantitative reliability across different classes of magnetic systems. In contrast, the NSC approach based on a frozen-potential approximation exhibits systematic quantitative deviations: it overestimates spin-spiral energies and exchange couplings in high-moment systems (bcc Fe and Mn-based Heuslers) while underestimating them in low-moment fcc Ni. The magnitude of these discrepancies increases with the magnetic moment size and can exceed several hundred percent in high-moment compounds. Our results demonstrate that while NSC evaluations are computationally efficient, fully SC spin-spiral calculations are essential for obtaining quantitatively reliable exchange interactions within the projector augmented-wave framework.

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References (52)

  1. W. Heisenberg, Zur Theorie des Ferromagnetismus, Z. Phys. 49, 619 (1928).
  2. 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).
  3. P.-W. Ma, C. H. Woo, and S. L. Dudarev, Large-scale simulation of the spin-lattice dynamics in ferromagnetic iron, Phys. Rev. B 78, 024434 (2008).
  4. A. V. Ruban, S. Shallcross, S. I. Simak, and H. L. Skriver, Atomic and magnetic configurational energetics by the generalized perturbation method, Phys. Rev. B 70, 125115 (2004).
  5. T. Archer, C. D. Pemmaraju, S. Sanvito, C. Franchini, J. He, A. Filippetti, P. Delugas, D. Puggioni, V. Fiorentini, R. Tiwari, et al., Exchange interactions and magnetic phases of transition metal oxides: Benchmarking advanced ab initio methods, Phys. Rev. B 84, 115114 (2011).
  6. A. I. Liechtenstein, M. Katsnelson, V. Antropov, and V. Gubanov, Local spin density functional approach to the theory of exchange interactions in ferromagnetic metals and alloys, J. Magn. Magn. Mater. 67, 65 (1987).
  7. X. Wan, Q. Yin, and S. Y. Savrasov, Calculation of magnetic exchange interactions in Mott-Hubbard systems, Phys. Rev. Lett. 97, 266403 (2006).
  8. H. J. Xiang, E. J. Kan, S.-H. Wei, M.-H. Whangbo, and X. G. Gong, Predicting the spin-lattice order of frustrated systems from first principles, Phys. Rev. B 84, 224429 (2011).
  9. L. Sandratskii, Noncollinear magnetism in itinerant-electron systems: Theory and applications, Adv. Phys. 47, 91 (1998).
  10. L. M. Sandratskii and P. Bruno, Exchange interactions and Curie temperature in (Ga,Mn)As, Phys. Rev. B 66, 134435 (2002).
  11. J. Kübler, Ab initio estimates of the Curie temperature for magnetic compounds, J. Phys.: Condens. Matter 18, 9795 (2006).
  12. S. V. Halilov, H. Eschrig, A. Y. Perlov, and P. M. Oppeneer, Adiabatic spin dynamics from spin-density-functional theory: Application to Fe, Co, and Ni, Phys. Rev. B 58, 293 (1998).
  13. The FLEUR project, https://www.flapw.de/.
  14. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
  15. 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).
  16. D. Hobbs, G. Kresse, and J. Hafner, Fully unconstrained noncollinear magnetism within the projector augmented-wave method, Phys. Rev. B 62, 11556 (2000).
  17. M. Marsman and J. Hafner, Broken symmetries in the crystalline and magnetic structures of γ-iron, Phys. Rev. B 66, 224409 (2002).
  18. S. Y. Savrasov, Linear response calculations of spin fluctuations, Phys. Rev. Lett. 81, 2570 (1998).
  19. E. Şaşıoğlu, A. Schindlmayr, C. Friedrich, F. Freimuth, and S. Blügel, Wannier-function approach to spin excitations in solids, Phys. Rev. B 81, 054434 (2010).
  20. M. Ležaić, P. Mavropoulos, G. Bihlmayer, and S. Blügel, Exchange interactions and local-moment fluctuation corrections in ferromagnets at finite temperatures based on noncollinear density-functional calculations, Phys. Rev. B 88, 134403 (2013).
  21. E. Şaşıog, L. Sandratskii, P. Bruno, et al., Magnetic exchange coupling and Curie temperature of Ni(1+x) MnSb (x=0, 0.25, 0.5, 0.75, 1) from first principles, J. Magn. Magn. Mater. 290, 385 (2005).
  22. J. Rusz, I. Turek, and M. Diviš, Random-phase approximation for critical temperatures of collinear magnets with multiple sublattices: GdX compounds (X= Mg, Rh, Ni, Pd), Phys. Rev. B 71, 174408 (2005).
  23. K. Binder and D. W. Heermann, Monte Carlo Simulation in Statistical Physics (Springer, 1992), Vol. 8.
  24. F. L. Durhuus, T. Skovhus, and T. Olsen, Plane wave implementation of the magnetic force theorem for magnetic exchange constants: Application to bulk Fe, Co and Ni, J. Phys.: Condens. Matter 35, 105802 (2023).
  25. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  26. J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B 45, 13244 (1992).
  27. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  28. S. Sanvito, C. Oses, J. Xue, A. Tiwari, M. Zic, T. Archer, P. Tozman, M. Venkatesan, M. Coey, and S. Curtarolo, Accelerated discovery of new magnets in the Heusler alloy family, Sci. Adv. 3, e1602241 (2017).
  29. I. Galanakis and E. Şaşıoğlu, Ab-initio calculation of effective exchange interactions, spin waves, and Curie temperature in L21-and L12-type local moment ferromagnets, J. Mater. Sci. 47, 7678 (2012).
  30. E. Şaşıoğlu, L. M. Sandratskii, and P. Bruno, First-principles calculation of the intersublattice exchange interactions and Curie temperatures of the full Heusler alloys Ni2MnX (X=Ga, In, Sn, Sb), Phys. Rev. B 70, 024427 (2004).
  31. See Supplemental Material at http://link.aps.org/supplemental/10.1103/pfn2-p6jb for additional computational details, convergence tests, and benchmarking results of the constrained self-consistent spin-spiral method, including analyses of the Wigner–Seitz radius, penalty parameter, and comparisons between NSC and self-consistent spin-spiral calculations.
  32. F. J. dos Santos, L. Binci, G. Menichetti, R. Mahajan, N. Marzari, and I. Timrov, Comparative study of magnetic exchange parameters and magnon dispersions in NiO and MnO from first principles, Phys. Rev. B 113, 024427 (2026).
  33. P. Buczek, A. Ernst, and L. M. Sandratskii, Different dimensionality trends in the Landau damping of magnons in iron, cobalt, and nickel: Time-dependent density functional study, Phys. Rev. B 84, 174418 (2011).
  34. P. Bruno, Exchange interaction parameters and adiabatic spin-wave spectra of ferromagnets: A “renormalized magnetic force theorem,” Phys. Rev. Lett. 90, 087205 (2003).
  35. A. Jacobsson, G. Johansson, O. I. Gorbatov, M. Ležaić, B. Sanyal, S. Blügel, and C. Etz, Efficient parameterisation of non-collinear energy landscapes in itinerant magnets, Sci. Rep. 12, 18987 (2022).
  36. M. Pajda, J. Kudrnovský, I. Turek, V. Drchal, and P. Bruno, Ab initio calculations of exchange interactions, spin-wave stiffness constants, and Curie temperatures of Fe, Co, and Ni, Phys. Rev. B 64, 174402 (2001).
  37. M. Stringfellow, Observation of spin-wave renormalization effects in iron and nickel, J. Phys. C 1, 950 (1968).
  38. J. Lynn, Temperature dependence of the magnetic excitations in iron, Phys. Rev. B 11, 2624 (1975).
  39. G. Shirane, V. Minkiewicz, and R. Nathans, Spin waves in 3d metals, J. Appl. Phys. 39, 383 (1968).
  40. R. Pauthenet, Experimental verification of spin-wave theory in high fields, J. Appl. Phys. 53, 8187 (1982).
  41. P. W. Mitchell and D. M. Paul, Low-temperature spin-wave excitations in nickel, by neutron triple-axis spectroscopy, Phys. Rev. B 32, 3272 (1985).
  42. T. Graf, C. Felser, and S. S. Parkin, Simple rules for the understanding of Heusler compounds, Prog. Solid State Chem. 39, 1 (2011).
  43. E. Şaşıoğlu, L. M. Sandratskii, P. Bruno, and I. Galanakis, Exchange interactions and temperature dependence of magnetization in half-metallic Heusler alloys, Phys. Rev. B 72, 184415 (2005).
  44. Y. Noda and Y. Ishikawa, Spin waves in Heusler alloys Pd2MnSn and Ni2MnSn, J. Phys. Soc. Jpn. 40, 690 (1976).
  45. K. Tajima, Y. Ishikawa, P. J. Webster, M. W. Stringfellow, D. Tocchetti, and K. R. Zeabeck, Spin waves in a Heusler alloy Cu2MnAl, J. Phys. Soc. Jpn. 43, 483 (1977).
  46. P. J. Webster and K. R. A. Ziebeck, Alloys and compounds of d-elements with main group elements, in Alloys and Compounds of d-Elements with Main Group Elements, Landolt-Börnstein, New Series, Group III Vol. 19/c, edited by H. R. J. Wijn (Springer, Berlin, 1988), pp. 2 and 75–184.
  47. E. Şaşıoğlu, L. M. Sandratskii, and P. Bruno, Role of conduction electrons in mediating exchange interactions in Mn-based Heusler alloys, Phys. Rev. B 77, 064417 (2008).
  48. L. Castelliz, Beitrag zum Ferromagnetismus von Legierungen der übergangsmetalle mit Elementen der B-Gruppe, Z. Metallk 46, 198 (1955).
  49. T. Kanomata, K. Shirakawa, and T. Kaneko, Effect of hydrostatic pressure on the Curie temperature of the Heusler alloys Ni2Mnz (z=Al, Ga, In, Sn and Sb), J. Magn. Magn. Mater. 65, 76 (1987).
  50. J. K. Desmarais, G. Vignale, K. Bencheikh, A. Erba, and S. Pittalis, Electron localization function for non-collinear spins, Phys. Rev. Lett. 133, 136401 (2024).
  51. J. K. Desmarais, A. Erba, G. Vignale, and S. Pittalis, Meta-generalized-gradient approximation made magnetic, Phys. Rev. Lett. 134, 106402 (2025).
  52. M. Desmarais, G. Vignale, and S. Pittalis, Physical spin torques from exactly constrained exchange-correlation torques, Phys. Rev. Lett. 136, 016403 (2026).

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Phys. Rev. B 113, 214401– Published 1 June, 2026
  • Received 30 October 2025
  • Accepted 1 May 2026
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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.

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