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Disordered local moment picture

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The disordered local moment (DLM) picture is a method, in condensed matter physics, for describing the electronic structure of a magnetic material at a finite temperature, where a probability distribution of sizes and orientations of atomic magnetic moments must be considered.[1][2][3][4] Its was pioneered, among others, by Balázs Győrffy, Julie Staunton, Malcolm Stocks, and co-workers.

The underlying assumption of the DLM picture is similar to the Born-Oppenheimer approximation for the separation of solution of the ionic and electronic problems in a material. In the disordered local moment picture, it is assumed that 'local' magnetic moments which form around atoms are sufficiently long-lived that the electronic problem can be solved for an assumed, fixed distribution of magnetic moments.[5] Many such distributions can then be averaged over, appropriately weighted by their probabilities, and a description of the paramagnetic state obtained. (A paramagnetic state is one where the magnetic order parameter, , is equal to the zero vector.)

The picture is typically based on density functional theory (DFT) calculations of the electronic structure of materials. Most frequently, DLM calculations employ either the Korringa–Kohn–Rostoker (KKR)[6] (sometimes referred to as multiple scattering theory) or linearised muffin-tin orbital (LMTO) formulations of DFT, where the coherent potential approximation (CPA) can be used to average over multiple orientations of magnetic moment. However, the picture has also been applied in the context of supercells containing appropriate distributions of magnetic moment orientations.[7]

Though originally developed as a means by which to describe the electronic structure of a magnetic material above its magnetic critical temperature (Curie temperature), it has since been applied in a number of other contexts. This includes precise calculation of Curie temperatures and magnetic correlation functions for transition metals,[3][8] rare-earth elements,[9][10] and transition metal oxides;[11] as well as a description of the temperature dependance of magnetocrystalline anisotropy.[12][13] The approach has found particular success in describing the temperature-dependence of magnetic quantities of interest in rare earth-transition metal permanent magnets such as SmCo5[14] and Nd2Fe14B,[15] which are of interest for a range of energy generation and conversion technologies.

References

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  1. ^ Pindor, A J; Staunton, J; Stocks, G M; Winter, H (1983). "Disordered local moment state of magnetic transition metals: a self-consistent KKR CPA calculation". Journal of Physics F: Metal Physics. 13 (5): 979–989. doi:10.1088/0305-4608/13/5/012. ISSN 0305-4608.
  2. ^ Staunton, J.; Gyorffy, B. L.; Pindor, A. J.; Stocks, G. M.; Winter, H. (1984). "The "disordered local moment" picture of itinerant magnetism at finite temperatures". Journal of Magnetism and Magnetic Materials. 45 (1): 15–22. doi:10.1016/0304-8853(84)90367-6. ISSN 0304-8853.
  3. ^ a b Staunton, J; Gyorffy, B L; Pindor, A J; Stocks, G M; Winter, H (1985). "Electronic structure of metallic ferromagnets above the Curie temperature". Journal of Physics F: Metal Physics. 15 (6): 1387–1404. doi:10.1088/0305-4608/15/6/019. ISSN 0305-4608.
  4. ^ Gyorffy, B L; Pindor, A J; Staunton, J; Stocks, G M; Winter, H (1985). "A first-principles theory of ferromagnetic phase transitions in metals". Journal of Physics F: Metal Physics. 15 (6): 1337–1386. doi:10.1088/0305-4608/15/6/018. ISSN 0305-4608.
  5. ^ Mendive Tapia, Eduardo (2020), Mendive Tapia, Eduardo (ed.), "Disordered Local Moment Theory and Fast Electronic Responses", Ab initio Theory of Magnetic Ordering: Electronic Origin of Pair- and Multi-Spin Interactions, Springer Theses, Cham: Springer International Publishing, pp. 29–54, doi:10.1007/978-3-030-37238-5_3, ISBN 978-3-030-37238-5, retrieved 2024-09-25
  6. ^ Faulkner, J. S.; Stocks, G. Malcolm; Wang, Yang (2018-12-01). Multiple Scattering Theory: Electronic structure of solids. IOP Publishing. doi:10.1088/2053-2563/aae7d8. ISBN 978-0-7503-1490-9.
  7. ^ Mendive-Tapia, Eduardo; Neugebauer, Jörg; Hickel, Tilmann (2022-02-17). "Ab initio calculation of the magnetic Gibbs free energy of materials using magnetically constrained supercells". Physical Review B. 105 (6): 064425. arXiv:2202.11492. doi:10.1103/PhysRevB.105.064425.
  8. ^ Pinski, F. J.; Staunton, J.; Gyorffy, B. L.; Johnson, D. D.; Stocks, G. M. (1986-05-12). "Ferromagnetism versus Antiferromagnetism in Face-Centered-Cubic Iron". Physical Review Letters. 56 (19): 2096–2099. doi:10.1103/PhysRevLett.56.2096. ISSN 0031-9007.
  9. ^ Hughes, I. D.; Däne, M.; Ernst, A.; Hergert, W.; Lüders, M.; Poulter, J.; Staunton, J. B.; Svane, A.; Szotek, Z.; Temmerman, W. M. (2007). "Lanthanide contraction and magnetism in the heavy rare earth elements". Nature. 446 (7136): 650–653. doi:10.1038/nature05668. ISSN 1476-4687.
  10. ^ Mendive-Tapia, Eduardo; Staunton, Julie B. (2017-05-11). "Theory of Magnetic Ordering in the Heavy Rare Earths: Ab Initio Electronic Origin of Pair- and Four-Spin Interactions". Physical Review Letters. 118 (19). arXiv:1610.08304. doi:10.1103/PhysRevLett.118.197202. ISSN 0031-9007.
  11. ^ Hughes, I D; Däne, M; Ernst, A; Hergert, W; Lüders, M; Staunton, J B; Szotek, Z; Temmerman, W M (2008-06-06). "Onset of magnetic order in strongly-correlated systems from ab initio electronic structure calculations: application to transition metal oxides". New Journal of Physics. 10 (6): 063010. arXiv:0802.3660. doi:10.1088/1367-2630/10/6/063010. ISSN 1367-2630.
  12. ^ Staunton, J. B.; Ostanin, S.; Razee, S. S. A.; Gyorffy, B. L.; Szunyogh, L.; Ginatempo, B.; Bruno, Ezio (2004-12-14). "Temperature Dependent Magnetic Anisotropy in Metallic Magnets from an Ab Initio Electronic Structure Theory: L 1 0 -Ordered FePt". Physical Review Letters. 93 (25). arXiv:cond-mat/0407774. doi:10.1103/PhysRevLett.93.257204. ISSN 0031-9007.
  13. ^ Staunton, J. B.; Szunyogh, L.; Buruzs, A.; Gyorffy, B. L.; Ostanin, S.; Udvardi, L. (2006-10-17). "Temperature dependence of magnetic anisotropy: An ab initio approach". Physical Review B. 74 (14). doi:10.1103/PhysRevB.74.144411. ISSN 1098-0121.
  14. ^ Patrick, Christopher E.; Kumar, Santosh; Balakrishnan, Geetha; Edwards, Rachel S.; Lees, Martin R.; Petit, Leon; Staunton, Julie B. (2018-02-28). "Calculating the Magnetic Anisotropy of Rare-Earth–Transition-Metal Ferrimagnets". Physical Review Letters. 120 (9). arXiv:1803.00235. doi:10.1103/PhysRevLett.120.097202. ISSN 0031-9007.
  15. ^ Bouaziz, Juba; Patrick, Christopher E.; Staunton, Julie B. (2023-01-05). "Crucial role of Fe in determining the hard magnetic properties of Nd 2 Fe 14 B". Physical Review B. 107 (2). arXiv:2301.02868. doi:10.1103/PhysRevB.107.L020401. ISSN 2469-9950.
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