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Pair- and Four-Spin Interactions in the Heavy Rare Earth Elements

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Ab initio Theory of Magnetic Ordering

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

Rare earth materials are at the origin of many applications with increasing importance. However, their complicated magnetism arising from the strongly correlated f-electrons clearly sets an outstanding problem with significant interest on fundamental physics grounds that is not fully understood yet. This motivates the ab initio description of the diverse magnetism in the heavy rare earth (HRE) elements.

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Notes

  1. 1.

    In addition, we checked that using either a fully relativistic or scalar relativistic version of our SDFT-DLM method produces the same f-electron magnetic ordering—valence electronic structure linkage.

  2. 2.

    Note that contrary to the lattice Fourier definition given in Eq. (3.68), here we sum over all magnetic positions, i.e. \(\mathcal {J}^\text {eff}(\mathbf q )=\sum _{nn'}\mathcal {J}^\text {eff}_{nn'}\exp \left[ \mathbf q \cdot (\mathbf x _n-\mathbf x _{n'})\right] \).

  3. 3.

    As an important note, we verified that the paramagnetic state is unstable to the formation of a HAFM structure prescribed by a 10 layer periodicity from the paramagnetic limit analysis based on the calculation of the direct correlation function, as described in Sect. 3.4. The long-range constants (\(n-n'>6\)) shown in the inset of Fig. 5.6 have been obtained from this calculation.

References

  1. Jensen J, Mackintosh AR (1991) Rare earth magnetism, estructure and excitations. Clarendon, Oxford

    Google Scholar 

  2. Gschneidner KA, Eyring LR (1978) Handbook on the physics and chemistry of rare Earths. North-Holand, Amsterdam

    Google Scholar 

  3. Zverev VI, Tishin AM, Chernyshov AS, Ya Mudryk KA, Jr G, Pecharsky VK (2014) Magnetic and magnetothermal properties and the magnetic phase diagram of high purity single crystalline terbium along the easy magnetization direction. J Phys: Condens Matter 26(6):066001

    Google Scholar 

  4. Herz R, Kronmüller H (1978) Field-induced magnetic phase transitions in dysprosium. J Magn Magn Mater 9(1):273–275

    Article  ADS  Google Scholar 

  5. Alkhafaji MT, Ali N (1997) Magnetic phase diagram of dysprosium. J Alloys Compd 250(1):659–661

    Google Scholar 

  6. Kida Y, Tajima K, Shinoda Y, Hayashi K, Ohsumi H (1999) Effect of magnetic field on crystal lattice in dysprosium studied by X-ray diffraction. J Phys Soc Jpn 68(2):650–654

    Article  ADS  Google Scholar 

  7. Chernyshov AS, Tsokol AO, Tishin AM, Gschneidner KA, Pecharsky VK (2005) Magnetic and magnetocaloric properties and the magnetic phase diagram of single-crystal dysprosium. Phys Rev B 71:184410

    Article  ADS  Google Scholar 

  8. Zverev VI, Tishin AM, Min Z, Mudryk Y, Gschneidner KA Jr, Pecharsky VK (2015) Magnetic and magnetothermal properties, and the magnetic phase diagram of single-crystal holmium along the easy magnetization direction. J Phys: Conden Matter 27(14):146002

    Google Scholar 

  9. Cowley RA, Bates S (1988) The magnetic structure of holmium. I. J Phys C: Solid State Phys 21(22):4113

    Google Scholar 

  10. Ali N, Willis F, Steinitz MO, Kahrizi M, Tindall DA (1989) Observation of transitions to spin-slip structures in single-crystal holmium. Phys Rev B 40:11414–11416

    Google Scholar 

  11. Jiles DC, Palmer SB, Jones DW, Farrant SP, Gschneidner KA Jr (1984) Magnetoelastic properties of high-purity single-crystal terbium. J Phys F: Metal Phys 14(12):3061

    Article  ADS  Google Scholar 

  12. Jiles DC, Blackie GN, Palmer SB (1981) Magnetoelastic effects in terbium. J Magn Magn Mater 24(1):75–80

    Article  ADS  Google Scholar 

  13. Kataev GI, Sattarov MR, Tishin AM (1989) Influence of commensurability effects on the magnetic phase diagram of terbium single crystals. Phys Status Solidi (a) 114(1):K79–K82

    Google Scholar 

  14. Yu J, LeClair PR, Mankey GJ, Robertson JL, Crow ML, Tian W (2015) Exploring the magnetic phase diagram of dysprosium with neutron diffraction. Phys Rev B 91:014404

    Article  ADS  Google Scholar 

  15. Chernyshov AS, Mudryk Y, Pecharsky VK, Gschneidner KA (2008) Temperature and magnetic field-dependent x-ray powder diffraction study of dysprosium. Phys Rev B 77:094132

    Article  ADS  Google Scholar 

  16. Nagamiya T, Nagata K, Kitano Y (1962) Magnetization process of a screw spin system. Prog Theor Phys 27(6):1253–1271

    Article  ADS  Google Scholar 

  17. Kitano Y, Nagamiya T (1964) Magnetization process of a screw spin system II. Prog Theor Phys 31(1):1–43

    Article  ADS  Google Scholar 

  18. Jensen J, Mackintosh AR (1990) Helifan: a new type of magnetic structure. Phys Rev Lett 64:2699–2702

    Article  ADS  Google Scholar 

  19. Evenson WE, Liu SH (1968) Generalized susceptibilities and magnetic ordering of heavy rare earths. Phys Rev Lett 21:432–434

    Article  ADS  Google Scholar 

  20. Evenson WE, Liu SH (1969) Theory of magnetic ordering in the heavy rare earths. Phys Rev 178:783–794

    Article  ADS  Google Scholar 

  21. Andrianov AV (1995) Helical magnetic structures in heavy rare-earth metals as a probable manifestation of the electronic topological transition. J Magn Magn Mater 140-144:749–750. International Conference on Magnetism

    Google Scholar 

  22. Palmer SB, McIntyre GJ, Andrianov AV, Melville RJ (1998) The c/a ratio of helical magnetic structures in rare-earth materials. J Magn Magn Mater 177-181:1023–1024. International Conference on Magnetism (Part II)

    Google Scholar 

  23. Hughes ID, Däne M, Ernst A, Hergert W, Lüders M, Poulter J, Staunton JB, Svane A, Szotek Z, Temmerman WM (2007) Lanthanide contraction and magnetism in the heavy rare earth elements. Nature 446:650–653

    Article  ADS  Google Scholar 

  24. Döbrich KM, Bostwick A, McChesney JL, Rossnagel K, Rotenberg E, Kaindl G (2010) Fermi-surface topology and helical antiferromagnetism in heavy lanthanide metals. Phys Rev Lett 104:246401

    Article  ADS  Google Scholar 

  25. Andrianov AV, Savel’eva OA, Bauer E, Staunton JB (2011) Squeezing the crystalline lattice of the heavy rare-earth metals to change their magnetic order: experiment and ab initio theory. Phys Rev B 84:132401

    Google Scholar 

  26. Oroszlány L, Deák A, Simon E, Khmelevskyi S, Szunyogh L (2015) Magnetism of gadolinium: a first-principles perspective. Phys Rev Lett 115:096402

    Article  ADS  Google Scholar 

  27. Liu SH (1978) Handbook of the physics and chemistry of rare Earths, vol 1. North-Holland, Amsterdam

    Google Scholar 

  28. Dugdale SB (2014) Probing the Fermi surface by positron annihilation and Compton scattering. Low Temp Phys 40(4):328–338

    Article  ADS  Google Scholar 

  29. Zhou L, Wiebe J, Lounis S, Vedmedenko E, Meier F, Blügel S, Dederichs PH, Wiesendanger R (2010) Strength and directionality of surface Ruderman-Kittel-Kasuya-Yosida interaction mapped on the atomic scale. Nat Phys 6:187–191

    Google Scholar 

  30. Peters L, Ghosh S, Sanyal B, van Dijk C, Bowlan J, de Heer W, Delin A, Di Marco I, Eriksson O, Katsnelson MI, Johansson B, Kirilyuk A (2016) Magnetism and exchange interaction of small rare-earth clusters; Tb as a representative. Sci Rep 6:19676

    Article  ADS  Google Scholar 

  31. Ohno H (1998) Making nonmagnetic semiconductors ferromagnetic. Science 281:951

    Article  ADS  Google Scholar 

  32. Ali M, Adie P, Marrows CH, Greig D, Hickey BJ, Stamps RL (2007) Exchange bias using a spin glass. Nat Mater 6:70

    Article  ADS  Google Scholar 

  33. Anisimov VI, Zaanen J, Andersen OK (1991) Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys Rev B 44:943–954

    Article  ADS  Google Scholar 

  34. Anisimov VI, Aryasetiawan F, Lichtenstein AI (1997) First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA + U method. J Phys: Conden Matter 9(4):767

    Google Scholar 

  35. Lüders M, Ernst A, Däne M, Szotek Z, Svane A, Ködderitzsch D, Hergert W, Györffy BL, Temmerman WM (2005) Self-interaction correction in multiple scattering theory. Phys Rev B 71:205109

    Article  ADS  Google Scholar 

  36. Perdew JP, Zunger A (1981) Self-interaction correction to density-functional approximations for many-electron systems. Phys Rev B 23:5048–5079

    Google Scholar 

  37. Hughes ID, Däne M, Ernst A, Hergert W, Lüders M, Staunton JB, Szotek Z, Temmerman WM (2008) Onset of magnetic order in strongly-correlated systems from ab initio electronic structure calculations: application to transition metal oxides. New J Phys 10(6):063010

    Article  Google Scholar 

  38. Marmodoro A, Ernst A, Ostanin S, Sandratskii L, Trevisanutto PE, Lathiotakis NN, Staunton JB (2016) Short-range ordering effects on the electronic Bloch spectral function of real materials in the nonlocal coherent-potential approximation. Phys Rev B 94:224205

    Article  ADS  Google Scholar 

  39. Langner MC, Roy S, Kemper AF, Chuang Y-D, Mishra SK, Versteeg RB, Zhu Y, Hertlein MP, Glover TE, Dumesnil K, Schoenlein RW (2015) Scattering bottleneck for spin dynamics in metallic helical antiferromagnetic dysprosium. Phys Rev B 92:184423

    Article  ADS  Google Scholar 

  40. Teichmann M, Frietsch B, Döbrich K, Carley R, Weinelt M (2015) Transient band structures in the ultrafast demagnetization of ferromagnetic gadolinium and terbium. Phys Rev B 91:014425

    Article  ADS  Google Scholar 

  41. Andres B, Christ M, Gahl C, Wietstruk M, Weinelt M, Kirschner J (2015) Separating exchange splitting from spin mixing in gadolinium by femtosecond laser excitation. Phys Rev Lett 115:207404

    Article  ADS  Google Scholar 

  42. Krieger K, Dewhurst JK, Elliott P, Sharma S, Gross EKU (2015) Laser-induced demagnetization at ultrashort time scales: predictions of TDDFT. J Chem Theory Comput 11(10):4870–4874

    Article  Google Scholar 

  43. Faulkner JS (1982) The modern theory of alloys. Prog Mater Sci 27(1):1–187

    Article  Google Scholar 

  44. Schadler G, Weinberger P, Gonis A, Klima J (1985) Bloch spectral functions for complex lattices: applications to substoichiometric TiN\(_x\) and the Fermi surface of TiN\(_x\). J Phys F: Metal Phys 15(8):1675

    Article  ADS  Google Scholar 

  45. Callen HB, Callen E (1966) The present status of the temperature dependence of magnetocrystalline anisotropy, and the \(l(l+1)2\) power law. J Phys Chem Solids 27(8):1271–1285

    Article  ADS  Google Scholar 

  46. McEwen KA (1978) Handbook on the physics and chemistry of rare Earths, vol 1. North-Holand, Amsterdam

    Google Scholar 

  47. Koehler WC, Cable JW, Child HR, Wilkinson MK, Wollan EO (1967) Magnetic structures of holmium II. the magnetization process. Phys Rev 158:450–461

    Article  ADS  Google Scholar 

  48. Gebhardt JR, Ali N (1998) Magnetic phase diagrams of holmium determined from magnetoresistance measurements. J Appl Phys 83(11):6299–6301

    Article  ADS  Google Scholar 

  49. Trushkevych O, Fan Y, Perry R, Edwards RS (2013) Magnetic phase transitions in Gd\(_{64}\)Sc\(_{36}\) studied using non-contact ultrasonics. J Phys D: Appl Phys 46(10):105005

    Google Scholar 

  50. Locht ILM, Kvashnin YO, Rodrigues DCM, Pereiro M, Bergman A, Bergqvist L, Lichtenstein AI, Katsnelson MI, Delin A, Klautau AB, Johansson B, Di Marco I, Eriksson O (2016) Standard model of the rare earths analyzed from the Hubbard I approximation. Phys Rev B 94:085137

    Article  ADS  Google Scholar 

  51. Rosen M (1968) Elastic moduli and ultrasonic attenuation of gadolinium, terbium, dysprosium, holmium, and erbium from 4.2 to 300K. Phys Rev 174:504–514

    Google Scholar 

  52. Palmer SB (1970) Debye temperatures of holmium and dysprosium from single crystal elastic constant measurements. J Phys Chem Solids 31(1):143–147

    Article  ADS  Google Scholar 

  53. Bodryakov VY, Povzner AA, Zelyukova OG (1999) Magnetic contribution to the Debye temperature and the lattice heat capacity of ferromagnetic rare-earth metals (using gadolinium as an example). Phys Solid State 41(7):1138–1143

    Article  ADS  Google Scholar 

  54. Gschneidner KA Jr, Pecharsky VK, Tsokol AO (2005) Recent developments in magnetocaloric materials. Rep Prog Phys 68(6):1479

    Article  ADS  Google Scholar 

  55. Staunton JB, Marmodoro A, Ernst A (2014) Using density functional theory to describe slowly varying fluctuations at finite temperatures: local magnetic moments in gd and the ’not so local’ moments of Ni. J Phys: Conden Matter 26(27):274210

    Google Scholar 

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  1. Department of Computational Materials Design, Max Planck Institute for Iron Research, Düsseldorf, Germany

    Dr. Eduardo Mendive Tapia

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Mendive Tapia, E. (2020). Pair- and Four-Spin Interactions in the Heavy Rare Earth Elements. In: Ab initio Theory of Magnetic Ordering. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-37238-5_5

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