Magnetization Densities in Material Science

Chapter
First Online:

Abstract

The aim of this chapter is to point out the relevance of magnetization density studies by means of polarized neutron diffraction (PND) for understanding the magnetic behaviour of materials. Recent advances in the PND technique are overviewed. Major improvements in PND data analysis concern magnetization density reconstruction using the Maximum of Entropy Method (MEM) and the new method based on the local susceptibility tensor approach for non collinear moments in strongly anisotropic materials. The well established model refinement methods are based on the atomic orbital (AO) model and the multipole model. The interest of magnetization density studies for studying novel molecule-based magnetic materials is demonstrated on the basis of selected examples.

Keywords

Spin Density Pure Spin Spin Crossover Magnetic Form Factor Magnetization Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Notes

Acknowledgments

The authors thank A. Gukasov for many helpful discussions.

References

  1. 1.
    Schweizer J (2006) Polarized neutrons and polarization analysis. In: Chatterji T (ed) Neutron scattering from magnetic crystals. Elsevier, Amsterdam, pp 153–213CrossRefGoogle Scholar
  2. 2.
    Lawson PK, Cooper MJ, Dixon MAG, Timms DN, Zukowski E, Itoh F, Sakurai H (1997) Magnetic-Compton-scattering study of spin moments in UFe2. Phys Rev B 56:3239–3243CrossRefGoogle Scholar
  3. 3.
    Tsutsui S, Sakurai Y, Itou M, Matsuda TD, Haga Y, Onuki Y (2005) Magnetic Compton scattering study of UCoAl. Phys B 359–361:1117–1119CrossRefGoogle Scholar
  4. 4.
    Kučera M, Kuneš J, Kolomiets A, Diviš M, Andreev AV, Sechovsky V, Kappler JP, Rogalev A (2002) X-ray magnetic circular dichroism studies of 5f magnetism in UCoAl and UPtAl. Phys Rev B 66:144405CrossRefGoogle Scholar
  5. 5.
    Muro T, Shishidou T, Oda F, Fukawa T, Yamada H, Kimura A, Imada S, Suga S, Park SY, Miyahara T, Sato K (1996) Magnetic circular dichroism of the S 2p, Co 2p, and Co 3p core absorption and orbital angular momentum of the Co 3d state in low-spin CoS2. Phys Rev B 53:7055CrossRefGoogle Scholar
  6. 6.
    Neubeck W, Vettier C, de Bergevin F, Yakhou F, Mannix D, Ranno L, Chatterji T (2001) Orbital moment determination of simple transition metal oxides using magnetic X-ray diffraction. J Phys Chem Solid 62:2173–2180CrossRefGoogle Scholar
  7. 7.
    Ito M, Tsuji N, Adachi H, Nakao H, Murakami Y, Taguchi Y (2005) Tokura, Y: direct observation of ordered orbital of YTiO3 by the X-ray magnetic diffraction technique. Nucl Instrum Method Phys Res B 238:237–241CrossRefGoogle Scholar
  8. 8.
    Tsuji N, Ito M, Sakurai H, Suzuki K, Tanaka K, Kitani K, Adachi H, Kawata H, Koizumi A, Nakao H, Murakami Y, Taguchi Y, Tokura Y (2008) Magnetic Compton profile study of orbital ordering state of 3d electrons in YTiO3. J Phys Soc Jpn 77:023705–1–023705–4Google Scholar
  9. 9.
    Javorsky P, Sechovsky V, Schweizer J, Bourdarot F, Lelièvre-Berna E, Andreev AV, Shiokawa Y (2001) Magnetization densities in UCoAl studied by polarized neutron diffraction. Phys Rev B 63:064423CrossRefGoogle Scholar
  10. 10.
    Kernavanois N, Ressouche E, Brown PJ, Henry JY, Lelièvre-Berna E (2003) Magnetization distribution in paramagnetic CoO: a polarized neutron diffraction study. J Phys Condens Matter 15:3433–3443CrossRefGoogle Scholar
  11. 11.
    Akimitsu J, Ichikawa H, Eguchi N, Miyano T, Nishi M, Kakurai K (2001) Direct observation of orbital ordering in YTiO3 by means of the polarized neutron diffraction technique. J Phys Soc Jpn 70:3475–3478CrossRefGoogle Scholar
  12. 12.
    Champion G, Arrio MA, Sainctavit P, Zacchigna M, Zangrando M, Finazzi M, Parmigiani F, Villain F, Mathoniere C, Cartier dit Moulin C (2003) Size effect on local magnetic moments in ferrimagnetic molecular complexes: an XMCD investigation. Monatshefte fur Chem 134:277–284Google Scholar
  13. 13.
    Moroni R, Cartier dit Moulin Ch, Champion G, Arrio M-A, Sainctavit Ph, Verdaguer M, Gatteschi D (2003) X-ray magnetic circular dichroism investigation of magnetic contributions from MnIII and MnIV ions in Mn12-ac. Phys Rev B 68:064407CrossRefGoogle Scholar
  14. 14.
    Schweizer J, Gillon B (1999) In: Lahti PM (ed) Magnetic properties of organic radicals. Marcel Dekker, Inc, New York, p. 449Google Scholar
  15. 15.
    Schweizer J, Ressouche E (2001) In: Miller J, Drillon M (eds) MagnetoScience – from molecules to materials. Wiley, Berlin, pp 325–357CrossRefGoogle Scholar
  16. 16.
    Zheludev A, Chiarelli R, Delley B, Gillon B, Rassat A, Ressouche E, Schweizer J (1995) Spin density in an organic biradical ferromagnetic crystal. J Mag Mag Mater 140–144:1439–1440CrossRefGoogle Scholar
  17. 17.
    Gillon B (2001) Spin distributions in molecular systems with interacting transition metal ions. In: Miller J, Drillon M (eds) MagnetoScience – from molecules to materials. Wiley, Berlin, pp 357–378CrossRefGoogle Scholar
  18. 18.
    Reynolds PA, Figgis BN (1990) On the charge density distribution in cobalt(III) ammine hexacyanochromate(III) complexes. Aust J Chem 43:1929–1934CrossRefGoogle Scholar
  19. 19.
    Figgis BN, Kucharski ES, Vrtis M (1993) Spin and charge transfer through hydrogen bonding in [Co(NH3)5(OH2)][Cr(CN)6]. J Am Chem Soc 115:176–181CrossRefGoogle Scholar
  20. 20.
    Pontillon Y, Caneschi A, Gatteschi D, Grand A, Ressouche E, Sessoli R, Schweizer J (1999) Experimental spin density in a purely organic free radical: visualization of the ferromagnetic exchange pathway in p-(methylthio)phenyl nitronyl nitroxide, Nit(SMe)Ph. Chem Eur J 5:3616–3624CrossRefGoogle Scholar
  21. 21.
    Pillet S, Souhassou M, Pontillon Y, Caneschi A, Gatteschi D, Lecomte C (2001) Investigation of magnetic interaction pathways by experimental electron density measurements: application to an organic free radical, p(methylthio)phenyl nitronyl nitroxide. New J Chem 25:131–143CrossRefGoogle Scholar
  22. 22.
    Baron V, Gillon B, Cousson A, Mathonière C, Kahn O, Grand A, Öhrström L, Delley B, Bonnet M, Boucherle JX (1997) Spin density maps for the ferrimagnetic chain compound MnCu(pba)(H2O)3,2H2O, (pba = 1,2 propylènebis(oxamato)): polarized neutron diffraction and theoretical studies. J Am Chem Soc 119:3500–3506CrossRefGoogle Scholar
  23. 23.
    Pillet S, Souhassou M, Mathonière C, Lecomte C (2004) Electron density distribution of an oxamato bridged Mn(II)-Cu(II) bimetallic chain and correlation to magnetic properties. J Am Chem Soc 126:1219–1228CrossRefGoogle Scholar
  24. 24.
    Carlisle CJ, Willis BTM (eds) (2009) Magnetic neutron diffraction. In: Experimental neutron scattering. Oxford University Press, New York, pp 172–193Google Scholar
  25. 25.
    Brown PJ (1992) Magnetic scattering of neutrons. In: Wilson AJC (ed) International tables for crystallography, vol C. Kluwer, Dordrecht, pp 512–514Google Scholar
  26. 26.
    Coppens P, Becker PJ (1992) Analysis of charge and spin densities. In: Wilson AJC (ed) International tables of crystallography, vol C. Kluwer, Dordrecht, pp 627–645Google Scholar
  27. 27.
    Gukasov A, Brown PJ (2002) Determination of atomic site susceptibility tensors from polarized neutron diffraction data. J Phys Condens Matter 14:8831–8839CrossRefGoogle Scholar
  28. 28.
    Gukasov A, Goujon A, Meuriot JL, Person C, Exil G, Koskas G (2007) Super-6T2, a new position-sensitive detector polarized neutron diffractometer. Phys B 397:131–134CrossRefGoogle Scholar
  29. 29.
    Tasset F (1995) Towards helium-3 neutron polarizers. Phys B 213&214:935–938CrossRefGoogle Scholar
  30. 30.
    Dreyer J, Regnault L-P, Bourgeat-Lami E, Lelièvre-Berna E, Pujol S, Thomas M, Thomas F, Tasset F (2000) Cryopol: a superconducting magnetostatic cavity for a 3He neutron spin filter. Nucl Instrum Method Phys Res A 449:638CrossRefGoogle Scholar
  31. 31.
    Hutanu V, Meven M, Lelièvre-Berna E, Heger G (2009) POLI-HEiDi: the new polarized neutron diffractometer at the hot source (SR9) at the FRMII – project status. Phys B 404:2633–2636CrossRefGoogle Scholar
  32. 32.
    Anderson IS, Cook J, Felcher G, Gentile T, Greene G, Klose F, Koetzle T, Lelièvre-Berna E, Parizzi A, Pynn R, Zhao J (2005) Polarized neutrons for pulsed neutron sources. J Neutron Res 13:193–223CrossRefGoogle Scholar
  33. 33.
    Tasset F, Brown PJ, Lelièvre-Berna E, Roberts T, Pujol S, Alibon J, Bourgeat-Lami E (1999) Spherical neutron polarimetry with Cryopad-II. Phys B 267–268:69CrossRefGoogle Scholar
  34. 34.
    Brown PJ (2006) Spherical neutron polarimetry. In: Chatterji T (ed) Neutron scattering from magnetic crystals. Elsevier, Amsterdam, pp 215–244CrossRefGoogle Scholar
  35. 35.
    Brown PJ, Forsyth JB, Lelièvre-Berna E, Tasset F (2002) Determination of the magnetization distribution in Cr2O3 using spherical neutron polarimetry. J Phys Condens Matter 14:1957–1966CrossRefGoogle Scholar
  36. 36.
    Reynolds PA, Gilbert EP, Figgis BN (1996) Powder neutron diffraction in an applied magnetic field: a novel tool for transition metal chemistry. Inorg Chem 35:545–546CrossRefGoogle Scholar
  37. 37.
    Wills AS, Lelièvre-Berna E, Tasset F, Schweizer J, Ballou R (2005) Magnetization distribution measurements from powders using a 3He spin filter: a test experiment. Phys B 356:254–258CrossRefGoogle Scholar
  38. 38.
    Goujon A, Gillon B, Gukasov A, Jeftic J, Nau Q, Codjovi E, Varret F (2003) Photoinduced molecular switching studied by polarized neutron diffraction. Phys Rev B 67:220401(R)CrossRefGoogle Scholar
  39. 39.
    Papoular RJ, Gillon B (1990) Maximum entropy reconstruction of spin density maps in crystals from polarized neutron diffraction data. Europhys Lett 13:429–434CrossRefGoogle Scholar
  40. 40.
    Schleger P, Puig-Molina A, Ressouche E, Schweizer J (1997) A general maximum-entropy method for model-free reconstructions of magnetization densities from polarized neutron diffraction data. Acta Crystallogr A 53:426–435CrossRefGoogle Scholar
  41. 41.
    Brown PJ (2004) Experimental attempts to measure non-collinear local magnetization. J Phys Chem Solid 65:1977–1983CrossRefGoogle Scholar
  42. 42.
    Sakata M, Sato M (1990) Accurate structure analysis by the maximum-entropy method. Acta Crystallogr A 46:263–270CrossRefGoogle Scholar
  43. 43.
    Gukasov A, Braden M, Papoular RJ, Nakatsuji S, Maeno Y (2002) Anomalous spin-density distribution on oxygen and Ru in Ca1.5Sr0.5RuO4: polarized neutron diffraction study. Phys Rev Lett 89:087202CrossRefGoogle Scholar
  44. 44.
    Brown PJ (1992) Magnetic form factors. In: Wilson AJC (ed) International tables for crystallography, vol C. Kluwer, Dordrecht, pp 391–399Google Scholar
  45. 45.
    Clementi E, Roetti C (1974) Atom Data and Nucl Data Tab 14:177CrossRefGoogle Scholar
  46. 46.
    Hansen NK, Coppens P (1978) Testing aspherical atom refinements on small-molecule data sets. Acta Crystallogr A 34:909–921CrossRefGoogle Scholar
  47. 47.
    Brown PJ, Capiomont A, Gillon B, Schweizer J (1979) Spin densities in free radicals. J Mag Mag Mater 14:289–294CrossRefGoogle Scholar
  48. 48.
    Boucherle JX, Gillon B, Maruani J, Schweizer J (1982) Determination by polarized neutron diffraction of the spin density distribution in a non-centrosymmetrical crystal of DPPH:C6H6. J de Physique ColloqueC7 43:227–234Google Scholar
  49. 49.
    Coppens P (1997) X-ray charge densities and chemical bonding. IUCr texts on crystallography 4. Oxford University Press, Oxford/New YorkGoogle Scholar
  50. 50.
    Claiser N, Souhassou M, Lecomte C, Gillon B, Carbonera C, Caneschi A, Dei A, Gatteschi D, Bencini A, Pontillon Y, Lelièvre-Berna E (2005) Combined charge and spin density experimental study of the yttrium(III) semiquinonato complex Y(HBPz3)2(DTBSQ) and DFT calculations. J Phys Chem B 109:2723CrossRefGoogle Scholar
  51. 51.
    Holladay A, Leung P, Coppens P (1983) Generalized relations between d-orbital occupancies of transition metal atoms and electron-density multipole population parameters from X-ray diffraction data. Acta Crystallogr A 39:377CrossRefGoogle Scholar
  52. 52.
    Squires GL (1978) Introduction to the theory of thermal neutron scattering. University Press, Cambridge, p. 139Google Scholar
  53. 53.
    Kernavanois N, Grenier B, Huxley A, Ressouche E, Sanchez JP, Flouquet J (2001) Neutron scattering study of the ferromagnetic superconductor UGe2. Phys Rev B 64:174509CrossRefGoogle Scholar
  54. 54.
    Hiess A, Bourdarot F, Coad S, Brown PJ, Burlet P, Lander GH, Brooks MSS, Kaczorowski D, Czopnik A, Troc R (2001) Spin and orbital moments in itinerant magnets. Europhys Lett 55:267–272CrossRefGoogle Scholar
  55. 55.
    Prokes K, Gukasov A (2009) Magnetization densities in URhSi studied by polarized neutron diffraction. Phys Rev B 79:024406CrossRefGoogle Scholar
  56. 56.
    Brown PJ, Neumann KU, Simon A, Ueno F, Ziebeck KRA (2005) Magnetization distribution in CoS2; is it a half metallic ferromagnet? J Phys Condens Matter 17:1583–1592CrossRefGoogle Scholar
  57. 57.
    Schweizer J (1980) Interpretation of magnetization densities. In: Becker P (ed) Electron and magnetization densities in molecules and crystals, vol 48, NATO advanced study institutes series, series B: physics. Plenum Press, New York, pp 501–519Google Scholar
  58. 58.
    Gukasov A, Cao H, Mirebeau I, Bonville P (2009) Spin density and non-collinear magnetization in frustrated pyrochlore Tb2Ti2O7 from polarized neutron scattering. Phys B 404:2509–2512CrossRefGoogle Scholar
  59. 59.
    Gukasov AG, Rogl P, Brown PJ, Mihalik M, Menovsky A (2002) Site susceptibility tensors and magnetic structure of U3Al2Si3: a polarized neutron diffraction study. J Phys Condens Matter 14:8841–8851Google Scholar
  60. 60.
    Borta A, Gillon B, Gukasov A, Cousson A, Luneau D, Jeanneau E, Ciumacov I, Sakiyama H, Tone K, Mikuriya M (2011) Local magnetic moments in a dinuclear Co2 + complex as seen by polarized neutron diffraction: Beyond the effective spin-1/2 model. Phys Rev B 83:184429Google Scholar
  61. 61.
    Kumazawa S, Kubota Y, Takata M, Sakata M, Ishibashi Y (1993) MEED: a program package for electron-density-distribution calculation by the maximum-entropy method. J Appl Crystal 26:453–457CrossRefGoogle Scholar
  62. 62.
    Ressouche E, Boucherle JX, Gillon B, Rey P, Schweizer J (1993) Spin density maps in nitroxide-Copper(II) complexes. A polarized neutron diffraction determination. J Am Chem Soc 115:3610–3617CrossRefGoogle Scholar
  63. 63.
    Matthewman JC, Thompson P, Brown PJ (1982) The CCSL library. J Appl Crystallogr 15: 167–173; Brown PJ (2006) Cambridge crystallographic subroutine library. documentation on https://www.ill.eu/sites/ccsl/html/ccsldoc.html Google Scholar
  64. 64.
    Frontera C, Rodriguez-Carvajal J (2003) FullProf as a new tool for flipping ratio analysis. Phys B 335:219–222CrossRefGoogle Scholar
  65. 65.
    Kahn O (1993) Molecular magnetism. VVH Publishers, Inc., New YorkGoogle Scholar
  66. 66.
    Pontillon Y, Bencini A, Caneschi A, Dei A, Gatteschi D, Gillon B, Sangregorio C, Stride J, Totti F (2000) Spin density map of the triplet ground state of a Titanium(IV) complex with the Schiff base diquinone radical ligands: a polarized neutron diffraction and DFT investigation. Angew Chem Int Eng Ed 39:1786–1788CrossRefGoogle Scholar
  67. 67.
    Aebersold M, Gillon B, Plantevin O, Pardi L, Kahn O, Bergerat P, von Seggern I, Tuczek F, Öhrström L, Grand A, Lelièvre-Berna E (1998) Spin density maps in the triplet ground state of [Cu2(t-bupy)4(N3)2](ClO4)2 (t-bupy = p-tert-butylpyridine): a polarized neutron diffraction study. J Am Chem Soc 120:5238–5245CrossRefGoogle Scholar
  68. 68.
    Baron V, Gillon B, Plantevin O, Cousson A, Mathonière C, Kahn O, Grand A, Öhrström L, Delley B (1996) Spin density maps in an oxamido-bridged Mn(II)Cu(II) binuclear compound; polarized neutron diffraction and theoretical studies. J Am Chem Soc 118:11822–11830CrossRefGoogle Scholar
  69. 69.
    Kahn O, Mathonière C, Srinavasan B, Gillon B, Baron V, Grand A, Öhrström L, Ramashesha S (1997) Spin distributions in antiferromagnetically coupled Mn2+Cu2+ systems: from the pair to the infinite chain. New J Chem 21:1037–1045Google Scholar
  70. 70.
    Caneschi A, Gatteschi D, Sessoli R, Schweizer J (1998) Magnetization density in a Mn high-spin (S = 12) magnetic cluster. Phys B 241–243:600Google Scholar
  71. 71.
    Robinson RA, Brown PJ, Argyriou DN, Hendrickson DN, Aubin DMJ (2000) Internal magnetic structure of Mn12 acetate by polarized neutron diffraction. J Phys Condens Matter 12:2805–2810CrossRefGoogle Scholar
  72. 72.
    Pontillon Y, Caneschi A, Gatteschi D, Sessoli R, Ressouche E, Schweizer J, Lelièvre-Berna E (1999) Magnetization density in an iron(III) magnetic cluster. A polarized neutron investigation. J Am Chem Soc 121:5342CrossRefGoogle Scholar
  73. 73.
    Gillon B, Sangregorio C, Caneschi A, Gatteschi D, Sessoli R, Ressouche E, Pontillon Y (2007) Experimental spin density in the high spin ground state of the Fe8pcl cluster. Inorg Chim Acta 360:3802–3806CrossRefGoogle Scholar
  74. 74.
    Ruiz E, Rajaraman G, Alvarez S, Gillon B, Stride J, Clérac R, Larionova J, Decurtins S (2005) Symmetry and topology determine the MoV–CN–MnII exchange interactions in high-spin molecules. Angew Chem Int Ed 44:2711–2715CrossRefGoogle Scholar
  75. 75.
    Gillon B, Larionova J, Ruiz E, Nau Q, Goujon A, Bonadio F, Decurtins S (2008) Experimental and theoretical study of the spin ground state of the high-spin molecular cluster [NiII{NiII(CH3OH)3}8(μ-CN)30{WV(CN)3}6],15CH3OH by polarized neutron diffraction and density functional theory calculations. Inorg Chem Acta 361:3609–3615CrossRefGoogle Scholar
  76. 76.
    Zheludev A, Garlea VO, Nishina S, Hosokoshi Y, Cousson A, Gukasov A, Inoue K (2007) Spin-density distribution in the partially magnetized organic quantum magnet F2PNNNO. Phys Rev B 75:104427CrossRefGoogle Scholar
  77. 77.
    Decurtins S, Gütlich P, Hasselbach MK, Spiering H, Hauser A (1985) Light-induced excited-spin-state trapping in iron(II) spin-crossover systems. Optical spectroscopic and magnetic susceptibility study. Inorg Chem 24:2174CrossRefGoogle Scholar
  78. 78.
    Ogawa Y, Koshihara S, Koshino K, Ogawa T, Urano C, Takagi H (2000) Dynamical aspects of the photoinduced phase transition in spin-crossover complexes. Phys Rev Lett 84:3181CrossRefGoogle Scholar
  79. 79.
    Sato O, Iyoda T, Fujishima A, Hashimoto K (1996) Photoinduced magnetization of a cobalt-iron cyanide. Science 272:704CrossRefGoogle Scholar
  80. 80.
    Matsuda K, Machida A, Moritomo Y, Nakamura A (1998) Photoinduced demagnetization and its dynamical behavior in a (Nd0.5Sm0.5) 0.6Sr0.4MnO3 thin film. Phys Rev B 58:R4023CrossRefGoogle Scholar
  81. 81.
    Becker PJ, Coppens P (1985) About the simultaneous interpretation of charge and spin density data. Acta Crystallogr A 41:177–182CrossRefGoogle Scholar
  82. 82.
    Qureshi N, Zbiri M, Rodriguez-Carvajal J, Stunault A, Ressouche E, Hansen TC, Fernandez-Diaz T, Rodriguez-Valazaman J, Sanchez-Montero J, Johnson MR, Fuess H, Ehrenberg H, Sakurai Y, Itou M, Gillon B (2009) Experimental magnetic form factors in Co3V2O8: A combined study of ab initio calculations, magnetic Compton scattering and polarized neutron diffraction. Phys Rev B 79:094417CrossRefGoogle Scholar
  83. 83.
    Gillet JM (2007) Determination of a one-electron reduced density matrix using a coupled pseudo-atom model and a set of complementary scattering data. Acta Crystallogr A 63: 234–238CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Laboratoire Léon Brillouin (CEA-CNRS)Centre d’Etudes de SaclayGif-sur-Yvette, CedexFrance
  2. 2.Structures, Properties and Modelling of Solids (SPMS) LaboratoryEcole Centrale ParisChatenay-MalabryFrance

Personalised recommendations