EMR-related problems at the interface between the crystal field Hamiltonians and the zero-field splitting Hamiltonians

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The interface between optical spectroscopy, electron magnetic resonance (EMR), and magnetism of transition ions forms the intricate web of interrelated notions. Major notions are the physical Hamiltonians, which include the crystal field (CF) (or equivalently ligand field (LF)) Hamiltonians, and the effective spin Hamiltonians (SH), which include the zero-field splitting (ZFS) Hamiltonians as well as to a certain extent also the notion of magnetic anisotropy (MA). Survey of recent literature has revealed that this interface, denoted CF (LF) ↔ SH (ZFS), has become dangerously entangled over the years. The same notion is referred to by three names that are not synonymous: CF (LF), SH (ZFS), and MA. In view of the strong need for systematization of nomenclature aimed at bringing order to the multitude of different Hamiltonians and the associated quantities, we have embarked on this systematization. In this article, we do an overview of our efforts aimed at providing a deeper understanding of the major intricacies occurring at the CF (LF) ↔ SH (ZFS) interface with the focus on the EMR-related problems for transition ions.

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  • 1. Figgis B. N. & Hitchman M. A. (2000). Ligand field theory and its applications. New York: Wiley-VCH.

  • 2. Mulak J. & Gajek Z. (2000). The effective crystal field potential. Amsterdam: Elsevier.

  • 3. Newman D. J. & Ng B. (Eds.) (2000). Crystal field handbook. Cambridge: Cambridge University Press.

  • 4. Wildner M. Andrut M. & Rudowicz C. (2004). Optical absorption spectroscopy in geosciences. Part I: Basic concepts of crystal field theory. In A. Beran & E. Libowitzky (Eds.) Spectroscopic methods in mineralogyEuropean Mineralogical Union Notes in Mineralogy. (Vol. 6 Chapter 3 pp. 93–143). Budapest: Eötvös University Press.

  • 5. Liu G. & Jacquier B. (Eds.). (2005). Spectroscopic properties of rare earths in optical materials. Berlin: Tsinghua University Press and Springer.

  • 6. Weil J. A. Bolton J. R. & Wertz J. E. (1994). Electron paramagnetic resonance elemental theory and practical applications. New York: Wiley.

  • 7. Bencini A. & Gatteschi D. (1990). EPR of exchange coupled systems. Berlin: Springer.

  • 8. Mabbs F. E. & Collison D. (1992). Electron paramagnetic resonance of d transition-metal compounds. Amsterdam: Elsevier.

  • 9. Misra S. K. (Ed.) (2011). Multifrequency electron paramagnetic resonance. Weinheim: Wiley-VCH.

  • 10. Boča R. (1999). Theoretical foundations of molecular magnetism. Amsterdam: Elsevier.

  • 11. Buschow K. H. J. & de Boer F. R. (2003). Physics of magnetism and magnetic materials. New York: Kluwer Academic.

  • 12. Boča R. (2006). Magnetic parameters and magnetic functions in mononuclear complexes beyond the spin-Hamiltonian formalism. Struct. Bond. 117 1–264.

  • 13. Gatteschi D. Sessoli R. & Villain J. (2006). Molecular nanomagnets. Oxford: Oxford University Press.

  • 14. Rudowicz C. & Karbowiak M. (2014). Terminological confusions and problems at the interface between the crystal field Hamiltonians and the zero-field splitting Hamiltonians – survey of the CF=ZFS confusion in recent literature. Physica B451 134–150.

  • 15. Rudowicz C. & Karbowiak M. (2015). Revealing the consequences and errors of substance arising from the inverse confusion between the crystal (ligand) field quantities and the zero-field splitting ones. Physica B456 330–338.

  • 16. Sorace L. Benelli C. & Gatteschi D. (2011). Lanthanides in molecular magnetism: old tools in a new field. Chem. Soc. Rev. 40 3092–3104.

  • 17. Rudowicz C. & Karbowiak M. (2015). Disentangling intricate web of interrelated notions at the interface between the physical (crystal field) Hamiltonians and the effective (spin) Hamiltonians. Coord. Chem. Rev. 287 28–63.

  • 18. Baldoví J. J. Cardona-Serra S. Clemente-Juan J. M. Coronado E. Gaita-Arino A. & Palii A. (2013). SIMPRE: A software package to calculate crystal field parameters energy levels and magnetic properties on mononuclear lanthanoid complexes based on charge distributions. J. Comput. Chem.34 1961–1967.

  • 19. Pandey S. & Kripal R. (2013). Zero-field splitting parameters of Cr3+ in lithium potassium sulphate at orthorhombic symmetry site. Acta Phys. Pol. A123 101–105.

  • 20. Rudowicz C. & Karbowiak M. (2014). Implications of invalid conversions between crystal-field splitting ones used in superposition model. Acta Phys. Pol. A125 1215–1219.

  • 21. Karbowiak M. & Rudowicz C. (2014). Software package SIMPRE – revisited. J. Comput. Chem. 35 1935–1941.

  • 22. Solano-Peralta A. Sosa-Torres M. E. Flores-Alamo M. El-Mkami H. Smith G. M. Toscano R. A. & Nakamura T. (2004). High-field EPR study and crystal and molecular structure of trans-RSSR-[CrCl2 (cyclam).] nX (X = ZnCl 4 2− Cl and Cl·4H2O·0.5HCl). Dalton Trans.2004 2444–2449.

  • 23. Kowalczyk R. M. Kemp T. F. Walker D. Pike K. J. Thomas P. A. Kreisel J. Dupree R. Newton M. E. Hanna J. V. & Smith M. E. (2011). A variable temperature solid-state nuclear magnetic resonance electron paramagnetic resonance and Raman scattering study of molecular dynamics in ferroelectric fluorides. J. Phys.-Condens. Matter 23 315402(16pp).

  • 24. Muralidhara R. S. Kesavulu C. R. Rao J. L. Anavekar R. V. & Chakradhar R. P. S. (2010). EPR and optical absorption studies of Fe3+ ions in sodium borophosphate glasses. J. Phys. Chem. Solids71 1651–1655.

  • 25. Padlyak B. V. Wojtowicz W. Adamiv V. T. Burak Y. V. & Teslyuk I. M. (2010). EPR spectroscopy of the Mn2+ and Cu2+ centres in lithium and potassium-lithium tetraborate glasses. Acta Phys. Pol. A117 122–125.

  • 26. Singh R. K. & Srinivasan A. (2010). EPR and magnetic susceptibility studies of iron ions in ZnOFe2 O3-SiO2-CaO-P2O5-Na2O glasses. J. Magn. Magn. Mater.322 2018–2022.

  • 27. Antal A. Janossy A. Forro L. Vertelman E. J. M. van Koningsbruggen P. J. & van Loosdrecht P. H. M. (2010). Origin of the ESR spectrum in the Prussian blue analog RbMn[Fe(CN)6]·H2O. Phys. Rev. B82 14422(5pp).

  • 28. Nagy K. L. Quintavalle D. Feher T. & Janossy A. (2011). Multipurpose high-frequency ESR spectrometer for condensed matter research. Appl. Magn. Reson.40 47–63.

  • 29. Nagy K. L. Náfrádi B. Kushch N. D. Yagubskii E. B. Herdtweck E. Fehér T. Kiss L. F. Forró L. & Jánossy A. (2009). Multifrequency ESR in ET2 MnCu[N(CN)2]4: A radical cation salt with quasi-two-dimensional magnetic layers in a three-dimensional polymeric structure. Phys. Rev. B80 104407(8pp).

  • 30. Aleshkevych P. Fink-Finowicki J. Gutowski M. & Szymczak H. (2010). EPR of Mn2+ in the kagomé staircase compound Mg2.97Mn0.03V2O8. J. Magn. Reson.205 69–74.

  • 31. Garcia F. A. Venegas P. A. Pagliuso P. G. Rettori C. Fisk Z. Schlottmann P. & Oseroff S. B. (2011). Thermally activated exchange narrowing of the Gd3+ ESR fine structure in a single crystal of Ce1-xGdxFe4P12 (x ≈ 0.001) skutterudite. Phys. Rev. B84 125116(7pp).

  • 32. Güler S. Rameev B. Khaibullin R. I. Lopatin O. N. & Aktaş B. (2010). EPR study of Mn-implanted single crystal plates of TiO2 rutile. J. Magn. Magn. Mater.322 L13–L17.

  • 33. Schweiger A. & Jeschke G. (2001). Principles of pulse electron paramagnetic resonance. Oxford: Oxford University Press.

  • 34. Gerson F. & Huber W. (2003). Electron spin resonance spectroscopy of organic radicals. Weinheim: Wiley-VCH.

  • 35. Kaupp M. Buhl M. & Malkin V. G. (2004). Calculation of NMR and EPR parameters. Weinheim: Wiley-VCH.

  • 36. Lushington G. H. (2004). The effective spin Hamiltonian concept from a quantum chemical perspective. In M. Kaupp M. Buhl & V. G. Malkin (Eds.) Calculation of NMR and EPR parameters (Chapter 4). Weinheim: Wiley-VCH.

  • 37. Neese F. (2004). Zero-field splitting. In M. Kaupp M. Buhl & V. G. Malkin (Eds.) Calculation of NMR and EPR parameters (Chapter 34). Weinheim: Wiley-VCH.

  • 38. Mobius K. & Savitsky A. (2009). High-field EPR spectroscopy on proteins and their model systems characterization of transient paramagnetic states. Cambridge: The Royal Society of Chemistry.

  • 39. Jeschke G. & Schlick S. (2006). Continuous-wave and pulsed ESR methods. In S. Schlick (Ed.) Advanced ESR methods in polymer research. New Jersey USA: John Wiley & Sons.

  • 40. Rudowicz C. (2008). Clarification of the confusion concerning the crystal-field quantities vs. the zero-field splitting quantities in magnetism studies: Part II – survey of literature dealing with model studies of spin systems. Physica B403 2312–2330.

  • 41. Rudowicz C. & Sung H. W. F. (2001). Can the electron magnetic resonance (EMR) techniques measure the crystal (ligand) field parameters? Physica B300 1–26.

  • 42. Rudowicz C. (2009). Truncated forms of the second-rank orthorhombic Hamiltonians used in magnetism and electron magnetic resonance (EMR) studies are invalid – why it went unnoticed for so long? J. Magn. Magn. Mater.321 2946–2955.

  • 43. Rieger P. H. (2007). Electron spin resonance analysis and interpretation. Cambridge: The Royal Society of Chemistry.

  • 44. Lund A. Shiotani M. & Shimada S. (2011). Principles and applications of ESR spectroscopy. Dordrecht: Springer Science+Business Media B.V.

  • 45. Brustolon M. & Giamello E. (2009). Electron paramagnetic resonance: A practitioner’s toolkit. New Jersey USA: John Wiley & Sons.

  • 46. Tang J. K. Wang Q. L. Si S. F. Liao D. Z. Jiang Z. H. Yan S. P. & Cheng P. (2005). A novel tetranuclear lanthanide(III)-copper(II) complex of the macrocyclic oxamide [PrCu3](macrocyclic oxamide = 14811-tetraazacyclotradecanne-23-dione): synthesis structure and magnetism. Inorg. Chim. Acta358 325–330.

  • 47. Li B. Gu W. Zhang L. Z. Qu J. Ma Z. P. Liu X. & Liao D. Z. (2006). [Ln2(C2O4)2 (pyzc)2 (H2O)2]n[Ln = Pr (1) Er (2)]: Novel two-dimensional lanthanide coordination polymers with 2-pyrazinecarboxylate and oxalate. Inorg. Chem. 45 10425–10427.

  • 48. Ouyang Y. Zhang W. Xu N. Xu G. F. Liao D. Z. Yoshimura K. Yan S. P. & Cheng P. (2007). Threedimensional 3d-4f polymers containing heterometallic rings: Syntheses structures and magnetic properties. Inorg. Chem.46 8454–8456.

  • 49. Xu N. Shi W. Liao D. Z. Yan S. P. & Cheng P. (2008). Template synthesis of lanthanide (Pr Nd Gd) coordination polymers with 2-hydroxynicotinic acid exhibiting ferro-/antiferromagnetic interaction. Inorg. Chem.47 8748–8756.

  • 50. Hou Y. L. Xiong G. Shen B. Zhao B. Chen Z. & Cui J. Z. (2013). Structures luminescent and magnetic properties of six lanthanide–organic frameworks: observation of slow magnetic relaxation behavior in the DyIII compound. Dalton Trans.42 3587–3596.

  • 51. AlDamen M. A. Cardona-Serra S. Clemente-Juan J. M. Coronado E. Martí-Gastaldo C. Gaita-Arino A. Luis F. & Montero O. (2009). Mononuclear lanthanide single molecule magnets based on the polyoxometalates [Ln(W5O18)2]9− and [Ln(β2-SiW11O39)2]13-(LnIII = Tb Dy Ho Er Tm and Yb). Inorg. Chem.48 3467–3479.

  • 52. Luzon J. Bernot K. Hewitt I. J. Anson C. E. Powell A. K. & Sessoli R. (2008). Spin chirality in a molecular dysprosium: the archetype of the noncollinear ising model. Phys. Rev. Lett.100 247205(4pp).

  • 53. Bartolomé J. Filoti G. Kuncser V. Schinteie G. Mereacre V. Anson C. E. Powell A. K. Prodius D. & Turta C. (2009). Magnetostructural correlations in the tetranuclear series of {Fe3LnO2} butterfly core clusters: magnetic and Mössbauer spectroscopic study. Phys. Rev. B80 014430(16pp).

  • 54. Pointillart F. Le Guennic B. Golhen S. Cador O. Maury O. & Ouahab L. (2013). High nuclearity complexes of lanthanide involving tetrathiafulvalene ligands: structural magnetic and photophysical properties. Inorg. Chem.52 1610–1620.

  • 55. Bayrakçeken F. Demir O. J. & Karaaslan İ. Ş. (2007). Theoretical investigations of the specific heat functions for the orthorhombic Nd+3 centers in some crystals. Spectrochim. Acta Part A66 462–466.

  • 56. Bayrakçeken F. Demir O. J. & Karaaslan İ. Ş. (2007). Specific heat functions for the orthorhombic Nd3+ in scheelite type of crystals. Spectrochim. Acta Part A66 1291–1294.

  • 57. Kim Y. H. Yeom T. H. Eguchi H. & Seidel G. M. (2007). Magnetic properties of erbium in single crystal Bi2Te3. J. Magn. Magn. Mater.310 1703–1705.

  • 58. Pedersen K. S. Ungur L. Sigrist M. Sundt A. Schau-Magnussen M. Vieru V. Mutka H. Rols S. Weihe H. Waldmann O. Chibotaru L. F. Bendix J. & Dreiser J. (2014). Modifying the properties of 4f single-ion magnets by peripheral ligand functionalisation. Chem. Sci.5 1650–1660.

  • 59. Rudowicz C. (2008). Clarification of terminological confusion concerning the crystal field quantities vs the effective spin Hamiltonian and zero-field splitting quantities in the papers by Bayrakçeken et al. [Spectrochim. Acta Part A 66 (2007). 462 & 1291]. Spectrochim. Acta Part A71 1623–1626.

  • 60. Baldoví J. J. Cardona-Serra S. Clemente-Juan J. M. Coronado A. Gaita-Ariñ o A. & Palii A. (2012). Rational design of single-ion magnets and spin qubits based on mononuclear lanthanoid complexes. Inorg. Chem.51 12565–12574.

  • 61. Baldoví J. J. Borrás-Almenar J. J. Clemente-Juan J. M. Coronado E. & Gaita-Ariño A. (2012). Modeling the properties of lanthanoid single-ion magnets using an effective point-charge approach. Dalton Trans.41 13705–13710.

  • 62. Baldoví J. J. Cardona-Serra S. Clemente-Juan J. M. Coronado E. & Gaita-Ariño A. (2013). Modeling the properties of uranium-based single ion magnets. Chem. Sci.4 938–946.

  • 63. Baldoví J. J. Clemente-Juan J. J. Coronado E. & Gaita-Ariñ o A. (2013). Two pyrazolylborate dysprosium(III) and neodymium(III) single ion magnets modeled by a radial effective charge approach. Polyhedron66 39–42.

  • 64. Yamashita A. Watanabe A. Akine S. Nabeshima T. Nakano M. Yamamura T. & Kajiwara T. (2011). Wheel-shaped ErIIIZnII 3 single-molecule magnet: A macrocyclic approach to designing magnetic anisotropy. Angew. Chem. Int. Ed.50 4016–4019.

  • 65. Chilton N. F. (2013). PHI User Manual v1.7.

  • 66. Clemente-Juan J. M. Coronado E. & Gaita-Arino A. (2012). Magnetic polyoxometalates: from molecular magnetism to molecular spintronics and quantum computing. Chem. Soc. Rev. 41 7464–7478.

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