5 f magnetism and its specific features

1. 5f magnetism and its specific features Ladislav Havela Charles University, Prague Czech Republic Yk-Workshop on Magnetism in Complex Systems Vienna 2009

2. Outline • Actinides - 5f (de)localization – between 3d and 4f • + strong s-o interaction • 2. Development of the localization throughout • the series • 3. Where magnetism appears (U) .. Specific features • of the 5f magnetism – exchange, anisotropy • 4. …and where it disappears (Pu)…5f occupancy • Character of the 5f states seen by different methods

3. Smith-Kmetko periodic tableof transition elements

4. Light actinides - Pauli paramagnets (exchange enhanced) Heavy actinides - ionic magnetism; “Hund’s rules” - but strong s-o coupling leads to j-j coupling

6. Th Pa U Np Pu Am….. g (mJ/mol K2) 4 6.6 10 14 22 2 0 (10-8 m3/mol) 0.12 0.34 0.48 0.68 0.64 0.85 • Cm Bk Cf Es • TN (K) 64 34 51 (TC) • meff (mB) 7.55 9.7 9.7 11.3 (?)

8. Hill limit separating the magnetic and superconducting regimes H.H. Hill, Plutonium and Other Actinides, Santa Fe 1970 THE EARLY “ACTINIDES”: THE PERIODIC SYSTEM’S f ELECTRON TRANSITION METAL SERIES Minimum inter-atomic spacing for appearance of magnetism Ce……...3.4 Å U……….3.4-3.6 Å Np……..3.25 Å Pu……..3.4 Å

9. U compounds –large variety of magnetic properties (Np parallel, Pu not..) Weak paramagnets – low g, approaching magnetic ordering (spin fluctuations) – g enhancement --> 5f band intersected by the Fermi level 5f-5f overlap…..U-U spacing…..Hill criterion Superconductiong Magnetic a-U U6Mn, U6Fe, U6Co, U6Ni…Tc < 3.7 K U3Ir U3Si2 UPt, UIr – ferro UFe2, UNi2 (Laves ph.) – Ferro UGa2 - Ferro UGa2, UIn3, UPt3 AF UPd3 UCu5, U2Zn17, UBe13

10. Exceptions – large dU-U …non-magnetic UAl3, UNi5 Other mechanism must be in the game – 5f hybridization with electronic states of ligands

11. Other mechanisms of delocalization suppress magnetism (in U, Np): hybridization of 5f states with ligand states. In compounds with transition metals, mutual position (given by different electronegativity) is decisive

12. Features of 5f-band magnetism: 1. Large orbital moments in itinerant systems

13. Features of 5f-band magnetism: 2. Anisotropic hybridization-induced exchange interaction: • stronger than conventional RKKY in strong f-bonding directions (if those can be specified), ferromagnetic • UGa2 – Tc = 126 K, GdGa2, TN = 12 K. • perpendicular to it weaker, ferro- or antiferromagnetic

14. Relation of actinide magnetism with the 5f band width – density of states at EF (concept of the d-magnetism, i.e. itinerant one) • Curie-Weiss law c 1/(T – Qp) • Spin waves E Dq2, D  T5/2….Bloch law • Near TC – critical behaviour c  1/(T-TC)4/3 …Heisenberg system • Resistivity – spin disorder scattering…..disordered moments above TC • Where the itinerant nature is manifest? • Ordered moments are in no relation to Hund’s rules • meff and ms apparently uncorrelated. Low magnetic entropy S < Rln2.. • Fast decrease of Tc by pressure

15. Features of 5f-band magnetism: 2. Giant anisotropy (hybridization-induced two-ion anisotropy)

16. Ising ferromagnets from easy-axis spin fluctuators Local moments from band states - no localized 5f states 5f band at EF (specific heat, PES) - except UPd3

17. Pressure effects 2 band model needed

18. For low J: RKKY wins For large J: Kondo wins

20. Electrical resistivity • Matthiessen’s rule tot = 0 + ph-e + e-e+spd

21. Antiferromagnet Sublattice magnetization Truncation factor – captures a possible gapping of the Fermi surface by additionalBZ boundaries in AF state

22. Hexagonal structure- ZrNiAl type

23. Upturn due to the Fermi sufrace gapping

24. Large superzone boundary gapping results of of strong coupling of direction of U moments and conduction electron sub-system… …also other features as large Kerr rotation due to large orbital moments

25. meff (mB) ms (mB) meff (mB) ms (mB) LS coupling intermediate coupling f3 3.62 3.27 3.68 3.33f4 2.68 2.40 2.75 2.46f5 0.85 0.71 1.01 0.86f6 0 0 Np - quite analogous to U, suggesting the same mechanisms at work Pu??? Free Pu ion - 5f6 Pu ion in solid - 5f5 (Johansson and Rosengren 1975) Pu solid in conventional band theory - 5fn, n 5.0 (magnetic)

26. d-Pu has low and very weakly temperature dependent susceptibility • Olsen 1992 • Fradin and Brodsky 1970 27Al NMR • Piskunov et al., PRB 71 (2005) 174410 69Ga NMR • Lashley et al. PRB 72 (2005) 054416 specific heat, neutron diffraction, scattering • Heffner et al. m+SR Physica B 374 (2006) 163 NO MAGNETISM!

27. Neither expansion makes any significant difference in c0. There cannot be any narrow band at EF - expansion would lead to a further narrowing But there is a high g coefficient of specific heat in d-Pu (53±10) mJ/mol K2Stewart and Elliott 1981 (64±3) mJ/mol K2Lashley et al. 2003 (41±1) mJ/mol K2 Havela et al. 2009

28. 5f5 - 5f6 (suggested e.g. by volume) 5f5

29. U Np Pu U Np Pu PuPt2 - TC = 6 K, m = 0.2 mB Also PuPt - TN = 44 K PuPt3 - TN = 40 K, meff = 1.3 mB/f.u. PuPd3 - TN = 24 K, meff = 1.0 mB/f.u. PuGa3 - TN = 24 K, meff = 0.78 mB/f.u. TC = 20 K, m = 0.2 mB/f.u. Suggestion A transfer from 5f states necessary to reach magnetic state in Pu. Does it mean that pure Pu has more 5f electrons?

30. Localization in the sequence of actinides observed by photoelectron spectroscopy

31. 5f

34. One trick to bridge the area between localized and itinerant behaviour is the Mixed level Model (MLM). It assumes integral 5f occupancy of localized states plus some itinerant 5f states. O. Eriksson, J.D. Becker, A.V. Balatsky, J.M. Wills, J.Alloys Comp. 287 (1999) 1 Conclude the 5f4 localized manifold plus  1 5f electron in itinerant states But Pu is quite stable against any attempt to make it magnetic! MLM and LDA, GGA…all lead to magnetic ground state L(S)DA+U “around mean field” calculations A.B. Shick, V. Drchal, L. Havela, Europhys. Lett. 69 (2005) 588 A.O. Shorikov, A.V. Lukoyanov, M.A. Korotin, and V.I. Anisimov, Phys.Rev.B 72 (2005) 024458 Conclude that n5f > 5.0 for d-Pu.

36. Am a reduced to 94.7% • Pu volume expands by 7 % for 30% Am • Am at 6.5 GPaa = 4.613 Å

37. Pu3Am LSDA+U+Hubbard I - open 5f shell embedded in the sea of conduction electrons spectral density

38. Can LDA+U calculations pick up the onset of magnetism when going from PuSe or PuTe to PuSb? PuSb - ferro state, 5f5 with ordered moment 0.75 mB/Pu G.H. Lander, A. Delapalme, P.J. Brown, J.C. Spirlet, L. Rebizant, O. Vogt, Phys.Rev.Lett. 53 (1984) 2262 Pu moments fast collapse in the Pu(Sb,Te) system K. Mattenberger et al., J.Less Common. Met 121 (1986) 285 Calculations: n5f = 5.2 - total magnetic moment 0.76 mB/Pu !!! In PuTe n5f = 5.68, m= 0

39. The 3 peaks reflect the 5f6 admixture into the 5f5 states. Beyond n5f non-magnetic on LDA+U level

40. Conclusions • U magnetism with large orbital moments and huge anisotropy has too low Tc to offer any room temperature applications. Hope in thin-films and other artificial structures combined with 3d metals. • To have U compounds magnetic: • - 5f band must be narrow and populated as much as possible • Large dU-U, compound with late transition metals with the d-states far below EF (d-band filled close to top) or with large p-metals • 3. To have Pu compounds magnetic: • - 5f states must be little depopulated to move away from non-magnetic 5f6. • (too high admixture of 5f6 suppresses magnetism even if dU-U is large)