1. Hyperfine fields of Lanthanides (and Actinides) in Fe: preliminary results and interpretations Nuclear condensed matter physics University of Leuven D. Torumba S. Cottenier M. Rots

2. Hyperfine fields  B hf Phys. Rev. B 62 (2000) 461 Condensed matter interest Nuclear physics interest E = -  ·B

3. Moments and fields of the electron system Magnetic moment M M tot = M spin + M orb M spin = # up - # down r v -e A L B orb M orb I L = mrv u z A = 2  r 2 u z I = - ev/2  r M orb = - ev/r u z B orb =  0 /4  r M orb (if external field: M orb // B ext ) Hyperfine field B hf B tot = B spin + B orb + B c B spin = electron as bar magnet B orb = electron as current loop B c = electrons in nucleus Sign: w.r.t. B ext that aligns the moments

4. What is special (or difficult) for lanthanides and actinides in Fe ? They are heavy For cubic point symmetry : B spin = B orb = 0 Heavy  Relativistic effects  SO-coupling  cubic symmetry broken  B orb and B spin not zero B orb is dominant (for transition metals: B c dominant) They show strong electron correlations f-orbitals are spatially localized  strong correlation effects correlation only partially described by LDA  LDA+U ?

5. Atomic physics : free lanthanide ions and Hund’s rules Hund 1 : maximize |S| Hund 2 : maximize L Hund 3 : 0 – 7 f-electrons: J=L-S 8 – 14 f-electrons: J=L+S

6. M orb M spin M tot LSJ M orb M spin M tot LSJ B ext Effective moment of Ln 3+ ions

7. Lanthanides in Fe : experimental facts (1965 – 2003) Highly reliable, sign measured (NMR/ON, TDPAC) LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm

8. Lanthanides in Fe : experimental facts (1965 – 2003) Highly reliable, sign measured (NMR/ON, TDPAC) Highly reliable, sign not measured (MS, TDPAC) LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm

9. Lanthanides in Fe : experimental facts (1965 – 2003) Highly reliable, sign measured (NMR/ON, TDPAC) Highly reliable, sign not measured (MS, TDPAC) Rather reliable, sign not measured (LTNO) LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm

10. Lanthanides in Fe : experimental facts (1965 – 2003) Highly reliable, sign measured (NMR/ON, TDPAC) Highly reliable, sign not measured (MS, TDPAC) Rather reliable, sign not measured (LTNO) Rather unreliable, sign measured (IPAC) LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm x

11. Lanthanides in Fe : experimental facts (1965 – 2003) Standard interpretation (unquestioned since 1965) M spin (Ln) antiparallel to M spin (Fe) M orb M spin M tot LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm = what we really know. LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm M orb M spin M tot

12. Computational details 16-atom supercell R mt K max = 7.5 k-mesh = 10x10x10 (75 in IBZ) Relaxation of nn for Eu, then fixed SO included, with RLO LDA (see soon: LDA+U) Initial Ln spin moment: parallel, zero, antiparallel

13. M spin M orb M tot E para - E anti LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm

14. B c and B spin B orb B tot LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm

15. What we knowReinterpretation of experimental systematics La Ce Pr NdPm SmEu Gd Tb Dy HoErTmYbLu M spin M orb LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm Comparison with experiment LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm

16. Improving on correlation: LDA+U (work in progress) Agreement if : U=0.4 Ry U=0.5 Ry Applying U increases an already positive orbital contribution. (What for initially negative contributions ?) Eu Er

17. La Ce Pr NdPm SmEu Gd Tb Dy HoErTmYbLu U=0.4 U=0.5 ? LaPrPmEuTbHoTmLu Ce NdGdDy ErYb Sm What can be expected from U ?

18. Conclusions LDA+SO suggests an ferromagnetic Ln-Fe coupling for Dy-Yb, in contrast to common belief (needs further verification with LDA+U) Values of hff are reasonably reproduced by LDA+SO, applying LDA+U looks promising LDA+U on all cases Free lanthanide atoms, as a comparison efg (without RLO) A similar study on Actinides in Fe Scanning literature for nuclear physics implications We continue with :