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Hyperfine fields of Lanthanides (and Actinides) in Fe: preliminary results and interpretations

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. Condensed matter interest Nuclear physics interest. Phys. Rev. B 62 (2000) 461. Hyperfine fields.

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Hyperfine fields of Lanthanides (and Actinides) in Fe: preliminary results and interpretations

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

  3. Hyperfine field Bhf Btot = Bspin + Borb + Bc Bspin = electron as bar magnet Borb = electron as current loop Bc = electrons in nucleus Sign: w.r.t. Bext thataligns the moments Moments and fields of the electron system Magnetic moment M Mtot = Mspin + Morb Mspin = # up - # down L A L = mrv uz A = 2r2 uz I = - ev/2r Morb = - ev/r uz Borb = 0/4r Morb r I v -e Morb Borb (if external field: Morb // Bext )

  4. What is special (or difficult) for lanthanides and actinides in Fe ? They are heavy • For cubic point symmetry : Bspin = Borb = 0 • Heavy  Relativistic effects  SO-coupling  cubic symmetry broken  Borb and Bspin not zero Borb is dominant (for transition metals: Bc 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. Morb Mspin Mtot Morb Mspin Mtot L S J L S J Effective moment of Ln3+ ions Bext

  7. La Pr Pm Eu Tb Ho Tm Lu Nd Sm Gd Dy Ce Er Yb Lanthanides in Fe : experimental facts (1965 – 2003) Highly reliable, sign measured (NMR/ON, TDPAC)

  8. La Pr Pm Eu Tb Ho Tm Lu Nd Sm Gd Dy Ce Er Yb Lanthanides in Fe : experimental facts (1965 – 2003) Highly reliable, sign measured (NMR/ON, TDPAC) Highly reliable, sign not measured (MS, TDPAC)

  9. La Pr Pm Eu Tb Ho Tm Lu Nd Sm Gd Dy Ce Er Yb 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)

  10. La Pr Pm Eu Tb Ho Tm Lu Nd Sm Gd Dy Ce Er Yb 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) x Rather unreliable, sign measured (IPAC)

  11. La La Pr Pr Pm Pm Eu Eu Tb Tb Ho Ho Tm Tm Lu Lu Nd Nd Sm Sm Gd Gd Dy Dy Ce Ce Er Er Yb Yb = what we really know. Morb Mspin Mtot Morb Mspin Mtot Lanthanides in Fe : experimental facts (1965 – 2003) Standard interpretation(unquestioned since 1965) Mspin(Ln) antiparallel to Mspin(Fe)

  12. Computational details 16-atom supercell RmtKmax= 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. La La La La La La La Pr Pr Pr Pr Pr Pr Pr Pm Pm Pm Pm Pm Pm Pm Eu Eu Eu Eu Eu Eu Eu Tb Tb Tb Tb Tb Tb Tb Ho Ho Ho Ho Ho Ho Ho Tm Tm Tm Tm Tm Tm Tm Lu Lu Lu Lu Lu Lu Lu Nd Nd Nd Nd Nd Nd Nd Sm Sm Sm Sm Sm Sm Sm Gd Gd Gd Gd Gd Gd Gd Dy Dy Dy Dy Dy Dy Dy Ce Ce Ce Ce Ce Ce Ce Er Er Er Er Er Er Er Yb Yb Yb Yb Yb Yb Yb Mspin Morb Mtot Epara - Eanti

  14. La La La La La La Pr Pr Pr Pr Pr Pr Pm Pm Pm Pm Pm Pm Eu Eu Eu Eu Eu Eu Tb Tb Tb Tb Tb Tb Ho Ho Ho Ho Ho Ho Tm Tm Tm Tm Tm Tm Lu Lu Lu Lu Lu Lu Nd Nd Nd Nd Nd Nd Sm Sm Sm Sm Sm Sm Gd Gd Gd Gd Gd Gd Dy Dy Dy Dy Dy Dy Ce Ce Ce Ce Ce Ce Er Er Er Er Er Er Yb Yb Yb Yb Yb Yb Bc and Bspin Borb Btot

  15. La La Pr Pr Pm Pm Eu Eu Tb Tb Ho Ho Tm Tm Lu Lu Nd Nd Sm Sm Gd Gd Dy Dy Ce Ce Er Er Yb Yb Ce Nd Pm Gd Dy La Pr Sm Eu Tb Ho Er Tm Yb Lu Comparison with experiment What we know Reinterpretation ofexperimental systematics Mspin Morb

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

  17. ? La Pr Pm Eu Tb Ho Tm Lu Nd Sm Gd Dy Ce Er Yb Ce Nd Pm Gd Dy La Pr Sm Eu Tb Ho Er Tm Yb Lu What can be expected from U ? U=0.5 U=0.4

  18. We continue with : • 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 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

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