Hyperfine fields of Lanthanides and Actinides in Fe
- Slides: 18
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
Hyperfine fields Bhf • Condensed matter interest • Nuclear physics interest Phys. Rev. B 62 (2000) 461 E = - ·B
Moments and fields of the electron system Magnetic moment M Hyperfine field Bhf Mtot = Mspin + Morb Btot = Bspin + Borb + Bc Mspin = # up - # down Bspin = electron as bar magnet Borb = electron as current loop Bc = electrons in nucleus A I Morb L L = mrv uz r A = 2 r 2 uz v -e I = - ev/2 r Morb = - ev/r uz Borb = 0/4 r Morb Borb (if external field: Morb // Bext ) Sign: w. r. t. Bext that aligns the moments
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+U ?
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
Effective moment of Ln 3+ ions Morb Mspin Mtot Bext L S J Morb Mspin Mtot L S J
Lanthanides in Fe : experimental facts (1965 – 2003) La Ce Pr Nd Pm Eu Tb Ho Tm Lu Sm Gd Dy Er Yb Highly reliable, sign measured (NMR/ON, TDPAC)
Lanthanides in Fe : experimental facts (1965 – 2003) La Ce Pr Nd Pm Eu Tb Ho Tm Lu Sm Gd Dy Er Yb Highly reliable, sign measured (NMR/ON, TDPAC) Highly reliable, sign not measured (MS, TDPAC)
Lanthanides in Fe : experimental facts (1965 – 2003) La Ce Pr Nd Pm Eu Tb Ho Tm Lu Sm Gd Dy Er Yb Highly reliable, sign measured (NMR/ON, TDPAC) Highly reliable, sign not measured (MS, TDPAC) Rather reliable, sign not measured (LTNO)
Lanthanides in Fe : experimental facts (1965 – 2003) La Ce Pr Nd Pm Eu Tb Ho Tm Lu Sm Gd Dy Er Yb 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)
Lanthanides in Fe : experimental facts (1965 – 2003) La Pr Pm Eu Tb Ho Tm Lu Ce Nd Sm Gd Dy Er Yb Standard interpretation (unquestioned since 1965) Mspin(Ln) antiparallel to Mspin(Fe) Morb Mspin Mtot La Pr Pm Eu Tb Ho Tm Lu Ce Nd Sm Gd Dy Er Yb = what we really know.
Computational details 16 -atom supercell Rmt. Kmax= 7. 5 k-mesh = 10 x 10 (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
Mspin Morb La Pr Pm Eu Tb Ho Tm Lu Ce Nd Sm Gd Dy Er Yb Mtot La Pr Pm Eu Tb Ho Tm Lu Ce Nd Sm Gd Dy Er Yb Epara - Eanti La Pr Pm Eu Tb Ho Tm Lu Ce Nd Sm Gd Dy Er Yb
Bc and Bspin Borb Btot La Pr Pm Eu Tb Ho Tm Lu Ce Nd Sm Gd Dy Er Yb La Pr Pm Eu Tb Ho Tm Lu Ce Nd Sm Gd Dy Er Yb
Comparison with experiment La Ce Pr Nd Pm Eu Tb Ho Tm Lu Sm Gd Dy Er Yb What we know Mspin Morb La Ce Pr Nd Pm Eu Tb Ho Tm Lu Sm Gd Dy Er Yb Reinterpretation of experimental systematics La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
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 ? )
What can be expected from U ? U=0. 5 U=0. 4 ? La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
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 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
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