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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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slide1

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

slide2

Condensed matter interest

  • Nuclear physics interest

Phys. Rev. B 62 (2000) 461

Hyperfine fields

Bhf

E = - ·B

slide3

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 )

slide4

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 ?
slide5

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

slide6

Morb

Mspin

Mtot

Morb

Mspin

Mtot

L

S

J

L

S

J

Effective moment of Ln3+ ions

Bext

slide7

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)

slide8

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)

slide9

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)

slide10

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)

slide11

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)

slide12

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

slide13

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

slide14

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

slide15

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

slide16

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 ?)

slide17

?

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

slide18

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