Correlation in Lanthanides

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Correlation in Lanthanides

• Erik Ylvisaker

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LDADMFT(HI)

• Construct auxilary isolated atom w/ same
  occupation
• Gk matrix includes 6s,6p,5d orbitals too.
  Self-energy only on 4fs.
• Solve self-consistently with occupation
• Two parameters U, ?f
• U is usual Hubbard U
• ?f handles double-counting
• J Exchange term?

Guess ?(?)
Use Gk(?) to get nf
Adjust ?at until nfat nf
Converged?
Calculate ?at
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Lanthanide Valency

• Most Lanthanides trivalent
• Yb and Eu divalent
• Large Molar Volume
• Small Bulk Modulus

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Yb Valence vs. Pressure

• Valence transition in agreement with experiment
• Vertical section volume collapse

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Idealized Hubbard Bands

• Usual Gap U-J
• Eu, Gd, Yb Gap U6J
• At n8, LHB picks up 7J

• ?0 linear in n
• U 6 eV, J 1 eV

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Calculation of Parameters

• U from constrained LDA

Yb
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Hubbard Bands (Real Parameters)

• No Exchange

• Exchange seems important for Eu and up.

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Effective U
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Valence vs. Pressure

• Adjusted ?f adjusted by 0.8 eV at all V
• Bad News
• Valence transition destroyed.
• Good News
• Volume collapse gone

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Yb Valence in DMFT(HI)

• Gradual transition predicted.
• Low T ? transition less complete.
• Valence goes back down at high pressures.
• Agrees with QMC at low pressure

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Summary

• Anisotropy parameter J important for 2nd half of
  Lanthanides
• Sensitivity to double-counting
• Reasonable agreement w/ experiment using good
  parameters