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Correlation in Lanthanides

Correlation in Lanthanides. Erik Ylvisaker. Construct auxilary isolated atom w/ same occupation G k matrix includes 6s,6p,5d orbitals too. Self-energy only on 4f’s. Solve self-consistently with occupation Two parameters: U,  f U is usual Hubbard U  f handles double-counting

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Correlation in Lanthanides

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  1. Correlation in Lanthanides Erik Ylvisaker

  2. Construct auxilary isolated atom w/ same occupation Gk matrix includes 6s,6p,5d orbitals too. Self-energy only on 4f’s. Solve self-consistently with occupation Two parameters: U, f U is usual Hubbard U f handles double-counting J Exchange term? LDA+DMFT(HI) Guess () Use Gk() to get nf Adjust at untilnfat = nf Converged? Calculate at

  3. Eu Yb Ce Sm Gd Tm Lu Lanthanide Valency • Most Lanthanides trivalent • Yb and Eu divalent • Large Molar Volume • Small Bulk Modulus

  4. Valence transition in agreement with experiment “Vertical” section volume collapse… Yb Valence vs. Pressure

  5. Idealized Hubbard Bands • “Usual” Gap U-J • Eu, Gd, Yb Gap U+6J • At n=8, LHB picks up 7J • 0 linear in n • U = 6 eV, J = 1 eV

  6. U – from constrained LDA Calculation of Parameters Yb

  7. No Exchange Hubbard Bands (Real Parameters) • Exchange seems important for Eu and up.

  8. Effective U

  9. Valence vs. Pressure • Adjusted f : adjusted by 0.8 eV at all V • Bad News • Valence transition destroyed. • Good News • Volume collapse gone

  10. 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

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

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