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Correlation in Lanthanides

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This study examines the correlation effects in lanthanides by employing the LDA+DMFT(HI) approach to analyze self-energy and valence transitions. It investigates key parameters such as Hubbard U and exchange J, highlighting the importance of double-counting corrections. The research shows notable differences in valence behavior under pressure, particularly for divalent Yb and Eu compared to trivalent lanthanides. Additionally, predictions of gradual valence transitions and volume collapse phenomena are discussed, with good agreement found with experimental data.

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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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