Computational Science Engineering Departmen CSE Daresbury Laboratory Self Self-Interaction Correction (SIC) Scheme Interaction Correction (SIC) Scheme and f and f-Electron Materials Electron Materials Z. (Dzidka) Szotek Z. (Dzidka) Szotek Daresbury Laboratory, UK Daresbury Laboratory, UK
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
§§ Introduction: some issues in fIntroduction: some issues in f--systemssystems
§§ SICSIC--LSD method: advantages and disadvantagesLSD method: advantages and disadvantages
Ø Full implementation (T=0K)•• Applications: valence and valence transitionsApplications: valence and valence transitions
Ø Local SIC (Multiple Scattering Theory implementation)•• Finite temperature phenomena: Ce phase diagramFinite temperature phenomena: Ce phase diagram•• Finite Temperature Magnetism of the Heavy Rare EarthsFinite Temperature Magnetism of the Heavy Rare Earths
Note different behaviour in the lattice constants Note different behaviour in the lattice constants between the chalcogenides and the pnictidesbetween the chalcogenides and the pnictides
Global energy minimum determines ground state configurationGlobal energy minimum determines ground state configuration
NNvalencevalence = Z = Z -- NNcorecore--NNSIC(loc)SIC(loc)
Self-interaction free total energy functional (Perdew & Zunger, 1981):
? Orbital dependent potential differentiates between localized Orbital dependent potential differentiates between localized and delocalised electronsand delocalised electrons
?? Gain in band formation Gain in band formation vs.vs. gain in localization (SIC energy)gain in localization (SIC energy)?? Study of various localization/delocalisation configurationsStudy of various localization/delocalisation configurations
Number of Itinerant fNumber of Itinerant f--ElectronsElectronsCalculated vs. Experimental Lattice ParametersCalculated vs. Experimental Lattice Parameters
ValenceValence is determinedby the number of
localized f-electrons, but valence transitionsvalence transitions
are driven bythe number of
itinerant f-electrons
NNvalencyvalency = Z = Z -- NNcorecore--NNSIC(loc)SIC(loc)
Structural and Localisation Transitions in CePStructural and Localisation Transitions in CeP
A. Svane et al., Solid State Commun. A. Svane et al., Solid State Commun. 102102, 473 (1997); A. Svane et al., J. Phys.: Condens. Matter , 473 (1997); A. Svane et al., J. Phys.: Condens. Matter 1010, 5309 (1998);, 5309 (1998);A. Svane et al., Phys. Rev. B A. Svane et al., Phys. Rev. B 5959, 7888 (1999)., 7888 (1999).
Rare EarthsRare Earths: P. Strange, A. Svane, W.M. Temmerman, Z.Szotek and H. Winter, : P. Strange, A. Svane, W.M. Temmerman, Z.Szotek and H. Winter, Nature 399 Nature 399 (1999) 756.(1999) 756.
ActinidesActinides: L. Petit, A. Svane, W.M. Temmerman and Z. Szotek, Solid State : L. Petit, A. Svane, W.M. Temmerman and Z. Szotek, Solid State Communications Communications 116 (2000) 379.116 (2000) 379.
Trivalency vs. Divalency in fTrivalency vs. Divalency in f--SystemsSystems
Until recently, PuOUntil recently, PuO22 was accepted to be the stable Pu oxidewas accepted to be the stable Pu oxide andanda compound of choice for long time storage of Pu a compound of choice for long time storage of Pu
2000: Discovery of PuO2000: Discovery of PuO2+x2+x by Haschke et al.by Haschke et al.
Oxidation reaction in the presence of water, at temperatures in Oxidation reaction in the presence of water, at temperatures in the the range 25range 25°° to 350to 350°° C : PuOC : PuO22+xH+xH22OO——>PuO>PuO2+x2+x+xH+xH22
Existence of PuOExistence of PuO2+x 2+x remains controversialremains controversial
SICSIC--LSDLSD: Theoretical study of the changes in electronic structure of : Theoretical study of the changes in electronic structure of PuOPuO2 2 under oxidation under oxidation
Full approach: DMFT or DCPAFull approach: DMFT or DCPA
Simplified approach:Simplified approach:– starting with the static limitstatic limit within multiple scattering theory (multiple scattering theory (KKRKKR))– self-interaction correction (SICSIC): identify important configurationsidentify important configurations– use CPACPA--DLMDLM (pseudo-alloys) to invoke valence and spin fluctuations–– NLNL--CPACPA to allow for SRO, and DLM technology for calculating TSRO, and DLM technology for calculating Tcc
–– dynamics dynamics (possibly two level system-like approach/R-matrix/ensemble averaging)
LSDLSD SICSIC--LSDLSD
ββ
αβαααα ψεψψ ∑=+= )( SICLDA VHHεψψ =LSDH
Valence, orbital, and charge orderValence, orbital, and charge order
HUTSEPOTHUTSEPOT
AbAb--initio Method for Strongly initio Method for Strongly Correlated Electron SystemsCorrelated Electron Systems
• itinerant electrons • good description for weakly
correlated metals
• electrons are localised
• good description for insulatorsIntermediate range: • partial localisation • fluctuations• DMFT
Coherent Potential Approximation (CPA):Coherent Potential Approximation (CPA):Effective medium: on average no extra scattering by impuritiesEffective medium: on average no extra scattering by impurities
For each temperature, volume and concentrations cFor each temperature, volume and concentrations cii
Identify different local (spin/valence) configurations lying cloIdentify different local (spin/valence) configurations lying close in energyse in energy
LL--SIC:Ce at Finite TemperaturesSIC:Ce at Finite Temperatures
Gibbs free energy
Free energy
),,(),),,,((),,( cTppVcTcTpVFcTpG +=V(a.u.)
p[kb
ar]
200 K400 K
600 K800 K
1000 K1200 K
1400 K1500 K
1600 K
LSICLSIC--KKRKKR--CPACPA with DLMwith DLM
Use alloy analogy (Hubbard III) Use alloy analogy (Hubbard III) with localised (SIC) and delocalised with localised (SIC) and delocalised (LSD) states.(LSD) states.
Disordered Local Moments for GdDisordered Local Moments for Gd
Combining SICCombining SIC--LSD with the disordered local moment (DLM) picture LSD with the disordered local moment (DLM) picture of magnetism:of magnetism:
• Using GdGd as a prototype for late rare earths (REs)
•• SICSIC--LSDLSD corrects the wrong magnetic structure of GdGd calculated by LSD.
•• DLMDLM: calculation of the magnetic susceptibility in the paramagnetic phase: peak in χ(q) provides the magnetic ordering vector and transition temperature.
Gd: Magnetic Order in Heavy Rare EarthsGd: Magnetic Order in Heavy Rare Earths
DLMDLM: calculation of the magnetic susceptibilityin the paramagnetic phase - peak in χχ(q)(q) provides the magnetic ordering vector.
Onset of Magnetic OrderOnset of Magnetic OrderBelow TTCC: paramagnetic state is unstable:an infinitesimal magnetic field will induce a finite magnetization. Divergence of the paramagnetic susceptibility indicates Curie (Neel) temperature.
Investigate magnetic order as a function of lattice parameters (Investigate magnetic order as a function of lattice parameters (Wigner Seitz radius Wigner Seitz radius and c/a ratio).and c/a ratio).
Magnetic Order in Heavy Rare EarthsMagnetic Order in Heavy Rare Earths
SICSIC--LSD provides improved treatment of localized statesLSD provides improved treatment of localized states
Competition between localization energy and band formation energCompetition between localization energy and band formation energy leads to a useful definition y leads to a useful definition of valence even for metallic systemsof valence even for metallic systems
Description of change in valence as a function of pressure and cDescription of change in valence as a function of pressure and chemical compositionhemical composition
Phase transitions of fPhase transitions of f--electron systems at finite temperatureselectron systems at finite temperatures
Localization energy and band formation energy are treated on equLocalization energy and band formation energy are treated on equal footingal footing
M. LM. Lüüdersders and W. M. Temmerman (and W. M. Temmerman (DaresburyDaresbury))A.A. Svane et al. (Svane et al. (AarhusAarhus))L. Petit (L. Petit (ORNL & AarhusORNL & Aarhus))
J.B. Staunton and I. Hughes (J.B. Staunton and I. Hughes (WarwickWarwick))B. L. GyB. L. Gyöörffy (rffy (BristolBristol))
D. KD. Köödderitzsch (dderitzsch (MunichMunich) ) M. DM. Dääne, A. Ernst and ne, A. Ernst and W. Hergert (W. Hergert (HalleHalle))
P. Strange et al. (P. Strange et al. (KeeleKeele//KentKent))H. Winter (H. Winter (KarlsruheKarlsruhe))J. Poulter (J. Poulter (BangkokBangkok))