Cerium is one of the most fascinating elements of the periodic system. In its elemental form it exhibits several phases like an antiferromagnetic-, a paramagnetic- and asuperconducting-phase. It is the only element with a solid-solid critical point and Kondo scatteringt. Many of these properties are attributed to the single localized 4f electron close to the Fermi level. 

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Eb, Jeroen Wichert van der,

van der Eb, Jeroen Wichert

Dissertations of the University of Groningen

   University of GroningenCerium, one of nature's purest puzzlesvan der Eb, Jeroen WichertIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2000Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):van der Eb, J. W. (2000). Cerium, one of nature's purest puzzles. [Thesis fully internal (DIV), Groningen].s.n.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 01-11-2023Chapter 6Puzzling the Cerium Pieces TogetherIn the foregoing chapters many individual conclusions and observations have been drawnfrom the different measurements. We will now attempt to fit the pieces together into aconsistent model and dwell on the implications it has for the general picture of cerium.How far have we come? Has our interpretation changed as a result of the measurementswe performed and what consequences do the measurements have on the theories available?Indeed, our interpretation has changed and this has significant consequences for the theoriesavailable! The interpretation of the γ phase has not been altered a great deal, but theinterpretation of the α phase has changed significantly. The reason for this is that we havebeen able to obtain the optical conductivity of cerium in the far infrared energy range andwere able to perform photoemission measurements at low photon energies. As far as weknow these are the first optical measurements performed on both the α and the γ phasein the low (infrared) energy range.Although there are some photoemission studies on cerium with low energy photons(< 40 eV ), no proper explanation has been given to account for the different features seenin the spectra. In addition the α phase spectra (e.g. 21 eV (HeI) photon energy) havenot been discussed (or have been avoided) in literature. This is probably due to the factthat HeI α phase data is very different from the data taken at higher energies. The reasonfor this discrepancy is threefold: (1) the HeI photon energy is on resonance, resulting indifferent cross section behaviour (see section 4.1.3); (2) an Auger structure is obscuringthe valance band, making it hard to compare with other spectra taken at different photonenergies (see section 5.2); (3) the bulk sensitivity has increased compared to the sensitivityhigher photon energies, especially 4d→ 4f resonance photoemission, (section 4.1.2).6.1 CeriumIn the foregoing we have put forward the uniqueness of the combination of the optical andphoto-emission data available and how this was used in the new analysis. In section 1.7the stage has been set for the discussion of the new results.The γ phase at high temperatures can be visualized by (b) in figure 1.7. Upon cooling109110 Chapter 6. Puzzling the Cerium Pieces Togetherdown without allowing the phase transition to take place, the hybridization increases some-what and the resonance at the Fermi level will occur: fig. 1.7(c). Going through the phasetransition to the α phase, there is a large increase in hybridization and a heavy electronband is formed at the Fermi level: fig. 1.7(d).Comparing the HeI photoemission results (fig. 4.9) with fig. 1.7 reveals in a very directway the assignment of the different phases. But the resemblance with a simplified pictureis not the only reason for the assignment.Considering a ’hot’ γ phase, where the temperature is much higher than the Kondotemperature (T >> TK), the lattice spacing is large and thus the 4f − 5d and especiallythe 4f − 4f hybridization are low. Because the γ phase is a magnetic system with localmoments and the hybridization is low, the bandwidth is small compared to the Coulombinteraction, leading to a picture as in figure 1.7b.Only when the γ phase is cooled well below the Kondo temperature, and is not goingthrough the phase transition, the hybridization increases due to the (normal temperature-dependent) contraction of the lattice. The increase in the hybridization will not only leadto broadening of the 4f 0 final state but also to a pushed-out bound state at the Fermilevel. In the Kondo picture this is the so called Kondo or Abricosov-Suhl resonance. In apromotional type picture, the 4f 1 initial state has partially been depopulated due to thehigher hybridization, resulting in the mixing of the 4f 0 state into the ground state, whichwill appear as an electron affinity state just above the Fermi level. In the Mott transitionpicture this pushed-out state at the Fermi level will not occur. The final state formed justabove the Fermi level will have a reasonable amount of atomic 4f character and thereforethe spin-orbit split peak will be visible in the photoemission spectra. The formation ofa sharp peak at the Fermi level, in a cold γ phase, can be seen figure 3.4: the valenceband, except the near Fermi level region, is distinctly different from the α phase. Thisinterpretation of a cold γ phase can be verified by performing temperature-dependent NeImeasurements on a γ phase film. The idea is to look at the Auger intensity during coolingdown.Contraction of the lattice towards the α phase volume will increase the hybridization.Even though the 4f − 4f hybridization is still low, as the overlap of the 4f wave functionsof neighbouring atoms is small, the hopping via the 5d bands has increased significantly.The result will be a broadening of the 4f band being pinned at the Fermi level at the costof weight of the ’incoherent’ 4f 0 removal and 4f 2 addition states. The band formed at theFermi level has a heavy renormalized band mass since the 4f states are still quite localizedbut form a highly hybridized band with the 5d states.The incoherent 4f 0 final state has almost disappeared in the HeI and NeI spectra(fig. 4.9) and weight has accumulated near the Fermi level. Interpreting the photoemissionspectra in this way is not without reason. A good deal of the arguments for this reasoningarise form the infrared spectroscopy we performed.The optical conductivity of α phase cerium (fig. 2.12) shows a pronounced Drude be-haviour; it is a fairly good and ’normal’ metal, that is Fermi liquid-like. In the γ phasethe frequency dependence as well as the DC conductivity is much lower and the rise at low6.2. Challenge and Outlook 111energies is too broad to be Drude-like, showing that the γ phase does not behave Fermiliquid-like.At low energies the mass enhancement is high in the α phase, a factor of 2 to 3 higherthen the γ phase (fig. 2.15). Due to the larger 5d bandwidth, the infrared measurements aremainly 5d-sensitive. The mass-enhancement indicates that the 5d band is highly hybridizedwith the 4f states.How does this interpretation stand against the theories described above? The promo-tional type of theories for describing the phase transition are already out of the picturesince the 4f occupancy stays more or less the same. What is left seems to be a bit of amixture. The γ phase is very much a Kondo system. The Mott transition is not appropri-ate since it can not account for the temperature-dependence of the γ phase. On the otherhand the α phase is more like a heavy band metal. This is, therefore more like the lowtemperature phase in the Mott picture.6.2 Challenge and OutlookNow, after going through the complete analysis, we can ask the question which stepsshould be taken to finish the cerium puzzle. More experiments, for instance photoemissionexperiments in the low photon energy range, are called for. The 5p → 4f resonance canreveal more information if careful synchrotron work is performed. The ’on and of’ switchingof the Auger structure in NeI photoemission can be used to verify the interpretation of the’hot and ’cold’ γ phase.Even though we worked carefully, one might comment that the films are not character-ized properly. To get the new results appreciated and accepted, a thorough investigationof the films is needed. In addition, a recipe should be found to make very smooth ceriumfilms, although we have attempted this by growing films on optically flat silicon. Thisis not only important for the infrared measurements but also for photoemission since itwill minimize the surface contribution to the spectra. Experiments of this kind need ultrahigh vacuum systems with a large amount of preparation and investigation facilities andif possible connected to a synchrotron in the low photon energy range (10 − 50eV ), withsufficient beam intensity and resolution. The quality of the vacuum should be exceedinglyhigh, in the low 10−11 mbar range and special care should be taken to keep hydrogencontamination of the vacuum to a minimum.112 Chapter 6. Puzzling the Cerium Pieces TogetherAbbreviationsbcc body centered cubicCEELS Core level Electron Energy LossDFT Density Functional TheoryDMFT Dynamical Mean Field TheoryDOS Density Of Statesfcc face centered cubicGS Gunnarsson and Schönhammer (model)dhcp double hexagonal close packedHeI Helium I light (21.2 eV )HeII Helium II light (40.8 eV )KE Kinetic EnergyKVC Kondo Volume Collapse (model)LAPW - LDA Local Agmented Plain Wave LDALDA Local Density ApproximationMIR Mid InfraredNeI Neon I light (16.8 eV )NeII Neon II light (26.8 eV )NIR Near InfraredPM Promotional ModelSIC-LDA Self Interaction Correction-Local Density ApproximationSPTHSF Site-Projected Two-Hole Spectral FunctionTK Kondo TemperatureUHV Ultra High VacuumUPS Ultra violet Photo-emission SpectroscopyVIS Visible light range113114 Chapter 6. Puzzling the Cerium Pieces Together

English

Cerium, one of nature's purest puzzles

Proceedings - University of Groningen

   University of GroningenCerium, one of nature's purest puzzlesvan der Eb, Jeroen WichertIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2000Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):van der Eb, J. W. (2000). Cerium, one of nature's purest puzzles. s.n.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 02-06-2022Chapter 6Puzzling the Cerium Pieces TogetherIn the foregoing chapters many individual conclusions and observations have been drawnfrom the different measurements. We will now attempt to fit the pieces together into aconsistent model and dwell on the implications it has for the general picture of cerium.How far have we come? Has our interpretation changed as a result of the measurementswe performed and what consequences do the measurements have on the theories available?Indeed, our interpretation has changed and this has significant consequences for the theoriesavailable! The interpretation of the γ phase has not been altered a great deal, but theinterpretation of the α phase has changed significantly. The reason for this is that we havebeen able to obtain the optical conductivity of cerium in the far infrared energy range andwere able to perform photoemission measurements at low photon energies. As far as weknow these are the first optical measurements performed on both the α and the γ phasein the low (infrared) energy range.Although there are some photoemission studies on cerium with low energy photons(< 40 eV ), no proper explanation has been given to account for the different features seenin the spectra. In addition the α phase spectra (e.g. 21 eV (HeI) photon energy) havenot been discussed (or have been avoided) in literature. This is probably due to the factthat HeI α phase data is very different from the data taken at higher energies. The reasonfor this discrepancy is threefold: (1) the HeI photon energy is on resonance, resulting indifferent cross section behaviour (see section 4.1.3); (2) an Auger structure is obscuringthe valance band, making it hard to compare with other spectra taken at different photonenergies (see section 5.2); (3) the bulk sensitivity has increased compared to the sensitivityhigher photon energies, especially 4d→ 4f resonance photoemission, (section 4.1.2).6.1 CeriumIn the foregoing we have put forward the uniqueness of the combination of the optical andphoto-emission data available and how this was used in the new analysis. In section 1.7the stage has been set for the discussion of the new results.The γ phase at high temperatures can be visualized by (b) in figure 1.7. Upon cooling109110 Chapter 6. Puzzling the Cerium Pieces Togetherdown without allowing the phase transition to take place, the hybridization increases some-what and the resonance at the Fermi level will occur: fig. 1.7(c). Going through the phasetransition to the α phase, there is a large increase in hybridization and a heavy electronband is formed at the Fermi level: fig. 1.7(d).Comparing the HeI photoemission results (fig. 4.9) with fig. 1.7 reveals in a very directway the assignment of the different phases. But the resemblance with a simplified pictureis not the only reason for the assignment.Considering a ’hot’ γ phase, where the temperature is much higher than the Kondotemperature (T >> TK), the lattice spacing is large and thus the 4f − 5d and especiallythe 4f − 4f hybridization are low. Because the γ phase is a magnetic system with localmoments and the hybridization is low, the bandwidth is small compared to the Coulombinteraction, leading to a picture as in figure 1.7b.Only when the γ phase is cooled well below the Kondo temperature, and is not goingthrough the phase transition, the hybridization increases due to the (normal temperature-dependent) contraction of the lattice. The increase in the hybridization will not only leadto broadening of the 4f 0 final state but also to a pushed-out bound state at the Fermilevel. In the Kondo picture this is the so called Kondo or Abricosov-Suhl resonance. In apromotional type picture, the 4f 1 initial state has partially been depopulated due to thehigher hybridization, resulting in the mixing of the 4f 0 state into the ground state, whichwill appear as an electron affinity state just above the Fermi level. In the Mott transitionpicture this pushed-out state at the Fermi level will not occur. The final state formed justabove the Fermi level will have a reasonable amount of atomic 4f character and thereforethe spin-orbit split peak will be visible in the photoemission spectra. The formation ofa sharp peak at the Fermi level, in a cold γ phase, can be seen figure 3.4: the valenceband, except the near Fermi level region, is distinctly different from the α phase. Thisinterpretation of a cold γ phase can be verified by performing temperature-dependent NeImeasurements on a γ phase film. The idea is to look at the Auger intensity during coolingdown.Contraction of the lattice towards the α phase volume will increase the hybridization.Even though the 4f − 4f hybridization is still low, as the overlap of the 4f wave functionsof neighbouring atoms is small, the hopping via the 5d bands has increased significantly.The result will be a broadening of the 4f band being pinned at the Fermi level at the costof weight of the ’incoherent’ 4f 0 removal and 4f 2 addition states. The band formed at theFermi level has a heavy renormalized band mass since the 4f states are still quite localizedbut form a highly hybridized band with the 5d states.The incoherent 4f 0 final state has almost disappeared in the HeI and NeI spectra(fig. 4.9) and weight has accumulated near the Fermi level. Interpreting the photoemissionspectra in this way is not without reason. A good deal of the arguments for this reasoningarise form the infrared spectroscopy we performed.The optical conductivity of α phase cerium (fig. 2.12) shows a pronounced Drude be-haviour; it is a fairly good and ’normal’ metal, that is Fermi liquid-like. In the γ phasethe frequency dependence as well as the DC conductivity is much lower and the rise at low6.2. Challenge and Outlook 111energies is too broad to be Drude-like, showing that the γ phase does not behave Fermiliquid-like.At low energies the mass enhancement is high in the α phase, a factor of 2 to 3 higherthen the γ phase (fig. 2.15). Due to the larger 5d bandwidth, the infrared measurements aremainly 5d-sensitive. The mass-enhancement indicates that the 5d band is highly hybridizedwith the 4f states.How does this interpretation stand against the theories described above? The promo-tional type of theories for describing the phase transition are already out of the picturesince the 4f occupancy stays more or less the same. What is left seems to be a bit of amixture. The γ phase is very much a Kondo system. The Mott transition is not appropri-ate since it can not account for the temperature-dependence of the γ phase. On the otherhand the α phase is more like a heavy band metal. This is, therefore more like the lowtemperature phase in the Mott picture.6.2 Challenge and OutlookNow, after going through the complete analysis, we can ask the question which stepsshould be taken to finish the cerium puzzle. More experiments, for instance photoemissionexperiments in the low photon energy range, are called for. The 5p → 4f resonance canreveal more information if careful synchrotron work is performed. The ’on and of’ switchingof the Auger structure in NeI photoemission can be used to verify the interpretation of the’hot and ’cold’ γ phase.Even though we worked carefully, one might comment that the films are not character-ized properly. To get the new results appreciated and accepted, a thorough investigationof the films is needed. In addition, a recipe should be found to make very smooth ceriumfilms, although we have attempted this by growing films on optically flat silicon. Thisis not only important for the infrared measurements but also for photoemission since itwill minimize the surface contribution to the spectra. Experiments of this kind need ultrahigh vacuum systems with a large amount of preparation and investigation facilities andif possible connected to a synchrotron in the low photon energy range (10 − 50eV ), withsufficient beam intensity and resolution. The quality of the vacuum should be exceedinglyhigh, in the low 10−11 mbar range and special care should be taken to keep hydrogencontamination of the vacuum to a minimum.112 Chapter 6. Puzzling the Cerium Pieces TogetherAbbreviationsbcc body centered cubicCEELS Core level Electron Energy LossDFT Density Functional TheoryDMFT Dynamical Mean Field TheoryDOS Density Of Statesfcc face centered cubicGS Gunnarsson and Schönhammer (model)dhcp double hexagonal close packedHeI Helium I light (21.2 eV )HeII Helium II light (40.8 eV )KE Kinetic EnergyKVC Kondo Volume Collapse (model)LAPW - LDA Local Agmented Plain Wave LDALDA Local Density ApproximationMIR Mid InfraredNeI Neon I light (16.8 eV )NeII Neon II light (26.8 eV )NIR Near InfraredPM Promotional ModelSIC-LDA Self Interaction Correction-Local Density ApproximationSPTHSF Site-Projected Two-Hole Spectral FunctionTK Kondo TemperatureUHV Ultra High VacuumUPS Ultra violet Photo-emission SpectroscopyVIS Visible light range113114 Chapter 6. Puzzling the Cerium Pieces Together

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 University of Groningen
Cerium, one of nature's purest puzzles
van der Eb, Jeroen Wichert
IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from
it. Please check the document version below.
Document Version
Publisher's PDF, also known as Version of record
Publication date:
2000
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
van der Eb, J. W. (2000). Cerium, one of nature's purest puzzles Groningen: s.n.
Copyright
Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the
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Download date: 11-02-2018
Cerium, one of
Nature’s Purest Puzzles
Printed by: Stichting Drukkerij C. Regenboog Groningen
ISBN 90-367-1322-6
RIJKSUNIVERSITEIT GRONINGEN
Cerium, one of
Nature’s Purest Puzzles
Proefschrift
ter verkrijging van het doctoraat in de
Wiskunde en Natuurwetenschappen
aan de Rijksuniversiteit Groningen
op gezag van de
Rector Magnificus Dr. D. F. J. Bosscher
in het openbaar te verdedigen op
dinsdag 7 november 2000
om 13.15 uur
door
Jeroen Wichert van der Eb
geboren op 19 september 1964
te Leiden
Promotor: Prof. Dr. D. van der Marel
Beoordelingscommissie: Prof. Dr. J. A. Mydosh
Prof. Dr. G. A. Sawatzky
Prof. Dr. Z.-X. Shen
Voor mijn grootouders
en voor Lars van der Loop
Contents
Abstract 11
1 Cerium and its Puzzle 13
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2 Scope of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3 Some General Properties of Cerium . . . . . . . . . . . . . . . . . . . . . . 14
1.3.1 Phase Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.2 Crystal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.3 The Valency of Cerium . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4 Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4.1 The Main (Resonant) Photoemission Results from Cerium . . . . . 17
1.4.2 Infrared Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4.3 Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.5 Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.5.1 The Promotional Models . . . . . . . . . . . . . . . . . . . . . . . . 21
1.5.2 The Mott Transition . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.5.3 The 4f Wave Function . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.5.4 The Kondo Volume Collapse Model . . . . . . . . . . . . . . . . . . 24
1.5.5 The Single Impurity Hamiltonian and the GS Model . . . . . . . . 24
1.5.6 LDA and LDA + U . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.6 The Volume Collapse from an Atomic Point of View . . . . . . . . . . . . . 27
1.7 The Main Pieces of the Cerium Puzzle . . . . . . . . . . . . . . . . . . . . 27
2 Infrared Spectroscopy 31
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2 Infrared Grazing Incidence Measurements on Ce . . . . . . . . . . . . . . . 32
2.3 The Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.1 The Design of the UHV Cryostat . . . . . . . . . . . . . . . . . . . 35
2.3.2 Optical Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4 Ce Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.5 MIR Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.5.1 Polarizer Correction . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.5.2 Gold Reference Correction For Non-Ideal Mirrors . . . . . . . . . . 43
7
8 Contents
2.6 Ellipsometry in the Visible Range . . . . . . . . . . . . . . . . . . . . . . . 46
2.7 Combining the MIR, NIR and Ellipsometry Data . . . . . . . . . . . . . . 46
2.8 Obtaining the Conductivity σ from the Reflectivity Data . . . . . . . . . . 48
2.9 The F-Sum Rule and Other Useful Formulas . . . . . . . . . . . . . . . . . 49
2.10 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.11 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3 Temperature-Dependent Photoemission of α and γ Phase Films 63
3.1 Film Deposition and Characterization . . . . . . . . . . . . . . . . . . . . . 63
3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.2.1 Hysteresis in Cerium Films . . . . . . . . . . . . . . . . . . . . . . . 70
3.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4 Energy-Dependent Photo Emission 75
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.1.1 Non-Resonant Photoionization Cross Sections . . . . . . . . . . . . 76
4.1.2 Escape Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.1.3 Resonant Enhancement of the 5d and 4f States . . . . . . . . . . . 78
4.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.2.1 In-Situ Thin Film Preparation . . . . . . . . . . . . . . . . . . . . . 80
4.2.2 Photo Electron Spectroscopy . . . . . . . . . . . . . . . . . . . . . . 80
4.2.3 Background and Satellite Corrections . . . . . . . . . . . . . . . . . 81
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.3.1 Core Level Features . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.3.2 The Valence Band . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3.3 Resonant Enhancement . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.3.4 Assignment of the Experimental Spectra . . . . . . . . . . . . . . . 92
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5 Valence Band Auger Spectroscopy of α- and γ-Phase Cerium 95
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.2 Near Threshold Auger Spectroscopy . . . . . . . . . . . . . . . . . . . . . . 97
5.2.1 Extracting the Auger Spectrum . . . . . . . . . . . . . . . . . . . . 99
5.2.2 The Valence Band . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6 Puzzling the Cerium Pieces Together 109
6.1 Cerium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2 Challenge and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Abbreviations 113
Samenvatting 115
Contents 9
Dankwoord 119
10 Contents


   University of GroningenCerium, one of nature's purest puzzlesvan der Eb, Jeroen WichertIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2000Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):van der Eb, J. W. (2000). Cerium, one of nature's purest puzzles. s.n.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 03-06-2022Chapter 6Puzzling the Cerium Pieces TogetherIn the foregoing chapters many individual conclusions and observations have been drawnfrom the different measurements. We will now attempt to fit the pieces together into aconsistent model and dwell on the implications it has for the general picture of cerium.How far have we come? Has our interpretation changed as a result of the measurementswe performed and what consequences do the measurements have on the theories available?Indeed, our interpretation has changed and this has significant consequences for the theoriesavailable! The interpretation of the γ phase has not been altered a great deal, but theinterpretation of the α phase has changed significantly. The reason for this is that we havebeen able to obtain the optical conductivity of cerium in the far infrared energy range andwere able to perform photoemission measurements at low photon energies. As far as weknow these are the first optical measurements performed on both the α and the γ phasein the low (infrared) energy range.Although there are some photoemission studies on cerium with low energy photons(< 40 eV ), no proper explanation has been given to account for the different features seenin the spectra. In addition the α phase spectra (e.g. 21 eV (HeI) photon energy) havenot been discussed (or have been avoided) in literature. This is probably due to the factthat HeI α phase data is very different from the data taken at higher energies. The reasonfor this discrepancy is threefold: (1) the HeI photon energy is on resonance, resulting indifferent cross section behaviour (see section 4.1.3); (2) an Auger structure is obscuringthe valance band, making it hard to compare with other spectra taken at different photonenergies (see section 5.2); (3) the bulk sensitivity has increased compared to the sensitivityhigher photon energies, especially 4d→ 4f resonance photoemission, (section 4.1.2).6.1 CeriumIn the foregoing we have put forward the uniqueness of the combination of the optical andphoto-emission data available and how this was used in the new analysis. In section 1.7the stage has been set for the discussion of the new results.The γ phase at high temperatures can be visualized by (b) in figure 1.7. Upon cooling109110 Chapter 6. Puzzling the Cerium Pieces Togetherdown without allowing the phase transition to take place, the hybridization increases some-what and the resonance at the Fermi level will occur: fig. 1.7(c). Going through the phasetransition to the α phase, there is a large increase in hybridization and a heavy electronband is formed at the Fermi level: fig. 1.7(d).Comparing the HeI photoemission results (fig. 4.9) with fig. 1.7 reveals in a very directway the assignment of the different phases. But the resemblance with a simplified pictureis not the only reason for the assignment.Considering a ’hot’ γ phase, where the temperature is much higher than the Kondotemperature (T >> TK), the lattice spacing is large and thus the 4f − 5d and especiallythe 4f − 4f hybridization are low. Because the γ phase is a magnetic system with localmoments and the hybridization is low, the bandwidth is small compared to the Coulombinteraction, leading to a picture as in figure 1.7b.Only when the γ phase is cooled well below the Kondo temperature, and is not goingthrough the phase transition, the hybridization increases due to the (normal temperature-dependent) contraction of the lattice. The increase in the hybridization will not only leadto broadening of the 4f 0 final state but also to a pushed-out bound state at the Fermilevel. In the Kondo picture this is the so called Kondo or Abricosov-Suhl resonance. In apromotional type picture, the 4f 1 initial state has partially been depopulated due to thehigher hybridization, resulting in the mixing of the 4f 0 state into the ground state, whichwill appear as an electron affinity state just above the Fermi level. In the Mott transitionpicture this pushed-out state at the Fermi level will not occur. The final state formed justabove the Fermi level will have a reasonable amount of atomic 4f character and thereforethe spin-orbit split peak will be visible in the photoemission spectra. The formation ofa sharp peak at the Fermi level, in a cold γ phase, can be seen figure 3.4: the valenceband, except the near Fermi level region, is distinctly different from the α phase. Thisinterpretation of a cold γ phase can be verified by performing temperature-dependent NeImeasurements on a γ phase film. The idea is to look at the Auger intensity during coolingdown.Contraction of the lattice towards the α phase volume will increase the hybridization.Even though the 4f − 4f hybridization is still low, as the overlap of the 4f wave functionsof neighbouring atoms is small, the hopping via the 5d bands has increased significantly.The result will be a broadening of the 4f band being pinned at the Fermi level at the costof weight of the ’incoherent’ 4f 0 removal and 4f 2 addition states. The band formed at theFermi level has a heavy renormalized band mass since the 4f states are still quite localizedbut form a highly hybridized band with the 5d states.The incoherent 4f 0 final state has almost disappeared in the HeI and NeI spectra(fig. 4.9) and weight has accumulated near the Fermi level. Interpreting the photoemissionspectra in this way is not without reason. A good deal of the arguments for this reasoningarise form the infrared spectroscopy we performed.The optical conductivity of α phase cerium (fig. 2.12) shows a pronounced Drude be-haviour; it is a fairly good and ’normal’ metal, that is Fermi liquid-like. In the γ phasethe frequency dependence as well as the DC conductivity is much lower and the rise at low6.2. Challenge and Outlook 111energies is too broad to be Drude-like, showing that the γ phase does not behave Fermiliquid-like.At low energies the mass enhancement is high in the α phase, a factor of 2 to 3 higherthen the γ phase (fig. 2.15). Due to the larger 5d bandwidth, the infrared measurements aremainly 5d-sensitive. The mass-enhancement indicates that the 5d band is highly hybridizedwith the 4f states.How does this interpretation stand against the theories described above? The promo-tional type of theories for describing the phase transition are already out of the picturesince the 4f occupancy stays more or less the same. What is left seems to be a bit of amixture. The γ phase is very much a Kondo system. The Mott transition is not appropri-ate since it can not account for the temperature-dependence of the γ phase. On the otherhand the α phase is more like a heavy band metal. This is, therefore more like the lowtemperature phase in the Mott picture.6.2 Challenge and OutlookNow, after going through the complete analysis, we can ask the question which stepsshould be taken to finish the cerium puzzle. More experiments, for instance photoemissionexperiments in the low photon energy range, are called for. The 5p → 4f resonance canreveal more information if careful synchrotron work is performed. The ’on and of’ switchingof the Auger structure in NeI photoemission can be used to verify the interpretation of the’hot and ’cold’ γ phase.Even though we worked carefully, one might comment that the films are not character-ized properly. To get the new results appreciated and accepted, a thorough investigationof the films is needed. In addition, a recipe should be found to make very smooth ceriumfilms, although we have attempted this by growing films on optically flat silicon. Thisis not only important for the infrared measurements but also for photoemission since itwill minimize the surface contribution to the spectra. Experiments of this kind need ultrahigh vacuum systems with a large amount of preparation and investigation facilities andif possible connected to a synchrotron in the low photon energy range (10 − 50eV ), withsufficient beam intensity and resolution. The quality of the vacuum should be exceedinglyhigh, in the low 10−11 mbar range and special care should be taken to keep hydrogencontamination of the vacuum to a minimum.112 Chapter 6. Puzzling the Cerium Pieces TogetherAbbreviationsbcc body centered cubicCEELS Core level Electron Energy LossDFT Density Functional TheoryDMFT Dynamical Mean Field TheoryDOS Density Of Statesfcc face centered cubicGS Gunnarsson and Schönhammer (model)dhcp double hexagonal close packedHeI Helium I light (21.2 eV )HeII Helium II light (40.8 eV )KE Kinetic EnergyKVC Kondo Volume Collapse (model)LAPW - LDA Local Agmented Plain Wave LDALDA Local Density ApproximationMIR Mid InfraredNeI Neon I light (16.8 eV )NeII Neon II light (26.8 eV )NIR Near InfraredPM Promotional ModelSIC-LDA Self Interaction Correction-Local Density ApproximationSPTHSF Site-Projected Two-Hole Spectral FunctionTK Kondo TemperatureUHV Ultra High VacuumUPS Ultra violet Photo-emission SpectroscopyVIS Visible light range113114 Chapter 6. Puzzling the Cerium Pieces Together

NARCIS 

University of Groningen

   University of GroningenCerium, one of nature's purest puzzlesvan der Eb, Jeroen WichertIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2000Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):van der Eb, J. W. (2000). Cerium, one of nature's purest puzzles. s.n.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 25-12-2020Chapter 6Puzzling the Cerium Pieces TogetherIn the foregoing chapters many individual conclusions and observations have been drawnfrom the different measurements. We will now attempt to fit the pieces together into aconsistent model and dwell on the implications it has for the general picture of cerium.How far have we come? Has our interpretation changed as a result of the measurementswe performed and what consequences do the measurements have on the theories available?Indeed, our interpretation has changed and this has significant consequences for the theoriesavailable! The interpretation of the γ phase has not been altered a great deal, but theinterpretation of the α phase has changed significantly. The reason for this is that we havebeen able to obtain the optical conductivity of cerium in the far infrared energy range andwere able to perform photoemission measurements at low photon energies. As far as weknow these are the first optical measurements performed on both the α and the γ phasein the low (infrared) energy range.Although there are some photoemission studies on cerium with low energy photons(< 40 eV ), no proper explanation has been given to account for the different features seenin the spectra. In addition the α phase spectra (e.g. 21 eV (HeI) photon energy) havenot been discussed (or have been avoided) in literature. This is probably due to the factthat HeI α phase data is very different from the data taken at higher energies. The reasonfor this discrepancy is threefold: (1) the HeI photon energy is on resonance, resulting indifferent cross section behaviour (see section 4.1.3); (2) an Auger structure is obscuringthe valance band, making it hard to compare with other spectra taken at different photonenergies (see section 5.2); (3) the bulk sensitivity has increased compared to the sensitivityhigher photon energies, especially 4d→ 4f resonance photoemission, (section 4.1.2).6.1 CeriumIn the foregoing we have put forward the uniqueness of the combination of the optical andphoto-emission data available and how this was used in the new analysis. In section 1.7the stage has been set for the discussion of the new results.The γ phase at high temperatures can be visualized by (b) in figure 1.7. Upon cooling109110 Chapter 6. Puzzling the Cerium Pieces Togetherdown without allowing the phase transition to take place, the hybridization increases some-what and the resonance at the Fermi level will occur: fig. 1.7(c). Going through the phasetransition to the α phase, there is a large increase in hybridization and a heavy electronband is formed at the Fermi level: fig. 1.7(d).Comparing the HeI photoemission results (fig. 4.9) with fig. 1.7 reveals in a very directway the assignment of the different phases. But the resemblance with a simplified pictureis not the only reason for the assignment.Considering a ’hot’ γ phase, where the temperature is much higher than the Kondotemperature (T >> TK), the lattice spacing is large and thus the 4f − 5d and especiallythe 4f − 4f hybridization are low. Because the γ phase is a magnetic system with localmoments and the hybridization is low, the bandwidth is small compared to the Coulombinteraction, leading to a picture as in figure 1.7b.Only when the γ phase is cooled well below the Kondo temperature, and is not goingthrough the phase transition, the hybridization increases due to the (normal temperature-dependent) contraction of the lattice. The increase in the hybridization will not only leadto broadening of the 4f 0 final state but also to a pushed-out bound state at the Fermilevel. In the Kondo picture this is the so called Kondo or Abricosov-Suhl resonance. In apromotional type picture, the 4f 1 initial state has partially been depopulated due to thehigher hybridization, resulting in the mixing of the 4f 0 state into the ground state, whichwill appear as an electron affinity state just above the Fermi level. In the Mott transitionpicture this pushed-out state at the Fermi level will not occur. The final state formed justabove the Fermi level will have a reasonable amount of atomic 4f character and thereforethe spin-orbit split peak will be visible in the photoemission spectra. The formation ofa sharp peak at the Fermi level, in a cold γ phase, can be seen figure 3.4: the valenceband, except the near Fermi level region, is distinctly different from the α phase. Thisinterpretation of a cold γ phase can be verified by performing temperature-dependent NeImeasurements on a γ phase film. The idea is to look at the Auger intensity during coolingdown.Contraction of the lattice towards the α phase volume will increase the hybridization.Even though the 4f − 4f hybridization is still low, as the overlap of the 4f wave functionsof neighbouring atoms is small, the hopping via the 5d bands has increased significantly.The result will be a broadening of the 4f band being pinned at the Fermi level at the costof weight of the ’incoherent’ 4f 0 removal and 4f 2 addition states. The band formed at theFermi level has a heavy renormalized band mass since the 4f states are still quite localizedbut form a highly hybridized band with the 5d states.The incoherent 4f 0 final state has almost disappeared in the HeI and NeI spectra(fig. 4.9) and weight has accumulated near the Fermi level. Interpreting the photoemissionspectra in this way is not without reason. A good deal of the arguments for this reasoningarise form the infrared spectroscopy we performed.The optical conductivity of α phase cerium (fig. 2.12) shows a pronounced Drude be-haviour; it is a fairly good and ’normal’ metal, that is Fermi liquid-like. In the γ phasethe frequency dependence as well as the DC conductivity is much lower and the rise at low6.2. Challenge and Outlook 111energies is too broad to be Drude-like, showing that the γ phase does not behave Fermiliquid-like.At low energies the mass enhancement is high in the α phase, a factor of 2 to 3 higherthen the γ phase (fig. 2.15). Due to the larger 5d bandwidth, the infrared measurements aremainly 5d-sensitive. The mass-enhancement indicates that the 5d band is highly hybridizedwith the 4f states.How does this interpretation stand against the theories described above? The promo-tional type of theories for describing the phase transition are already out of the picturesince the 4f occupancy stays more or less the same. What is left seems to be a bit of amixture. The γ phase is very much a Kondo system. The Mott transition is not appropri-ate since it can not account for the temperature-dependence of the γ phase. On the otherhand the α phase is more like a heavy band metal. This is, therefore more like the lowtemperature phase in the Mott picture.6.2 Challenge and OutlookNow, after going through the complete analysis, we can ask the question which stepsshould be taken to finish the cerium puzzle. More experiments, for instance photoemissionexperiments in the low photon energy range, are called for. The 5p → 4f resonance canreveal more information if careful synchrotron work is performed. The ’on and of’ switchingof the Auger structure in NeI photoemission can be used to verify the interpretation of the’hot and ’cold’ γ phase.Even though we worked carefully, one might comment that the films are not character-ized properly. To get the new results appreciated and accepted, a thorough investigationof the films is needed. In addition, a recipe should be found to make very smooth ceriumfilms, although we have attempted this by growing films on optically flat silicon. Thisis not only important for the infrared measurements but also for photoemission since itwill minimize the surface contribution to the spectra. Experiments of this kind need ultrahigh vacuum systems with a large amount of preparation and investigation facilities andif possible connected to a synchrotron in the low photon energy range (10 − 50eV ), withsufficient beam intensity and resolution. The quality of the vacuum should be exceedinglyhigh, in the low 10−11 mbar range and special care should be taken to keep hydrogencontamination of the vacuum to a minimum.112 Chapter 6. Puzzling the Cerium Pieces TogetherAbbreviationsbcc body centered cubicCEELS Core level Electron Energy LossDFT Density Functional TheoryDMFT Dynamical Mean Field TheoryDOS Density Of Statesfcc face centered cubicGS Gunnarsson and Schönhammer (model)dhcp double hexagonal close packedHeI Helium I light (21.2 eV )HeII Helium II light (40.8 eV )KE Kinetic EnergyKVC Kondo Volume Collapse (model)LAPW - LDA Local Agmented Plain Wave LDALDA Local Density ApproximationMIR Mid InfraredNeI Neon I light (16.8 eV )NeII Neon II light (26.8 eV )NIR Near InfraredPM Promotional ModelSIC-LDA Self Interaction Correction-Local Density ApproximationSPTHSF Site-Projected Two-Hole Spectral FunctionTK Kondo TemperatureUHV Ultra High VacuumUPS Ultra violet Photo-emission SpectroscopyVIS Visible light range113114 Chapter 6. Puzzling the Cerium Pieces Together

ARTS repository - University of Groningen

   University of GroningenCerium, one of nature's purest puzzlesvan der Eb, Jeroen WichertIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2000Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):van der Eb, J. W. (2000). Cerium, one of nature's purest puzzles. s.n.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 06-06-2022Chapter 6Puzzling the Cerium Pieces TogetherIn the foregoing chapters many individual conclusions and observations have been drawnfrom the different measurements. We will now attempt to fit the pieces together into aconsistent model and dwell on the implications it has for the general picture of cerium.How far have we come? Has our interpretation changed as a result of the measurementswe performed and what consequences do the measurements have on the theories available?Indeed, our interpretation has changed and this has significant consequences for the theoriesavailable! The interpretation of the γ phase has not been altered a great deal, but theinterpretation of the α phase has changed significantly. The reason for this is that we havebeen able to obtain the optical conductivity of cerium in the far infrared energy range andwere able to perform photoemission measurements at low photon energies. As far as weknow these are the first optical measurements performed on both the α and the γ phasein the low (infrared) energy range.Although there are some photoemission studies on cerium with low energy photons(< 40 eV ), no proper explanation has been given to account for the different features seenin the spectra. In addition the α phase spectra (e.g. 21 eV (HeI) photon energy) havenot been discussed (or have been avoided) in literature. This is probably due to the factthat HeI α phase data is very different from the data taken at higher energies. The reasonfor this discrepancy is threefold: (1) the HeI photon energy is on resonance, resulting indifferent cross section behaviour (see section 4.1.3); (2) an Auger structure is obscuringthe valance band, making it hard to compare with other spectra taken at different photonenergies (see section 5.2); (3) the bulk sensitivity has increased compared to the sensitivityhigher photon energies, especially 4d→ 4f resonance photoemission, (section 4.1.2).6.1 CeriumIn the foregoing we have put forward the uniqueness of the combination of the optical andphoto-emission data available and how this was used in the new analysis. In section 1.7the stage has been set for the discussion of the new results.The γ phase at high temperatures can be visualized by (b) in figure 1.7. Upon cooling109110 Chapter 6. Puzzling the Cerium Pieces Togetherdown without allowing the phase transition to take place, the hybridization increases some-what and the resonance at the Fermi level will occur: fig. 1.7(c). Going through the phasetransition to the α phase, there is a large increase in hybridization and a heavy electronband is formed at the Fermi level: fig. 1.7(d).Comparing the HeI photoemission results (fig. 4.9) with fig. 1.7 reveals in a very directway the assignment of the different phases. But the resemblance with a simplified pictureis not the only reason for the assignment.Considering a ’hot’ γ phase, where the temperature is much higher than the Kondotemperature (T >> TK), the lattice spacing is large and thus the 4f − 5d and especiallythe 4f − 4f hybridization are low. Because the γ phase is a magnetic system with localmoments and the hybridization is low, the bandwidth is small compared to the Coulombinteraction, leading to a picture as in figure 1.7b.Only when the γ phase is cooled well below the Kondo temperature, and is not goingthrough the phase transition, the hybridization increases due to the (normal temperature-dependent) contraction of the lattice. The increase in the hybridization will not only leadto broadening of the 4f 0 final state but also to a pushed-out bound state at the Fermilevel. In the Kondo picture this is the so called Kondo or Abricosov-Suhl resonance. In apromotional type picture, the 4f 1 initial state has partially been depopulated due to thehigher hybridization, resulting in the mixing of the 4f 0 state into the ground state, whichwill appear as an electron affinity state just above the Fermi level. In the Mott transitionpicture this pushed-out state at the Fermi level will not occur. The final state formed justabove the Fermi level will have a reasonable amount of atomic 4f character and thereforethe spin-orbit split peak will be visible in the photoemission spectra. The formation ofa sharp peak at the Fermi level, in a cold γ phase, can be seen figure 3.4: the valenceband, except the near Fermi level region, is distinctly different from the α phase. Thisinterpretation of a cold γ phase can be verified by performing temperature-dependent NeImeasurements on a γ phase film. The idea is to look at the Auger intensity during coolingdown.Contraction of the lattice towards the α phase volume will increase the hybridization.Even though the 4f − 4f hybridization is still low, as the overlap of the 4f wave functionsof neighbouring atoms is small, the hopping via the 5d bands has increased significantly.The result will be a broadening of the 4f band being pinned at the Fermi level at the costof weight of the ’incoherent’ 4f 0 removal and 4f 2 addition states. The band formed at theFermi level has a heavy renormalized band mass since the 4f states are still quite localizedbut form a highly hybridized band with the 5d states.The incoherent 4f 0 final state has almost disappeared in the HeI and NeI spectra(fig. 4.9) and weight has accumulated near the Fermi level. Interpreting the photoemissionspectra in this way is not without reason. A good deal of the arguments for this reasoningarise form the infrared spectroscopy we performed.The optical conductivity of α phase cerium (fig. 2.12) shows a pronounced Drude be-haviour; it is a fairly good and ’normal’ metal, that is Fermi liquid-like. In the γ phasethe frequency dependence as well as the DC conductivity is much lower and the rise at low6.2. Challenge and Outlook 111energies is too broad to be Drude-like, showing that the γ phase does not behave Fermiliquid-like.At low energies the mass enhancement is high in the α phase, a factor of 2 to 3 higherthen the γ phase (fig. 2.15). Due to the larger 5d bandwidth, the infrared measurements aremainly 5d-sensitive. The mass-enhancement indicates that the 5d band is highly hybridizedwith the 4f states.How does this interpretation stand against the theories described above? The promo-tional type of theories for describing the phase transition are already out of the picturesince the 4f occupancy stays more or less the same. What is left seems to be a bit of amixture. The γ phase is very much a Kondo system. The Mott transition is not appropri-ate since it can not account for the temperature-dependence of the γ phase. On the otherhand the α phase is more like a heavy band metal. This is, therefore more like the lowtemperature phase in the Mott picture.6.2 Challenge and OutlookNow, after going through the complete analysis, we can ask the question which stepsshould be taken to finish the cerium puzzle. More experiments, for instance photoemissionexperiments in the low photon energy range, are called for. The 5p → 4f resonance canreveal more information if careful synchrotron work is performed. The ’on and of’ switchingof the Auger structure in NeI photoemission can be used to verify the interpretation of the’hot and ’cold’ γ phase.Even though we worked carefully, one might comment that the films are not character-ized properly. To get the new results appreciated and accepted, a thorough investigationof the films is needed. In addition, a recipe should be found to make very smooth ceriumfilms, although we have attempted this by growing films on optically flat silicon. Thisis not only important for the infrared measurements but also for photoemission since itwill minimize the surface contribution to the spectra. Experiments of this kind need ultrahigh vacuum systems with a large amount of preparation and investigation facilities andif possible connected to a synchrotron in the low photon energy range (10 − 50eV ), withsufficient beam intensity and resolution. The quality of the vacuum should be exceedinglyhigh, in the low 10−11 mbar range and special care should be taken to keep hydrogencontamination of the vacuum to a minimum.112 Chapter 6. Puzzling the Cerium Pieces TogetherAbbreviationsbcc body centered cubicCEELS Core level Electron Energy LossDFT Density Functional TheoryDMFT Dynamical Mean Field TheoryDOS Density Of Statesfcc face centered cubicGS Gunnarsson and Schönhammer (model)dhcp double hexagonal close packedHeI Helium I light (21.2 eV )HeII Helium II light (40.8 eV )KE Kinetic EnergyKVC Kondo Volume Collapse (model)LAPW - LDA Local Agmented Plain Wave LDALDA Local Density ApproximationMIR Mid InfraredNeI Neon I light (16.8 eV )NeII Neon II light (26.8 eV )NIR Near InfraredPM Promotional ModelSIC-LDA Self Interaction Correction-Local Density ApproximationSPTHSF Site-Projected Two-Hole Spectral FunctionTK Kondo TemperatureUHV Ultra High VacuumUPS Ultra violet Photo-emission SpectroscopyVIS Visible light range113114 Chapter 6. Puzzling the Cerium Pieces Together

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Cerium, one of nature's purest puzzles

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