In Memory of GHK: Correlated electrons from intermetallics to organometallics Presented at the George Hsing Kwei Memorial Symposium, Los Alamos, June 27, 2006 Corwin H. Booth Chemical Sciences Division Glenn T. Seaborg Center Lawrence Berkeley National Laboratory
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In Memory of GHK: Correlated electrons from intermetallics to organometallics Presented at the George Hsing Kwei Memorial Symposium, Los Alamos, June 27,
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In Memory of GHK: Correlated electrons from intermetallics to
organometallics
Presented at the George Hsing Kwei Memorial Symposium, Los Alamos, June 27, 2006
Corwin H. BoothChemical Sciences Division
Glenn T. Seaborg CenterLawrence Berkeley National
Laboratory
Outline
1. George and me2. George and correlated electrons3. INTRODUCTION: Kondo effect in f-electron
intermetallics4. RESEARCH DIRECTIONS: Possible correlated
electron effects in organometallics
A second career…
• Of George top 50 most-cited papers, nearly 70% came after 1986, 26 in High Tc, 10 in CMR, 7 in mixed valence/heavy fermions and 4 in fullerenes
• During this time, George became a Rietveld jock, solving the 4th most crystal structures using IPNS (I believe, after Jorgensen, Lawson and somebody else)
• George’s mode of operation: facilitator (“vector boson”)— Took a broad view— Put teams of people together— Learned to play to people’s strengths
• From susceptibility, would get 28% and 69% 4f13 in bipy and terpy at RT, with sharp temperature dependence*
• Yb XANES: no observed T-dep in nf from 30-400 K
• Cannot be due to a chemical equilibrium between 4f13 and 4f14 configurations *Veauthier et al., Inorg. Chem. 44, 5911 (2005).
Cerocene and bis(pentalene)cerium
• Temperature-independent paramagnetism (TIP)
• Very low susceptibility: nearly all tetravalent 4f0?
• Ce LIII says more 4f1 character than 4f0 ?!?!?!
• CePn*2 looks same (same electron count)
5700 5720 5740 57600.0
0.5
1.0
1.5
2.0
___2p 4f 1 L 5d
__2p 4f 0 5d
__2p 4f 1 5d
Nor
mal
ized
Abs
orpt
ion
Energy (eV)
Ce(III) Ce(IV) Cerocene
5700 5720 5740 57600.0
0.5
1.0
1.5
2.0
No
rma
lize
d A
bso
rptio
n
Energy (eV)
Cerocene CePn*
2
0 50 100 150 200 250 3000.00010
0.00015
0.00020
0.00025
0.00030
0 50 100 150 200 250 3000.0001
0.0002
0.0003
0.0004
0.0005
(e
mu/
mol
Ce)
T (K)
Ce(cot)2
Booth et al., PRL 95, 267202 (2005)
Metallic bonding in organic compounds
• Benzene discovered in 1825 by Faraday
• Kekulé proposed correct structure in 1858
• Problems include x-ray measurements: 1.53A for typical C-C, 1.34A for typical C=C, and 1.39A for the 6 carbon-carbon bonds in benzene
• Linus Pauling determined the solution: hybrid orbitals!
• Like metals, bonding electrons are delocalized over the ring
• Unlike metals, energy bands are atomic-like (narrow)
A new idea… for 1989!
Ce
Ce(COT)2
Dolg, Fulde and coworkers(1989-1995): intermediate valence state closer to Ce(III) (nf=0.81), but forms a magnetic singlet with the cyclooctatetraene -ligands: a multiconfigurational ground state of 4fe2u
1e2u3 (81%) and 4f0e2u
4 (19%)
The energy difference to the magnetic (triplet) excited state is on the order of 1 eV (TK~11,600 K).
Kondo: a mechanism for f-bonding
Ce
Ce(COT)2
delocalized ’s (HOMO) do the screening of the f-moment
• If Kondo involved, TK is large enough as to swamp crystal fields
• Could we be thermally occupying a new orbital that also is hybridized strongly with the f hole?
fHOMO
kBTK~Wexp[-f /N(0) Vfc2]
N(0) is density of states at the Fermi level
Wrap up
•George’s contributions to strongly correlated electron systems were broadly based
•For me (and many others) George’s biggest contribution was recognizing a problem and the talents in other people to tackle that problem
• I focussed on f-electron intermetallics
•My work on intermetallics lead me to cerocene and the conjecture that these weird properties of some f-electron organometallics is due to strongly correlated electronic effects
Collaborators and Acknowledgements
Million Daniel, Sang-Wook Han, Evan Werkema,Wayne Lukens, Daniel Kazdan, Dick Andersen (LBNL)
Marc Walter (TU-Kaiserslautern, LBNL)Jon Lawrence (UC Irvine)E. D. Bauer, John Sarrao (Los Alamos National Laboratory)Andrew Ashley, Dermot O’Hare (Oxford)
This research was supported by the Director, Office of Science, Office of Basic Energy Science, Chemical Sciences, Geosciences and Biosciences Division, US Department Energy under Contract Number DE-AC-03-76F00098.
Data were collected on Beamlines 2-3, 10-2 and 11-2 at the Stanford Synchrotron Radiation Laboratory (SSRL), which is operated by the DOE, OBES.
And of course…
George!
Metallocene summary
Attack: Overall lineshape not in the Kondo limit. Impurity model in Kondo limit probably not appropriate HOMO/LUMO gap should become more important for lower TK (?) Better models (for instance, NCA, DFT+correlations, DMFT)
Create molecules with different TK and or HOMO/LUMO gap Explore relationships between the ligand, TK and Other phenomena: valence transitions? U? Np? Pu?
Kondo impurity vs. Anderson lattice
• Kondo investigated the problem of a magnetic impurity in a nonmagnetic host:
• An alternate model was developed by Anderson in 1961 for magnetic alloys, i.e. so-called “concentrated” or “lattice” systems:
,
)0(2k
ckk JnH sS
,
†mix
imp
,band
miximpband
)H.c.(k
k
d
kkk
dcVH
nUnH
nH
HHHH
Kondo Hamiltonian
Anderson Hamiltonian
Kondo=Anderson when d-VU
V2/d=Jc
CeCerocene Ce(COT)2:
Ce
N
N N
N
N N
NN
Ce(Mac)2:
N
N
Yb
R
R
bipy: R=H
bipy-OMe: R= OCH 3
Cp*2Yb(bipy):
bipy: R=H
bipy-OMe: R=OCH3
N
N
Yb
R
Rtbudad: R= C(CH3)3
p-methyldad: R= CH3N
N
Yb
R
Rtbudad: R= C(CH3)3
p-methyldad: R= CH3
Cp*2Yb(dad):
A family of rare-earth metallocenes
Advantages of ytterbium
N
N
Yb
R
R
bipy: R=H
bipy-OMe: R= OCH 3
Cp*2Yb(bipy):
bipy: R=H
bipy-OMe: R=OCH3
Cp*2 Yb (bipy)
N
N
Yb
R
Rtbudad: R= C(CH3)3
p-methyldad: R= CH3N
N
Yb
R
Rtbudad: R= C(CH3)3
p-methyldad: R= CH3
Cp*2Yb(dad):
• Can’t observe the expected temperature dependences if TK is large, like in cerocene!
• Get TK down, need to tune…
• Using Cp* and attached functional groups, can vary the f/ coupling!
The Anderson lattice and the “slow crossover”
0 100 200 3000.000
0.025(e)
YbAgCu4
(c)
(em
u/m
ol)
0.000
0.005
YbTlCu4
(b)
0.000
0.005
YbMgCu4
(a)
0.00
0.05
YbZnCu4
(d)
T(K)
0.000
0.025
YbCdCu4
0.0
0.5
1.0
(ef
f)2 =T/
CJ
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
J. M. Lawrence et al., Phys. Rev. B, 63:054227, 2001. LBNL-46027
A. L. Cornelius et al., Phys. Rev. Lett., 88:117201, 2002. LBNL-49405
nc
0.52
~2
1.2
0.9
1.6
Local moment in a Pu intermetallic
Sarrao et al., Nature 420, 297 (2002)
=Cel/T~m*~1/TK
=77 mJ/mol·K2
Curie-Weiss behavior above Tc
CeAl2 nanoparticle properties
• Primary Kondo evidence is from ~following:
TK(H)2=TK(0)2+(JgBH)2
• Powder diffraction indicates a ~1.1% volume expansion.
• Gruneisen relation gives TK~2-4K
• The rest is attributed to size effects (generic…)
• Claim is TN is suppressed due to inability to support spin waves over such small distances.
• In addition, TK decreases from ~5K to 0.7K
CePt2+x contracts, rather than expands
Cp*2 Yb (bipy)
8900 8920 8940 8960 8980 9000
-0.2
0.0
0.2
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Yb(bipy) Yb(bipy)I
dt)
/dE
E (eV)
Yb L3 XANES Yb(bipy)
Yb(bipy)I
t (
norm
aliz
ed)
• Yb L3 XANES show a divalent component, indicating a valence of 2.80.1
• The valence does not change with temperature from 20 – 300 K
• This result rules out a chemical equilibrium
• Indicates that TK must be at least 750 K
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Bickers, Fig. 14
nf(T
)/n
f(o)
log10 (T/TK)
X-ray absorption spectroscopy
• Main features are single-electron excitations.• Away from edges, energy dependence fits a power
law: AE-3+BE-4 (Victoreen).• Threshold energies increase roughly as Z2.
• Real system 1023 electrons• 1/r2 interaction is long
range• Compute 1023 interactions
with 1023-1 other fermions
• 1023-1 electrons form a Fermi sea of non-interacting “quasiparticles” excitations
• q.p.’s have same quantum numbers (spin, charge), but a renormalized mass m*
• Amazing fact: FLT describes most pre-1985 behavior in the solid state, including metals, superfluid 3He, BCS superconductivity, quantum Hall liquid state, heavy fermions, mixed valence, Kondo, etc. etc. etc
Fermi gas + interactions = Fermi liquid
• Real system 1023 electrons• 1/r2 interaction is long
range• Compute 1023 interactions
with 1023-1 other fermions
• Ground state properties of a Fermi Liquid: T2
= 0
• C~ T
“Kondo Box”
Liang et al., Nature 2002
• A lot of recent attention on the Kondo effect in quantum dots
• In most of these systems, conduction electrons are injected
• Self-contained “Kondo Box” has been lightly explored:Thimm, Kroha and von Delft, PRL 82, 2143 (1999).
Schlottmann, PRB 65, 024420 (2001).
Schlottmann, PRB 65, 022431 (2001).
Chen et al., PRL 84, 4990 (2000).
Kondo: a mechanism for f-bonding
Ce
Ce(COT)2
delocalized ’s (HOMO) do the screening of the f-moment
f-shell is close to fully occupied
• Benzene discovered in 1825 by Faraday
• Linus Pauling determined the solution: hybrid orbitals!
• Like metals, bonding electrons are delocalized over the ring
• Unlike metals, energy bands are atomic-like (narrow)
Kondo: a mechanism for f-bonding
Ce
Ce(COT)2
delocalized ’s get partially localized
localized f’s get partially delocalized
• Benzene discovered in 1825 by Faraday
• Linus Pauling determined the solution: hybrid orbitals!
• Like metals, bonding electrons are delocalized over the ring
• Unlike metals, energy bands are atomic-like (narrow)
Inspiration from the Dark Side?
Cerocenebis-cyclooctatetraene cerium
Ce(COT)2
Ce(C8H8)2
Dolg, Fulde and coworkers(1989-1995): intermediate valence state closer to Ce(III) (nf=0.81), but forms a magnetic singlet with the cyclooctatetraene -ligands
The energy difference to the magnetic (triplet) excited state is on the order of 1 eV (TK~11,600 K).
This picture is very closely analogous to the Kondo effect in the heavy-fermion and mixed valence intermetallics…
A molecular magnetic mystery…
Ce
Ce(COT)2Quick history of CEROCENE, Ce(C8H8)2
Cerocene discovered in 1976 (Greco) following uranocene in 1968 (Streitwieser)
NMR, gas phase photoemission, structure consistent with Ce(IV)
Basic behavior of IV metals
High temperature limit: LOCAL MOMENT PARAMAGNET
Integral valence: nf 1 z = 2+nf = 3 Yb 4f13(5d6s)3
Curie Law: CJ/T where CJ = N g2 B2 J(J+1)/ 3 kB J = 7/2 (Yb)