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f-electron Fermi surface exclusion above TK in CeRu_2Si_2
Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 1
University of Michigan LLNL Talk--April 10, 2002
ff--electron electron Fermi Fermi surface exclusion above Tsurface exclusion above TKK in CeRuin CeRu22SiSi22
LDA“ band 4” hole Fermi surfaceno f- electron
Luttinger counting theorem ⇒⇒
f-electrons counted in Fermi surface IF f-moments quenched.
(no matter what route to Fermi liquid)
dHvA paradigm (Tautz et al, 1995)
•• large Z-po int hole FS f0 LaRu2Si2f1 CeRu2Si2 high field (metamag)f1 CeRu2Ge2 ferromagnet
•• reduced "pil low" hole FS counts ≈≈ ½ Ce f- electronin Kondo CeRu2Si2
--at low temperature
Conjecture (Fulde & Zwick nagl, 1988)
f-electrons exc luded from FS above Kondo temperature TK
Diff icult to test with low-T dHvA.
( ≈≈½ f-electron in o ther multiply-conn ectedcomplex FS piece)
≈≈½ extra f-electronhere
University of Michigan LLNL Talk--April 10, 2002
LDA for LaRuLDA for LaRu22SiSi22 and CeRuand CeRu22SiSi22 comparedcompared
band 4Z- hole pocket
La Ce
f-electron Fermi surface exclusion above TK in CeRu_2Si_2
Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 2
University of Michigan LLNL Talk--April 10, 2002
Fermi Fermi surface of CeRusurface of CeRu22SiSi22
γ = 350 mJ/mol-K2
Γ •
Γ •
Ζ-
• Χ• Χ• Χ
Zwicknagl ‘88Lonzarich ‘88 Tautz ’95
ξξ, µµ, , νν ε ε αα δδ, , γγ, , ββm*/me 120 20 13 4, 2.5,1.6C*/T 194 64
ξξ, µµ, , νν ε ε αα δδ, , γγ, , ββm*/me 120 20 13 4, 2.5,1.6C*/T 194 64
-0.2
-0.1
0.0
0.1
0.2
Bin
ding
Ene
rgy
(eV
)
ΓΓ ΓΓ X ΓΓ(Σ)(Σ)Z
-2
-1
0
1
2
Bin
ding
Ene
rgy
(eV
)
Z ΓΓ ΓΓ(Σ)(Σ)ΓΓ X
Relativistic LDA
Renormalized LDA
G. Zwicknagl, Adv. Phys. 41, 203 (1992).
E.K.R. Runge, R.C. Albers, N.E. Christensen & G. Zwicknagl, Phys. Rev B. 51, 10375 (1995).
University of Michigan LLNL Talk--April 10, 2002
4
6
81
2
4
6
810
2
4
Fre
quen
cy (
kT)
80 40 0 -40
Field Direction (deg)
[001] [100] [110]
LaRu2Si
2 CeRu
2Ge
2
ω
4
6
81
2
4
6
810
2
4
Frr
eque
ncy
(kT
)
15105
H (T)
CeRu2Si
2: H//[001]
below, above
Hm
β
γ
δ
ψ
ω
4
6
81
2
4
6
810
2
4
Fre
quen
cy (
kT)
80 40 0 -40
Field Direction (deg)
[001] [100] [110]
LaRu2Si
2 CeRu
2Si
2
αβ
γ δ
εη
ψ
ω
Ce Ce Spin State & Spin State & FermiFermi Surface of Surface of CeRuCeRu22SiSi22
• LaRu2Si2• CeRu2Ge2
• CeRu2Si2: H>Hm
• CeRu2Si2: H<Hm
Exclude f’sfrom FS forfor T>>TK ???
*ZwicknaglPhysica Scripta
T49, 34 (1993)
f 0
ω
f 1
ψ
ferromagneticCeRu2Ge2FS likeLaRu2Ge2
high fieldmetamagCeRu2Si2FS likeLaRu2Ge2
& T<<TK *or T>>TK
f-electron Fermi surface exclusion above TK in CeRu_2Si_2
Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 3
University of Michigan LLNL Talk--April 10, 2002
XRuXRu22SiSi22——3d crystal3d crystalkk--space arcs for varying photon energyspace arcs for varying photon energy
Brill ou in Zone
ARPES arcs
ΓΓ
ΖΖ
ΧΧ
ΖΖ
ΓΓ
((ΣΣ))
7
6
5
4
3
2k
z
-3 -2 -1 0 1 2 3k
x
200
Ζ Ζ Γ Γ Χ Χ Γ Γ
Ζ Ζ
<100> <110>
3525
15
175
150
125
100
75
Ζ Ζ Γ Γ Χ Χ ΓΓ
kz
kx
<100> <110>
<100>
<110>
University of Michigan LLNL Talk--April 10, 2002
-2
-1
0
1
2
k y (
Å-1
)
-2 -1 0 1 2
kX ( Å
-1)
ΓΖ
Χ
-2
-1
0
1
2
k y (
Å-1
)
152 eV-2
-1
0
1
2
k y (
Å-1
)
122 eV
(a) (c)(b)
LaRuLaRu22SiSi22 FermiFermi surface from ARPESsurface from ARPESJ.D. J.D. Denlinger Denlinger (data from ALS)(data from ALS)
Hole sheets (center = Z) Electron sheets (center = ΓΓ)
hνν fixes kz andmap center' s BZ point
hνν = 122 eV 152 eV LDA
f-electron Fermi surface exclusion above TK in CeRu_2Si_2
Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 4
University of Michigan LLNL Talk--April 10, 2002
Same large hole FS for LaRuSame large hole FS for LaRu22SiSi22and CeRuand CeRu22SiSi22 for Tfor T≈≈≈≈ 120K > 6120K > 6TTKK
J. D. Denlinger et al, 2001
samplesJ. SarraoLANL
University of Michigan LLNL Talk--April 10, 2002
-2
-1
0
1
2
k y (
Å-1
)
-2 -1 0 1 2
kX ( Å
-1)
Γ
Χ
Ζ
-2
-1
0
1
2
k y (
Å-1
)
122 eV-2
-1
0
1
2
k y (
Å-1
)
91 eV
(a) (b) (c)
Experimental Experimental FermiFermi Surface Surface —— 4f weight at low 4f weight at low mass mass ΓΓΓΓ, Z points, Z points for CeRufor CeRu22SiSi22
hνν = 91 eV
dHvA: m/me = 4, 2.5, 1.6,m/me=13,20
m/me = 120
Hole sheets (center = Z)
hνν = 122 eV LDA
Electron sheets (center = ΓΓ)
f-electron Fermi surface exclusion above TK in CeRu_2Si_2
Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 5
University of Michigan LLNL Talk--April 10, 2002
CeRuCeRu22SiSi22 ARPES good and bad cleavesARPES good and bad cleaves
good
bad
University of Michigan LLNL Talk--April 10, 2002
CeRuCeRu22SiSi22 angle integratedangle integrated
6
4
2
0-6 -5 -4 -3 -2 -1 0
Binding Energy (eV)
Avg All80
60
40
20
0
806040200
Polar (deg)
∆θ = ±4°
“ Good” sur faceangle-integrated 4d RESPES from ARPES
53 angles, normalize at 5 eV, average
f-electron Fermi surface exclusion above TK in CeRu_2Si_2
Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 6
University of Michigan LLNL Talk--April 10, 2002
Surface effect in CeRuSurface effect in CeRu22SiSi22
Dashed lines—extremumbehavior in set with better angle resolution
Solid lines—extremumbehavior of this data set
Bold—angle summedspectrum
University of Michigan LLNL Talk--April 10, 2002
Low hLow hνννν OK forOK for CeRuCeRu22SiSi22
(a) and (b)ARPES from center of normal emission Z-point
(d) Ce 3d edge RESPESwith 0.2 eV resolution
(consistent with SPr ing8 data)(c) angle summed 4d edge
RES-ARPES
Evidence that bulk behavior can be seen in 4d RESPES of thismaterial
Denlinger et al, SCES’01 proceedings
f-electron Fermi surface exclusion above TK in CeRu_2Si_2
Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 7
University of Michigan LLNL Talk--April 10, 2002
CeRuCeRu22SiSi22 why bulk at low hwhy bulk at low hνννν??
• Crystal structure admits two cleavage planes, with and without Ce
“ Good cleaves” probably from sur face without Ce.
I .e., bur ied active layer—impor tant for cuprates
• Really flat sur face missing edges and steps, less “ sur face sensitive.
University of Michigan LLNL Talk--April 10, 2002
Anderson Latt ice ModelAnderson Latt ice Model22--band low energy band low energy ansatzansatz
-0.2
0.0
0.2
E -
E F(e
V)
0.40.20.0-0.2-0.4k (Å
-1)
E+
E-
εd(k)
εf
εf 'EF
kFkF'
-0.2
0.0
0.2
E -
EF
(eV
)
-0.4 -0.2 0.0 0.2 0.4
k (Å-1
)
d
-0.4 -0.2 0.0 0.2 0.4
k (Å-1
)
f
(a)
(b)
(c)
Qualitatively s imilar to LDA for CeRu2Si2poss ible origin of success for LDA FS of Ce materials
• renormalized f near EF• renormalized
hybridization to d
f-electron Fermi surface exclusion above TK in CeRu_2Si_2
Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 8
University of Michigan LLNL Talk--April 10, 2002
ff--d mixingd mixing
CeRu2Si2 (122 eV, ~Z)
4f, γ=350
J. D. Denlingeret al, 2001samples: Maple, Fisk,Sarrao
5f, γ=180
URu2Si2 (108 eV, ~X)