f-electron Fermi surface exclusion above TK in CeRu 2Si 2online.itp.ucsb.edu/online/cem02/allen1/pdf/Allen_f... · 2002-09-24 · f-electron Fermi surface exclusion above TK in CeRu_2Si_2

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


LDA for LaRuLDA for LaRu22SiSi22 and CeRuand CeRu22SiSi22 comparedcompared

band 4Z- hole pocket

La Ce




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).


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




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>


-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




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


-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)




CeRuCeRu22SiSi22 ARPES good and bad cleavesARPES good and bad cleaves

good

bad


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




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


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




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.


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




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)

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f-electron Fermi surface exclusion above TK in CeRu 2Si 2online.itp.ucsb.edu/online/cem02/allen1/pdf/Allen_f... · 2002-09-24 · f-electron Fermi surface exclusion above TK in CeRu_2Si_2