Bulk and surface
electronic properties
of RERh2Si2 compounds(RE = rare-earth element)
as observed by ARPES
C. Laubschat,Technische Universität Dresden,
GermanyAknowledgement:

RET2Si2 compounds (RE = rare-earth, T = Co, Rh, Ir)
Si-terminated
RET

Cleavageplanes• ThCr2Si2-structure• Tightly bond Si-T-Si blocks→ cleavage between RE and Si layers• Surface state at Si-terminated surfaces
M. Güttler et al., PRB 90,195138 (2014)RE-terminatedYbRh2Si2, mean valence ~2,9
Yb-terminatedsuface signal

Yb2+
surfaceSi-terminatedbulk signal

Yb2+
bulk

S. Danzenbächer et al., PRB 75, 45109 (2007)

YbRh2Si2: Analysis within SIAM

4f13

4f12
surfacebulk• Bulk emission governed by stron 4f12 final-state multiplet and weak 4f13
doublet → mixed valent, valence 2,93
SIAM-Parameter: Epsilon_f = 0.1 eV, Delta = 0.12 eV, Uff = 6 eV
• Surface emission: Purely divalentYbRh2Si2: Yb and Si-termination

Binding Energy (eV)EF1.0
Yb-terminatedSi-terminated• Induced 4f-dispersion due to “avoid crossing“ of Rh-4d-band• Bulk: 4f crystal field splittings + 4f Fermi-level crossing → HF system• Yb surface: No CEF splittings and Fermi-level crossings → stable Yb2+
D.V. Vyalikh, PRL 105, 237601 (2010)

CeRh2Si2: Surface termination• Surface termination may be
determinated by watching thesurface state within the large
gap of the projected bandstructure around the M-point(marked by star) which only
exists at Si-terminated surfaces• Also the surface resonance atthe Γ-point (Dirac cone) is
characteristic for Si-termination
although there are underlying
bulk bands weakly visible alsoat Ce termination.
• Data taken off-resonance at112 eV photon energy
S. Patil et al., Nature Comm. 7,
11029 (2016)

Si-terminatedCe-terminatedCeRh2Si2: Bulk and surface electron structure• Ce at surface sites:
Well defined ionization
peak (4f0),
4f1 signal only aroundΓ-point consisting almostof 4f15/2 component at EF..
⇒ weakly hybridized• Ce in the bulk:
4f0-character fully merged
into the valence band.
Intense 4f15/2 emission
with crystal field splitting
and 4f17/2 side band.
⇒ strongly hybridized
S. Patil et al., Nature Comm. 7,11029 (2016)

4 f 51/ 2
4 f 71/ 2

4f0

4 f 51/ 2
4 f 71/ 2

Valence f-DOS on Ce (arb.units)

Different hybridization in the bulk and at the surface
0.3

CeRh2Si2

f-LDOSburied Ce
Si-terminated0.2

buried Ce
Ce-terminated

0.1

0.0-3

surface Ce
Ce-terminated-2-10

Energy (eV)• hybridization ~ hopping probability 4f ↔ valence band f-LDOS• surface: coordination reduced → hopping probability reduced• surface: f-LDOS near EF reduced → hopping probability reduced• bulk: f-LDOS large around 2 eV → strong hybridization of 4f0-stateSimulation within the Single-Impurity Anderson-ModelPES Intensity (arb.units)

0.5
0.4

CeRh2Si2

experiment,
Ce-termination

SIAM-2

4f0

0

Ce at Ce-terminated surface+ residual Ce bulk emission

4f1

0.3

-1

experiment,
Si-termination

0.2-2-100.1

Ce buried (bulk)

0.0

Ce at Ce-terminated surface-3-2-10

Energy (eV)Parameter: Bulk:
Epsilon_f = - 1.7 eV, Delta = 1.05 eV, Uff = 6 eV.
Surface: Epsilon_f = - 1.9 eV, Delta = 0.7 eV (70% from bulk),→ strong 4f1-signal for bulk Ce, shift and smearing of weak 4f0 component→ weak4f1-signal for Ce at surface, well pronounced 4f0 component

Thermochemical model: Valence of rare-earth elements
ΔEII,III : free atom excitation energy[Xe]4fn(5d6s)2→ [Xe]4fn-1(5d6s)3⇒ all rare-earths except La, Gd, Lu
are divalent in the gas phase

B. Johansson, Phys. Rev. B20, 1315 (1979)

Valence of rare-earth elements
ΔEII,III : free atom excitation energy[Xe]4fn(5d6s)2→ [Xe]4fn-1(5d6s)3⇒ all rare-earths except La, Gd, Lu
are divalent in the gas phase

ΔEcohII,III = EcohIII – EcohII⇒ zero line shifts downwards

ΔEcohIII,IIMetals: Gain in cohesive energy⇒ only Eu, Yb remain divalent
BULK

B. Johansson, Phys. Rev. B20, 1315 (1979)

Valence of rare-earth elements
ΔEII,III : Free atom excitation energy[Xe]4fn(5d6s)2→ [Xe]4fn-1(5d6s)3⇒ all rare-earths except La, Gd, Lu

Metals: Gain in cohesive energy
ΔEcohII,III = EcohIII – EcohII⇒ zero line shifts downwards

ΔEcohsurf

are divalent in the gas phase⇒ only Eu, Yb remain divalent

SURFACEBULKSurfaces: Cohesive Energy reduced
ΔEcohsurf ≈ 0,8*ΔEcohbulk⇒ Sm-metal reveals surface valencetransition to divalent state
B. Johansson, Phys. Rev. B20, 1315 (1979)

Photoemission of 4f-states
Divalent systems:
Fully screened final state
EBIN = ΔEII,III + EIMP
Impurity term considers that
not the whole system undergoes
valence transition
pure metals: EIMP ≈ 0.6 eVcompounds: EIMP ≈ 0,1 eV
SURFACE
BULK

B. Johansson, Phys. Rev. B20, 1315 (1979)

Photoemission of 4f-states
Divalent systems:
Fully screened final state
EBIN = ΔEII,III + EIMP
Impurity term considers that
not the whole system undergoes
valence transition
pure metals: EIMP ≈ 0.6 eVcompounds: EIMP ≈ 0,1 eV
SURFACEAt surfaces EBIN larger:surface core-level shift

B. Johansson, Phys. Rev. B20, 1315 (1979)

BULK

Photoemission of 4f-states
RERh2Si2 compounds:
RE = Yb: mixed-valent
EBIN ≈ 0 eV,
EBINsurf ≈ 0,7 eV

Photoemission of 4f-states
RERh2Si2 compounds:
RE = Yb: mixed-valent
EBIN ≈ 0 eV,
EBINsurf ≈ 0,7 eV
RE = Eu: divalent
EBIN ≈ 0,2 eV,
EBINsurf ≈ 1,0 eV

Photoemission of 4f-states
RERh2Si2 compounds:
RE = Yb: mixed-valent
EBIN ≈ 0 eV,
EBINsurf ≈ 0,7 eV
RE = Eu: divalent
EBIN ≈ 0,2 eV,
EBINsurf ≈ 1,0 eV
Prediction for whole series:
All RE except Eu, Yb
trivalent in the bulk
and at the surface!

SURFACE
BULK

Inclination of lines due todifferent atomic volumes!

Photoemission of 4f-states
RERh2Si2 compounds:
RE = Yb: mixed-valent
EBIN ≈ 0 eV,
EBINsurf ≈ 0,7 eV
RE = Eu: divalent
EBIN ≈ 0,2 eV,
EBINsurf ≈ 1,0 eV
Prediction for whole series:
All RE except Eu, Yb
trivalent in the bulk
and at the surface!
RE = Sm; EBIN ≈ -1,1 eV
EBINsurf ≈ -0,2 eVTrivalent in the bulk
and at the surface

SURFACE
BULK

SmRh2Si2
Si-terminatedSm-terminated
(a)
(b)

(c)

(d)

• Si-termination identified by surface state around M-point
A. Chikina et al., PRB 95, 155127 (2017)

SmRh2Si2
Si-terminatedSm-terminated
(a)
(b)

(c)

Surface signal(d)Bulk signal• Si-termination identified by surface state around M-point• Bulk and surface spectra dominated by 4f4 multiplets• Clear surface-shift of 4f4 multiplet → almost trivalent in the bulk and at the surfaceBulk signal broadened by hybridization, surface shift 0.3-1.0 eV

SmRh2Si2
Si-terminatedSm-terminated
(a)
(b)

(c)

Sm-terminatedSm-terminated(d)• Si-termination identified by surface state around M-point• Bulk and surface spectra dominated by 4f4 multiplet• Clear surface-shift of 4f4 multiplet → almost trivalent in the bulk and at the surface• Non-dispersive stripe-structure near EF → additional 4f5 multiplet?

SmRh2Si2
Si-terminatedSm-terminated(a)(b)

Si-terminatedSm-terminatedoff-resonance
(c)

(d)

• Spectral shape similar for bulk and surface• H. Yamaoka et al, PRB 85, 115120 (2012)
Similar stripes observed in SmSn3 assigned toshifted 4f5 multiplet

SmRh2Si2
Si-terminatedSm-terminated
(a)
(b)

(c)

Si-terminatedSm-terminated

(d)

2.0

1.5

1.0

0.5

0.0

• For mixed-valent Sm 4f5-multiplet must
Surface f-DOS
be pinned at EF both for bulk and surface• Intensity of individual multiplet terms may be altered due to resonance• Mixed-valent in the bulk and at the surface with mean valence around 2.9

Sm-valence in SmRh2Si2: SIAM
• Neglect of multiplet effects
and double-excitations• Estimation of Δ-parameterfrom interpolation between
Ce- and Yb-system
Bulk:
Δ = 0.7 eV

SIAM simulation
without multiplets• Assumption: Reduction ofΔ at surface to 70% of bulk
value
• Setting ε = -EBIN(4f4)Bulk:
ε = -6.0 eV
Surface: ε = -6.3 eV• With Uff = 7 eV from LDA+U
we get for -EBIN(4f5) ≈ ε + Uff
Bulk: EBIN = -1.0 eV (-1.1 eV)
Surf: EBIN = -0.7 eV (-0.3 eV)thermochemical estimate inparentesis

Result of SIAM:
Bulk:
mean Sm-valence:
2.94
Surface: mean Sm-valence:
2.95
Behavior qualitatively similar to Ce!

Why is EuRh2Si2 stable divalent?
• Assuming for Eu similar Δ as for Sm and ε = 0.2 eV→ EuRh2Si2 should be mixed-valent, mean valence ~2.5!
• Photoemission: No trace of 4f5 final-state multiplet characteristic for Eu3+

6F

4f6

7F

6H

4f6
EuRh2Si2hv = 142 eV

Expected
Eu-spectrum

4f5

4f7

Sm3+Eu2+7F• Hopping directly or via virtual low-energy excitations of 4fn-configurations• Sm: Strong overlapp of 4f5 6F and 4f6 7F terms• Eu: No low-energy excitations possible in 4f7 (spin-flip requires ΔE > 4 eV)→ hybridization strongly reduced! A. Chikina et al., PRB 95, 155127 (2017)

Summary:•clear determination of surface termination by inspection of surface
state characteristic for Si-termination• different degree of 4f-hybridization in the bulk and at the surface:
YbRh2Si2: bulk intermediate valent close Yb3+, surface stable divalent
CeRh2Si2: strongly hybridized in the bulk, weakly at the surface• estimation of surface valence by means of thermochemical model
SmRh2Si2: bulk and surface intermediate valent close to Sm3+
- explanation whithin SIAM in analogy to Ce-compounds- possible Kondo-phenomena in Sm-compounds ?
EuRh2Si2: bulk and surface stable divalent, although mixed-valence
expected from analogy to Sm-compound- strongly reduced hybridization due to lacking low-energy multiplet ?
- phenomenon generally encountered in Eu-compounds, wherein contrast to weak T-dependent valence changes in Yb and Ce-systems
strong abrupt 1st-order transitions take place upon T or p-changes