resonance x-ray refectvity — a tool to extract valence profles ......ue46-pgm1 beamline at bessy...
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Resonance X-ray refectvity — a tool to extract valence profles and atomic scatering factors
Dresden, December 2018
Volodymyr Zabolotnyy
Experimental Setup
Image http://www.is.mpg.de
Image http://www.is.mpg.de
RSXS Endstation
1. (Resonant) Soft X-ray Scattering (RSXS) / X-Ray reflectometry- 10-motion UHV diffractometer (4-circle diffractometer + x,y,z and detector motions)- Detectors: Channeltron, Photodiode, with multiple slits and filters, 2D Micro-Channelplate (MCP), Polarization Analyzer, Multi-channel Scaler, Electrometer.
2. X-ray Absorption Spectroscopy (XAS) - by total electron yield (TEY), total fluorescence yield (TFY)
3. Magnetic Circular Dichroism (MCD)- full polarization control of the incoming beam.
REIX beamline at CLS
CLS, Canada
RSXS Scattering Chamber
In-Vacuum Diffractometer He4 closed cycle cryostat
Permanentmagnet
Selected Applications
• Resonant diffraction from magnetic, charge, and orbital order superstructures
• Spectroscopy of electronic ordering phenomena
• Magnetization states of single molecular magnets
• Element-specific magnetic hysteresis loops
UE46-PGM1 beamline at BESSY
CLS, Canada
Calculatng refectvity from a stack
A. Single interface Fresnel equations ⇒ B. Thick sample iterative Parrat approach ⇒
Calculatng refectvity from a stack
incident σ
incident πreflected σ
reflected π
transmitted σ
transmitted π
incident σ
M
C. Thick sample, arbitrary polarization+anisotropic ε(z) matrix approach⇒
Continuity condition:
SUBSTRATE
SURFACE
12
10
8
6
4
2
0
(1-n
) 1
0-3
302520151050
distnce (Å)
Where does element sensitvity comes from?
cO~χO (E)
cFe~χFe(E)
n−1=∑a
2π ca r0
k 2( f ' (E )+if ' ' (E))
sum over chemical elements atomic concentration in mol/cm³
atomic scattering length
n−1=∑a
ca~χa(E)
Lab-based of single-energy reflectivity measurements cannot be element sensitive.
R(qz)n(z)
``
Where does element sensitvity arise from?
100806040200distance (Å)
0.16
0.12
0.08
0.04
0.00Co
nce
ntra
tion
(m
ol/c
m³)
O Cu
10-10
10-8
10-6
10-4
10-2
100
0.60.40.20.01/Å
E = 926.0eV
10-10
10-8
10-6
10-4
10-2
100
0.60.40.20.01/Å
E = 500.0eV
20151050-5
1000
900
800
700
600
“Habitable zone„ for sof X-ray refectvity
█ K- edges█ L-edges█ M-edges
Optcal constants
1. Theoretical calculation away from resonances
● Chantler et al. AIP 652, 370 (2003) ● Chantler et al. J Phys Chem Ref Data 24, 71 (1995)● Chantler et al. J Phys Chem Ref Data 29, 597 (2000)
2. Total Electron Yield used as absorption
next most red 563 pages:
fit regions fit regions
Kramers– Kronig
R(qz)
12
10
8
6
4
2
0
(1-n
) 1
0-3
302520151050
distnce (Å)
Where the vicious circle begin...
cO~χO (E)
cFe~χFe(E)
wanted, but close to impossible n−1=∑a
ca~χa (E)
n(z)R(qz) n(z)
optimize & try again
trivial and rarely needed
Fitting R(q) to chemical profles
Totally unrestricted fit:
1) 4 elements2) 300Å thik sample (3Å x100 slices)3) Elemental concentration in the range 0–0.100cm³ at Δc = 0.005cm³ resolution (5%)
Size of the “phase space” 400 fit parameters, each with 20 levels = 20400
~ 2 x 10520
0.030
0.025
0.020
0.015
0.010
0.005
0.000
Co
nce
ntr
atio
n (
mo
l/cm
³)
200150100500distance (Å)
d
σc
Parametrization in terms of Roughness σ, thickness d, concentration c, brings the number of “free” fit parameters typically below 3 x 3 layers x 4 elements = 36
20⇒ 36 ~7 x 10
46 distinct points in “phase space” with plenty of local minima.
⇒ Necessity of sophisticated fit methods.
Fitness profle
Commonly used gradient descent methods are not suitable to fit reflectivity data, due to large number of local minima and strong non-linearity
parameter 1 para
met
er 2
Fitting approaches:
Some modification of an Evolution algorithms appear to be the most suited to fit reflectivity data.
Fitting R(q) to chemical profles
RemagX (S. Macke)
Simulation:● Parrat formalism ● Matrix formalism
Fit:● Evolution ● Simplex ● Levenberg&Marquardt
Own code under IgorPro
Simulation:● Parrat formalism ● Coupling with theory (Quanty)
Fit:● Evolution+dynamic mutation
● direct import of SPECS data ● preprocessing (cutting, resampling, backround)
Fitting R(q) to chemical profles
Param. distribution in the populationTime convergence of χ²(p1, ...pN)
Overview of all experimental and simulated spectraAtomic conc. profiles dcσ-model
“Real life” example: ZnO/Fe3O4
10-5
10-4
10-3
10-2
10-1
Det
/Mon
itor
0.300.200.10
1/Å 10-5
10-4
10-3
10-2
10-1
100
Det
/Mon
itor
0.200.150.100.05
1/Å 10-6
10-4
10-2
100
Det
/Mon
itor
0.200.150.100.05
1/Å
10-6
10-4
10-2
100
Det
/Mon
itor
0.250.200.150.100.05
1/Å 10-6
10-4
10-2
100
Det
/Mon
itor
0.250.200.150.100.05
1/Å10
-5
10-4
10-3
10-2
10-1
100
Det
/Mon
itor
0.300.200.100.00
1/Å
10-5
10-4
10-3
10-2
10-1
Det
/Mon
itor
0.300.200.10
1/Å 10-6
10-5
10-4
10-3
10-2
10-1
Det
/Mon
itor
0.40.30.20.1
1/Å 10-6
10-4
10-2
Det
/Mon
itor
0.40.30.20.1
1/Å
10-6
10-4
10-2
Det
/Mon
itor
0.40.30.20.1
1/Å 10-6
10-4
10-2
Det
/Mon
itor
0.50.40.30.20.1
1/Å 10-6
10-4
10-2
Det
/Mon
itor
0.50.40.30.20.1
1/Å
Sc_15E = 650.0eVchi = 0.0014
Sc_16E = 350.0eVchi = 0.0038
Sc_17E = 400.0eVchi = 0.0024
Sc_18E = 450.0eVchi = 0.0020
Sc_19E = 500.0eVchi = 0.0060
Sc_20E = 550.0eVchi = 0.0084
Sc_21E = 600.0eVchi = 0.0008
Sc_24E = 750.0eVchi = 0.0007
Sc_25E = 800.0eVchi = 0.0011
Sc_26E = 850.0eVchi = 0.0011
Sc_27E = 900.0eVchi = 0.0013
Sc_28E = 950.0eVchi = 0.0011
Sc_29E = 1000.0eVchi = 0.0008
Sc_34E = 709.6eVchi = 0.0043
Sc_35E = 719.7eVchi = 0.0017
Sc_36E = 721.6eVchi = 0.0027
Sc_37E = 723.2eVchi = 0.0021
Sc_38E = 561.0eVchi = 0.0020
Sc_40E = 650.0eVchi = 0.0015
Sc_52E = 250.0eVchi = 0.0080
Sc_53E = 300.0eVchi = 0.0041
Sc_64E = 710.0eVchi = 0.0049
Sc_76E = 720.0eVchi = 0.0013
Sc_77E = 721.0eVchi = 0.0006
Sc_78E = 722.0eVchi = 0.0006
Sc_79E = 723.0eVchi = 0.0019
Sc_80E = 724.0eVchi = 0.0026
Sc_81E = 725.0eVchi = 0.0025
Sc_82E = 726.0eVchi = 0.0023
Sc_83E = 727.0eVchi = 0.0022
Sc_84E = 728.0eVchi = 0.0020
Sc_85E = 729.0eVchi = 0.0019
Sc_86E = 730.0eVchi = 0.0018
Sc_90E = 541.0eVchi = 0.0021
Sc_91E = 547.5eVchi = 0.0013
0.10
0.08
0.06
0.04
0.02
0.00
Co
nce
ntr
atio
n (
mo
l/cm
³)
200150100500distance (Å)
Fe O Zn C
Off-resonance spectra, E = 350–1000eVFe optical constants, Chantler
Chemical profile
30
25
20
15
10
5
0
-51000900800700600500400300
Energy (eV)
Fe f' f''
“Real life” example: ZnO/Fe3O4
0.10
0.08
0.06
0.04
0.02
0.00
Co
nce
ntr
atio
n (
mo
l/cm
³)
200150100500distance (Å)
Fe O Zn C
on-resonance spectra, E = 700–730eVFe optical constants, Chantler
Chemical profile
30
25
20
15
10
5
0
-51000900800700600500400300
Energy (eV)
Fe f' f''
10-6
10-5
10-4
10-3
10-2
10-1
Det/M
onito
r
0.40.30.20.1
1/Å 10-6
10-5
10-4
10-3
10-2
10-1
Det/M
onito
r
0.40.30.20.1
1/Å10
-6
10-5
10-4
10-3
10-2
10-1
De
t/Monito
r
0.40.30.20.1
1/Å
10-6
10-5
10-4
10-3
10-2
10-1
Det/M
onito
r0.40.30.20.1
1/Å 10-6
10-5
10-4
10-3
10-2
10-1
Det/M
onito
r
0.40.30.20.1
1/Å 10-6
10-5
10-4
10-3
10-2
10-1
De
t/Monito
r
0.40.30.20.1
1/Å
0.0001
0.001
0.01
0.1
Det/M
onito
r
0.200.150.100.05
1/Å0.0001
0.001
0.01
0.1
Det/M
onito
r
0.40.30.20.1
1/Å0.0001
0.001
0.01
0.1
De
t/Monito
r
0.250.200.150.100.05
1/Å
10-6
10-5
10-4
10-3
10-2
10-1
Det/M
onito
r
0.40.30.20.1
1/Å10
-6
10-5
10-4
10-3
10-2
10-1
Det/M
onito
r
0.40.30.20.1
1/Å10
-6
10-5
10-4
10-3
10-2
10-1
De
t/Monito
r
0.40.30.20.1
1/Å
Sc_24E = 750.0eVchi = 0.0008
Sc_34E = 709.6eVchi = 0.0213
Sc_35E = 719.7eVchi = 0.0031
Sc_36E = 721.6eVchi = 0.0055
Sc_37E = 723.2eVchi = 0.0052
Sc_64E = 710.0eVchi = 0.0213
Sc_76E = 720.0eVchi = 0.0026
Sc_77E = 721.0eVchi = 0.0025
Sc_78E = 722.0eVchi = 0.0027
Sc_79E = 723.0eVchi = 0.0044
Sc_80E = 724.0eVchi = 0.0064
Sc_81E = 725.0eVchi = 0.0070
Sc_82E = 726.0eVchi = 0.0068
Sc_83E = 727.0eVchi = 0.0062
Sc_84E = 728.0eVchi = 0.0054
Sc_85E = 729.0eVchi = 0.0047
Sc_86E = 730.0eVchi = 0.0041
“Real life” example: ZnO/Fe3O4
0.10
0.08
0.06
0.04
0.02
0.00
Co
nce
ntr
atio
n (
mo
l/cm
³)
200150100500distance (Å)
Fe O Zn C
on-resonance spectra, E = 700–730eVFe optical constants, corrected
Chemical profile
80
60
40
20
0
-20
-40
-601000900800700600500400300
Energy (eV)
Fe f' f''
10-5
10-4
10-3
10-2
10-1
Det
/Mon
itor
0.40.30.20.1
1/Å10
-5
10-4
10-3
10-2
10-1
Det
/Mon
itor
0.40.30.20.1
1/Å10
-5
10-4
10-3
10-2
10-1
Det
/Mon
itor
0.40.30.20.1
1/Å
0.0001
0.001
0.01
0.1
Det
/Mon
itor
0.200.150.100.05
1/Å0.0001
0.001
0.01
0.1
Det
/Mon
itor
0.40.30.20.1
1/Å0.0001
0.001
0.01
0.1
Det
/Mon
itor
0.250.200.150.100.05
1/Å
10-5
10-4
10-3
10-2
10-1
Det
/Mon
itor
0.40.30.20.1
1/Å10
-5
10-4
10-3
10-2
10-1
Det
/Mon
itor
0.40.30.20.1
1/Å10
-5
10-4
10-3
10-2
10-1
100
Det
/Mon
itor
0.40.30.20.1
1/Å
10-5
10-4
10-3
10-2
10-1
100
Det
/Mon
itor
0.40.30.20.1
1/Å10
-5
10-4
10-3
10-2
10-1
100
Det
/Mon
itor
0.40.30.20.1
1/Å10
-5
10-4
10-3
10-2
10-1
Det
/Mon
itor
0.40.30.20.1
1/Å
Sc_24E = 750.0eVchi = 0.0007
Sc_34E = 709.6eVchi = 0.0043
Sc_35E = 719.7eVchi = 0.0017
Sc_36E = 721.6eVchi = 0.0027
Sc_37E = 723.2eVchi = 0.0021
Sc_64E = 710.0eVchi = 0.0049
Sc_76E = 720.0eVchi = 0.0013
Sc_77E = 721.0eVchi = 0.0006
Sc_78E = 722.0eVchi = 0.0006
Sc_79E = 723.0eVchi = 0.0019
Sc_80E = 724.0eVchi = 0.0026
Sc_81E = 725.0eVchi = 0.0025
Sc_82E = 726.0eVchi = 0.0023
Sc_83E = 727.0eVchi = 0.0022
Sc_84E = 728.0eVchi = 0.0020
Sc_85E = 729.0eVchi = 0.0019
Sc_86E = 730.0eVchi = 0.0018
Ozan190 – O terminated
0.10
0.08
0.06
0.04
0.02
0.00
conce
ntr
atio
n (
mol/c
m³)
200150100500
distance (Å)
Zn O Fe
σ(Zn) = σ(Fe) independent from σ(O)
Surface contaminaton effectively accounted
by oxygen
0.10
0.08
0.06
0.04
0.02
0.00
con
cent
ratio
n (
mo
l/cm
³)
250200150100500
distance (Å)
Zn O Fe
Ozan194 – Zn terminated
σ(Zn) = σ(Fe) independent from σ(O)
Surface contaminaton effectively accounted
by oxygen
11Å
Comparison to STEM
O terminated Zn terminated
exfoliation?
O. Kirilmaz et al. in preparation
Optcal constants
1. Theoretical calculation away from resonances
● Chantler et al. AIP 652, 370 (2003) ● Chantler et al. J Phys Chem Ref Data 24, 71 (1995)● Chantler et al. J Phys Chem Ref Data 29, 597 (2000)
2. Total Electron Yield used as absorption
next most red 563 pages:
fit regions fit regions
Kramers– Kronig
Hydrogen atom
f2 → σabs → transition rate → matrix element
0.4 0.6 0.8 1.0 1.20.0
0.2
0.4
0.6
0.8
1.0
Energy (Ry)
f 2(e
/ato
m)
Analytical expressions for f2(E) can be derived:
Comparison to C.T. Chanter data:
10-10
10-8
10-6
10-4
10-2
100
f 2(e
/ato
m)
101
102
103
104
105
Energy (eV)
Chantleranalytical
Comparison to experimental polarizability:
H atom is a suitable test system, since its discrete and continuous spectrum of is known analytically
Total mass attenuation coefficients [µ/ ρ]tot silver.
C. Q. Tran et al., J. Phys B 38, 89 (2005)
2p
3p
4p
1s
∞p
1 2 5 10
0.01
0.05
0.10
0.50
1
f 2(e
/ato
m)
Energy (Ry)
Theoretcal optcal constants
Crystal/Ligand field cluster calculation
M. W. Haverkort et al. PRB 85, 165113 (2012)
================================================================= written by Maurits W. Haverkort ======== with contributions from: ======== Yi Lu, Robert Green and Sebastian Macke ======== (C) 1995-2015 All rights reserved ======== www.quanty.org ======== Beta version, be critical and report errors!!! ===================================================================== Version compiled at: Mar 14 2015 at 10:24:16 ===================================================================== When used in scientific publications please cite ======== Phys. Rev. B 85, 165113 (2012) ======== Phys. Rev. B 90, 085102 (2014) ======== Euro Phys. Lett. 108, 57004 (2014) =================================================================
2.0
1.5
1.0
0.5
0.0
f''(
E)
(a
rb.
u.)
3020100-10-20
Comparison to experimental polarizability:
~
NiO – Theory restricted ft
10-5
10-4
10-3
10-2
10-1
100
R(q
)
0.40.30.20.1Momentum q (1/Å)
0.40.30.20.1 0.40.30.20.1 0.40.30.20.1 0.40.30.20.1 0.40.30.20.1
E = 855.1eV E = 856.3eV E = 859.3eV E = 866.7eV E = 870.2eV E = 870.9eV
10-5
10-4
10-3
10-2
10-1
R(q
)
0.40.30.20.1
1/Å
0.250.05
1/Å
0.300.200.10
1/Å
0.40.30.20.1
1/Å
0.50.40.30.20.1
1/Å
0.200.10
1/Å
E = 800.0eV E = 700.0eV E = 600.0eV E = 900.0eV E = 1000.0eV E = 500.0eV
Momentum q (1/Å)
860840 860840 860840 860840 860840 880860840
th = 5.0°tth = 10.0°
th = 10.0°tth = 20.0°
th = 12.5°tth = 25.0°
th = 15.0°tth = 30.0°
th = 17.5°tth = 35.0°
th = 20.0°tth = 40.0.°
R(q
)
Energy (eV)
0.10
0.05
0.00
Con
cent
ratio
n (m
ol/c
m³)
120100806040200z(Å)
NiOMgC
off-resona nton-resona nt
150
100
50
0870860850
Energy (eV)
Experimental f2(E)Theoretical f2(E)
f 2(E
)
150
100
50
0870860850
Energy (eV)
NiO NiO
NiO, Measured R(E, q) NiO, Model R(E, q)
undershoot in TEY at L3
q, (
1/Å
)
overshoot in TEY at L2
NiO – Theory restricted ft
K. Fürsich, V. Zabolotnyy, E Schierle et al. PRB 97, 165126 (2018)
M. Neupane et al. Nat Comm 4, 2991 (2013)
● Mixed valent system● Kondo insulator● Topologically protected ingap surface state
Heming et al. B 90, 195128 (2014)
Disrupted stoichiometry at the cleaved surface?
SmB6 — Intro
SmB6 – samples
Often samples with polished surfaces are used for resonant x-ray experiments
Surface contaminated and unstable
It is too rough for reflectivity
We use floating-zone samples, cut in rods, pre-oriented
Cleavage in fast entry at 10-8 mBar, transfer to 2*10-10 mBar in reflectivity chamber
Cleaves along (100) even if cut along (111) Surface size ~ 1mm x 1mm Sufficiently large terraces (beam ~ 100 mm)
No indications of oxygen in TEY spectrum
SmB6 – a multivalent system
SmB6 – a multivalent system
V. Zabolotnyy, K. Fürsich, R. J. Green et al. PRB 97, 205416 (2018)
Thank you for your atentonQuestons are welcome.
Acknowledgements and contributions:
K. Fürshich,A. Tcakaev, M. Dettbarn, B. Katter Uni WürzburgChul-Hee Min, O. KirilmazF. Reinert, V. Hinkov
R. Green University of British Columbia, Vancouver
M. Haverkort MPI for CPS, Dresden/Uni Heidelberg
D. Inosov TU-Dresden
R Suatro Canadian Light SourceFeizhou He
E. Schierle BESSYC. Schüssler-Langeheine
E. Weschke
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