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Resonant Elas+c and Inelas+c X ray sca2ering George A Sawatzky
Physics department and Max Planck/UBC center for Quantum Materials
UBC
The main people involved • Ilya Elfimov UBC • Maurits Haverkort MP/
UBC • Robert Green CLS/UBC • Steve Johnston UBC/MP • Shadi Balendeh UBC • Mona Berciu UBC • Jeroen van den Brink
(Dresden) IFW • Subhra sen Gupta (Riken)
• Vladimir Hinkov MP/UBC • Sesbas+an Make MP/UBC • Valen+na Bisogni PSI • Thorsten Schmi2 PSI • Sara Catalano Geneva • Marta Gibert Geneva • Jean-‐Marc Triscone
Geneva • Ronny Sutarto CLS • Feizou He CLS
What would we like to Study
• The ordering of atoms • The valence electron states of the elements • The ordering of the magne+c moments (Spins) • The ordering of the quadrupole moments of the elements
• Phase transi+ons in these orderings • Elementary excita+ons; phonons, magnons, orbitons
• The above for the new ar+ficial super laYces
O
Cu
La,Sr
a
c
La2-‐x-‐yNdySrxCuO4
The cuprates are charge-‐transfer insulators à the doped holes go into the O 2p orbitals
Vojta, Advances is Physics (2009)
, Nd
Cuprate structure
Cu here is 2+ and has 9 3d electrons so Spin =1/2
Ordering in strongly correlated systems Stripes in Nd-LSCO
ΔQC ~ 1 e ΔQO ~ 0
ΔQ < 0.5 e
Charge inhomogeneity in Bi2212
Pan, Nature, 413, 282 (2001); Hoffman, Science, 295, 466 (2002) ΔQ ~ 0.1 e
ΔQ/Qtotal~1/500 Quadrupole moment ordering
Crystal fields, mul+plets, and Hunds rule for cubic (octahedral) point group
d5; Mn2+, Fe3+
Free ion Cubic Oh
t2g
t2g
eg
eg 4J
(4)J is the energy to flip One of spins around 10DQ= crystal field
S=5/2 No degeneracy
d4; Mn3+, Cr2+
t2g
t2g
eg 3J
S=2 two fold degenerate
10DQ
Mizokawa et al PRB 63, 024403 2001
Charge ,spin,orbital,laYce polaron in manganites controling orbital ordering using interface pinning.
Can we get LaNiO3 to look like Cuprates at interfaces (Khaliulin Phys. Rev. Le5. 102, 017205 (2009) )?
POLAR catastrophies in ar+ficial superstructures The basic physics involved in the new discoveries of Spectacular proper+es of some oxide interfaces
LaAlO3/SrTiO3 Interface of two insulators = superconductor
We need to probe the (electronic)Structure Of these buried interfaces
Phonons, Magnons
Similar picture For d-‐d excita+ons CT excitons in TM compounds
We need informa+on on all the Elementary excita+ons
Or a typical TM Oxide
CT Excitons Orbitons
In solids we have collec+ve excita+ons i.e.Phonons , Magnons , Excitons,-‐-‐-‐
Q = 2π/λ
Combine x ray spectroscopy with sca2ering (both Elas+c and Inelas+c)
Resonant x ray sca2ering
Mn 2p – 3d transiIons (L23 edge) At about 650 eV Fe 2p-‐3d is at about 730eV ResoluIon is about 0.2 eV!!! Element selecIve!!!
Note the mul+plet structure Due to the 2p53d6 coulomb and exchange interac+ons. This Structure depends on the details Of the star+ng ground state!!
States I have a core hole on atom i and a valence electron This depends on the local electronic structure Enhancement by 3-4 orders of magnitude at resonance.
At resonance we have contrast for:
– Elements
– Valence electron density
– Bond orientation; orbital ordering quadrupole moment orientation [linear pol. light]
– Spin density
• 4-‐circle diffractometer (9 in-‐vacuum mo+ons)
• ultra-‐high vacuum (P = 2 x 10-‐10 Torr)
• Photodiode, channeltron and 2D channelplate detectors with variable slits and filters • cooling to 18 K with closed-‐cycle cryostat
• Full polariza+on control of incident light (EPU) with unique dual EPU rapid switching of polariza+on mode • 80 – 2500 eV photon energy range • High energy resolu+on (E/ΔE > 15000 at Nitrogen K edge)
• A2ached chambers for in-‐situ sample growth (MBE) and characteriza+on (XPS, AFM/STM, EELS, scanning Auger spectroscopy, SEM, UV photoemission)
Resonant sor x-‐ray sca2ering at the Canadian Light Source
University of British Columbia funded by Canada Founda+on for Innova+on, Bri+sh Columbia Knowledge
Development Fund and Western Economic Diversifica+on
David Hawthorn (Waterloo) Feizhou He (CLS) Luc Venema (Groningen) Harold Davis (UBC) Ronny Sutarto (UBC) Hiroki Wada+ (Tokyo) Jochen Geck (IFW Dresden) Kyle Shen (Cornell) Andrew Achkar (Waterloo) George Sawatzky
The Canadian Light Source
h2p://www.lightsource.ca/experimental/reixs.php
channeltron
support structure
heat shield
photodiode
MCP
sample recepticle
sample heater
closed-cyclecryostat
z stage
x stage
y stage
!
"
#
2# in-vacuum stepper motor
slit wheel
Hawthorn et al. Rev. Sci. Instrum. 2011
Reminder λ E
= 1Å 12000 eV
3d Transition Metal Compounds
L2,3 edge 2p à 3d
500 eV à 900 eV
20 Å à 12 Å
Rare Earth’s (4f compounds)
M4,5 edge 3d à 4f
800 eV à 1800 eV
12 Å à 8 Å
C1s - 280 eV à 40 Å
N1s - 390 eV à 35 Å
O1s - 530 eV à 25 Å
S1s - 3000 eV à 4 Å
Analyzing RSXS energy dependence
Kramers-‐Kronig Transform • Determine f ʹ′ (ω) from f ʹ′ʹ′ (ω)
relate x-‐ray absorp+on, σ(ω) to sca2ering form factor, f ʹ′ʹ′ (ω)
Scheme: We can use the x-‐ray absorp+on to determine the real and imaginary parts of the
atomic sca2ering form factor
1.
2.
• Fink et al. PRB (2009). • Abbamonte et al. Nature Physics (2005).
• Schüβler-‐Langeheine et al., PRL (2005) • …
950940930920Incident photon energy (eV)
TEY
(a. u
.)
X-ray absorptionL3
L2
XAS and RSXS Cu L edge XAS
fCu Kramers-‐ Kronig
-80
-40
0
40
f (ele
ctr
ons/a
tom
)
960940920
Photon energy (eV)
Re{f} Im{f}
LCu 3,2
LNSCO
Doped holes in cuprate
C. T. Chen et al. PRL 66, 104 (1991)
Cu2+ d9 S=1/2
O 2-‐ full shell
La2-‐xSrxCuO4 Sr -‐-‐-‐doped holes
Huge contrast for Cu2+ 3d9 as in CuO and Cu1+ 3d10 as in Cu2O
YBCO oxygen ordering
2p 3d transition
Experimental Geometry
θ
θ
φ
Cu2+ 3d9 Cu1+ 3d10
Huge contrast for Cu2+ 3d9 as in CuO and Cu1+ 3d10 as in Cu2O
Zooming-in on different Cu’s: Tuning Polarization
E//ab E//ac
Photon energy (eV)
At L3 edge, 1.3 I(E//ab) / I(E//ac) =
Spin and charge stripes
Cuprate phase diagram
CDW in 1/8 doped Cuprates from Resonant SoZ x ray sca5ering
La1.8-‐xEu0.2SrxCuO4
Cu L3
La1.875Ba0.125CuO4
Fink et al, PRB (2009)
model
model
meas
meas
TFY
TFY
meas
model
TFY
Abbamonte et al, Nature Physics (2005)
O K O K [0.25 0 0.72] CDW
YBa2Cu3O6+x RIXS G. Ghiringhelli et al Science 2012
Note the peak in the zero Loss line at q=0.30 indicaIve Of a super structure!!
G. Ghiringhelli et al Science 2012
Temperature dependence of the CDW instensity and correlaIon length (width) indicate that CDW Competes with superconducIvity
A. J. Achkar et al PRLin press YBCO ORTHO 3 demonstrates CDW is in plane and should Not be confused with the Chain ordering superstructure At q=0.33
An RXS study of Pr.5Ca.5MnO3 Films on LSAT
Hiroki Wada+ et al
Hiroki Wada+ et al
Note XAS has li5le Structure and is independent of Temp. IT IS ACTUALLY RATHER BORING
Thin film 50nm of PCMO on LSAT
Hiroki Wada+ et al
Although XAS shows li5le change at various phase transiIons The energy dependent superstructure Bragg peaks exhibit strong changes On going thoug the phase transiIons
Theory of resonant elas+c and inelas+c sca2ering
• Haverkort; PRL 105, 167404 (2010) • This extends the Hannon type work based on spherical symmetry for the intermediate state (impulse approxima+on) to include lower symmetry and changes sum rules.
• We then need a sca2ering tensor who’s elements can to a large degree be determined by a generalized X ray absorp+on Greens func+on matrix involving two polariza+ons and a strong dependence on the spin direc+on in magne+cally ordered materials
• Resonant elas+c sca2ering requires informa+on about the generalized X ray absorp+on Greens func+on (not only the diagonal elements) for each atom in the unit cell
On trying to fit the Mn data as well as Co, Ni in Nickelates we note that we have a very bad understanding of the spectral shapes in resonant sca2ering.
This is especially the case in high oxida+on state systems i.e. involving Mn4+, Co4+, Ni3+ etc. (See the talk on
Monday about whats special) Perhaps the local cluster models used are breaking down or perhaps the
holes are largely on O
Resonant “x-ray cartography”
X-ray reflectivity maps for the non-destructive determination of the chemical and valence state
depth profiles with atomic resolution
Vlaimir Hinkov and Sebastian Macke main players at the MP/UBC center for Quantum Materials at UBC
Resonant x ray reflectometry
• Structure and elementary excita+ons in solids determining the proper+es of solids
• The special role of resonant x ray sca2ering • Examples of resonant elas+c x ray sca2ering for charge , spin and atomic structure
• Examples of resonant inelas+c x ray sca2ering for the elementary excita+ons in solids
• Non-‐destrucIve element specific depth profiling of the electronic
structure – Element, Thickness, Roughness,
– Magne+c-‐, Orbital-‐, Valence-‐state
Resonant x-ray reflectivity (RXR)
LaNiO3
LaAlO3
LaNiO3
LaAlO3
• Each material has an E-dependent, complex dielectric function ε (more general: matrix) • ε strongly increases at the absorption edge (e.g. 2p → 3d transition) → element specific and sensitive to the valance electrons
• Refraction and reflection if ε (or equiva-lently the refractive index n) changes at an interface • Polarisation analysis of the outgoing beam would provide even more information at the expense of intensity
500 600 700 800 900 1000
0.0
0.2
0.4
0.6
0.8
1.0
1.2
abso
rptio
n (T
EY
)
Energy (eV)
Pr
Ni O Ti
Using RXE, one can measure the complete chemical, valence state, magnetic and orbital profile
Model
26/06/2013 41 MPG/UBC Workshop
Solving of Maxwells-‐equa+on for op+cally isotropic material and thin films leads to |𝑅|↑2 ≅ |𝑟↓01 + 𝑟↓12 𝑒↑2𝑖𝑘↓𝑧1 𝑑 +O(𝑟↑3 )|↑2
with 𝑟↓𝑎𝑏 = 𝑘↓𝑧,𝑎 − 𝑘↓𝑧,𝑏 /𝑘↓𝑧,𝑎 + 𝑘↓𝑧,𝑏 ∙ 𝑒↑−2𝑘↓𝑧,𝑎 𝑘↓𝑧,𝑏 𝜎 Fresnel coefficient
(+roughness)
Wave vector 𝑘↓𝑧 = 𝑘↓0 √𝑁↑2 − 𝑐𝑜𝑠↑2 𝜃
Op+cal constant defined as
𝑁=1−𝛿+𝑖𝛽
film
substrate
0
1
2
d
θ θ
Energy dependent and Kramers-‐Kronig consistent
𝛿=𝛿(𝐸) 𝛽=𝛽(𝐸)
Reflec+vity highly nonlinear in terms of N
In reality: dielectric tensor 𝜀(𝐸), Transfer matrix method
Element specific depth profiling
NdGaO3
LaCoO3
NdGaO3
LaCoO3
LaAlO3
XAS
Reflec+vity fits of LCO//NGO
43
26/06
/201
3
Theta 2 Theta or constant energy Q scans.
Energy dependence at constant Q At the points on the ler plot
Note the Fresnel interferences on the ler . At the minima there is destruc+ve interference From sca2ering from upper and lower interfaces and at the maxima this is construc+ve . This is indica+ve of changes in the composi+on and electronic structure as seen in the Spectroscopy shown in the right panel.
Reflec+vity of LAO/LCO//NGO
44
26/06
/201
3
Density profiling of LCO/NGO Density profiling LAO/LCO/NGO
26/06/2013 45
Note the Co2+ at the surface Note the Water/CO2 on surface
Note the absence of Co2+
Example of depth profiling /burried layer
SrTiO3 Substrate
SrTiO3 Buffer Layer
1. u.c. La0.005Sr0.995TiO3
SrTiO3
Can we see the single layer containing La burried deep in the material and determine where it exactly is? YES: For La concentraIon larger than about 0.01
Buried layers
SrTiO3 Substrate
SrTiO3 Buffer Layer
1. u.c. La0.2Sr0.8TiO3
SrTiO3
La M5
La M5
La M5
La M4
La M4
Sebas+an Macke Vladimir Hinkov
Sample from Stemmer At UCSB
Buried layers
La M5
La M5
La M5
La M4
La M4
48
26/06
/201
3
Addi+onal examples of theore+cal studies
(c): all kinds of electronic structure change (d): different profiles for different entries in the tensor. E. g. exchange bias
49
26/06
/201
3
Analysis tool • Frequency-‐domain Maxwell-‐equa+on simulator with Full-‐Matrix approach
• Fit measurements • Graphical user interface
26/06/2013 50
remagx.org
Grou
p mee+n
g
SebasIan Macke
t2g
t2g
eg
eg 3J
S=2, 3 fold degenerate d6; Fe2+, Co3+
Energy Loss is t2g-‐eg spliYng These form d-‐d excitons or also called orbitons
t2g
t2g
eg
eg
Resonant inelas+c x ray sca2ering
PRL 105, 157006 (2010) SLS Ghiringhelli et al RIXS on Sr2CuO2Cl2
d-‐d excitons Due to crystal fields
Magnon dispersion
Resonant inelas+c x ray sca2ering
New Journal of Physics 13 (2011) 043026 M Morel et al
For the Cuprates the Theory works very well indeed as it does for NiO i.e. Ni2+
Phonon excita+ons via core to valence excited state local bonding change resul+ng In excited O-‐TM vibra+onal modes. INFORMATION ABOUT THE D ELECTRON PHONON COUPLING
w.a.Lee et al con mat 301.4267 accepted in PRL. Ca2+5xY2−5xCu5O10 a 1D chain cuprate.
igure 2: Experimental data.
Detailed Magnon (or are they magnons?) dispersion in cuprates Keimers Group
Doped holes in cuprate
C. T. Chen et al. PRL 66, 104 (1991) As we hole dope the system the O1s to 2p first peak rises very strongly indica+ng That the doped holes are mainly on O 2p.
Kuiper et al PRL 62 221 (1989) LixNi1-‐x O A CHARGE TRANSFER GAP SYSTEM HOLES IN O
Note the high “pre-‐ Edge feature and the Spectral weight Transfer from high To low energy scales Just as in the cuprates The holes are mainly on O and not on Ni.!!
LNO thin film on LSAT Sutarto, Wada+, Stemmer UCSB
Note the huge O 1s -‐2p prepeak just as in the cuprates HOLES ON O
Torrance et al PRB 42, 8209
Recent RIXS results demonstrate that the cluster interpreta+on of the XAS used by everyone is not valid for the
Nickelate’s
results obtained by Valen+na Bisogni and Thorsten Schmi2 from PSI
Sara Catalano, Marta Gibert , Raoul Scherwitzl Jean-‐Marc Triscone, and Pavlo Zubko From Geneva
PSI, V. Bisogni – T. Schmi5
RIXS spectra of NdNiO3 – 15 K
α=50°
[110]
LH
PSI, V. Bisogni – T. Schmi5
RIXS map of NdNiO3 – 15 K insulaIng phase
Ni 2p XAS energy region : Up to now the peaks A and B were considered to be ,multiplet structure in the final 2p5 3d8 local states
RIXS demonstrates that a local d-d like description is OK for peak A with photon energy independent peak positions in RIXS
Near linear dependence of the “Loss” energy With photon energy show that this is not RIXS but simple x ray flourescence.
So peak A in XAS involves the excited d Electron intimately while peak B must involve an excitation into a delocalized continuum band state in the intermediate state. The continuum starts at most 1 eV above the bound state. This has implications for the ground state and low energy excitations and the properties.
PSI, V. Bisogni – T. Schmi5
RIXS map of NdNiO3 – 300 K Metallic Phase
Here the con+nuum states merge With the “bound states or resonances”
Strong T dependence of the XAS
NNO On LSAT 300K metallic phase
NNO on LAST 15K Insula+ng phase
Conven+onally RENiO3 would involve Ni3+ which is expected to be low spin
i.e. S=1/2 with 6 electrons in t2g orbitals and 1 in an eg orbital
STRONG JT WHICH IS NOT OBSERVED!
RIXS and XAS indicate The lowest energy states in Nickelates before Ni d
–O2p hybridiza+on could well be par+ally filled O band with the Ni in d8
S=1 states
How to get rid of JT ?
Charge dispropor+ona+on into d6 and d8 would solve this problem. But experiments show only very low amplitude in the insula+ng phase
High oxida+on states
• In general we expect the charge transfer energy to strongly decrease for higher oxida+on states
• This could mean a different star+ng point i.e. • Cu3+ Cu2+L Ni3+ Ni3+L Co4+ Co3+L • Fe4+ Fe3+L Mn4+??? The charge degrees of freedom are on Oxygen
Charge dispropor+ona+on without moving charge
Consider ReNiO3 Ni3+ on average but label it as Ni2+L Then each Ni is surrounded by 2 L holes in ReNiO3 ( 1 hole per 3 O) 2Ni3++
Ni2+ + Ni4+
Two holes in O2p Orbital in octahedron With central eg symmetry
Ni2+ no JT Each second Ni2+ has an octahedron of O with two holes of Eg symmetry in bonding orbital's I.e. d8 L2
No Jahn Teller problem anymore
The nickaltes i.e. RENiO3
Lets associate the two holes (with S=1) with one Ni which will then be a S=0 cluster Because of Jpd. The octahedron will contract leaving the other Ni neighbors in a d8 S=1 state. This gives the correct structure at low T and in fact also gives the correct spin structure . Effec+ve dispropor+ona+on without moving charge. THIS STATE SEEMS TO BE NEARLY DEGNERATE WITH A METALLIC ITINERANT O HOLE STATE
The theory of systems with nega+ve charge transfer gap energies
• This is really complicated since we now cannot use our simple non metallic ansatz. We then have a problem of a laYce of local spins in d states with strong hybridiza+on and exchange with the holes on O.
• The case I alluded to of LaNiO3 is perhaps such an example.
• Perhaps viewed as a Kondo laYce model but with a charge density wave instability driven by an exhaus+on principle since only ½ of the Ni spins can be compensated by O 2p holes