resonantelas+c(and(inelas+c((x ray(scaering(( ·...

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

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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

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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

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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

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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


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.


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

resonantelas+c(and(inelas+c((x ray(scaering(( ·...

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