Charge Dynamics in (ω, Q)-SpaceStudied by Inelastic X-ray Scattering

Jun’ichiro Mizuki
Quantum Beam Science Directorate
Japan Atomic Energy Agency (JAEA)

Inelastic X-ray scattering• The first term: non-resonant inelastic scattering‒ All electrons （Ze） are contributed ⇒ phonon excitation• The second term: resonant inelastic scattering (RIXS)‒ Electrons on the specific atom are contributed.
‒ Resonance enhancement‒ Element specific ⇒ electronic excitation

RIXS of 3d transition elements
Ｋ-edge （1s→4p、several keV）
(a) absorption(b) interaction between
1s core-hole and 3d electron(c) X-ray emission

Inelastic Scattering
2[I (Q, E ) ~ [V (Q)] 1 # e] • Im ! (Q, E )# "E #1

Interaction of probe

Generalized susceptibility

For neutrons

Spin susceptibility
Nuclear susceptibility

For X-rays
For electrons

Charge susceptibility

χ(Q,E )= -(Q2/4π2N) 1/ε(Q,E)
Dynamical dielectric function

P. R. B. 61 (’00) 16423: including
ele. –ho. inter.
: not including
ele.-ho. Inter.

LiF
insulator

GaNsemiconductor

Non resonant IXS on Diamond
Propertied of an indirect band gap
Band gap

ele. and hol. interaction
between the band gap●Band engineering ofSemiconductors,●Supercondctor based on

Semiconductors

0.37eVInt.
?

180meVCaliebe et al., P.R.L. 84 (’00) 3907

higher E

M. Hoesch, J. M. et al., P. R. B. 75 (‘07) 140508(R)Electrons in mean field
Quantum Hall effect

Heavy fermion

Strongly correlated electrons
Organic molecules

Colossal magnetoresistanceHigh TC superconductor

Complex interplay between Charge, Spin, Orbital
degrees of freedom

Elementary Excitations in Solids
Text book
100eV
10eV
1eV

Compton scatt.

PlasmonInterband electron transition
magnonStoner excitation

100meV

Strongly
Correlated
systems

Crystal field tran.
phonon10meV1020Q(A-1)

Set-up of Inelastic Scattering Spectrometer at BL-11XU

Observed energy
Resolution
at 6.5 keV

Schematic diagram of electronic states
energyenergyOt, t”

CuUt”

Ut

DOS
DOS(ii) Hole doped (iii) Electron doped
systemsystem

Electron doping

X=0.154Calculated by K. Tsutsui

1.000

Energy (eV)

302

10
(!,!)

(!/2,!/2)(0,0)

Momentum Transfer q(!/2,0)(!,0)
Theory(small cluster)

RIXS spectra
Dynamical density response function

The electron involved in dynamical density response function
can be selected by RIXS !
K. Ishii, J. M. et al.,PRL. 94 (’05)207003

toward future
Required energy resolution● Inter-band excitation: “U”~2eV
Excitations across the Mott / charge-transfer gap● Intra-band excitation: “t”~0.4eV
Excitations within bands across the Fermi level

ΔE~0.5eV

ΔE~0.1eV● Low-energy excitation: “J”~0.1eV
Excitations related to the spin degree of freedom

ΔE~0.05eV

Dynamical structure factor of IXS in the phonon energy region

ε(Q,ω)=εel(Q, ω)+εion(Q, ω)-1
χ(Q, ω)= -(Q2/4π2N) 1/ε(Q, ω)I(Q, ω)= F(εel)+G(εel)·H(εion)
I(Q,E)=E+

How to get the information on electric dynamical function
Collaboration between X-rays and Neutrons
1. Measure the phonon spectrum anddispersion by Neutron Inelastic Scattering.
2. Derive the information on the width,
eigenvector and structure factor of phonons,and calculate the phonon intensity of IXS.
(C-IXS)
3. Compare the C-IXS with the observed
IXS spectrum.

IXS spectrum

I(q, ω)(electric + phonon) partB-doped Diamond

Spectral intensity ofthe bare LO-phonon

M. Tachiki et al., Phys. Rev. B38, (‘88) 218.

Phonon DOS of Fe-based super.
Based on LDA cal.

TC=48 K

TC=27 K

T. Fukuda, et al., J. Phys. Soc. Jpn. 77 (‘08) 103715

Observation space

In what space should we measure physical properties?

Real time (t)Energy space (ε)

Real space (r)Momentum space (q)Dynamics in time domain
Tracking the motion of charges in a terahertz
light field by femtosecond X-ray diffraction
A. Cavalleri et al., Nature 442 (‘06) 664

Time-dependent
Structure factor

Excitation of phonon polaritons in LiTaO3

Collaborators for RIXS:
Experiment

TheoryBeamlineCollaborators for Fe- based Superconductors:
JAEA● T. Fukuda, S. Shamoto, M. Ishikado, J. Mizuki, M. Arai,
SPring-8/RIKEN, JASRI● A. Q. R. Baron, S. Tsutsui, H. Uchiyama

JST● H. Nakamura, M. Machida
AIST● A. Iyo, H. Kito, H. Eisaki
TIT● H. Hosono

Importance of the collaboration between
Experiment and theory

Elastic

Resonant

R-time (t)R-space (r)Inelastic

N-Resonant

E-space (ε)

M-space (q)