Metal-Insulator Transitions in
Complex Oxides probed by
Compton Scattering
B. Barbiellini, Northeastern University, Boston, USA
Theory Group, Northeastern [NU]
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Arun Bansil [NU]
Robert S. Markiewicz [NU]
Bernardo Barbiellini [NU]
Peter Mijnarends [NU & Delft, Holland]
Stanislas Kaprzyk [NU & AGH, Poland]
Matti Lindroos [NU & TTKK, Finland]
Jouko Nieminen [ “
“ ]
Seppo Sahrakorpi [NU]
Dan Nissenbaum [NU]*
Ville Arpiainen [TTKK, Finland]
Hsin Lin [NU]*
Tanmoy Das [NU]
Wael Al-Sawai [NU]
Susmita Basak [NU]
Ray Wang [NU]
Cristian Kusko [Romania]
Millard Baublitz [NU and Boston U.]
Many Experimental Collaborations
DFT
QMC
One-body
Many-body
Interactions
STM
Matrix
Elements
Spectroscopies
ARPES
RIXS
X-ray
Compton
Positron
Annihilation
Motivation & Outline
• Coulomb repulsion tends to localize
individual d electrons on atoms.
• Hybridization with the oxygen p electron
states tends to de-localize the d electrons.
• These competing effects explain the MIT.
• Compton scattering is a unique MIT probe
in Y1-xPrxCu3O7, La2-2xSr1+2xMn2O7, Fe3O4.
The Compton cross section


dd
/ 2
d

d

c
o
n
s
t
(
p
)
e

The cross section is related to the Electron Momentum Density (EMD)
G. Kaplan, B. Barbiellini and A. Bansil, Phys. Rev. B 68, 235104 (2003).
Electron Momentum Density
The EMD is given by the formula:

()
p
2
n


i p
i
2
Important information on the wave functions and the occupation
numbers values can be extracted from the EMD.
The occupation ni can be calculated within AGP or RVB.
Barbiellini & Bansil, J. Phys Chem. Solids 62, 2181 (2001).
Occupation number sum rule
The occupation numbers are the eigenvalues of the oneparticle density and they satisfy the relations:
0n
1
i 

ˆ)2
T
r(
n

i N
i
1
For independent particles the orbitals are either occupied or empty.
Virtual orbitals appear because of electronic correlation.
MIT in RBa2Cu3O7 (R=Y or Pr)
The [100]-[110] Compton profile anisotropy displays a remarkable difference
between insulating PBCO and metallic YBCO.
The theory gives good agreement
for the shape in the metallic YBCO
but it must be rescaled.
A. Shukla, B. Barbiellini, A. Erb, A.A. Manuel, T. Buslaps V. Honkimaki and P. Suortti,
Phys. Rev. B 59,12127 (1999); ESRF Highlights (1997)
MIT in La2-2xSr1+2xMn2O7
• The Colossal Magneto-Resistance (CMR)
phenomenon is a huge decrease of resistance
induced by application of a magnetic field.
• We have considered x=0.35 under 3 conditions:
(1) FM metallic T<Tc, (2) PM insulating, (3) CMR.
B. Barbiellini, A. Koizumi, P. E. Mijnarends,
W. Al-Sawai, Hsin Lin, T. Nagao, K. Hirota,
M. Itou, Y. Sakurai and A. Bansil, Phys.
Rev. Lett. 102, 206402 (2009)
eg
t2g
2d-EMD in the FM phase
Yinwan Li, P. A. Montano, J.F. Mitchell, B. Barbiellini, P. E. Mijnarends,
S. Kaprzyk, and A. Bansil, Phys. Rev. Lett. 93, 207206 (2004).
KKR LDA calculation
in good agreement
with Magnetic
Compton scattering.
In the C4v anisotropy
FS & p and d
wave function effects
become visible.
The amplitude of the
t2g and eg peaks is
about 9 % while the
amplitude of the p
related peaks is less
than 4 %.
[100]-[110] CP anisotropy
Oxygen p electrons
play a major role at low
momentum range.
FT reveals electron localization
Coherence peaks have
shorter range in the PM
phase.
Number of electrons involved in MIT
In the present case we do
need to rescale the theory
CP anisotropy.
We can therefore estimate the
number of electron displaced
in the MIT:
0.71 FM-PM
0.67 CMR-PM
The role of p electrons is
important.
Fe3O4 studied by Magnetic Compton
Scattering
Magnetite is ferrimagnetic with a Curie temperature > 800 K.
Below TV= 122 K a MIT occurs (Verwey)
MCS allows us to study the magnetic electrons behavior at the MIT.
7.5
Fe3O4
log () (cm)
6.0
4.5
3.0
1.5
0.0
-1.5
-3.0
4
8
12
16
20
24
-1
1000/T (K )
H. Kobayashi, M. Itou, S. Todo, B.Barbiellini, P.E. Mijnarends and A. Bansil,
Manuscript submitted in Phys. Rev. B (2009)
Tetra (A) site
octa (B) site
O2-
(Fe2+, Fe3+) octa
Fe3+ tetra
Cubic spinel structure above Tv
Magnetic electron contributions
Contribution from ferromagnetic
B sites
This contribution is cancelled
by anti-ferromagnetic A B sites
Magnetite Spin MD
3d-Spin MD in the basal plane.
KKR LDA calculation.
FS breaks, p and d wave
function effects are visible.
Magnetic Compton Profile
Good agreement between the calculation and the experiment.
MCP anisotropy
The MCP anisotropy decreases
below the Verwey temperature.
This was also observed by
Y. Li, P.A. Montano,
B. Barbiellini, P.E. Mijnarends,
S. Kaprzyk, and A. Bansil,
J. Phys. Chem. Solids 68, 1556
(2007).
2d-reconstruction (expt.)
T=300 K
The reconstructed 2d-EMD changes from
being negative at 300 K to positive at 12 K in
the low momentum region.
T=12 K
The number of electrons per cell (with two Fe
B sites) whose wave functions localize ne=0.59
should be compared to the charge ordering on
the iron B-sites of about 0.40 electrons per unit
cell (from RXS).
The higher value of ne indicates that the
iron-oxygen hybridization plays also a role in
the MIT.
Conclusion
• Compton scattering in transition-metal oxides
shows clearly that and valence electrons are
shared in states that cannot be assigned solely
to metal or oxygen.
• Models in which oxides are simulated in terms of
cation charge fluctuations with an on-site
Coulomb interaction, ignoring oxygen states are
too schematic to describe correctly the MIT.
Japan Synchrotron Radiation Research Institute,
Press Release May 19, 2009
FS topology and Fe-based superconductivity
Y. J. Wang, Hsin Lin, B. Barbiellini, P.E. Mijnarends,R.S. Markiewicz, S. Kaprzyk and A. Bansil
Please see poster by Y.J. Wang
LaOFeAs is a member of the Fe-based
superconductors with simple
tetragonal crystal structure stacking
with FeAs layers and LaO layers.
Calculated Lock-Crisp-West
(LCW) folding in the
paramagnetic tetragonal
Brillouin zone of LaOFeAs.