Electron-hole counts in Al-substituted MgB
2
superconductors from x-ray Raman scattering
A. Mattila,
1,2,
* J. A. Soininen,
1
S. Galambosi,
1
T. Pylkkänen,
3
S. Huotari,
3
N. D. Zhigadlo,
4
J. Karpinski,
4
and K. Hämäläinen
1
1
Department of Physics, University of Helsinki, P.O. Box 64, 00014 Helsinki, Finland
2
STUK – Radiation and Nuclear Safety Authority, P.O. Box 14, 00881 Helsinki, Finland
3
European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble Cedex, France
4
Solid State Physics Laboratory, ETH, CH-8093 Zürich, Switzerland
Received 13 April 2007; revised manuscript received 14 May 2008; published 21 August 2008
We have investigated the electronic structure of Mg
0.83
Al
0.17
B
2
and MgB
2
single crystals using x-ray Raman
scattering at the B-K edge. Utilizing the momentum transfer dependence of the scattering process, together
with first-principles multiple scattering calculations, we have extracted the site and symmetry projected density
of empty B states in Mg
0.83
Al
0.17
B
2
in the presence of a core hole. In comparison to the density of states for
pure MgB
2
, we find the B--band hole count to decrease at the Fermi level by 35 9%. The -band hole count
is relatively stable with a 4 7% increase compared to MgB
2
. These results shed light on the role of band
filling in lowering the T
c
. Our work opens an application area for x-ray Raman scattering and density of states
extraction scheme in studies of doped systems.
DOI: 10.1103/PhysRevB.78.064517 PACS numbers: 74.25.Jb, 71.15.-m, 74.70.Ad, 78.70.Ck
I. INTRODUCTION
Atomic substitutions and doping are used to modify and
engineer the physical properties of compounds and have
been naturally applied to alter the superconducting properties
of various systems. For understanding and predicting the ef-
fects of substitution or doping, knowledge of the electronic
structure is crucial, and especially for elucidating changes in
the superconductivity, the density of states at the Fermi level
is an important characteristic of the system. Atomic substitu-
tions have been also employed for MgB
2
, whose high critical
temperature of superconductivity T
c
39 K has been ex-
plained to arise from a phonon-mediated mechanism with
different coupling strengths to the electronic B- and
bands.
1–4
Even though the different coupling strengths lead
to a realization of two-band superconductivity,
5
MgB
2
still
has only one transition temperature due to weak interband
phonon scattering between and bands.
4
The high density
of empty electronic states at the Fermi level, provided by the
B- band, is one of the essential features behind the high T
c
in MgB
2
. The quasi-two-dimensional 2D band, deriving
from the hybridized B sp
x
p
y
orbitals, resides within the B
sheets and couples strongly to B-B E
2g
bond oscillations,
6,7
leading to the larger superconducting energy gap. The
smaller gap originates from the three-dimensional 3D
band, formed by B p
z
orbitals, with a weaker electron-
phonon coupling strength.
In MgB
2
, atomic substitutions can be used to change the
phonon scattering rates and to modify the electronic density
of states. Two studied substitutions have been the ones of Al
for Mg and of C for B. Although both modifications dope the
system with additional electrons, the effects on the scattering
of electrons from phonons are different.
8–11
The Al substitu-
tion is expected to mostly affect the scattering in the band,
whereas C substitution should increase both the and
band scattering. In both cases the modification leads to a
decrease in the critical temperature and the eventual disap-
pearance of superconductivity.
12
Recent work has suggested
that the lowering of the critical temperature in MgB
2
would
result from the reduction of the electron phonon coupling
constant due to band filling, with the gap region staying
constant due to the compensating effect of a changing inter-
band scattering rate.
13,14
To elucidate the role of the band
filling versus the changes in the phonon spectra or in the
interband scattering rate, further experimental work on the
substituted MgB
2
compounds is needed.
The exact details of the electron doping induced changes
in MgB
2
are still uncertain, and until recently, the effect of
substitution was mainly investigated on polycrystalline
samples.
15–18
Single crystal MgB
2
and AlB
2
have been al-
ready characterized,
19
however high quality Al and C, sub-
stituted crystals with intermediate substitution levels, have
only lately become available, enabling more detailed studies
of the anisotropies.
10,11,20
In a recent de Haas–van Alphen
study of Al substituted single crystal MgB
2
,
14
the authors
found a 16% reduction in the number of band holes with
7.5% Al content, but were unable to derive a number for the
band.
In this context, x-ray Raman scattering XRSRef. 21 is
well suited to probe both the and band hole counts on
equal footing in Al substituted MgB
2
single crystals. The
anisotropies and symmetries of the empty electronic states in
pure MgB
2
have been already investigated using XRS
22
to
separate the s, , and band contributions. Later theoretical
developments
23
have also made it possible to quantitatively
extract the site and symmetry projected local density of
states DOS from the experimental XRS data, allowing a
direct comparison to theoretical calculations of the electronic
structure. The power of this scheme has already been dem-
onstrated on pure MgB
2
.
24
In the following we will extend
this scheme to doped systems, opening completely new areas
for the applications of x-ray Raman scattering.
In this paper we present an XRS investigation at the B-K
edge on Al-substituted single crystal Mg
0.87
Al
0.17
B
2
and on
pure MgB
2
. We probe the electron doping-induced changes
in the empty B electronic states, especially in the interesting
and bands. As we use hard x-rays, we probe the bulk of
PHYSICAL REVIEW B 78, 064517 2008
1098-0121/2008/786/0645175 ©2008 The American Physical Society 064517-1