Magnetic and electronic structure of „ Ga
1 Àx
Mn
x
… As
L. Bergqvist,
1
P. A. Korzhavyi,
2
B. Sanyal,
1
S. Mirbt,
1
I. A. Abrikosov,
1
L. Nordstro
¨
m,
1
E. A. Smirnova,
3
P. Mohn,
4
P. Svedlindh,
5
and O. Eriksson
1
1
Department of Physics, Uppsala University, Box 530, SE-75121, Uppsala, Sweden
2
Department of Materials Science, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
3
Department of Theoretical Physics, Moscow Institute of Steel and Alloys, 119991 Moscow, Russia
4
Center for Computational Materials Science, TU Wien, A-1060 Wien, Austria
5
Department of Materials Science, Uppsala University, Box 530, SE-75121, Uppsala, Sweden
Received 5 November 2002; published 6 May 2003
We present theoretical calculations of the magnetic and electronic structure of Mn-doped GaAs in the
zinc-blende structure. The magnetic properties are shown to be very sensitive to structural defects, in particu-
lar, As antisite defects and Mn at interstitial positions. Only when considering such defects can the experimen-
tal magnetic moments be reproduced by first-principles theory. We present a simple model for understanding
the connection between the magnetic ordering and the As antisites, and the way in which the defects help to
stabilize a partial disordered local-moment state. The connection between the energetics of the Mn substitution
and the As antisite concentration is also analyzed. In addition, we compare the calculated magnetic properties
and electronic structures of Mn situated on substitutional sites Mn replacing a Ga atom and on interstitial
sites, where in agreement with observations the interstitial site is found to be less favorable. Finally, combining
our first-principles calculations of the spin-wave excitation energies with a classical Heisenberg Hamiltonian
we have calculated interatomic exchange interactions, and using Monte Carlo simulations we present theoret-
ical values of the critical temperature as a function of Mn concentration.
DOI: 10.1103/PhysRevB.67.205201 PACS numbers: 75.25.+z, 75.70.-i, 85.75.-d
I. INTRODUCTION
Dilute magnetic semiconductors are argued to be of sci-
entific and technological importance,
1
e.g., due to applica-
tions in spin electronics.
2
Substitution of Mn for Ga in GaAs,
forming Mn
x
Ga
1 -x
As with Mn concentrations up to 10%,
has been shown to result in a particularly promising material.
Although the magnetic structure and critical temperature are
known to be sensitive to the way in which the samples have
been prepared, e.g., annealing conditions, etc., one can con-
clude that in favorable cases a critical temperature of
100 K has been observed.
1,3,4
Quite recently it was also
shown that Mn implanted in GaP can in very specific cases
have a critical temperature close to room temperature.
5
The
fact that the magnetic properties are affected by the anneal-
ing suggests that there may be lattice defects and/or inhomo-
geneties in the samples, and arsenic antisite defects denoted
As
Ga
) have been observed.
6
Due to a high equilibrium vapor
pressure of As, epitaxial growth of GaAs is usually per-
formed at a certain As overpressure that produces an As-rich
GaAs.
7
Combined with the high concentration of Mn atoms
which act as acceptors, such experimental conditions make
the formation of As antisites which act as donors energeti-
cally favorable. In the work of Ref. 6 it was also shown that
the As
Ga
are connected to a local lattice deformation that can
be as large as 10% in the bond length. The replacement of
Mn for Ga is shown to result in a small lattice distortion
around the Mn atom, deduced both from experimental
8
and
theoretical
9
techniques. Also, the electronic properties of
Mn
x
Ga
1 -x
As have been studied using optical probes
10
and
by angle-resolved photoemission.
11
The magnetic properties
of Mn
x
Ga
1 -x
As/GaAs/Mn
x
Ga
1 -x
As trilayers have been
measured, with an unexpected large interlayer exchange con-
stant and a proposed metallic behavior of the GaAs spacer.
12
The intense experimental efforts to understand these ma-
terials are paralleled with equally intense theoretical efforts.
Hence both the electronic structure and magnetic properties
of defect-free Mn-GaAs have been studied.
9,13–24
In addition,
the transport properties of Mn
x
Ga
1 -x
As/GaAs heterostruc-
tures have been calculated using first-principles theory.
25
The
origin of the ferromagnetism in these systems is under dis-
cussion, and models including the Ruderman-Kittel-Kasuya-
Yosida model,
14
the competition between the double- and
superexchange mechanisms,
13
and a double-resonance
mechanism
15
have been proposed. First-principles calcula-
tions on defect-free Mn-GaAs give total magnetic moments
of 4
B
/Mn atom for ferromagnetically coupled Mn impuri-
ties on the Ga sublattice in GaAs.
9,18,21–24
This result is in
sharp contrast to the experimental results obtained by satu-
ration magnetization measurements that are significantly
smaller, 2.4
B
/Mn atom.
26
This marked disagreement be-
tween experimental saturation magnetization data and the
theory was recently argued by us
26
to be due to As antisite
defects.
27
By considering the presence of As
Ga
, theory
showed that a disordered local-moment DLM state
28
mini-
mized the total energy. This state has only a part of the
randomly distributed Mn atoms ferromagnetically aligned
while the remaining fraction of the Mn atoms has an orien-
tation of their magnetic moments antiparallel to the global
magnetization direction, and this magnetic configuration re-
produced the observed macroscopic magnetic moment with
good accuracy. We remark here that subsequently a different
mechanism involving spin disorder of the Mn atoms with a
spin-glass-type structure has been proposed.
29
Other defect
structures have also been suggested and, in particular, Mn
atoms situated at interstitial positions have been detected
30
PHYSICAL REVIEW B 67, 205201 2003
0163-1829/2003/6720/2052019/$20.00 ©2003 The American Physical Society 67 205201-1