Facile synthesis of 3-(diarylmethylene)isobenzofuranones, 4-(diarylmethyl)-1(2H)-phthalazinones and diarylmethanes

Article abstract of DOI:10.1016/j.commatsci.2005.07.004

Reflux of 2,2-diaryl-1,3-indanediones in ethyleneglycol with a catalytic amount of triethylamine affords 3-(diarylmethylene)isobenzofuranones in very good yields. The latter produces 4-diarymethyl-1(2H)-phthalazinones under reflux in hydrazine hydrate (99%), and diarylmethanes upon stirring in ethylenediamine.

Full text of DOI:10.1016/j.commatsci.2005.07.004

Computational Materials Science 36 (2006) 84–90
www.elsevier.com/locate/commatsci
Dilute magnetic III–V semiconductor spintronics
materials: A first-principles approach
a,
b
c
G.P. Das *, B.K. Rao b,z, P. Jena , Y. Kawazoe
a
Department of Materials Science, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
b
Department of Physics, Virginia Commonwealth University, Richmond, VA 23284, USA
c
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
Abstract
Group-III nitride semiconductors, such as GaN, when doped with 3d transition metals such as Mn or Cr show ferromagnetism
with high Curie temperature. Such dilute magnetic semiconductors (DMS) with larger band gaps and smaller lattice constants com-
pared to GaAs based DMS, are potential candidates for room temperature spintronics devices. We have investigated the magnetic
coupling between doped Mn (or Cr) atoms in clusters as well as crystals of GaN from first principles using molecular orbital theory
for (GaN)xTM2 clusters and TB-LMTO band calculations for wurtzite structured (Ga14TM2)N16 supercells. Our calculations reveal
that the coupling between TM-impurity atoms is ferromagnetic with a bulk magnetic moment of ꢀ3.5 lB per Mn atom and ꢀ2.7 lB
per Cr atom.
Ó 2005 Elsevier B.V. All rights reserved.
Keywords: Dilute magnetic semiconductors; Spintronics; First-principles calculations; Cluster calculations; LMTO supercell
1. Introduction
‘‘Spintronics’’ is the short form of spin-based electronics
where one exploits electronÕs spin, over and above its
charge, in order to carry information. This new disci-
pline exploits the inherent quantum properties of elec-
trons for various kinds of logic, storage and sensor
applications via spin-polarization, spin-injection, spin-
transport, spin-coherence, spin-tracing, spin-valve etc.
[1]. The first successful example of spintronics is the
giant magneto-resistance (GMR) effect in Fe/Cr metallic
multilayers [2]. GMR is defined as the relative change in
conductivity between parallel and anti-parallel spin con-
figurations of the ferromagnetic layers. This effect arises
due to confinement of electrons in quantum wells
formed in the nonmagnetic layer by the spin-dependent
potentials of the ferromagnetic layers [3]. Semiconduc-
tor spintronics is a relatively new field that started in
the late 90s when it was shown that nonmagnetic III–
V semiconductors (such as GaAs) can be made ferro-
magnetic via doping of transition metal atoms (such as
Mn) and the Curie temperature Tc was found to be
The information revolution that we are experiencing
today puts increasing demand for faster, smaller, low
power and high storage capacity devices for processing
of information. Current state of the art semiconductor
devices have already come to the stage where it is
approaching the fundamental limit of miniaturization,
e.g., the width of gate electrodes in a Si-based micropro-
cessor has reduced to 61.5 nm where quantum effects
become predominant. Question is what next? Scientists,
especially device physicists are looking for radically new
pastures such as molecular electronics, magneto-
electronics, spin electronics and polymer electronics.
*
Corresponding author. Tel.: +91 33 24734971; fax: +91 33
24732805.
E-mail address: msgpd@iacs.res.in (G.P. Das).
Deceased.
z
0927-0256/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.commatsci.2005.07.004

G.P. Das et al. / Computational Materials Science 36 (2006) 84–90
85
ꢁ110 K [4]. The explanation was given by Dietl et al. [5]
in terms of exchange coupling between the localized
spins of d5 configuration Mn with the delocalized (or
weakly localized) holes residing in a p-like valence band,
and the same argument was used to estimate TcÕs for
other III–V and II–VI semiconductors doped with 5%
Mn. It was predicted that Tc can be pushed above room
temperature when some 3d TM is doped into GaN or
ZnO which are two most extensively studied wide
band-gap semiconductors because of their applications
in blue lasers and optoelectronic devices [6]. Following
this prediction of achieving ferromagnetism in GaN,
there was an avalanche of experimental works on the
(GaMn)N system, which however resulted in more
controversies than consensus. While some groups have
reported antiferromagnetic behavior, others have
observed ferromagnetism with various different values
of Tc ranging from 20 K to 940 K [7]. Most of these
results are on thin film samples for which substrate con-
ditions play a crucial role. In the flurry of experimental
attempts to synthesize ferromagnetic semiconductors
with Tc close to room temperature, Cr doped GaN has
also been recently grown successfully in the form of bulk
single crystal using a sodium flux grown method, and
the Tc is observed to be around 280 K [8].
(d) Using local density supercell band calculations for
3d transition metal (TM) doped III–V zinc-blende
semiconductors, van Schilfgaarde and Mryasov
[10] had shown that the anomalous exchange inter-
actions between the impurity atoms deviate
strongly from the RKKY-like simple models and
undergo a transition from ferromagnetic (for Mn
and Cr) to antiferromagnetic (for Fe) as a function
of d-band filling.
(e) Sato and Katayama-Yoshida [11], had carried out
KKR-CPA calculations in randomly substituted
3d TM impurities in GaN and found ferromag-
netic state to be stable for half-filled or less than
half-filled impurities such as V, Cr, and Mn, while
a spin-glass like state is found to be stable for more
than half-filled impurities Fe, Co, and Ni.
The investigations by these latter two groups [10,11]
independently confirm the experimental observations
of Mn and Cr atoms coupling ferromagnetically in
GaN. For further details, the reader may refer to some
of the recent theoretical works reported in this field [12].
3. First principles calculations
We have carried out first principles investigation of
TM2 dimer (TM = Mn and Cr) doped GaN in various
structural forms that simulate binding of TM onto surface
as well as bulk sites [13,14]. The reason why we have used
TM2-dimer rather than a single TM impurity atom is that
we are interested to see the strength of magnetic coupling
and compare it with our cluster results. All the results re-
ported in this work are based on density functional theory
with gradient corrected exchange-correlation functional.
The details of the methodologies used, both for cluster
and crystal calculations are given elsewhere [13,14]. Here,
we only give the salient features of our results.
2. Ferromagnetism in GaN DMS
This discovery of high Tc ferromagnetism in Mn (Cr)-
doped GaN samples have given rise to several important
observations.
(a) Cr and Mn are both antiferromagnetic in bulk
phase and when doped into GaN, these impurity
atoms go to Ga-substitutional site as Cr3+ and
Mn3+ valence state in d3 and d4 configurations
respectively. This indicates that a magnetic impu-
rity such as Mn or Cr contributes spins as well
as holes (p-type doping) to the III–V semiconduc-
tors such as GaN.
3.1. Cluster results
(b) The origin of ferromagnetism in Mn doped III–V
semiconductors was first explained by Dietl et al.
[5] in terms of carrier-mediated RKKY interaction
or Zener model, in which antiferromagnetic
(AFM) exchange coupling partially spin polarizes
the holes present in the system, which in turn
causes an alignment of the local Mn spins. This
model, however, assumes high hole density ꢀ1020
and the existence of Fermi surface.
(c) Later, Litvinov and Dugaev [9] used a model based
on virtual acceptor level to valence band transi-
tions, and provided a detailed quantitative predic-
tion of the dependence of the Curie temperature
on the Mn concentration for various wurtzite
III–V alloys.
The possibility of Mn forming stable clusters around
N, with the manifestation of giant magnetic moment in
MnxN clusters, was first predicted by Rao and Jena [15].
This opens up the question as to whether a TM impurity
such as Mn can indeed go to the Ga substitutional site
and form a local bond with N in GaN, while retaining
the tetrahedral configuration of the lattice. The recently
observed ferromagnetic coupling in MBE grown
(GaMn)N sample with 14% Mn (Tc ꢁ 750 K) [7] reiter-
ates this claim. As a precursor to full-fledged band cal-
culations, we have carried out SCF-LCAO-MO cluster
calculations on (GaN)x and (GaN)xTM2 (TM = Mn
and Cr) clusters. Considering all possible spin multiplic-
ities M = 2S + 1, we have obtained the optimized
ground state geometries of these clusters (Fig. 1), using

86
G.P. Das et al. / Computational Materials Science 36 (2006) 84–90
(a)
(b)
(c)
Cr
Mn
1.88
2.54
2.72
1.78
1.78
Ga
N
1.32
1.77
2.18
1.77
2.69
2.73
2.05
2.23
2.73
1.92
1.88
1.93
1.36
2.07
Fig. 1. Ground state cluster geometries for (a) (GaN)x (b) (GaN)xMn2 and (c) (GaN)xCr2 clusters (x = 1, 2, and 3).
Table 3
Gaussian-98 code with LANL2DZ basis [16]. Our
results are summarized in Tables 1–3. It is instructive
to see first the results for dimers involving a cation
and an anion or two cations (Table 1). For example,
pure Mn2 dimer is weakly bound, in sharp contrast to
its neighbor Cr2 which is very strongly bound. Mn–N
has a higher binding energy and a smaller bond length
compared to Ga–N, thereby indicating that Mn binds
to N more strongly than Ga. Tables 2 and 3 summarize
our calculated results for (GaN)x and (GaN)xTM2 clus-
ters, respectively. The TM–TM distance in (GaN)xTM2
Energetics and magnetic moment of (GaN)x TM2
x
1
2
3
˚
TM–TM dist (A)
Mn:GaN
Cr:GaN
3.11
3.29
2.52
2.62
2.44
2.74
˚
TM–N dist (A)
Mn:GaN
Cr:GaN
1.78
1.78
1.77
1.77
1.92
2.05
˚
Ga–N dist (A)
Mn:GaN
Cr:GaN
2.88
2.85
2.73
2.68
1.88
1.89
DE (eV)
Mn:GaN
Cr:GaN
5.39
5.43
3.73
3.21
4.34
4.47
˚
˚
˚
˚
varies from ꢀ3.1 A (ꢀ3.3 A) to ꢀ2.4 A (ꢀ2.7 A) for
TM = Mn (Cr), respectively. Guided by this, we carried
out subsequently supercell band calculations with the
Multiplicity (lB)
Mn:GaN
Cr:GaN
8
8
4
2
8
10
˚
Mn–Mn distance as 3.1 A and Cr–Cr distance as
˚
3.3 A. The energy values quoted in Table 2 correspond
to the following standard definitions viz:
Table 1
Calculated ground state properties of dimers
(a) BE of (GaN)x clusters: Eb = [xE(GaN) ꢂ E(GaN)x]/x,
(b) Energy gain in adding a GaN dimer to an existing
(GaN)xꢂ1 cluster: DE0 = E(GaN) + E[(GaN)xꢂ1] ꢂ
E[(GaN)x],
(c) Energy gain in adding a TM2 dimer to an existing
(GaN)x cluster: DE = E[(GaN)x] + 2E(TM) ꢂ
E[(GaN)xTM2].
Dimer
Bond
length (A)
Binding
energy (eV)
Magnetic
moment (lB)
˚
Ga–N
Mn–N
Cr–N
1.88
1.60
1.59
2.60
2.18
3.07
2.06
1.36
2 [Ga: 0.31 N: 1.69]
4 [Mn: 4.09 N: ꢂ0.09]
3 [Cr: 3.51 N: ꢂ0.51]
4 [Mn: 4.66 Ga: ꢂ0.66]
Ga–Mn
Table 2
Energetics and magnetic moment of (GaN)x (see text for definitions)
The DE values for x = 1, 2, and 3 follow the same
trend in the case of Mn and Cr-doping. The total mag-
netic moments of pure (GaN)x cluster for x = 1 turns
out to be 2 lB (most of the moment being located at
the N-site that is antiferromagnetically coupled to the
moment at Ga site). With increasing cluster size, the
x
Eb (eV)
DE0 (eV)
Magnetic
moment (lB)
1
2
3
0
2.99
3.33
–
4.02
3.66
2
0
0

G.P. Das et al. / Computational Materials Science 36 (2006) 84–90
87
Table 4
individual moments at Ga and N sites decrease and
(Ga14TM2)N16 supercell: parameters and results
eventually vanish since bulk GaN is nonmagnetic. On
doping with TM2 the magnetic nature changes com-
pletely as seen from the optimized ground–state spin
multiplicities (M = 2S + 1) of (GaN)xTM2 clusters.
For example, the total magnetic moment of (GaN)1Cr2
is 8 lB out of which 4.28 lB, 0.07 lB and ꢂ0.648 lB mo-
ments reside at Cr, Ga and N site, respectively. Bulk of
the moments are localized at the TM site which are
found to couple ferromagnetically, while the N sites ac-
quire small moments and couple antiferromagnetically
to those at TM sites. Thus, the ground states for both
Mn2 and Cr2 doped (GaN)x are found to be ferromag-
netic, with a lowering of energy by ꢀ0.4 eV.
(Ga14Mn2)N16
˚
(Ga14Cr2)N16
˚
Lattice parameters
a = 3.189 A
a = 3.189A
˚
˚
c = 5.185 A
c = 5.191A
u = 0.377
u = 0.377
VB Top + 1.6 eV
2.5 eV
TM d-band position
TM d-band width
VB Top + 1.4 eV
2.4 eV
Magnetic moment (lB)
Mn = 3.5
Cr = 2.69
Ga = 0.02
N = ꢂ0.02
Ga = 0.025
N = ꢂ0.025
doped GaN DMS system and has formula unit
(TM2Ga14)N16 whose cell parameters (see Table 4) have
been taken from experimental data. TM–TM distance is
˚
fixed at nearest neighbor cation separation (ꢁ3.19 A)
3.2. Supercell band strucure
˚
which is more than the critical separation of 2.5 A ob-
tained from our cluster calculations reported in Section
3.1. Self-consistent spin-polarized TB-LMTO calcula-
tions [19] have been performed within the simplified
atomic sphere approximation [20]. For details of the
methodology followed, readers may refer to a recent
Bulk GaN crystallizes in wurtzite structure (space
group P63mc) which has lattice vectors (in units of a)
p
ð 3=2; ꢂ1=2; 0Þ, (0,1,0) and (0,0,c/a) and an unit cell
containing two cations at (0,0,0) and (2/3,1/3,1/2),
and two anions at (0,0,3/8) and (2/3,1/3,7/8). There
have been numerous first-principles investigations of
the electronic properties of bulk GaN [17] as well as
doped GaN [18]. In order to simulate TM2 dimer doped
GaN, we construct a 32 atom supercell with lattice vec-
tors doubled along all the three directions, and then
selectively replacing two Ga atoms with the impurity
TM atom. Thus the supercell represents a ꢀ12% Mn-
˚
review [21]. The atomic sphere radii (sGa = 1.227 A,
˚
sN = 1.015 A), fixed by Hartree potential plot prescrip-
tion, are found to be roughly proportional to the cova-
˚
˚
lent radii (rGa = 1.62 A, rN = 1.26 A). We have used
(6,6,4) k-mesh in all our supercell calculations, which
corresponds to 144 k-points in the irreducible wedge
of the Brillouin zone. Effect of structural relaxation
Fig. 2. Total DOS for majority-spin and minority-spin of (a) (Ga14Mn2)N16 and (b) (Ga14Cr2)N16 supercells.

88
G.P. Das et al. / Computational Materials Science 36 (2006) 84–90
has been neglected, since the replacement of a Ga atom
of the semiconductor host by the impurity atom (Mn or
Cr) is not expected to relax the lattice substantially
[13,22].
Fig. 3. Partial DOS projected on to the TM impurity site, for majority-spin and minority-spin of (a) (Ga14Mn2)N16 and (b) (Ga14Cr2)N16 supercells.
Fig. 4. Energy band structures of (a) (Ga14Mn2)N16 and (b) (Ga14Cr2)N16 supercells along high symmetry directions. Fermi level is at 0 of energy
scale. The Ôfat-bandsÕ correspond to TM-eg projected (top panel) and TM-t2g projected (bottom panel). See text for details.

G.P. Das et al. / Computational Materials Science 36 (2006) 84–90
89
Self-consistent spin-polarized (only ferromagnetic) to-
tal densities of states of Mn- and Cr-doped GaN (Fig. 2)
show the half-metallic behavior with 100% spin-polariza-
tion, that is ideal for injection of spin-polarized charge
carriers into the non-magnetic semiconductor. Partial
(TM-projected) DOS (Fig. 3) clearly shows that the
states appearing in the gap are originating from the eg
and t2g levels of the TM impurity, whose dispersions
are seen from the so-called ‘‘fat-bands’’ projected onto
the corresponding impurity d-orbitals (Fig. 4). Each of
the fat bands has been allocated a width proportional
to the (sum of the) weight(s) of the corresponding ortho-
normal orbital(s) [23]. The Mn-projected fat-bands show
the minimum gap (direct) appearing at the M-point,
while the Cr-projected fat-bands show the minimum
gap at the C-point (Fig. 4). The Fermi level passes right
through the fattened impurity band in both cases, indi-
cating the possibility of double exchange mechanism
to be the most likely mechanism for the ferromagnetic
coupling in this family of DMS systems [24].
The paramagnetic DOS shows a ꢀ2.4 eV wide Mn 3d-
band hybridized with N 2p. The t2g band lies above the eg
band, thereby indicating that the Mn is sitting in tetrahe-
dral, rather than octahedral crystal field environment
(i.e., if eg. would have been above the t2g band) in the
GaN lattice. This is in conformity with the earlier results
[10,11]. When spin-polarization is switched on, there is a
further spin-splitting which we observe in the partial
DOS as well as in the fat-bands. The peak of the major-
ity-spin impurity d-band lies ꢀ1.4 eV and 1.6 eV above
the top of the valence band of GaN for Mn and Cr, respec-
tively. This conforms to the accepted view that Mn is in d4
configuration acting as an effective mass acceptor
(d5 + h), while Cr is in d3 configuration. Deep-level
optical spectroscopy measurements performed on lightly
Mn-doped samples indeed show that Mn forms a deep
acceptor level at 1.4 eV above the GaN band gap.
between doped TM atoms is an indirect exchange mech-
anism mediated by N. These results are in agreement
with the results earlier reported by van Schilfgaarde
and Mrysaov [10]. Clustering of TM impurity atoms
around N in GaN seems to play a crucial role in the man-
ifestation of ferromagnetism in this class of dilute mag-
netic semiconductors. The sensitivity of the measured
TcÕs to experimental growth conditions may very well
be due to the clustering of Mn around N that has been
studied by several groups in the recent past [15,22,25].
Since clusters represent an extreme case of surface
states and crystal sites represent a substitutional bulk
environment, we conclude that doping of Mn in GaN
whether they are porous, crystalline, or thin layers would
lead to ferromagnetic coupling between Mn atoms. This
allows great flexibility in synthesizing DMS systems
involving Mn- and Cr-doped GaN. In fact, there are
vigorous experimental efforts to realize DMS ferromag-
netism in porous GaN that contains large internal
surfaces and hence more substitutional sites. We are also
now exploring the possibility of doping both Mn and Cr
atoms together in the nearest neighbour and second
nearest neighbour sites of host GaN lattice, and looking
into the manifestation of DMS ferromagnetism.
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spin, while the minority-spin band merges with the
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