Theoretical prediction of magnetism induced by defects or doping in non-metallic colloids has gained a renewed interests recently. In this work, we investigated the possible appearance of magnetism in Cu doped CaO nanocolloids activated by SPAN-80 in the framework of density functional theory (DFT). Despite of strong antiferromagnetic superexchange interaction between Cu$^{2 + }$ ions, the local magnetic moment of Cu may arise due to attachment of colloidal agent onto the surface of CaO nanocluster. The ferromagnetism attributes to the degeneration of Cu 3d orbitals in CaO crystal fields, the aspects of electron correlation and quantum spin fluctuation. %PACS number: 42.30.R, 42.40.Ht, 42.30.K

Nhat, Hoang Nam

Trang, Nguyen Thuy

Vietnam Academy of Science and Technology: Journals Online

Communications in Physics, Vol. 25, No. 4 (2015), pp. 359-365
DOI:10.15625/0868-3166/25/4/0
STRONG ELECTRON CORRELATION IN CU-DOPED CAO NANOCOLLOID
NGUYEN THUY TRANG
Faculty of Physics, Hanoi University of Science, Vietnam National University, Hanoi
HOANG NAM NHAT
Faculty of Engineering Physics and Nano Technology, University of Engineering and Technology,
Vietnam National University, Hanoi
E-mail: nhathn@vnu.edu.vn
Received 29 November 2015
Accepted for publication 24 December 2015
Abstract. Theoretical prediction of magnetism induced by defects or doping in non-metallic colloids has gained a
renewed interests recently. In this work, we investigated the possible appearance of magnetism in Cu doped CaO
nanocolloids activated by SPAN-80 in the framework of density functional theory (DFT). Despite of strong antiferro-
magnetic superexchange interaction between Cu2+ ions, the local magnetic moment of Cu may arise due to attachment
of colloidal agent onto the surface of CaO nanocluster. The ferromagnetism attributes to the degeneration of Cu 3d
orbitals in CaO crystal fields, the aspects of electron correlation and quantum spin fluctuation.
Keywords: DFT, band-gap, CaO, calcium-oxide, mBJ, PBE, functional.
I. INTRODUCTION
Owing to the wide scope of application from optoelectronics to biology the rock salt com-
pounds continuously attract the growing interests of scientists worldwide. A defect induced pho-
toemission in CaO was a subject of many researches [1] and this popular rock salt proposed itself
as a brilliant candidate for application in laser windows, IR domes, IR optical fiber. . . Recently,
there has been a renewed interest in CaO due to a possibility of magnetism in doped (non-metallic)
CaO and defect-induced metallic CaO compounds [2–5]. On the basis of tight-binding-like model,
I. S. Elfimov et al. [2] showed that the cation vacancies in the divalent monoxides with rock salt
structure as well as in any other compounds with octahedral coordination might possess the local
magnetic moments if the on-site Coulomb repulsion U was taken into account. Their ab initio
calculation for CaO with 3.125% Ca vacancies revealed some local magnetic moments at the va-
cancy sites and the obtained numerical results were in good agreement with the theoretical expec-
tation. Their calculation demonstrated the importance of inclusion of strong electron correlation
when modeling the divalent monoxides. They also showed that CaO with vacancies exhibited a
half-metallic ferromagnetic ground state. The experimental verification was obtained from the
c©2015 Vietnam Academy of Science and Technology
360 NGUYEN THUY TRANG AND HOANG NAM NHAT
magnetization measurements taken at room temperature for CaO nanopowder [3]. Another possi-
ble mechanism to induce the local magnetic moments in CaO without doping of transition metals
was proposed by K. Kenmochi et al. [4] was to dope CaO with non-metallic elements such as C,
N and B. The calculations in the framework of Korringa-Kohn-Rostocker method predicted that
these materials should exhibit the room temperature ferromagnetism with local moments origi-
nating from 2p orbitals of dopants. The effects of the Coulomb repulsion U within 2p orbitals
were investigated in more details by V. Pardo and W. E. Pickett [5]. According to their results, the
inclusion of U had an effect of strengthening the localization of magnetic moments and reducing
the possible magnetic interaction.
In this work, we show that the local magnetic moments may be obtained in Cu-doped CaO
nanocolloids activated by using SPAN-80 as colloidal agent. It is well-known that the high tem-
perature superconducting cuprates possess the antiferromagnetic Mott-insulating ground state due
to the superexchange interaction between the strongly correlated spin 1/2 Cu2+ cations situating
in the octahedral crystal field of surrounding oxygen atoms. It is thus reasonable to expect that
the octahedral field substitution of Cu2+ for Ca2+ may inject some amounts of local magnetic
moments while introducing no extra electrons or holes. However, the question is whether or not
Cu2+ remains spin-polarized in the crystal field of rock salt as expected and if polarized then
which magnetic interaction, ferromagnetic or antiferromagnetic, is preferable. In the framework
of density functional theory (DFT), we aim at clarifying this problem
II. CALCULATIONS DETAILS
Both conventional orbital-independent exchange-correlation functionals i.e. generalized
gradient approximation (GGA) type and orbital-dependent correlation functionals, i.e. GGA+U
were used. The GGA functional is PBE of which the exchange part was formulated by Beck
and the correlation part was by Perdew-Wang [6]. The GGA+U is a kind of a mixture between
density functional theory method and Hubbard model theory in which the semilocal formulation
of exchange-correlation of a considered orbital is substituted with the Hubbard one to give a better
description of strongly-correlated system [7]. To formulate the orbitals for system considered, the
numerical atomic-like basis set and plane wave basis set with norm-conserving pseudopotential
(PWPP) were used in combination with GGA and GGA+U methods respectively. The numerical
atomic-like basis set is composed of a double-numeric quality basis set, i.e. 2 atomic orbitals
for each 1 occupied in free atom plus polarization functions with angular momentum one higher
than that of the highest occupied orbital in free atom (DNP basis set). The sets of DNP/GGA and
PWPP/GGA+U methods were provided by Dmol3 and CASTEP codes respectively [8, 9].
III. RESULTS AND DISCUSSIONS
First, we examined the periodic boundary condition (PBC) by using the DNP/GGA method
how two Cu atoms can be inserted into Ca sites using a large suppercell 2×2×2 (Fig. 1(a)), which
particularly corresponds to the impurity level of 6.25%. Three doping configurations with highest
symmetry were considered: two Cu atoms aligned along (111), (101) and (001) directions. At
each configuration, the initial ordering of spins was set to ferromagnetic (FM) and antiferromag-
netic (AFM) respectively. The comparison of obtained total ground state energies revealed that
the (001) configuration was the most preferable one which had Etotal(001) 7 eV lower than that
STRONG ELECTRON CORRELATION IN CU-DOPED CAO NANOCOLLOID 361
of the other two. Table 1 summarizes the total energy Etotal , concentrated charge QCu and spin
µCu from Mulliken’s electron population analysis, lattice constant and effective exchange constant
Je f f calculated using Heisenberg model. According to the data presented, while (111) configu-
ration preferred the AFM ordering state, the (101) preferred the FM one. However the obtained
Cu local moments were very small, i.e. µCu ≈ 0.2% of the moment of Cu2+. For the (001)
configuration with both FM and AFM initial magnetic orderings, the electron density converge to
the nonmagnetic state with zeroed Cu local moments.
Table 1. Summarization of total energy Etotal , concentrate atomic charge on Cu QCu, lo-
cal magnetic moment of Cu µCu, effective exchange interaction Je f f and magnetic ground
state for Ca0.9375Cu0.0625O
(111) (101) (001)
Initial
FM AFM FM AFM FM AFM
magnetic order
Etotal -26748.586702 -26748.586706 -26748.586707 -26748.586702 -26748.609028 -26748.609028
(Ha/cell)
QCu (|e|) 0.539 0.539 0.539 0.539 0.464 0.464
|µCu| (µB) 0.002 0.002 0.002 0.002 0 0
Je f f (meV) -0.055 0.070 0
Ground state AFM FM Paramagnetic or spin-glass?
Investigating the response of the PBC doped structure putting within the cavity of addi-
tional Coulomb force-field introduced by solvent by using the Conductor-like Screening Model
(COSMO) for the surrounding media with dielectric constants from 2 (common oils) to 80 (wa-
ter) we observed a slight enhancement of local moments (less then 0.1%) of doped sites when
the dielectric constant of medium decreased. This effect may be assigned to the strengthening of
Coulomb repulsion between occupied and unoccupied states due to the occurrence of additional
Coulomb field at the surface of the PBC structure. However, the prediction of COSMO for oils
(including SPAN-80) was known to be twice as large as the prediction by ab initio using the direct
attachment of colloidal agent onto the nanocluster surface.
The strong reduction of Cu local moment in the PBC structure can be assigned to three
possible reasons: (1) the strong antiferromagnetic quantum spin fluctuation (2) the intrinsic split-
ting of 3d Cu orbital in crystal field of CaO and (3) the inadequate treatment on strong correlation
aspects, i.e. insufficient on-site Coulomb repulsion U. Because the Cu local moment are the same
for both FM and AFM magnetic ordering states in (111) and (101) configurations, the quantum
spin fluctuation should be possible. It is easy to see that Cu atoms occupy sites so that Cu-O chains
were formed in two and three dimensions The situation is quite similar to the one as in Sr2CuO3
and Ca2CuO3 where the CuO layers are separated from each other by two (Sr/Ca)O layers. Con-
sequently, the interlayer coupling was small in comparison with the intrachain interaction [10]. To
be specific, the value is about 10 times smaller than the effective exchange Je f f ≈ 1 meV as
obtained for Ca0.9375Cu0.0625O in (111) and (101) configuration. Therefore, it is possible that the
small local magnetic moment µCu = 0.05 µB was due to the strong quantum spin fluctuation which
suppresses 95% magnetic moment of Cu site [11, 12].
362 NGUYEN THUY TRANG AND HOANG NAM NHAT
In order to figure out the roles of crystal field splitting and on-site Coulomb repulsion we
note that the calculation on basis of tight binding-like model for a cluster of oxygen octahedron
by I. S. Elfimov et al. [2] indicated that whether or not the vacancy will possess the spin-polarized
ground state depends on the crystal field splitting of orbitals. It was the nature of hole orbitals
which were formed mainly by 2p orbitals of oxygen that they were degenerate, therefore in the
presence of strong Coulomb repulsion the singlet states should be lifted to higher energy in com-
parison with the triplets. It is also well-known that the on-site Coulomb repulsion prefers the
single occupancy of spin-polarized states while the crystal splitting induces the double occupancy
of spin-unpolarized state. According to this, when Cu was substituted for Ca in its octahedral
field of surrounding oxygen, five Cu 3d orbitals are three-fold degenerate orbitals t2g (which are
full-filled) and two-fold degenerate orbitals eg (which are partial-filled). With a lack or inadequate
treatment of electron repulsion a ground state of the doped compound may appear as spin glass or
nearly spin glass, with µCu= 0 or nearly zero.
(a) (b)
Fig. 1. (a) CaO supercell 2×2×2 modeling a doping level 6.25%. The green dash line
indicate (001), (101) and (111) direction. (b) A supercell of octahedral nanocluster CuO6
embedded in vacuum; the inset shows the SPAN-80 molecule with its H(1) center.
Then we utilized the model cluster as given in Fig. 1(b). The approximation of choice was
the PWPP/GGA+U as described above. First we tested the model with U = 0,2.5,3,4,5,6 eV
applied on the Cu 3d orbitals. The results showed that the total magnetic moment was around the
nominal value of 1 µB and nearly 50% was concentrated on Cu for all values of U (Fig. 2(a)).
The local magnetic moment even appeared for U = 0 which indicated that the plane wave basis
set can reproduce the electron correlation in octahedral coordination better than the numerical
atomic-like basis set. Fig3(a) and (b) show the partial density of spin states (DOS) calculated with
various values of U. The addition of the on-site Coulomb term seemed to make the Cu 3d spins
more tightly bound to the core, in other words, they were more localized. This in turn reduced the
exchange constants which were observed to usually be larger than the measured ones.
STRONG ELECTRON CORRELATION IN CU-DOPED CAO NANOCOLLOID 363
(a) (b)
Fig. 2. (a) Plot of the local magnetic moment according to U for CuO6 nanocluster (black
close squares) and Cu doped CaO (red close round). The red dash line denotes the nom-
inal magnetic moment of Cu. (b) The dependence of total energy of AFM state of Cu
doped CaO on U value
Applying this methodology on the PBC structure of Cu doped CaO with doping concentra-
tion 25% using a supercell of the size 1×1×2 and initial spin ordering set to AFM, we found a
smaller local moment of maximum 0.66 µB (corresponding to U = 2.5, 3, 4 eV) The value reduced
to 0.48 µB for U = 0 eV and to 0.38 µB for large U = 5 eV. Fig 2 expresses the dependence of
local moment and energy difference between AFM and nonmagnetic spin ordering states ∆E on
U. Fig. 3(c) and (d) show the partial density of spin states (DOS) calculated for U = 0 and 4 eV. It
appeared reasonably that almost all spin-polarization was originated from O 2p and Cu 3d states.
As expected, the reduction of ∆E when U increased seemed to correspond with the reduction of
exchange amplitude due to the localization of spins.
With the settings given we studied the COSMO effect on final local moment for the sur-
rounding media having the dielectric constant from 2 to 80. Again we have observed a slight en-
hancement of measure not greater than 0.5%. This result argued for the fact that on PBC structure
of 25% doping the COSMO effect only limited response. However, the increase was observably
larger if one applied COSMO on doped nanocluster with 25% Cu content. We recorded the in-
crease of almost 27%, that is the maximum local moment over Cu site achieved 0.84 µB But as
noted above, the COSMO results were usually overestimated by the ratio approximately equal
100% for oils (thus for SPAN-80 in our case of interest). Its error is small only for the polar
solvents like water (with dielectric constant near 80). For the purpose of more exact estimation
of the effect of solvent binding on surface of doped cluster we built H(1) center of one molecule
SPAN-80 (Fig.1 (b)) onto the O center of doped CaO nanocluster. The previous study from our
group [13] showed that the binding through H(2) and O centers of SPAN-80 were not preferred.
Such the bindings resulted in the higher ground state energy (¿1 eV) of the binary nanoparticle-
colloid system in comparison with the case of binding through H(1). The optimized geometry was
achieved at the O...H(1) distance of 1.7 A˚ This distance is short enough to replicate the COSMO
effect on the Cu site directly bound to the given O center. As expected, the local moment reduced
to smaller value of 0.76 µB, that is the binding induced only ≈ 14% increase of local moment.
364 NGUYEN THUY TRANG AND HOANG NAM NHAT
Fig. 3. The partial density of spin states (DOS) calculated by using PWPP/GGA+U
method for the octahedral CuO6 nanocluster (a) U = 0 eV; (b) U = 4 eV. The same for Cu
doped CaO (c) U = 0 eV; and (d) U = 4 eV.
However, we should note here the difference between modeling the additional Coulomb force
field (ACFF) by COSMO and by direct surface binding of surfactant. While COSMO estimates
ACFF by putting solute inside a cavity of surfactant so the charge polarization (like in a capaci-
tor) is built-up onto two sides of a vacuum layer between solute and surfactant thus introducing
the ACFF on solute, the modeling of ACFF by direct binding of surfactant onto surface of solute
estimates ACFF by the strength of exchange interaction between bonding atoms. In our case,
more electrons were depleted from H(1) center of SPAN-80 and pumped onto the O 2p orbital,
raising its overall occupation level, which in turn induced a stronger Coulomb repulsion between
occupied and unoccupied states.
IV. CONCLUSION
The possible appearance of ferromagnetism in non-magnetic insulating materials was al-
ways exciting phenomenon. Here we examined such possibility in Cu doped CaO nanocolloid
within the framework of DFT methods. We showed that the inclusion of strong electron correla-
tion was important to discover the electron localization effect The obtained results argued for a
large local magnetic moment upon Cu doping sites and possible appearance of ferromagnetism in
doped nanoclusters where the ferromagnetic penetration depth is comparable with the cluster size.
We leave this for future consideration.
STRONG ELECTRON CORRELATION IN CU-DOPED CAO NANOCOLLOID 365
ACKNOWLEDGEMENT
This research is funded by Vietnam National Foundation for Science and Technology
Development (NAFOSTED) under grant number 103.02-2014.17. One of the authors, Nguyen
Thuy Trang, would like to thank TRIG A Project of Hanoi University of Science, Vietnam Na-
tional University, Hanoi for supporting.
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Strong Electron Correlation in Cu-doped CaO Nanocolloid

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Strong Electron Correlation in Cu-doped CaO Nanocolloid

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