Precursor synthesis and magnetic properties of Cd1-xFexO (0?≤?x?≤?0.07) polycrystalline solid solutions

Article abstract of DOI:10.1016/j.jallcom.2017.07.255

Polycrystalline solid solutions Cd_1-xFe_xO (0 < x ≤ 0.07) have been synthesized by the precursor method using formate of the composition Cd_1-xFe_x(HCOO)₂·2H₂O as a precursor. For the production of Cd_1-xFe_xO, the precursor was annealed in air at a maximal temperature of 400 °C. At x ≥ 0.075, an impurity CdFe₂O₄ ferrite phase with cubic spinel structure was detected in the samples. The examination of the magnetic properties of Cd_1-xFe_xO at 5 and 300 K revealed that they are ferromagnets, whose magnetization increases with the concentration of iron both at low and room temperature reaching the maximal values in samples with х = 0.07. In order to determine the degree of oxidation and the spin state of iron atoms, the main interatomic interactions giving rise to ferromagnetism as well as to estimate the Curie temperatures, we also performed first-principle calculations of the electronic band structure. They showed the existence of chemical bonding between adjacent iron atoms leading to the appearance of ferromagnetism by direct exchange. The value of the Curie temperature calculated by the mean field method on the basis of the first-principle calculations is 507 K, which is in reasonable agreement with the experimental value of 560 K.

Full text of DOI:10.1016/j.jallcom.2017.07.255

Accepted Manuscript
Precursor synthesis and magnetic properties of Cd Fe O (0 ≤ x ≤ 0.07)
1-x
x
polycrystalline solid solutions
V.N. Krasilnikov, V.P. Zhukov, О.I. Gyrdasova, Т.V. Dyachkova, А.P. Tyutyunnik,
Yu.А. Perevozchikova, H.W. Weber, A. Zaleski, V.V. Marchenkov
PII:
S0925-8388(17)32631-2
10.1016/j.jallcom.2017.07.255
JALCOM 42671
DOI:
Reference:
To appear in: Journal of Alloys and Compounds
Received Date: 9 February 2017
Revised Date: 24 July 2017
Accepted Date: 25 July 2017
Please cite this article as: V.N. Krasilnikov, V.P. Zhukov, О.I. Gyrdasova, Т.V. Dyachkova, А.P.
Tyutyunnik, Yu.А. Perevozchikova, H.W. Weber, A. Zaleski, V.V. Marchenkov, Precursor synthesis and
magnetic properties of Cd Fe O (0 ≤ x ≤ 0.07) polycrystalline solid solutions, Journal of Alloys and
1-x
x
Compounds (2017), doi: 10.1016/j.jallcom.2017.07.255.
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ACCEPTED MANUSCRIPT
PRECURSOR SYNTHESIS AND MAGNETIC PROPERTIES
OF Cd1-xFexO (0 ≤ x ≤ 0.07) POLYCRYSTALLINE SOLID SOLUTIONS
V.N. Krasilnikov1, V.P. Zhukov1, О.I. Gyrdasova1, Т.V. Dyachkova1, А.P. Tyutyunnik1,
Yu.А. Perevozchikova2, H.W. Weber3, A. Zaleski5, V.V. Marchenkov2, 4, 6
1 Institute of Solid State Chemistry of the Ural Branch of RAS, 620990 Ekaterinburg, Russia
2 M.N. Mikheev Institute of Metal Physics of the Ural Branch of RAS, 620990 Ekaterinburg, Russia
3 Atominstitut, TU, 1020 Vienna, Austria
4 Ural Federal University, 620002 Ekaterinburg, Russia
5 Institute of Low Temperatures and Structure Research, PAS, 50-422 Wroclaw, Poland
6 International Laboratory of High Magnetic Fields and Low Temperatures, 53-421 Wroclaw, Poland
Polycrystalline solid solutions Cd1-xFexO (0<x≤0.07) have been synthesized by the precursor method
using formate of the composition Cd1-xFex(HCOO)2ꢀ2H2O as a precursor. For the production of
Cd1-xFexO, the precursor was annealed in air at a maximal temperature of 400 oC. At x≥0.075, an impurity
CdFe2O4 ferrite phase with cubic spinel structure was detected in the samples. The examination of the
magnetic properties of Cd1-xFexO at 5 and 300 K revealed that they are ferromagnets, whose
magnetization increases with the concentration of iron both at low and room temperature reaching the
maximal values in samples with х = 0.07. In order to determine the degree of oxidation and the spin state
of iron atoms, the main interatomic interactions giving rise to ferromagnetism as well as to estimate the
Curie temperatures, we also performed first-principle calculations of the electronic band structure. They
showed the existence of chemical bonding between adjacent iron atoms leading to the appearance of
ferromagnetism by direct exchange. The value of the Curie temperature calculated by the mean field
method on the basis of the first-principle calculations is 507 K, which is in reasonable agreement with the
experimental value of 560 K.
Keywords: precursor synthesis, magnetization, cadmium oxide, spintronics, mean field method.
Highlights:
• simple-to-use precursor synthesis is proposed;
• homogeneous polycrystalline solid solutions Cd1-xFexO are promising materials for spintronics;
• Cd1-xFexO are ferromagnets at 5 and 300 K;
Curie temperature is calculated by the mean field method.

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INTRODUCTION
The development of advanced areas of modern science and engineering, such as spintronics based
on the idea of spin polarization in semiconductors, is impossible without the creation of novel functional
materials, which effectively combine the valuable properties of semiconductors and of ferromagnets and
allow to control their magnetic, semiconducting, and optical properties [1-3]. Zinc oxide is among such
materials. Doping of zinc oxide with transition metal cations gives rise to anomalies in the physical
(including magnetic) properties [3, 4]. In spite of the presence of only a few atomic percent of magnetic
impurities with negligibly small exchange interactions between them, ferromagnetic ordering can appear
in ZnO even at room temperature. At the same time, it was established that the magnetic properties of
materials based on zinc oxide depend not only on the presence and concentration of magnetic impurities,
but also on the method of their production. The low-temperature precursor synthesis with
Zn1-xFex(HCOO)2ꢀ2H2O formate as a precursor was used to synthesize stable ferromagnetic solid
solutions of the composition Zn1-xFexO (0<x≤0.07) with wurtzite structure [5-7]. The value of the
magnetic moment of Zn0.95Fe0.05O at room temperature was 0.42 µB/at Fe, which is much higher than
those for all known materials of analogous composition. A similar value (0.44 µB/at Fe) was obtained
o
only as a result of heating mechanically mixed ZnO and Fe3O4 at 700 C under a pressure of 5 GPa [8].
This indicates advantages of the simple-to-use precursor synthesis, the most important of which is the
possibility to very accurately specify the elemental composition both of the precursor, for example, in the
form of solid solutions Zn1-xFex(HCOO)2ꢀ2H2O, and of the product of its thermolysis. The logic of the
precursor synthesis approach for Zn1-xFexO developed by the authors [5-7] is based in the first place on
the exact knowledge of the precursor composition and the conditions of its transformation into the oxide
containing no impurity phases.
Along with zinc oxide, cadmium oxide can be used as a semiconducting matrix. Owing to its defect
structure, in particular, the presence of oxygen vacancies, cadmium oxide is an n-type semiconductor with
a broad forbidden band of ~2.2 eV showing a unique complex of physical properties, which explains the
wide range of its practical applications. CdO is used in various photoelectric devices, such as solar cells,
phototransistors, photodiodes, photosensors, flat-panel displays, IR detectors etc. [9-16]. The electrical
and optical properties of cadmium oxide depend on the degree of its imperfection, the presence and the
nature of heteroatomic impurities as well as on the morphology, surface microstructure, and particle size,
which are in turn determined by the synthesis conditions. The presence of even small amounts of intrinsic
defects or impurities has a profound effect on the bulk electronic properties of cadmium oxide [17, 18].
Thermal treatment of powder-like CdO in vacuum or in hydrogen atmosphere gives rise to room
temperature magnetization of 1.15 and 1.2 memu/g (10-3 A m2/kg), respectively, [18]. In our opinion, this
effect is due to an increase in the structural imperfection of cadmium oxide: annealing in vacuum leads to
the formation of oxygen bonds, while vacancies in the cadmium sublattice are formed in hydrogen

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atmosphere. According to first-principle calculations [18], vacancies in the cadmium and oxygen
sublattice induce spin-polarized states of O2p and 4d-orbitals of Cd in the vicinity of the Fermi level,
which determines its ferromagnetic properties. The introduction of transition element ions into the crystal
structure of cadmium oxide affects appreciably its electronic and optical properties [19-32]. Doping CdO
with small amounts (~1-2 at %) of iron leads to an abrupt enhancement of the electrical conductivity [25]
and to the appearance of weak ferromagnetic properties, which are enhanced upon exposing the samples
to vacuum or hydrogen atmosphere [28, 29]. An analogous effect is observed when cadmium oxide is
codoped with copper and gadolinium [30]. Nanodispersed solid solutions Cd1-xNixO (x = 0.047, 0.102,
0.163) exhibiting paramagnetic and ferromagnetic properties were synthesized by thermolysis of the
mixed oxalate of the composition Cd1-xNixC2O4ꢀnH2O [33]. Nanodispersed solid solutions Cd1-xMnxO
[20] and Cd1-xCoxO produced by thermolysis of mixed oxalates in air [31] and by electrochemical
deposition [32] show magnetic properties at 5 K. Ferromagnetic solid solutions of the composition
Cd1-xMnxO capable of room temperature magnetization were synthesized by a thermal treatment at 400 oC
of the precipitates formed as a result of the addition of ammonium hydroxide to aqueous solutions of
cadmium and manganese [34]. However, the best effect, as in the case of ZnO [5-8], was achieved when
cadmium oxide was doped with iron [28, 29]. Thus, along with Zn1-xFexO, diluted magnetic
semiconductors in the form of homogeneous polycrystalline solid solutions Cd1-xFexO are promising
materials for spintronics, which can be used for the fabrication of magnetoresistive memory cells, spin
light-emitting diodes (spin-LEDs), field-effect transistors, magnetic field sensors, electrically triggered
magnetic transducers, as well as components of quantum computers [1]. The aim of this work is to
develop a precursor method for the synthesis of polycrystalline solid solutions of the composition
Cd1-xFexO with the maximal possible degree of iron for cadmium substitution and to examine their
structural and magnetic properties using experimental and theoretical approaches. Cadmium formate of
the composition Cd(HCOO)2ꢀ2H2O, in the structure of which a certain part of Cd2+ positions is replaced
by Fe2+ cations, was chosen as a precursor. Cadmium formate belongs to the group of isostructural
compounds, which are highly soluble in water, of the general composition M(HCOO)2ꢀ2H2O (M = Mg,
Mn, Fe, Co, Ni, Cu, Zn, Cd), which crystallize in the monoclinic system (sp. gr. P21/c) and are able to
form solid solutions with each other [35-43]. A continuous series of solid solutions
Cd1-xFex(HCOO)2ꢀ2H2O was established for isostructural cadmium and iron formates [41].
EXPERIMENTAL
Cd1-xFex(HCOO)2ꢀ2H2O (0≤x≤0.2) was synthesized by dissolution of mixtures of cadmium and iron
formates in hot distilled water and by subsequent evaporation of the solutions at 60 oC in air until a solid
residue was formed:
(1-x)Cd(HCOO)2ꢀ2H2O + xFe(HCOO)2ꢀ2H2O = Cd1-xFex(HCOO)2ꢀ2H2O
(1)

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Before evaporation, a small amount of concentrated formic acid was added to the formate solutions to
suppress iron oxidation and to retain iron in the oxidation state +2. Cadmium and iron formates necessary
for the synthesis of Cd1-xFex(HCOO)2ꢀ2H2O were prepared by the following rections [42-44]:
CdCO3 + 2HCOOH + H2O = Cd(HCOO)2ꢀ2H2O + CO2
Fe + 2HCOOH + H2O = Fe(HCOO)2·2H2O + H2
(2)
(3)
Because of the possible oxidation of Fe2+ to Fe3+ by atmospheric oxygen [44], the iron formate was
crystallized by evaporation of the solution in nitrogen. The synthesized samples were kept in air-tight
glass vessels. The samples of Cd1-xFex(HCOO)2ꢀ2H2O dried at 100 oC were ground in a porcelain mortar
o
and heated on an electric stove at 300 C. The dark-brown mass, formed as a result of the thermal
decomposition of the precursors, was thoroughly ground, placed into a porcelain crucible, and annealed in
o
a muffle furnace at 400 C for 6 h. Finely dispersed samples of the nominal composition Cd1-xFexO (x =
0.01, 0.025, 0.05, 0.07, 0.075, 0.1, 0.15, 0.2) were synthesized.
The phase analysis of the precursors and the products of their thermolysis was carried out by means
of a polarizing microscope in transmitted light (the refraction indices were determined by the immersion
method at room temperature) and a STADI-P X-ray powder automatic diffractometer (STOE, Germany)
using CuKα1 radiation and the X-ray diffraction database PDF-2 (ICDD Release 2009). The shape and
size of the particles were determined by scanning electron microscopy (SEM) using a JSM JEOL 6390LA
device. The magnetic properties were measured in an MPMS XL7 SQUID magnetometer (Quantum
Design) in magnetic fields to 7 T. The density of the Cd1-xFexO powders was determined with an
automatic helium pycnometer AccuPyc II 1340 equipped with a 1 cm3 working chamber.
EXPERIMENTAL RESULTS AND DISCUSSION
The precipitates of cadmium formate Cd(HCOO)2ꢀ2H2O and iron formate Fe(HCOO)2·2H2O
deposited from the solution are white and light green powders, respectively. Cadmium formate forms
flattened crystals with moderate cleavage in the direction parallel to flattening and with poor cleavage in
other orientations. The refraction indices of the Cd(HCOO)2ꢀ2H2O crystals are Ng = 1.548, Nm = 1.509,
and Np = 1.497. Iron formate is characterized by the formation of plate-like and hexagonal scaly crystals
with the refraction indices: Ng = 1.563, Nm = 1.536, and Np = 1.524 [5, 7]. During evaporation of the
solutions of cadmium and iron formate mixtures, solid solutions of the composition
Cd1-xFex(HCOO)2ꢀ2H2O are formed, whose powders have a weak yellow-green color. The
Cd1-xFex(HCOO)2·2H2O crystals also have a plate-like shape, and their refraction indices differ
inconsiderably from those of pure cadmium formate. The refraction indices of the
Cd0.95Fe0.05(HCOO)2·2H2O crystals are equal to Ng = 1.551, Nm = 1.509, and Np = 1.499. The
Cd1-xFex(HCOO)2·2H2O crystals with an iron content of more than 5 at % are characterized by undulating
extinction, which impedes their orientation and measurement of refraction indices.

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Figure 1 shows the morphology of aggregates of CdO and Cd1-xFexO (x = 0.07) powders produced
by thermolysis of Cd(HCOO)2·2H2O and Cd1-xFex(HCOO)2·2H2O during heating in air at the maximal
o
annealing temperature of 400 C. The particles of undoped cadmium oxide have a typical round shape
(Fig. 1а). Such particles with a size of ~100 nm are formed during thermolysis of some precursors, such
as oxalate CdC2O4ꢀ2H2O [45] and malonate CdC3H2O4ꢀ2H2O [15], complex compounds of cadmium
containing mixed ligands [46], as well as during low-temperature thermolysis of precursors in oleic acid
[47, 48]. For the solid solutions Cd1-xFexO formed as a result of thermal decomposition of
Cd1-xFex(HCOO)2·2H2O, the round shape of particles is retained, but their size decreases as the iron
concentration grows (Fig. 1b), in agreement with the X-ray diffraction data of the coherent scattering
regions (SCR) estimated by the Scherrer equation (Table 1).
a
b
Fig. 1. SEM image of the morphology of CdO (a) and Cd1-xFexO (b) aggregates synthesized by
thermolysis of Cd(HCOO)2ꢀ2H2O and Cd1-xFex(HCOO)2ꢀ2H2O (x = 0.07).
Table 1. Lattice parameters, particle sizes (CSR), and density of cadmium oxide and solid solutions
Cd1-xFexO synthesized by thermolysis of formates
No.
1
Composition
a, nm
(CSR), nm
104.85
87.35
ƍ, g/cm3
CdO
Cd0.99Fe0.01
Cd0.975Fe0.025
0.46962(5)
0.46956(5)
0.46946(5)
0.46941(5)
0.46934(5)
8.058±0.006
7.962±0.008
7.820±0.03
7.674±0.02
7.657±0.02
2
O
3
O
90.42
4
Cd0.95Fe0.05
Cd0.93Fe0.07
O
80.33
5
O
80.48
According to the analysis of the X-ray diffraction data, the products of thermal decomposition of
Cd1-xFex(HCOO)2·2H2O (0≤x≤0.07) in air during heating in an electric stove consist mainly of an oxide
with CdO structure and small amounts (~ 0.5 mass %) of metallic cadmium impurities, whereas upon

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o
annealing at 400 C in a muffle furnace monophase samples of solid solutions of the composition
Cd1-xFexO with preset iron concentration and cubic NaCl type structure (sp. gr. Fm3m) typical of undoped
cadmium oxide are found (Table 1). Figure 2 displays the X-ray diffraction patterns of the powders of
pure cadmium oxide and solid solutions Cd1-xFexO with x = 0.01, 0.025, 0.05, and 0.07. At iron
concentrations of 7.5 at % and higher, lines of the impurity ferrite phase CdFe2O4 with cubic spinel
structure appear in the X-ray diffraction patterns [49-53]. The formation of metallic cadmium during
thermal decomposition of precursors can be induced by thermally stimulated intramolecular interaction of
the cationic and anionic components of the Cd(HCOO)2 (Cd2+ + 2HCOO- = Cd0 + H2O + CO + CO2)
formate. Indeed, as a result of heating in air at 300 oC, Cd(HCOO)2·2H2O decomposes with the formation
of CdO containing ~1 mass % Cd, whereas heating at the same temperature in helium atmosphere leads to
a thermal decomposition of the formate and to metallic cadmium in the form of a grey powder. During
heating of Fe(HCOO)2·2H2O in inert atmosphere, it transforms into a black magnetic pyophoric powder,
which spontaneously ignites in air at room temperature and transforms into Fe3O4 or γ-Fe2O3. The
reduction of cadmium to a metal was observed during examination of the thermal decomposition of
cadmium oxalate CdC2O4·3H2O [54] and cadmium acetate Cd(CH3COO)2·2H2O [56, 56]. In order to
improve the magnetic properties of cadmium oxide codoped with iron and copper and with gadolinium
o
and copper, the samples were held in hydrogen atmosphere at a temperature of 350 C [28-30]. Under
these conditions, cadmium was partly reduced to the elemental state:
CdO + H2 = Cd0 + H2O,
(4)
which, according to the authors [28-30], increased the structural imperfection of the samples and,
consequently, improved their magnetic properties. The iron, copper, and gadolinium cations present in the
structure of cadmium oxide catalyze this process. The largest growth of the room temperature magnetic
moment (from 2.93 memu/g to 837 memu/g, i.e. from 2.93·10-3 A m2/kg to 837·10-3 A m2/kg) was
observed for iron-doped CdO [28]. However, the formation of non-monophase ferromagnetic material as
a result of the isolation of cadmium from the oxide structure in the form of a metal reduces the
importance of these. In addition, the authors [28-30] did not take into account the possibility of a
reduction of iron and copper, when the samples are in contact with hydrogen, although this is quite
probable considering the data on the thermal decomposition of manganese, iron, cobalt, nickel, and
copper formates in an inert gas atmosphere [57-60]. Since Cd2+ can be partially reduced to Cd0 during
thermal decomposition of Cd1-xFex(HCOO)2·2H2O in air, the annealing of primary thermolysis products
is expected to yield the solid solutions Cd1-xFexO with enhanced structural imperfection. The presence of
point defects may affect the magnetic behavior of the synthesized samples of Cd1-xFexO, as upon heating
under hydrogen atmosphere [28-30].

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Fig. 2. X-ray diffraction patterns of CdO (1) and solid solutions Cd1-xFexO synthesized by thermal
treatment of Cd(HCOO)2ꢀ2H2O and Cd1-xFex(HCOO)2ꢀ2H2O in air at the maximal annealing temperature
of 400 oC (2 - x = 0.01, 3 - x = 0.025, 4 – x = 0.05, 5 – x = 0.07).
Figure 3 shows the magnetization curves of the Cd1-xFexO samples (0 ≤ x ≤ 0.07) at T = 5 K (Fig.
3a) and T = 300 K (Fig. 3b). All iron-containing samples are ferromagnetic. This is confirmed by the
presence of hysteresis and residual magnetic moments (see the insets in Figs. 3a and 3b). According to
Fig. 3 and Table 2 the value of the magnetic moment increases with iron concentration both at low
temperature and at room temperature reaching the maximal value for the sample with х = 0.07: mS = 2.4
A m2/kg at T = 5 K and mS = 0.9 A m2/kg at T = 300 K (Table 2). A similar trend at room temperature
was observed for nanocrystalline powders of CdO doped with iron atoms from 0.25 % Fe to 1.8 % Fe
[29]. By measuring the temperature dependence of the magnetization for Cd1-xFexO in the range from 300
to 800 K in a field of 50 mT, we determined the Curie temperature to be 560 K.
The experiments show that pure CdO behaves as a diamagnetic with a ferromagnetic component at
both temperatures, as observed in [18, 28]. As done there, we subtracted the diamagnetic component and
determined from the ferromagnetic component the coercive force HC and the saturation magnetic moment
mS. The values of HC and mS for all samples are listed in Table 2. At room temperature the saturation
magnetization of pure CdO is mS = 1.2·10-3 A m2/kg, in good agreement with previous data [18, 28, 29].
The magnetic characteristics of the Cd1-xFexO samples were compared with literature data [28, 29] using
Cd0.99Fe0.01O as an example (Table 1), since powders of the same composition were examined there at
room temperature.

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a
b
1
0
3
2
0.3
1
0.0
-0.3
-1
1
-0.1
0.0
Field (T)
0.1
-0.03
0.00
Field (T)
0.03
0
0
CdO
CdO
-1
-2
-3
Cd0.99Fe0.01
O
Cd0.99Fe0.01
O
Cd0.975Fe0.025
O
Cd0.975Fe0.025
O
Cd0.95Fe0.05
O
Cd0.95Fe0.05
O
-1
Cd0.93Fe0.07
O
Cd0.93Fe0.07
O
-8
-6
-4
-2
0
2
4
6
8
-8
-6
-4
-2
0
2
4
6
8
Field (T)
Field (T)
Fig. 3. Magnetization curves of CdO and solid solution Cd1-xFexO samples at 5 (a) and 300 K (b).
The hysteresis loops are shown in the insets.
Table 2. Coercivity HC and saturation magnetic moment ms for samples from different precursors at T = 5
K and T = 300 K
No
Sample
Coercivity Saturation magnetic Saturation magnetic
Temperature (K)
HC (mT)
moment
ms (10-3 A·m2/kg)
moment
ms (ꢁB/Fe)
-
1
2
3
4
5
CdO
23
5
7.5
1.2
5
300
5
-
Cd0.99Fe0.01
O
80
1
476
17.9
810
139
1520
502
2446
905
2.5
0.09
1.68
0.29
1.54
0.51
1.74
0.64
300
5
Cd0.975Fe0.025
O
58
1
300
5
Cd0.95Fe0.05
Cd0.93Fe0.07
O
46
1.2
45
2.2
300
5
O
300
In our work, the saturation magnetization of the Cd0.99Fe0.01O sample at Т = 300 K is mS = 17.9·10-3
A m2/kg, which is higher than reported in [28, 29], where mS = 2.93·10-3 A m2/kg and mS = 5.5·10-3
A m2/kg, respectively. Annealing of the Cd0.99Fe0.01O powder in vacuum [28] increased the saturation
magnetization by almost 7 times – up to mS = 19.73·10-3 A m2/kg, which the authors of [28] explain by
the appearance of oxygen vacancies strengthening the magnetic interaction between Fe atoms. Then these
powders were annealed in hydrogen atmosphere [28, 29], which led to a considerable increase in the

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saturation magnetization up to mS = 837·10-3 A m2/kg [28] and mS = 594·10-3 A m2/kg [29]. This large
increase in mS by two orders of magnitude was explained in [28, 29] by the appearance of metallic
cadmium and, correspondingly, cadmium vacancies. The latter can lead according to [28, 29] to a
strengthening of the magnetic Fe-Fe interaction and to the appearance of long-range order. Apparently,
calculations of the electronic structure of doped Cd1-xFexO oxides could confirm or disprove the
suppositions made in [28, 29].
THEORETICAL RESULTS AND DISCUSSION
First-principle calculations of the electronic structure were carried out in order to determine the degree of
oxidation, the spin state of the iron atoms and the main interatomic interactions giving rise to ferromagnetism in
iron-doped cadmium oxide as well as to estimate the Curie temperature. The calculations were performed for
the supercells produced by threefold translation of the primitive CdO cell along each crystallographic
direction. Accordingly, the supercell contains 27 primitive cells; with one cadmium atom and one oxygen atom
per a primitive cell, the supercell contains altogether 58 atoms. In this supercell, two cadmium atoms were
replaced by iron atoms, which corresponds to a doping concentration of 7.4 at %. The VASP program (Vienna
ab initio simulation package, version 5.2) [61], in which the plane-wave pseudopotential method of the electron
density functional theory is realized, was used for the calculations. The ultrasoft pseudopotentials supplied with
the program were employed. The calculations were carried out for 13 wave vectors in the irreducible part
of the Brillouin zone obtained automatically by means of the VASP computer code. The generalized
gradient approximation was used in the calculation of the exchange-correlation potentials. The wave
functions were decomposed in the basis with the plane wave energy to 500 eV, whereas for the
decomposition of the electronic density, the basis with the plane wave energy to 300 eV was used.
The Curie temperature was estimated on the basis of the mean field theory [62] employing an
approach for the Curie temperature expressed by the equation:
2 ∆
TC =
,
(5)
3kB N
where ꢂ is the difference in the energies of the ferromagnetic and antiferromagnetic states and N is the
number of magnetic centers in the supercell. Since the value of ꢂ is of the order of several tens of eV,
the total energy calculations can be performed with very high accuracy. We used the methods proposed
by the authors of the VASP program [61] for the calculation of forces and for searching for structures
with minimal energy. We assumed that the system of the crystal structure did not change, but that the
cell volume and the coordinates of the atoms were optimized. The process of relaxation was considered
to be completed, when the variation in the total energy after eight steps of volume optimization and
after eight steps of coordinate optimization did not exceed 0.01 eV and the values of residual forces
acting on the atoms did not exceed 0.15 eV/nm.

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The calculations of the ferromagnetic state were initiated by assigning similar values of the
starting magnetic moment (5 ꢁB) projection to two iron atoms, and the same with opposite values to the
antiferromagnetic state. Almost in all cases, the assigned magnetic ordering was retained in the self-
consistency process, the achieved accuracy of the total energy self-consistency being better than
0.00001 eV. The extended cell assumed for the calculations makes it possible to perform calculations
for different arrangements of the doping iron atoms in the cubic lattice of cadmium oxide and finally to
deduce the arrangement, in which ferromagnetic ordering is realized. These arrangements of iron atoms
are illustrated in Fig. 4. The electronic structure characteristics were calculated for three arrangements
of Fe atoms in the Cd sublattice sites. The iron atoms in positions 1 and 2 (hereafter arrangement 1-2)
are located at the minimal distance of 0.319 nm leading to direct exchange between them. If the Fe
atoms are located in positions 1 and 3 at a distance of 0.469 nm (arrangement 1-3), the interaction
between them is due to superexchange through an oxygen atom. Direct exchange, but at a larger
distance of 0.576 nm, corresponds to the arrangement of Fe atoms in positions 1 and 4 (arrangement 1-
4).
Fig. 4. Unit cell of CdO. The large spheres denote the positions of the iron and the cadmium
atoms, the small spheres denote the positions of the oxygen atoms. The numbering of the atoms
corresponds to different arrangements of the iron atoms – see the text.
Figure 5 shows the densities of electronic states for ferromagnetic ordering in arrangement 1-2. This
arrangement has the minimal total energy of the cell; the densities of states for the other calculated
arrangements do not differ considerably. In the energy interval from -9 to -7 eV, there are bands with
almost no spin polarization of the 4dCd states. In the interval from -6.2 to -5.3 eV, the 3dFe states with
positive spin orientation dominate. In the interval from -5.7 to -1 eV, the band states formed mainly by
the 2рO orbitals are located, but, as shown in Fig. 5В, they have also a hybridized contribution from the
3dFe orbitals. The band states in the interval from 0 to 2 eV are mainly formed by the 3dFe orbitals and
have negative spin polarization. The narrow band of states in the vicinity of the Fermi level contains one

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electron, i.e. it is half occupied by electrons. The states with a higher energy are formed basically of the
5sCd orbitals.
Fig. 5. Spin-projected total density of states (panel A) and density of the 3d Fe states (panel B) for
the ferromagnetic band structure of Fe-doped CdO with short-range direct exchange between iron atoms.
The value of the Fermi energy was set equal to zero. The DOS for spin-up and spin-down states is
indicated by positive and negative values, respectively.
From the above band structure it becomes apparent that the redistribution of electrons arising from
the substitution of a cadmium atom by an iron atom is as follows. The iron atom gives two electrons to
the band of oxygen states and is in the oxidation state +2 retaining six electrons. Five of six electrons are
in the band states with positive spin projection, and one electron is in the state with negative projection.
Consequently the Fe2+ ion is in the high-spin state with a magnetic moment close to 4 ꢁB, which promotes
magnetic ordering. In addition, the calculations show that the oxygen atoms have small magnetization, -
0.04 ꢁB, owing to the band 2pO states in the energy interval from -5.7 to -4.5 eV, which are hybridized

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with the 3dFe states and have a negative spin direction. Therefore, the magnetic moment at the iron atoms
decreases to 3.74 ꢁB.
Table 3 lists the calculated values of the total energy and the Curie temperature for the examined
arrangements. The arrangement 1-2 with short-range direct exchange between the iron atoms is most
stable. The Curie temperature calculated for this configuration corresponds to the presence of room-
temperature ferromagnetism. Considerably higher values of the total energy correspond to the
arrangements 1-3 and 1-4, which indicates a small probability for their realization. Moreover, for
arrangement 1–3 antiferromagnetic ordering turns out to be stable, which does not agree with the
available experimental data. For arrangement 1-4, the calculations with antiferromagnetic initial ordering
do not yield an antiferromagnetic, but a ferromagnetic solution, the magnetic moments being 4.02 and -
3.73 ꢁB, which does not allow the Curie temperature to be determined for this configuration. It is obvious,
however, that this configuration has only a small probability for realization too because of its higher
energy. From the above data it can be concluded that chemical bonding exists between the adjacent iron
atoms in the structure of Cd1-xFexO leading to a total energy reduction and to the appearance of
ferromagnetic ordering by means of direct exchange. This is confirmed by the analysis of the crystal
structure parameters of doped CdO. The optimized distance between the iron atoms for arrangement 1-2,
i.e. 0.293 nm for ferromagnetic and 0.324 nm for antiferromagnetic ordering, is much smaller than the
Cd–Cd distance for pure CdO (0.334 nm), which indicates the presence of chemical bonding between
atoms. Note that an analogous effect of the appearance of chemical bonding between adjacent substituent
atoms was observed for vanadium-doped anatase [63].
Table 3. Calculated values of the total energy of the extended cell and Curie temperatures
Arrangement
1 - 2
Arrangement
1 - 3
Arrangement
1 - 4
ЕT (eV) - FM
ET (eV) - AFM
TC (K)
-227.57
-227.44
507
-227.23
-227.28
180
-227.26
-212.60*
- *
*see the text
It should also be noted that for a study of defects and their role in the magnetic properties, very
informative experimental methods such as photoluminescence (PL) and electron paramagnetic resonance
(EPR) are available (see, e.g., Refs [64-67] and references therein). In Ref. [64], the structure, optical and
magnetic properties of thin ZnO films and ZnO films doped with manganese were studied. With a
combination of the defect analysis based on PL and XPS, the effect of these defects on the nature and
origin of ferromagnetism was investigated by EPR. These findings suggested that zinc and oxygen

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defects, especially zinc interstitials and singly ionized oxygen vacancies, play a crucial role in mediating
ferromagnetism in undoped ZnO. In Ref. [65] the PL properties of amorphous ε-FeSi/Si core–shell
nanofibers were studied and a strong PL peak was observed between 600 nm and 700 nm. According to
Ref. [65], this peak may be the result of intra-band transitions due to impurity and vacancy defect states in
the FeSi structure. The magnetic characteristics of a composite film containing vanadium and tungsten
oxides were reported in Ref. [66]. The analysis of the ESR data showed some sharp changes in the
magnetic properties near the metal-to-insulator transition, which was theoretically interpreted as the
ordering or alignment of the electron spins from a net moment to a parallel alignment of the magnetic
moments. The VSM results confirmed a paramagnetic phase with a small amount of a magnetically
ordered phase [66]. Finally, using EPR-measurements allowed us to find a correlation between the
number of oxygen vacancies and the ferromagnetic ordering in bulk Fe-doped ZnO in Ref. [67].
CONCLUSION
Using formate Cd1-xFex(HCOO)2·2H2O as a precursor, it is possible to produce stable ferromagnetic
solid solutions of the composition Cd1-xFexO with a wide homogeneity region of iron, which, are
considerably superior to samples of the same compositions synthesized earlier regarding their room-
temperature saturation magnetization,. The advantage of the developed synthesis method lies in the
possibility to preset very accurately the composition of elements both of the precursor and of the product
of its thermolysis. Samples with high magnetization values can be produced without the need for
annealing in hydrogen atmosphere or under high pressures. In terms of the saturation magnetization
values (Table 2), the synthesized solid solutions of Cd1-xFexO are comparable with Zn1-xFexO, which we
obtained earlier by the precursor method using the formate Zn1-xFex(HCOO)2·2H2O as a precursor [5-7].
The calculations of the electronic band structure show that the iron atoms at a concentration of about 7 at
% in Fe-doped cadmium oxide are in the high-spin state with magnetic moment values close to 3.7 ꢁB.
The calculations reveal the presence of chemical bonding between adjacent iron atoms leading to a
stabilization of ferromagnetic order by means of direct exchange. The calculated value of the Curie
temperature, 507 K, is in reasonable agreement with the experimental value, 560 K.
ACKNOWLEDGEMENTS
The study was carried out within the state assignment of FASO of Russia (theme “Spin” No
01201463330), supported in part by the RFBR (project No. 15-03-02908-а) and the Presidium of the Ural
Branch of Russian Academy of Sciences (projects No. 15-9-3-31 and No. 15-17-3-44). The first-principle
calculations were carried out at the computer cluster Uran at the Institute of Mathematics and Mechanics
of the Ural Branch of RAS.

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