Spin wave study and optical properties in Fe-doped ZnO thin films prepared by spray pyrolysis technique

Spin wave study and optical properties in Fe-doped ZnO thin fi lms prepared by spray pyrolysis technique

F. Lmai ^a , R. Moubah ^{b , *} , A. El Amiri ^b , Y. Abid ^b , I. Soumahoro ^{c , d} , N. Hassanain ^c , S. Colis ^d , G. Schmerber ^d , A. Dinia ^d , H. Lassri ^b

a

LPAT, Universit e Hassan II de Casablanca, Facult e des Sciences Ain Chock, B.P. 5366 Ma^ arif, Casablanca, Morocco

b

LPMMAT, Universit e Hassan II de Casablanca, Facult e des Sciences Ain Chock, B.P. 5366 Ma^ arif, Casablanca, Morocco

c

LPM, Facult e des Sciences, B.P. 1014, Universit e Mohammed V, Rabat, Morocco

d

Institut de Physique et Chimie des Mat eriaux de Strasbourg (IPCMS), UMR 7504 CNRS-UdS, 23 rue du Loess, BP 43, 67034, Strasbourg Cedex 2, France

a r t i c l e i n f o

Article history:

Received 7 February 2016 Received in revised form 1 April 2016

Accepted 6 April 2016

Keywords:

Optical properties

Diluted magnetic semiconductors Spray pyrolysis

Magnetic properties Spin wave theory

a b s t r a c t

We investigate the magnetic and optical properties of Zn

1-x

Fe

x

O (x ¼ 0, 0.03, 0.05, and 0.07) thin films grown by spray pyrolysis technique. The magnetization as a function of temperature [M (T)] shows a prevailing paramagnetic contribution at low temperature. By using spin wave theory, we separate the M (T) curve in two contributions: one showing intrinsic ferromagnetism and one showing a purely para- magnetic behavior. Furthermore, it is shown that the spin wave theory is consistent with ab-initio cal- culations only when oxygen vacancies are considered, highlighting the key role played by structural defects in the mechanism driving the observed ferromagnetism. Using UVevisible measurements, the transmittance, re fl ectance, band gap energy, band tail, dielectric coef fi cient, refractive index, and optical conductivity were extracted and related to the variation of the Fe content.

© 2016 Elsevier B.V. All rights reserved.

1. Introduction

ZnO is an interesting material for use in various potential ap- plications, ranging from optoelectronics and quantum well to spintronic devices [1,2]. This is related to its excellent properties which combine large band gap (E

g

) (3.37 eV) and exciton binding energy (60 meV) with intrinsic magnetic properties obtained upon doping and control of structural defects [1 e 3]. In order to func- tionalize ZnO for a wider range of applications, intensive research activities have been devoted to doping with different elements and using various preparation techniques [4 e 11]. The use of transition metals as dopant for ZnO offers several advantages such as the enhancement of the Curie temperature and magnetization, with signi fi cant improvement of both optical and electrical properties [12 e 15]. Usually, transition metal dopants are supposed to replace, at least partly, Zn

^2þ

ions in the ZnO host matrix. Among the most used magnetic dopants, Fe has been particularly investigated.

Several studies have indeed reported the effect of Fe doping on the

optical and magnetic properties of ZnO thin fi lms grown by various techniques [16,17]. However, only few of them reported on the optical constants, re fl ectance, dielectric coef fi cient, refractive in- dex, optical conductivity and absorption coef fi cient of Fe-doped ZnO thin fi lms. In order to use Fe-doped ZnO thin fi lms in opto- electronic and optical devices, an accurate knowledge of the above optical properties is mandatory [18].

On the other hand, transition metals contain a partially fi lled 3d level, where unpaired electrons are present and thus affecting signi fi cantly the magnetic properties of ZnO [19]. The origin of the observed magnetism in transition metal-doped ZnO is not fully established. The theoretical explanation of the mechanism driving the observed magnetism is still a subject of intense debate. Thus, additional magnetic studies are necessary to improve the under- standing of magnetism in transition metals-doped ZnO system. So far, the spin wave theory has never been used to study the ZnO system. The spin wave theory is one of the milestones in magnetism and is recognized to be of fundamental importance [20]. This method allows an appealing modeling of long range magnetic or- ders. Here, we investigate both the magnetic and optical properties of Zn

1-x

Fe

x

O thin fi lms with different Fe content deposited by spray pyrolysis method.

* Corresponding author.

E-mail address: reda.moubah@hotmail.fr (R. Moubah).

Contents lists available at ScienceDirect

Optical Materials

j o u r n a l h o me p a g e : w w w . e l s e v i e r . c o m / l o c a t e / o p t m a t

http://dx.doi.org/10.1016/j.optmat.2016.04.009

0925-3467/© 2016 Elsevier B.V. All rights reserved.

2. Experimental details

Zn

1-x

Fe

x

O thin fi lms were grown on SiO

2

substrates at 450

C by spray pyrolysis technique. Different Fe concentrations were used (x ¼ 0, 0.03, 0.05, and 0.07). ZnCl

₂

[0.05 M] and FeCl

₂

, 4H

₂

O were dissolved in distilled water at room temperature. A small amount of CH

3

COOH was added while stirring the solution during 30 min. The SiO

₂

substrates were cleaned before deposition and heated grad- ually to reach the deposition temperature of 450

C. The deposition time was about 77 min and the fl ow speed of solution of 2.6 mL/

min. The fi lm thicknesses were around 300 nm. The structural and chemical analyses were studied previously using x-ray diffraction (XRD) and scanning electron microscopy (SEM) [21]. All Zn

1-x

Fe

x

O thin fi lms (x ¼ 0, 0.03, 0.05, and 0.07) are polycrystalline and pre- sent, as expected, the wurtzite (hexagonal) structure without any additional phases, indicating the incorporation of Fe within ZnO matrix. The SEM measurements show that all samples are uniform, and are chemically homogeneous in a good agreement with the XRD data. Optical measurements were performed using a U-3000 Hitachi spectrophotometer [22,23]. Magnetic measurements were carried out using a superconducting quantum interference device (SQUID) magnetometer with an external fi eld up to 5 T.

3. Electronic structure calculations

Ab-initio calculations were carried out by using Korringa-Kohn- Rostoker (KKR) combined with the coherent potential approxima- tion (CPA) technique [24,25]. In the ZnO cell, it is supposed that the form of the crystal potential is estimated by a muf fi n-tin potential.

The wave functions in the muf fi n-tin spheres were extended in real harmonics up to l ¼ 2. The spin-orbit coupling and relativistic effect were considered as well. The Morruzi, Janack, Williams functional setting is utilized for the exchange-correlation energy. All calcula- tions have been made considering the lattice constants deduced from XRD data of Ref. [21] (a ¼ 3.24 Å and c ¼ 5.19 Å).

4. Results and discussion

4.1. Magnetic properties

Fig. 1 shows the experimental change of magnetization as a function of temperature recorded at a fi eld of 5 T for a Zn

_0.93

Fe

_0.07

O sample (black spheres). While increasing temperature, the magnetization shows a rapid decrease which is a signature of a paramagnetic phase. Above 50 K, the magnetization decreases slowly with increasing temperature, which can be attributed to a weak ferromagnetic contribution. This M(T) variation was investi- gated in the framework of the spin wave theory. As mentioned above for T > 50 K, the M (T) curve presents a ferromagnetic-like behavior. Thus, we have modeled this part of magnetization using Block's law. By using the spin wave theory, the M (T) curve for ferromagnetic materials can be expressed using the following formula:

Mð4:2KÞ MðTÞ

Mð4:2KÞ ¼ BT ³⁼² (1)

Where B is the spin-wave constant and M (4.2 K) is the magneti- zation at 4.2 K. Equation (1) is a good estimate of the change of magnetization as a function of temperature for ferromagnetic materials [26].

As can be observed in the inset of Fig. 1, the spin wave theory equation fi ts nicely with the experimental results for temperatures above 50 K. The extrapolation of the linear part for temperatures lower than 50 K, allows us to determine the whole temperature

range of the intrinsic ferromagnetic contribution of M (T) curve, which is shown in Fig. 1 (blue stars). Thus, the subtraction of the raw M (T) curve and the determined intrinsic ferromagnetic part allows deducing the paramagnetic contribution (red square) to the M (T) curve.

The spin-wave constant (B) expressed in equation (1) is linked to the spin wave stiffness constant (D) by this formula:

B ¼ 2:612 g m B

Mð4:2KÞ k _B

4 p ^D ₃₌₂

; (2)

In this equation, g is the spectroscopic g-factor (for iron g is equal to 2), m

B

is the Bohr magneton and k

B

is the Boltzmann constant. Using the fi t displayed in the inset of Fig. 1, we found the B parameter (Table 1), which is de fi ned as the slope of the linear fi t.

Finally, by knowing B and using equation (2), the spin wave stiffness constant (D) was also extracted.

On the basis of the itinerant electron model, the correlation between D and T

C

have discussed previously by Katsuki and Wolhfarth [27]. By using the effective mass estimate these authors have found the following formula:

D ¼ p ^k B T _C 6 ffiffiffi

p 2

k ² _F ; (3)

Where k

F

is the Fermi wave-vector.

By using the Heisenberg model, the spin wave stiffness constant (D) can be expressed as [28,29]:

D ¼ k _B r _FeFe ² T _C

2ðS Fe þ 1Þ : (4)

Where r

FeFe

is the interatomic distance between nearest Fe ions, S

Fe

is the spin moment of Fe ions. From equation (4), we calculate r

_Fe-Fe

which is found to be equal to 7.2 ± 0.1 Å. The exchange con- stant (J) is related to spin wave stiffness constant (D) mentioned above by this formula: J ¼

_2Sr^D2

FeFe

. Finally, we calculate the difference

0 50 100 150 200 250 300

0 50 100 150 200 250

M

_tot

Intrinsic ferromagnetic contribution Purely paramagnetic contribution M

tot

(em u /c m

3

)

T (K)

0 500 1000 1500

25 30 35 40 45

M (emu/cm

3

)

T

^3/2

(K

^3/2

)

Fig. 1. Raw experimental temperature dependence of magnetization for a Zn

0.93

Fe

0.07

O

sample measured in an external magnetic field of 5 T (black spheres) and extracted

contributions to magnetization due to the ferromagnetic (blue stars) and paramagnetic

(red square) phases of Zn

0.93

Fe

0.07

O. The inset shows the change of magnetization as a

function of T

^3/2

for temperatures above 50 K, the red line is the corresponding fit,

which was obtained using spin wave theory using equation (1). (For interpretation of

the references to color in this figure legend, the reader is referred to the web version of

this article.)

in energy between the antiferromagnetic and ferromagnetic states, which is de fi ned as: D ^E ¼ E

AFM

E

FM

¼ JS(S þ 1). All the calculated magnetic parameters are displayed in Table 1 .

We have performed ab-initio calculations using KKR-CPA approach. Fig. 2 shows the total DOS for Zn

0.93

Fe

0.07

O. The Zn-3d and O-2p states appear at around 6.5 and 3.5 eV below the Fermi level (valence band), respectively. However, the conduction band consists mainly of Zn-4s and Fe-3d states. The incorporation of Fe within the ZnO matrix allows having additional electrons in the conduction band. As mentioned above, the origin of magnetism in transition metal doped ZnO system is not trivial. In this light, it was shown that the structural defects play a key role in inducing ferromagnetism in the ZnO system. To reveal the in fl uence of structural defects on the magnetism of Fe-doped ZnO thin fi lms, we have calculated D ^E ¼ E

AFM

E

FM

for Zn

0.93

Fe

0.07

O without and with O vacancies. A negative value of D E means that the AFM interaction is dominant and if D E is positive the FM one is overcoming. As can be seen in Table 2, the sample without O vacancies exhibits a negative D E meaning a stabilization of an AFM interaction. The Fe ions within the ZnO matrix are exchanged through oxygen atoms which lead to a superexchange interaction with an AFM interaction.

However, for samples with O vacancies, D E is found to be positive highlighting the importance of O vacancies in inducing ferromag- netism. O vacancies are believed to induce defect-related hybridi- zation at the Fermi level and thus a ferromagnetic ordering can take place [30]. It is interesting to point out that the found D ^{E value is} comparable to the one deduced by spin wave theory (0.42 mRy) only by taking into account O vacancies. The exchange interaction deduced from spin wave theory was deduced from experimental data. The agreement between the spin wave theory and ab-initio calculations can be considered as a validation of the importance of structural defects in the mechanism driving the ferromagnetism in Fe-doped ZnO. As already known, all crystals exhibit some defects.

In ZnO, the type of defects that can be easily found are O vacancies, O interstitials, Zn vacancies, and Zn interstitials. However, due to

the lightness nature of oxygen, it is more probable to have oxygen related defects. In this perspective, several authors have reported that the oxygen vacancies could be responsible for the ferromag- netism in ZnO [31,32] which is in line with the results presented here.

4.2. Optical properties

4.2.1. Transmittance and re fl ectance

The transmittance T ( l ^{), and re} fl ectance R ( l ) spectra of Zn

1- x

Fe

_x

O thin fi lms (x ¼ 0, 0.03, 0.05, and 0.07) are presented in Fig. 3. For all samples, a signi fi cant transmission of around 80% in the visible range is observed, which can be understood considering the high structural quality of the present samples. With increasing Fe content, the transmission edge is shifted down to long wave- length. The observed shift shows a modi fi cation in the band structure of ZnO fi lms as a result of the insertion of Fe ions within the ZnO matrix. The re fl ectance R ( l ^{) at the} fi lm surface was determined by using both transmittance T ( l ) and absorbance A ( l ⁾ spectra, through the following relation [33]:

R ¼ 1 ffiffiffiffiffiffiffiffiffiffi Te ^A p

(6) The re fl ectance spectra of the Zn

1x

Fe

x

O fi lms for various Fe concentrations are shown in Fig. 3(b). As can be observed the re fl ectance increases slowly in region with wavelength ranging from 850 to 600 nm and then increases sharply with the decrease of wavelength in the range of 600 to 400 nm. The doped samples are more re fl ective than the pure ones. The increase of re fl ectance with Fe content suggests that the refractive index of Zn

1x

Fe

x

O fi lms is changed upon Fe doping.

4.2.2. Optical band gap and Urbach energy

The optical band gap energies were determined by means of Tauc's model [34]:

a ^h y ¼ a 0 ðh y EgÞ ^m (7)

In this formula, a is the absorption coef fi cient, a

0

is a constant, h n is the photon energy, and Eg is the optical band gap. The a ^coef fi - cient was determined from the absorbance by using the following formula: a ¼ 2 : 3026

^At

, where A is the absorbance and t is the fi lm thickness. The index m in equation (7) is associated with the nature of the electronic transitions. Since ZnO has a direct band gap, m is equal to 1/2. The plot of ( a ^h n ⁾

²

^{against h} n allows obtaining the values of Eg by extrapolating the linear variation to ( a ^h n ⁾

²

¼ 0. The deduced Eg values are reported in Fig. 4. As can be seen, with increasing the Fe content from x ¼ 0. to 0.07, Eg decreases from 3.278 to 3.264 eV, respectively. This band gap decrease is usually observed in semiconductors doped by transition metals. In our case, such decrease can be understood by considering the s e p and p e d interactions between band electrons and 3d electrons of Fe substituting Zn. Doping induces additional band tail states, which leads to a shrinkage of Eg. One can notice that close to the ab- sorption edge, the transmission spectra present an exponential change as a function of wavelength. This exponential tail, called the Urbach tail, can be explained by the disorder introduced by doping [35], and it is associated with the Urbach energy (E

U

). E

U

is the width of the exponential absorption edge which is calculated from Table 1

Some magnetic parameters of Zn

0.93

Fe

0.07

O deduced from spin wave theory at 4.2 K.

M (emu cm

³

) B (10

⁴

K

^3/2

) T

C

(K) k

F

(Å

¹

) D (meV Å

²

) J (mRy) D E (mRy)

45 2.2 260 0.2 197.75 0.069 0.41

-8 -6 -4 -2 0 2 4 6

-100 -50 0 50 100

Zn-4s O 2p

Fe 3d Zn 3d

Energie (eV)

DOS ( states/Ry )

EF

Fig. 2. Total DOS for Zn

0.93

Fe

0.07

O thin films obtained using the KKR-CPA approach.

Energy is relative to the Fermi level.

the slope of ln( a ^{) versus h} y , by using the following formula:

a ¼ a 1 exp h y

E _U

(8)

Where a

1

is a constant. Fig. 4 shows the change of E

U

versus Fe concentration (x). As can be observed, E

U

increases with increasing Fe content. Dopants induce localized states within the band gap.

Therefore, both a reduction in Eg and expansion of the Urbach tail occur. As the Fe concentration increases, the disorder effect in- creases as well. The steepness parameter b

U

¼ kT/E

U

de fi nes the widening of the absorption edge as a result of the exciton e phonon or electron e phonon interactions [36]. Therefore, equation (8) can be expressed as:

a ¼ a 0 exp b U

kT ðEÞ

(9)

It is found that b U values change from (1.84, 1.51, 1.46, and 0.9) 10

¹

with increasing Fe concentrations from 0, 3, 5, and 7%

respectively. b U presents a similar trend as that of E

U

, which con- fi rms the change of the absorption edge as a function of Fe content.

4.2.3. Complex optical refractive index

The complex optical refractive index can be written using the following formula:

_ n

¼ nð l Þ þ ikð l Þ (10)

Where n ( l ^{) and k (} l ) are the real and imaginary parts or refractive index. When k is negligible, n ( l ) can be expressed as a function of R ( l ) using the following relation [33]:

nð l Þ ¼ 1 þ ffiffiffi p R 1 ffiffiffi

p R (11)

Table 2

Simulated D ^E ¼ E

AFM

E

FM

for Zn

0.93

Fe

0.07

O without and with O vacancies.

Zn

0

.

93

Fe

0.07

O Zn

0

.

93

Fe

0.07

V

O0.03

O

0.97

Zn

0

.

93

Fe

0.07

V

O0.05

O

0.95

Zn

0

.

93

Fe

0.07

V

O0.07

O

0.93

D ^E ¼ E

AFM

E

FM

(mRy) - 0.32 0.17 0.3 0.5

0 10 20 30 40 50 60 70 80 90

Transmittance (%)

x=0 x=0.03 x=0.05 x=0.07

(a)

400 500 600 700 800

0 10 20 30 40 50

(b)

Reflectance (%)

Wavelength (nm)

Fig. 3. (a) Transmittance and (b) reflectance spectra of Zn

1x

Fe

x

O thin films (x ¼ 0, 0.03, 0.05, and 0.07).

0 1 2 3 4 5 6 7

3.264 3.267 3.270 3.273 3.276 3.279

Band gap energy Urbach energy

x (%)

Eg (eV)

0.12 0.14 0.16 0.18 0.20 0.22 0.24

Eu (eV)

Fig. 4. Change of band gap (Eg) and Urbach (E

U

) energies as a function of Fe content (x) in Zn

1-x

Fe

x

O thin films.

400 500 600 700 800

2 3 4 5 6

Refractive index

Wavelength (nm) x=0 x=0.03 x=0.05 x=0.07

Fig. 5. Refractive index n( l ) for different Fe concentrations (x) in Zn

1-x

Fe

x

O thin films.

By using equation (11) and the experimental re fl ectance data, n ( l ⁾ was calculated for different Fe contents in the visible window.

Fig. 5 shows the deduced n ( l ) for different samples. For all samples, the refractive index is found to increase signi fi cantly with decreasing wavelength. With increasing Fe content, the refractive index is increased. n ( l ) displays a usual dispersion, suggesting that all samples are homogeneous. One can notice that the refractive index is an important parameter of materials for technological applications in optical based devices, due to its direct relationship with the dispersion energy.

4.2.4. Dielectric characterization and optical conductivity

The real and imaginary parts of complex dielectric function,

3 1

( l ^{) and}

3 2

( l ) respectively, were determined using the following equations: ε

1

ð l Þ ¼ n

²

ð l Þ k

²

ð l Þ and ε

2

ð l Þ ¼ 2n ð l Þ k ð l Þ , respectively [37]. Where k ( l ) is the imaginary part of refractive index or extinction coef fi cient expressed as: k ð l Þ ¼

₄

^al _p . The change of

3 1

( l ⁾ and

3 2

( l ) as a function of wavelength is shown in Fig. 6. Both

31

( l ⁾ and

32

( l ) are constants at long wavelengths. For wavelengths smaller than 500 nm an important increase of both

31

( l ^{) and}

³2

( l ⁾ is observed which is due to the strong absorption at these wave- lengths. Since k is negligible compared to n for all samples, the behavior of real part

3 1

( l ) is identical to n

²

.

The complex optical conductivity s ⁽ l ⁾ ¼ s

1

( l ⁾ þ i s

2

( l ^{) is} correlated to the real

31

( l ) and imaginary

32

( l ) parts of dielectric function by the following relations [38]:

s 1 ¼ u ε 2 ε 0 (13)

s 2 ¼ u ε 1 ε 0 (14)

Where u is the angular frequency and ε

0

is the vacuum permittivity constant. Figs. 7 (a) and (b) show the change of s

1

( l ⁾ and s

2

( l ) as a function of wavelength. We note that the variations of both s

1

and s

2

with wavelength follow similar trends for the different Fe concentrations. With increasing Fe doping, the metallic contribution of the fi lms increases and causes an increase of con- ductivity. The optical conductivity is associated with the free charges [39]. Both s

1

( l ^{) and} s

2

( l ) increase signi fi cantly with Fe doping close to the absorption edge. The available free carriers absorb photon energy and thus an important increase of optical conductivity is observed. At long wavelength, a decrease in the optical conductivity in the visible region is seen which is due to the fact that the free carriers do not have enough energy to pass the conduction band as a result the conductivity is small.

5. Conclusion

Spin wave theory and UV e visible measurements were used to investigate the magnetic and optical properties of Zn

1-x

Fe

x

O thin fi lms. The temperature dependence of magnetization curve was separated in two contributions: one ferromagnetic and one purely paramagnetic. Using ab-initio calculations, we have shown that the

Fig. 6. Real (a) and imaginary (b) contributions of the dielectric function,

3 1

( l ) and

3 2

( l ) respectively, versus wavelength ( l ).

Fig. 7. Change of the (a) real and (b) imaginary contributions of s ( l ) as a function of

wavelength l for Zn

1x

Fe

x

O (x ¼ 0.03, 0.05, 0.07 and 0.1) thin films.

observed ferromagnetism can be attributed to oxygen vacancies. All Fe-doped ZnO samples are transparent with a transmission of about 80% in the visible widow, due to their high structural quality.

We have found that the band gap energy Eg decreases with increasing the Fe content. The optical constants (dielectric constant and optical conductivity) change with the Fe content to reach high values for the 7% Fe-doped ZnO fi lms. The fact that the optical properties can be improved by Fe doping and that homogeneous fi lms can be obtained by a simple and cheap method such as spray pyrolysis make these fi lms interesting for optoelectronic devices.

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