Structural, magnetic and transport study of DBPLD fabricated magnetic semiconductors 4

Experimental values of anisotropy fields are commonly obtained by measuring magnetic polarization curves with the field applied parallel and perpendicular to the easy magnetization direc

CHAPTER 7 STUDIES ON THE MAGNETIC MECHANISM

7.1 Introduction

For the purpose of fabrication of room temperature DMSs, Co-doped ZnO materials have been widely studies, and a considerable amount of experimental data have been already accumulated However, many discrepancies on magnetic behaviors were involved Even for those that were reported to be ferromagnetic, the origin of ferromagnetism is often questioned The origin of ferromagnetism in Co-doped ZnO remains an issue of debates

Till now, some investigations of the origin of magnetism in Co-doped ZnO were reported However, they studied the origin of ferromagnetism of Zn1-xCoxO thin films either with Co clusters [1], or precluding the Co clusters by controling processing parameters [2] It seems that the origin of magnetic behaviors for Zn1-xCoxO thin films

is still not well understood, especially when the Co concentration is low (x < 0.1)

Since it is easier to understand that Co clusters may occur if more Co are incorporated, which will definitely contribute to the ferromagnetic behavior of the Zn1-xCoxO thin films To be a candidate material to develop device in spintronics, it is essential to ensure that the magnetism does not originate from the second phases Thus, it is

significant to understand the origin of M-H hysteresis loops of Zn 1-xCoxO thin films

Several theories can be used to explain the magnetism in the absence of Co clusters [4] One is that ferromagnetism itself can be understood as being carrier induced, in a similar fashion as the ferromagnetic state in the double-exchange model for manganites at intermediate doping [5] Another is related to Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between the impurity spins For the former, carrier density is the crucial parameter determining the magnetization behavior [6] And, for the latter, RKKY might lead to spin glass behaviors in certain spin lattices [7]

One important criteria for DMSs to be intrinsic has been suggested to be the observation of the anomalous Hall effect (AHE) in the thin films [8] Though the criteria was questioned when both superparamagnetism and AHE were observed to co-exist in highly reduced Co-doped Rutile TiO2- δ films [9] However, AHE testing is

still a tool to show the spin-orbital interactions in the materials In this case, the interactions need to be analyzed further Photo-induced phenomena in diluted magnetic semiconductors have attracted much attention due to the possible interpretations of the origin of magnetic behaviors, in terms of the exchange interaction between the photo-generated carriers and magnetic ions, if the magnetization could be manipulated

[10] Ref [11] studied the influence of magnetic anisotropy to indicate the role of the hole concentration in the DMS system of (Ga,Mn)As in order to unveil the carrier induced magnetism

In the first part of this chapter, we will investigate whether magneto-crystalline anisotropy exists or not It is known that a magnetic material is said to possess magnetic anisotropy if its internal energy depends on the direction of its spontaneous magnetization with respect to the crystallographic axies [12] Experimental values of anisotropy fields are commonly obtained by measuring magnetic polarization curves with the field applied parallel and perpendicular to the easy magnetization direction [12,13] It is also noted that anisotropy energy is also produced by magnetostatic energy due to magnetic free poles appearing on the outside surface or internal surfaces

of an inhomogeneous magnetic material To proceed, we fabricated the film with c-axis perpendicular and parallel to the substrate surfaces, and compared the magnetic behaviors of these two kinds of thin films, hence to determine whether magneto-crystalline anisotropy exists or not To fabricate the Zn1-xCoxO thin films with c-axis perpendicular and parallel to the substrate surfaces, we used different sapphire substrates for matching of crystal lattice between the film and the substrate It is well known that substrates strongly affect crystal growth behaviors of films [14] In the second part of this chapter, we report on the relationship between the magnetism and

carrier density by comparing M-H loops with different carrier density in the films

From our experimental results, we found no magneto-crystalline anisotropy in

Zn1-xCoxO thin films were proposed based on a picture of spins in a carrier sea

7.2 Magnetic Anisotropy Study

Zn1-xCoxO with x = 0.05 precipitate-free single crystal thin films have been fabricated by a DBPLD method under the optimum experimental condition The films were grown on (0001) sapphire (c-plane) and (11 0) sapphire substrates (r-plane)

using the DBPLD method The room temperature M-H curves were obtained by an

AGM with the magnetic field applied parallel to and perpendicular to the film planes at room temperature A Hall effect system was employed to measure the film conductivity and carrier density with a Van der Pauw configuration at room temperature The sample was analyzed by X-ray diffraction (Philips, X’PERT-MRD)

to identify different crystal planes in the film Detailed lattice structure and possible precipitates were obtained by a HRTEM

7.2.1 Structures of Zn1-xCoxO Thin Films Grown on c- and r- Sapphire Substrates

XRD images of the Zn0.95Co0.05O thin films are shown in Fig 7-1 The film grown

on c-plane sapphire substrate is a single crystal with a wurtzite structure whose c-axis is parallel to that of the substrate [Fig 7-1(a)] The lattice parameters of the film

was determined to be c = 0.5207 nm, which is a little larger than the reported values

for ZnO [15] Figure 7-1(b) gives the XRD pattern of the Zn1-xCoxO (x = 0.05) film grown on r-plane substrate Diffraction peaks corresponding to (1120)plane of

Zn1-xCoxO thin film, (1012), (2024) and (3036)planes of Al2O3 were clearly

observed No peak of other planes was detected by XRD It is also wurtzite structure with the film (1120) plane aligned with the substrate(1012) planes The (11 0)peak of the Zn1-xCoxO is located at 56.57 ° Insets of Fig 7-1 show the Co 2p3/2 XPS spectra for the films grown on c- and r-plane sapphire substrates From the shape of the spectra and position of the peaks, there is only Co – O bonding existed in the films in both cases From these results we referred that Co had substituted Zn-site in ZnO and

Co – O bonding exists in the host lattice Based on the results of XPS and XRD, we conclude that this material is a single compound with the replacement of Zn by Co Figure 7-2 gives X-ray rocking curves of thin films The curves were taken from the diffraction peaks at 34.44° for c-plane and 56.57° for r-plane substrates, respectively The FWHM is 0.18° for c-plane and 0.37° for r-plane sapphire substrates This indicates that the film grown on c-plane substrate has a more concentrated crystalline orientation In our view it is due to the higher surface energy of {0001} facet of ZnO grown on sapphire substrate

) 0006 ( ( 10 1 0 )f

s

) 0 11 (

f

) 0002 (

Film

Sapphire

) 0006 (

)

0002

( (10 0)

) 0 11 (

) 0 11

(

) 4 10 (

) 4 20 (

) 0002 (

f

) 0 11 (

f

) 0002 (

Sapphire

Film

s

) 4 10 (

s

) 4 20 (

Fig 7-3 HRTEM images for Zn0.95Co0.05O films on c-plane substrate (a) film, substrate and interface, (b) electron diffraction pattern taken on the interface; r-plane substrate (c) film, substrate and interface, (d) electron diffraction pattern taken on the interface

HRTEM images of Zn0.95Co0.05O thin film-substrate interface are shown in Fig 7-3

In Fig 7-3(a), the interface between the film and c-plane substrate was found to be smooth The micrographs reveal well ordered lattice planes with few defects No precipitate was observed From these images, the epitaxial relationship between the

film (f) and substrate (s), expressed by Exp (5-2), agrees well with the XRD results

In Fig 7-3(c), the micrographs for those grown on r-plane sapphire substrate also showed well ordered lattice planes with few defects No precipitates was observed Although the interface between the Zn0.95Co0.05O thin film and r-plane sapphire substrate was found to be clear, and the (1120)plane of the film parallel to the )

in Fig 7-3(d) The tilt angle ϕ1 is 6° From the HRTEM diffractions and imaging

studies, the relationship between the film (f) and substrate (s), was determined to be as

follows: (11 0)f //(1012)s, (0002)f and (1014)s with an angle ϕ1 of 6° between the (0002)f and (1014)s To determine the direction of c-axis of the Zn0.95Co0.05O relative to the r-plane substrate, we can calculate the angle ϕ2 using crystallographic relationship,

4 10 4 20

4 10 4 20 2

cos

G G

Substrates

The curves of Figure 7-4 show the M-H loops of the Zn 1-xCoxO (x = 0.05) thin films

grown on c- and r-plane sapphire substrates The coercivity Hc is about 100 Oe This

result indicates in both cases, they are magnetic at room temperature We emphasize

that different M-H loops can be obtained under different experimental conditions, as

shown in Fig 7-4 From this figure, the film grown on the c-plane sapphire substrate

has a remanent squareness S of 0.056 when the applied magnetic field H is perpendicular to c-axis of the film, and 0.041 when H is parallel to c-axis For the r-plane substrate, S is about 0.107 when H is perpendicular to [1120] of the film and

0.066 in the case of H perpendicular to c-axis S is small for both r-plane and c-plane

substrates There is no evidence of magneto-crystalline anisotropy for both film orientations

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000 -1.0

-0.5 0.0 0.5 1.0

(Out of plane) (In plane)

-2000 0 2000 -0.5

0.0 0.5

Magnetic Field (Oe)

axis C

H// −

axis C

-0.5 0.0 0.5 1.0

(Out of plane) (In plane)

-2000 0 2000 -0.5

0.0 0.5

Magnetic Field (Oe)

] 0 2 11 [

⊥

H

axis C

Fig 7-4 Hystersis loops for Zn0.95Co0.05O films grown on (a) c-plane and (b) r-plane

sapphire substrate normalized to the saturation magnetization Ms The data were taken

at room temperature with the external field both in plane and out of plane of the films

and r- Sapphire Substrates

Electrical resistance is affected by the orientation of the crystal and strain produced

by stress, as shown in Table 7-1 From it, a smaller resistance is obtained for the r-plane substrate film It is reported that there is an effect of mechanical stress on the electrical resistance of a conducting crystal [16] Under our experimental conditions, the c-axis of the film grown on c-plane substrates is perpendicular to the surface, while the c-axis of the film grown on r-plane substrate lies in the surface plane Therefore Hall current must be associated with electrons jump in the plane which is perpendicular to the c-axis for the film grown on c-plane sapphire substrate, while the electrons jump in the plane of c-axis for r-plane substrate The mismatch for Zn1-xCoxO / Al2O3 in r-plane system is smaller than that in c-plane sapphire system The smaller lattice mismatch and a tilt angle in r-plane system result in the strain in the film partially relaxed [17] Hence, the film grown on r-plane substrate has a smaller strain

A smaller resistance is obtained for the r-plane substrate film The larger strain is the reason for a higher resistivity

Table 7-1 Electrical transport properties for Zn0.95Co0.05O films grown on c- and r-plane sapphire substrates at room temperature from the Hall effect measurements

(mΩ cm)

Carrier density (cm-3)

Both the Zn1-xCoxO with x = 0.05 thin films have a wurtzite single crystal structure There was no precipitates observed in both cases under HRTEM The thin film c-axis

is perpendicular to the film plane for samples grown on c-plane substrates, and lies in

the film plane for samples grown on r-plane substrates By comparing the M-H curves

of the two kinds of thin films, they are soft magnetic materials with small remanent squareness for both film orientations Hence, based on our experimental results, no crystalline anisotropy was observed in the Zn1-xCoxO system From the physical point

of view, a magnetic material is said to possess magnetic anisotropy if its internal energy depends on the direction of its spontaneous magnetization with respect to the crystallographic axies In hexagonal crystal structures, in most cases, the preferred agnetization direction will be along the c-axis [12] As it has been reported in [10, 18, 19], the strain induced anisotropy of the valence band can result in a sizable anisotropy

of spin properties in (Ga,Mn)As DMS system However, in our studies, no evidence was found to verify the magneto-crystalline anisotropy in this Zn0.95Co0.05O system In addition, the lattice mismatch of the Zn Co O thin films grown on c-plane

films grown on c-plane substrates leads to the distortion of the lattice This effect contributes to the Co ions locating at the center of the octahedron, which we have discussed in Chapter 5

7.3 AHE and Light Response Study

7.3.1 Anomalous Hall Effect (AHE)

In our studies, a Hall bar specimen of the 6-point Hall bar geometry with (1-2-2-1) configuration was used The size of the Hall bar has been illustrated earlier Figure 7-5 shows the schematic geometry of the AHE measurement

H

x y

z

α

Fig 7-5 Geometry of the AHE measurement α is the angle between the applied field

H and the normal to the sample

In the Hall effect measurement for a ferromagnetic material with the B field lying

in the plane of current and the normal of the surface, there are two Hall voltage components [20] The Hall resistivity ρB can be defined by

ϑα

ρH =R0Bcos +R A Mcos (7-2) where is the ordinary Hall coefficient, B is the magnetic flux density, is the

anomalous Hall coefficient, M is the magnetization of the film, α is the angle between

0

the applied field and the normal to the sample, θ is the angle between the

magnetization and the normal to the sample The first term in Eq 7-2 is the ordinary Hall effect (OHE) and arises from the Lorentz force acting on conduction electrons

The OHE depends on the z-component of the B field ( ), and produces an electric field perpendicular to and the current density The second term is the AHE and is due to spin dependent scattering mechanisms The AHE depends on the perpendicular

component of M, and produces an electric field perpendicular to the perpendicular component of M to the surface plane and the current density

Z

B

Z

B

Figure 7-6 shows a small Hall AHE signal of Zn1-xCox O thin film with x = 0.05 after

proper data extractions under the condition of α = 45°, though the signal is small It is

an evidence that AHE was observed in the Zn1-xCoxO thin film It is known that there is

no AHE reported in Zn1-xCoxO thin films in which Co is suggested to be more uniformly distributed In the light of our experimental conditions, the AHE signal is dominant for lower magnetic field and can be evaluated by subtracting the linear background Under our experimental conditions, only a few samples show the AHE signals and they are not pronounced

-400 -200 0 200 400 -0.04

Fig 7-6 AHE signal of Zn1-xCoxO with x = 0.05 thin film

It is universal thought that AHE relies on spin-orbit coupling between the carrier and the lattice, which produces a left-right asymmetry in the scattering [21] AHE is considered as a tool to test the ferromagnetic response of charge carriers in ferromagnetic semiconductors [22] In general, skew scattering provides a mechanism

of AHE Namely, the skew scattering is caused by an anisotropy of the sp-d interaction Hence, the observation of AHE shows that there presents sp-d interactions, indicating

that the magnetization direction follows the field direction [17] The shape of the Hall

resistance can be understood as the reflection of the field dependence of M, though the

magnetic field range did not reach the saturation value due to the limits of the experimental conditions

Applying the Hall effect measurements results, the evaluation of

0 0

∆ B (7-3)

as a function of B for a given direction of I and B with respect to the crystal axes were

obtained, where ρ is the Hall resistivity at a field of B, B ρ0 is the ρ with B B=0

To compare the effect in constancy, we evaluated it while setting B at 500 Gauss In this experimental arrangement, B rotates from α = 0 to α = 90° The result of ∆ρ/ρ0dependence on α is depicted in Fig 7-7 It can be seen that ∆ρ/ρ0 decreases as α decreases, following a cosine dependence on α It agrees with the first term in the Eq

7-2 It is well known that the OHE depends on the perpendicular component of the B field, and produces an electric field perpendicular to the perpendicular component of B and the current density From Eq 7-2, at the point of B = 500 Gauss, the AHE’s

contribution is small compared to the OHE term

0 20 40 60 80 100 -0.002

0.000 0.002 0.004 0.006 0.008 0.010

α ρ

on angle α obtained by Hall effect measurement of the

Zn1-xCoxO thin film with x = 0.05

7.3.2 Magnetism Response to Light Irradiation

From the physical point of view, DMSs should exhibit AHE However an observed AHE signal might not be enough to fulfill the criteria of DMS For example, AHE can

be found from a spin-orbit coupling in the interaction between band quasiparticles and crystal defects [23] In fact, AHE were observed in ferromagnetic metals, anti-ferromagnetic metals and semiconductors [21] Probably it is the reason for the co-occurrence of superparamagnetism and AHE in Cobalt-doped Rutile TiO2 [9]

To clarify the origin of magnetism, we applied the light source in the Hall effect system, as shown in the Fig 7-8 The relationship between the magnetism and carrier

is directly reflected through the response of the Zn1-xCoxO thin film (x = 0.05) to the light irradiation with the wavelength of 313 nm Figure 7-9 shows that under the condition of light irradiation, the Hall resistivity decreases while the carrier density increases In contrast, when the light is off, the Hall resistivity increases while the carrier density decreases It indicates that the light irradiation can increase the carrier density of the film

Fig 7-8 Schematic diagram of AHE measurement under the light irradiation of a

hand-held light source

light light light

Fig 7-9 Hall resistivity and carrier density response to light irradiation obtained by the

Hall effect measurement

The Zn1-xCoxO thin films are n-type semiconductors When the film was irradiated

with a light with photon energy larger than the band gap of the film, electrons near the valence band will be excited into the conduction band The amount of the electrons contributing to the un-equilibrium local spin-density distribution due to the double exchange mechanism will also be changed Hence the variance in the carrier density characterized by the Hall effect measurement may be a point to the variance in the electrons contributing to magnetism in DMS, if this mechanism works And vice versa Hence to clarify the spin-orbit interactions in Fig 7-6, we repeated the testing under a light irradiation with the wavelength of 313 nm However we failed to obtain an enhanced AHE signal after the light irradiation (not shown here) If the correlations between the global ordering of the Co2+ local moments and carrier density work in this

spin system, the magnetic moment can be mediated by carrier density, and the AHE signals should be enhanced Otherwise, there is no evidence to show the correlations between magnetic and transport properties in the magnetic system

Following this, we also applied the light source in the AGM system to compare the

M-H curves at different carrier densities, as shown in Fig 7-10(a) Figure 7-10(b)

presents typical M-H curves of the Zn 1-xCoxO thin film (x = 0.05) before and after light irradiation with the wavelength of 313 nm Here we give an explanation about the

plotting The M-H loops are plotted with the same scale of y-axis but a shift of x-axis

in order to give a clear comparison It can be seen that there is no observable difference

between the M-H curves obtained before and under the condition of light irradiations

In our view, if the correlation between the global ordering of the Co2+ local moments and carrier density in this spin system exists, the magnetic moment should be mediated

by carrier density On account of our experimental results, we conclude that there is no such correlation

Magnet for AGM

Sample

Light source Filter

Light irradiation

(b)

Fig 7-10(a) Schematic diagram of the light response measurement for M-H curves

under the light of a hand-held light source (b) Comparative M-H curves before and

under that light of a hand-held light source

7.4 Magnetic Mechanisms Proposal

7.4.1 Electron Configuration and Exchange Interactions in Zn1-xCoxO Thin Films

On account of our experimental results and understanding, the Zn1-xCoxO system can be regarded as the case of Co2+ (d7) in a tetrahedral field [24] From our absorption

results, the many electron ground states are singlet A2 We observed the absorption

band to the d-d transition of the Co2+ impurity in Zn1−xCoxO, indicating the band splitting, i.e., the trigonal splitting of 4 1( )

P T

Our experimental results show that Zn1-xCoxO thin films have similar band

structures to that of ZnO, in particular when x is small Here, it is reasonable to

consider that locates in the center of the bandgap, and the relative position of Fermi level and the top of the valence band,

F

E

v

E − for Zn1-xCoxO is that

eV, similar to that of ZnO [25] In Fig 5-14(b), band structures

presenting Zn 3d, O 2p hybridization with Zn s(p), non-bonding O 2p with Co 3d were

observed It is also known that Zn

8

Γ

2-) p orbitals The hybridization related to Γ is 8

important We will concentrate ourselves on this p-d hybridization in the following

discussions

In the Zn1-xCox O thin films, since the tetrahedral field resolves the d levels of Co 3d into and representations but in inverted order, the outer electron configuration of Co

doubly degenerate levels (eg) The orbital degeneracy is shift by increasing the energy

of the three t2g orbitals hybridizing with Γ -band states as compared to the two 8orbitals In these states, all the orbitals are singly occupied, while the sixth and seventh electrons occupy orbitals [26]

g e

g

t2

g e

) , , (

2g dxy dxz dyz

t

*) (

g

e

(a)

Fig 7-12 A schematic energy diagram of the p - d band of interest in Zn 1-xCoxO

magnetic system with O 2p states by the Co 3d states (a), (b) and (c) show the atomic

unpolarized level, the exchange split atomic levels and the final interacting states, respectively

In summary, under our experimental conditions, Co atoms substitute Zn-sites in ZnO, hence there is a tetrahedral crystal field applied on the Co ions The Zn1-xCoxO system can be regarded as the case of Co2+ (d7) in a tetrahedral field of ZnO, as shown in Fig

7-12 The exchange interaction between the p band in the valence band and the d electrons is mainly derived from the p-d hybridization Especially at the point, the top of the valence band is constructed purely from the anion p orbitals that can only hybridize with the d orbitals of t

Γ

2 symmetry In Co2+ impurities, where the t2 orbitals are half-filled, only those ligand band whose spins are antiparallel to that of the

transition-metal impurity can be transferred into the unoccupied t2 orbitals [27]

In DMSs, two fundamental interaction mechanisms are considered: the direct Coulomb exchange and the kinetic exchange The former is known to favor the parallel,

or ferromagnetic, alignment of the interacting spins, and the latter can lead to an antiferromagnetic-like interaction if the hybridization exchange constant is negative Let us estimate the exchange interaction in the Zn1-xCoxO thin films by calculating the

p-d exchange constant per unit volume ( N0β)

Kinetic exchange, i.e., the hybridization of the band states with localized ionic d

orbitals, may be viewed as a second-order perturbation effect involving virtual transition of an electron between the band states and ionic orbitals [26] As we have discussed before, Zn1-xCoxO thin films have similar electrical structure to that of ZnO,

in particular when x is small In Zn 1-xCoxO, the conduction band is mainly formed by

the s orbitals of the cation, and the valence band by the p orbitals of the anion The

hand, the exchange interaction between the p band in the valence band and the d electrons is mainly determined by p-d hybridization When the magnetic moments of

the transition-metal impurities are aligned in a strong magnetic field, the valence and conduction bands are split through the exchange interaction [27] Kinetic exchange in

Zn1-xCoxO is considered as a band electron interacting with a single Co2+ having 7d

electrons We cite the results of spin-dependent interaction resulting from hybridization

of the Bloch function of the band-edge electron with ionic orbitals [26-28]

The exchange coupling constant Nβ between the Co2+ 3d electrons and the anion

p electrons at the -point valence-band maximum has also been estimated using the parameters obtained from [24] and our experimental results, by a formular based on the second order of perturbation with respect to the hybridization term [24]

Γ

2

11

16

pd eff eff eff

V U

−

−

=

δδ

The meanings of the symbols in expressions are as follows:

(1) , the multiplet-averaged charge-transfer energy between the ligand and the transition-metal atom, is defined as the difference between the multiplet-averaged energies of the and configurations at the transition-metal atom, where

denotes n-electron occupancy at the transition-metal site in the presence of fully filled

ligand levels, and is derived by transferring one electron from one of the

∆

n

1 1

L

d n+

)()

av

d E L d

E d

E

expressed by Kanamori parameters u, u′, j, and j′

(3) The two parameters, and U are related through the relation∆ ∆≡εd −εp +nU , where εd and εp are the bare energies of the 3d transition metal and the 2p ligand

orbitals, respectively

(4) ∆eff and Ueff denote the charge-transfer and Coulomb interaction energy defined with respect to the lowest term of each multiplet, respectively

(5) δeff , the energy difference between the lowest terms of and , is

V

∆ ∆eff =δeff +W V /2 Here WV is the width of the host

valence band contributing to the hybridization term

(6) The energy of the lowest term of n− 1 is larger than that of by

the transition-metal atom defined in terms of the Slater-Koster parameters

pd

V

)( ai pd

(8) The d shell in free Co ions with N = 7 electrons has a non vanishing orbital momentum S

According to our experimental results and electronic-structure parameters for Co2+

[24] , we set ∆ = 5 eV, U = 6.0 eV, δeff = 6.8 eV, u = 8 eV, (pdδ) = -1.6 eV, S =1.5 The β

N values thus is estimated to be about 3.6 eV by Eq (7-4), where

)(9

32)

From the physical point of view, there are two reasons for the large Nβ in

Zn1-xCoxO First, The shorter distance of Co2+ and O2- in Zn1-xCoxO leads to the larger

p – d hybridization strength due to the increase in the transfer integral (pdσ) Second, among the host semiconductors ZnO, a large electronegativity of anion ligand leads to the larger charge-transfer energy ∆ In addition, for the Equ (6-1), sin ∆ (6.8 effeV) is as larg s U eff (9.8 eV), the contribution eff +U eff)

ce

becomes substantial and gives the large Nβ [24]

It is known that the final state of d electrons is determined by the competition of

crystal field splitting energy and intro-atomic exchange energy [29] On the other hand, there is another effect resulting from a strong trigonal distortion when Co2+ in hexagonal structure [30] In the following section, these effects will be discussed, and possible magnetic mechanisms involved in the films will be given

7.4.2 Proposal on Magnetic Mechanism

The results of our experiments show that the FC/ZFC curves of the Zn1-xCoxO

thin films exhibit discrepancy points on at low magnetic fields The M-H curves have

low squareness These results suggest that these magnetic behaviors probably could be explained by a spin glass system

Our experiments also showed that there exists spin-orbital interactions in the

Zn1-xCoxO thin films at room temperature, but there is no evidence to show the correlations between the magnetism and the carriers

Taking account all of our experimental results, schematically as shown in Fig 7-13,

it suggests that both ferromagnetic coupling and antiferromagnetic coupling are involved in the Zn1-xCoxO films Namely there is a competition between them In a wurtzite structure, which is a trigonal distortion system, the competition between ferromagnetic coupling and antiferromagnetic coupling probably could lead to a frustrated system Hence, we suppose that the magnetism of Zn1-xCoxO thin films at room temperature does not originate from the spin-orbit interactions in a long range order, but originates from a short range order More reasons are given as follows

delocalized

electrons

intermediate state

high value of

exchange constant

strong exchange interaction

structure

frustrated system

spin glass

Fig 7-13 Schematic diagram of experimental results leading to a spin glass system

Based on the electron configuration of Co2+ in Zn1-xCoxO, the t2 orbitals are half filled in Co2+ When an electron is located at the valence band maximum with spin

antiparallel to the Co spin, the t2 electron can be transferred into the unoccupied valence-band state with parallel spin and the valence-band electron with antiparallel

spins On the other hand, when an electron is located at valence band maximum with

spin parallel to the Co spin, there is no intermediate state available Therefore, the p-d

exchange interaction between the hole carriers and the Co spins is antiferromagnetic [31] Hence the key point for this issue is that there exist an amount of delocalized electrons in the system Hence we propose that under our experimental conditions, though there are electrons localized, there still exist delocalized electrons (For example,

in the case of U > , the compensating holes would be in O 2p states) There are some

exchange interactions in Zn

∆

1-xCoxO system The spins may be aligned themselves and ferromagnetic orientation can also hold

Taking account of all such, as our experimental results show high d-d interactions,

high Nβ , and strong trigonal distortion in hexagonal structure, probably we could explain it using a spin glass system, something like spins in a carrier sea [7] In the

Zn1-xCoxO system with less Co concentrations, Co ions substitute some Zn ions We take account the second nearest neighbors of Co ions in the Zn1-xCoxO with wurtzite structure, there are 12 second nearest neighbors of Co ions, they are arranged with hexagonal symmetry in three-dimensional (3D) lattice, as show in Fig 7-14, where the shadowed balls depict Zn and the solid balls with arrows depict Co ions which substitute Zn-site in ZnO The Co substitute Zn-site in ZnO randomly Let us suppose that over two Co ions happened to be nearest neighbors, like A, B, C in Fig 7-14 Once the direction of atom A is up, the direction of surrounding spins should be down, and once the direction of C is down, B should be up Namely, there are two

possibilities for the Co ion B spin orientation In this trigonal lattice (wurtzite structure), the strength of the ferromagnetic and antiferromagnetic interaction is the same order Hence the spins cannot find a most favorable direction for all the Co ions

In contrast, they randomly spaced, which results in the competing interactions to form the spin glass state In a word, the exchange interaction failed to be propagated

A

C B

Fig 7-14 Schematic illustration of the arrangement of the Zn (Co) ions and its next

nearest neighbors of Zn(Co) ions in this hexagonal close-packed lattice (wurtzite structure), where shaded balls depict Zn ions, solid balls (A, B and C) depict Co ions, the arrow on A, B, C depict the spin orientation

Co ions are located at the center of octahedron Therefore we have a coupling of d-like

cationic orbitals (Co2+ 3d) with covalent mixing of the six near neighbor anionic

orbitals (O2- 2p), as shown in Fig 7-15 Taking into account of the electronic

configuration of Co2+ in CoO (octerhedral symmetry) [32], it is reasonable to consider that the coupling band between the Co ions and O2- is the σ bond of the eg via collinear orientation of the moments In this case, if over two Co ions happened to be the second nearest neighbors, it leads to an anti-ferromagnetic coupling through a covalent mixing

of the p band (ball C in the Fig 7-15) The main reason is that an intervening O

2-transfers an electron to the neighboring magnetic Co2+ ion Some covalent mixing of p and d wave functions occurs with spins pointing in the same direction Because the

two anion O2- p-spins point in opposite in directions (Pauli exclusion principle), they will cause antiparallel pairing with the d-electrons on the magnetic atoms on the both

sides This will lead to an antiferromagnetic coupling via the ligand situated between

the two magnetic Co atoms (J < 0) So, the antiferromagnetic orientation can be held

With increasing Co concentration, this may happen more easily Hence this may be an explanation for our previous findings that the magnetic moment per Co decreases with increasing Co concentrations

The competing of the ferromagnetic and antiferromagnetic interaction leads to a frustrated spin system Spin glass can be used to explain the magnetic behaviors

-Fig 7-15 Schematic graph of arrangement of the Co ions and its next nearest

neighbors of Co ions in an octahedral structure, where shaded balls depict O ions, solid balls (A and B) depict Co ions, the arrow near A and B depict the spin orientation

7.5 Summary

In this chapter we obtain the following conclusions:

z There is no evidence of crystalline anisotropy for the Zn1-xCoxO thin films

z The observation of AHE indicates the present of sp-d interactions in the Zn 1-xCoxO

thin films However there is no observable difference between the M-H curves

obtained before and under the condition of light irradiations Our experimental results show that there does not exist such correlation between magnetism and carriers in the Zn1-xCoxO thin films

z The outer electron configuration of Co 3d 7 is The exchange coupling constant

2 3 2

N between the Co2+ 3d electrons and the anion p electrons at the

-point valence-band maximum has been estimated to be 3.6 eV, by a formular

Γ