PDF Journal of Alloys and Compounds - NJU

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Strain-tuned optical property in magnetoelectric LiFe ₅ O ₈ thin ﬁ lm

Hua Li

^a

, Xin Wang

^a^,^b

, Pengxia Zhou

^a^,^c^,^**

, Hua Wu

^d

, Chonggui Zhong

^a^,^b^,^*

, Zhengchao Dong

^a^,^c

, Junming Liu

^c

aSchool of Sciences, Nantong University, Nantong, 226019, China

bSchool of Physical Science and Technology, Soochow University, Suzhou, 215006, China

cLaboratory of Solid State Microstructures and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China

dCollege of Science, Donghua University, Shanghai, 201620, China

a r t i c l e i n f o

Article history:

Received 4 October 2019 Received in revised form 25 November 2019 Accepted 26 November 2019 Available online 27 November 2019

Keywords:

Optical property Magnetism Magnetostriction Strain

Photovoltaics

a b s t r a c t

Based on the density-functional theory, we investigated the energy band structure and optical property of LiFe5O8thinfilm with different biaxial strains using thefirst-principles calculations for ferrimagnetic (FI) and ferromagnetic (FM) states. The calculations indicated that a great magnetostriction exists in LiFe5O8films, and both FI and FM LiFe5O8films have the strong and wide absorption peak in visible region. The investigations found that, different from the other semiconductor photovoltaic material, both tensile strain and compressive strain decrease the band gap of LiFe5O8whether it’s in FM or FI state. The FI LiFe5O8possesses the direct band gap that can be adjusted from 1.33 to 1.47 eV under3% biaxial strain, while the FM ones are of relative smaller indirect band gaps with 0.61~0.82 eV in these strains.

Furthermore, by comparing the variations of carrier effective mass and concentration, as well as the electronic and optical band gaps in different strains, we found that the effects of compressive strain on broadening optical absorption and increasing carrier concentration of LiFe5O8thinfilms is obviously more helpful than those of the tensile strain, particular in FM state. These results indicated that the strain-tuned LiFe5O8films possess the extensively application prospects in magnetoelectric photovoltaic fields.

1. Introduction

Anomalous photovoltaic effect refers to an effect caused by intrinsic spontaneous polarization existing in ferroelectric materials, which is completely different from the traditional photovoltaic effect, and its photovoltaic voltage is proportional to the polarization intensity and is not limited by the band gap of materials [1,2].

Moreover, the direction of photocurrent varies with the polarization that can be controlled by electricﬁeld [3,4]. Higher photoelectric conversion efﬁciency makes ferroelectrics play an important role in the exploration and application of photovoltaic materials.

The main factors affecting the photovoltaic conversion efﬁ- ciency of materials are the band gaps of materials, the combination

of electrons and holes, blackbody radiation and so on [2]. When the photon energy is lower than the band gap, it cannot be absorbed by the material, while the photon energy is higher than the band gap, it can excite electron transitions. Therefore, appropriate band gap is the key to improve the photoelectric conversion efficiency of ferroelectric materials. Moreover, ferroelectrics can greatly reduce the recombination of electrons and holes due to the effect of internal electric field caused by spontaneous polarization, which improves the photoelectric conversion efficiency of ferroelectrics.

Some common ferroelectrics, such as LiNbO3, BiFeO3and BaTiO3, have been extensively studied as photovoltaic materials [5e8].

However, most ferroelectrics shave the wide band gaps, which are not suitable for visible light (1.59e3.3eV) absorption. Researchers have devoted themselves to reducing the band gaps of ferroelectric materials by doping and applying stress methods since many years ago, but little great progress have been made [9e11].

Lithium ferrite LiFe5O8(LFO) has attracted considerable atten- tion due to its large saturation magnetic moment, square hysteresis loop and high Curie temperature (950 K) [12,13]. Attribute to its excellent magnetic properties and low loss at high microwave

*Corresponding author. School of Sciences, Nantong University, Nantong, 226019, China.

**Corresponding author. School of Sciences, Nantong University, Nantong, 226019, China

E-mail addresses: [email protected] (P. Zhou), [email protected] (C. Zhong),[email protected](Z. Dong).

Contents lists available atScienceDirect

Journal of Alloys and Compounds

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

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frequencies, LFO plays important roles in microwave devices, for instance, gyrators, isolators, circulators, phase shifter [14e16].

Signiﬁcantly, some recent reports have indicated that LFO exhibits a lager magnetoelectric coupling [17,18], doping-tuned optical property [19,20] and a proper band gap at relatively high temper- atures [21], implying its potential as a ferroelectric photovoltaic material. However, since for a long time, the dielectric and optical properties of LFOﬁlms have never been investigated carefully for different magnetic states although the LFO has a suitable band gap closed to the ideal optical absorption.

In the present work, thefirst-principles calculations have been used to investigate the properties of the different strained FI and FM LFO films, including electronic and energy band structure, dielectric optical absorption, effective mass and concentration of carriers. The purpose of this work is to obtain the tunable strain that can provide a wider optical band gap and the higher carrier concentration for photovoltaic application, and explain these variations according to the strain-tuned shifts in the electronic structure. The results show that the application of tensile or compressive strain reduce the band gap, increase the concentration of carriers of LFOfilms for both FM and FI state, meanwhile, the region of optical absorption can be widen, and the FI LFO always keeps the direct band gap while there holds the smaller indirect band gap in the FM state. Moreover, in the FM LFO films, the effect of the biaxal compressive on band gap and the concentration of carriers perform most notably in all considered cases.

2. Structure and computation

Structurally, LFO has the inverse cubic spinel structure with a

space group P4₃32 and the lattice parameters are a¼ b¼ c¼ 8:324Å at room temperature [17,22]. LFO presents two crystallo- graphic phases, including the ordered and disordered, based on the experimental observations [23,24]. We here only consider the ordered case, where the Li^þand partial Fe³^þions inhabit the slightly distorted oxygen octahedral B-site (FeB), every three Fe³^þions are spaced by one Li^þions, and remainder Fe^3þions areﬁlled in the oxygen tetrahedral A-sites (Fe_A) [20,22,24].

In this cubic spinel structure, although the antiparallel spin alignment between FeBand FeAcauses the FI feature of LFO, the ferromagnetism of this material is very prominent due to not only existing a net molecular magnetic moment of 2.5mBper unit [25]

but also extremely high FM transition temperature (950 K) [12,26].

Thus, in this work we focus on the effect of FI and FM states under different biaxial strains. A supercell, which contains 4 Li^þions, 20 Fe^3þions, 32 O atoms, has been constructed for our calculations, as shown in Fig. 1(a). At the same time, the considered FI and FM states are given inFig. 1(b) and (c), respectively.

We performed the ﬁrst-principles calculations based on the density-functional theory (DFT) to investigate strain-tuned dielectric and optical properties in FI and FM LFOﬁlms. The projector- augmented plane wave (PAW) method implemented in the Viennaab initiosimulation package (VASP) [25e27] was used for both structural relaxation and static calculations, in which 2s¹, 3d⁷4s¹and 2s²2p⁴were treated as valence states for Li, Fe and O atoms, respectively. In calculations, notice that the strong electronic correlations from the Fe atoms, the Perdew-Burke-Ernzerhoff-type (PBE) exchange-correction potential was chose instead of the simple generalized gradient approximation (GGA) [25e27], and U¼4 eV for Fe is added into our PBE calculations because this value

Fig. 1.(a) The crystal structure, where a supercell including 4 Li^þions, 20 Fe^3þions, 32 O atoms is given, (b) FI and (c) FM structure of LiFe5O8ﬁlm.

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leads to the good agreement with the experimental results on band gap of LFO [28] and has also been discussed and veriﬁed in some DFT calculations for BiFeO3[29,30].

In addition, for the electronic structure calculations, the plane wave cutoff energy of 600 eV and the 10⁵eV convergent energy of supercell were adopted in lattice optimization process. Brillouin zone integrations were performed with the standard MonkhorstePackmethods in a 555 k-point mesh centered atG^. For simplicity, we considered an isotropous biaxial strain in LFO ﬁlms to simulate the effect of the lattice mismatch between the LFO ﬁlms and square rigid substrate. The equilibrium lattice constantc and internal atom positions as a function of biaxial strain were obtained by full relaxation in our DFT calculations.

3. Results and discussion

Firstly, for the free strained LFOﬁlms, the lattice constantsa¼ b¼ c¼ 8:40Å are obtained in FI state via PBE calculations.

Compared with the experimental results, the constant of LFOfilms is only 0.9% higher than the experimental data [17,22], indicating a perfect agreement. While the lattice constants ofa¼ b ¼ c¼ 8:47Å are obtained for the FM state, as shown inFig. 2(a). Although the steady energy of FM LFO is only 6.60 eV higher than that of FI state in a supercell, the lattice constants of LFO in FM state increase byl¼^Daâ¼0:83% (8300 ppm) compared with that of FI LFO, indicating a great magnetostriction in ferrite LFOfilm [31,32]. Because of this great magnetostriction effect, the dielectric and optical property can also be tuned by more ways. Combined with the high Curie temperature (950 K) of LFO [26], it shows the broad application prospects in room temperature environment.

To explore the strain-tuned optical properties of LFO thinfilms in different magnetic states, we assume the±1%,±2%,±3% biaxial strain imposed on the LFO film plane, where the positive and negative signs denote the tensile and compressive strain, respectively. Indeed, these strains can be achieved easily by growing LFO film on the appropriate tetragonal substrates in experiment [33,34].

Although bulk ferroic oxides are brittle and typically crack under moderate strains of 0.1%, about±3% strains are common in epitaxial oxideﬁlm [35,36], so we consider a strain magnitude of no greater than 3% for our calculations. Then, as shown inFig. 2(b) and (c), we ﬁnd the supercell energy increases for both FI and FM state when lattice constant deviates from equilibrium position due to strain, and the supercell volume increases almost linearly with the lattice constant, which indicates the reliability of our structure optimization when considering strain effect.

Fig. 3shows the band structures of the FI and FM LFOfilms under strain of3%, 0,þ3%. Firstly, as seen fromFig. 3(aec), both the valence bands maximum and conduction bands minimum occurs at theGpoint, indicating that a direct band gap exists in FI LFO films for different strains, and the intrinsic absorption can occurs without electron-phonon coupling. However, fromFig. 3(def) for the FM LFOfilms, it can be seen that the FM LFOfilms under strain of3%, 0,þ3% all have indirect but smaller band gaps. That is, although the optical absorption in FM LFOfilms must resort to the electron-phonon coupling, the energy required for the electron transition is rather smaller, meaning that a wider optical absorption can be occurs in FM LFOfilms [20,21]. In conclusions, magnetic transition can change the band structures from direct one to indirect band gap, and decreased the band gaps at the same time.

In addition, it also can be seen fromFig. 3that band gap has maximum value in the case of no strain, and reduce with increasing the compressive and tensile strains. However, it is noteworthy that the effect of compressive strain on band gap is more obvious than tensile strain for whether FI or FM state, as shown inFig. 4.

Besides the suitable band gap, the effective mass and

concentration of carriers are two important factors for character- izing optical properties of LFO ﬁlms. Thus, we calculated the effective massm* of carriers in different directions byﬁtting the band structure around the conduction band minimum for electron and valence band maximum for hole using the equation [36,37]:

m^*¼Z². d²E.

dk²

: (1)

Meanwhile, the carrier concentration n_i is calculated as following [38,39]:

n_i¼

2:51010¹⁹m^*_n m₀

m^*_p m₀

³4

T

300 ³²

e²^Eg^kBT; (2)

in which, m^*_n, m^*_p are the effective mass of electron and hole, respectively.m₀is the inertia mass of electron.Egis the electronic Fig. 2.(a) Energy variations in a supercell with lattice constants (a¼b¼c), energy and volume of the supercell for (b) FI and (c) FM LFOﬁlms under different strains.

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band gap,k_B is the Boltzmann constant, andT refers to thermo- dynamic temperature. Here, we take the room temperature T¼300 K.

The calculated results are shown inTable 1, where we only give the effective mass along the [0, 1, 0] and [0, 0, 1] direction on account of the symmetry in strained crystal. In the strain free case, the electron (hole) has the almost identical effective mass in different directions, showing the isotropy feature of cubic phase LFOﬁlms.

However, the obtained effective mass of carriers along different directions shows contrary and signiﬁcantﬂuctuations, regardless of compressive or tensile strain. When under different strain, the effective mass almost increases slightly except that the increase of electronic one at [010] direction is very obviously in the FM state, which also result in the average mass of carriers at different directions under strain is greater than that in strain free.

The carrier concentration also shows the stronger anisotropy in different direction because of the anisotropic carrier mass and the different band gap under different strains. The carrier concentration increases at [0, 1, 0] direction and reduces at [0, 0, 1] direction under tensile strain while the opposite changes occur under compressive strain. However, average carrier concentration under strain is increased, which means that photogenerated carrier transport is easier in LFOﬁlms under strain than in strain free. The strain can regulate carrier transport to great extent not only due to the change of carrier mass but mainly because of the decrease of energy gap.

To investigate further the strain-tuned optical property of LFO ﬁlm for different magnetic states, we calculated the real (ε1) and imaginary (ε2) parts of dielectric functions of LFO ﬁlm under different strains. By considering the allowed transitions from populated Kohn-Sham states jfikD of energy E_iðkÞto unoccupied Kohn-Sham statesfjkDof energyE_jðkÞwith the same wave vectork, the imaginary partε2of dielectric function can be calculated according to the following equation [40]:

ε_2ð_ab_Þð

u

Þ ¼4

p

²^e² m²

u

²

X

i;j

ð

BZ

2dk ð2

p

Þ³

CfjkP_bjfikD

CfjkPajfikD,

d

^EjðkÞ E_iðkÞ Z

u

⁽³⁾

whereuis the angular frequency of the incident radiation, anda; b are polarization directions.m; eare the rest mass and charge of electron, Zis the reduced Planck constant,P is the momentum operator. The real partε1 is obtained using the Kramers-Kronig relations. Then, the absorption coefﬁcient a is calculated using the expression [16,37]:

Fig. 3.Band structure of FI LFOﬁlms with (a)3%, (b) 0%, (c)þ3% strain and FM LFOﬁlms with (d)3%, (e) 0%, (f)þ3% strain.

Fig. 4.Band gap variation of LFOﬁlm under various strains.

Table 1

Effective mass and concentrations of carriers of LFOﬁlms with strain3%, 0%, 3% at different directions.

Direction Compressive strain (3%)

Unstrain Tensile strain (3%)

FI FM FI FM FI FM

m^*_pð m0Þ (0,1,0) 1.995 0.912 1.878 1.800 2.483 2.652 (0,0,1) 1.766 3.565 1.881 1.798 1.269 0.202 Average 1.919 2.385 1.879 1.799 2.078 1.427 m^*nð m0Þ (0,1,0) 1.615 2.173 1.745 1.006 1.945 1.247 (0,0,1) 2.024 1.047 1.727 1.006 1.699 3.142 Average 1.751 1.798 1.742 1.006 1.863 1.879 ni(10¹⁹) (0,1,0) 6.023 4.189 6.099 3.900 8.157 6.146 (0,0,1) 6.509 6.734 6.059 3.900 4.456 1.785 Average 6.216 7.472 6.093 3.911 6.911 5.253

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a

¼ ffiffiffi p2 E

Zc

ε²₁þε²₂ ¹₂

ε1

3 75

1 2

; (4)

whereEis the photon energy, andchas its usual meaning. Then, according to the Tauc plotða^EÞ^bE, whereb¼2 for direct band gap and b¼1=2 for indirect band gap [41,42], we obtained the optical band gap by a linear extrapolation ofða^EÞ^bEto zero.

The absorption coefficientsa^{of LFO}films under different strains are presented inFig. 5(a) for the FI state and (b) for the FM state, respectively, where the strain of3%,2%,1%,þ1%,þ2%,þ3% are taken into account. Wefind that both FI and FM LFOfilms have the strong absorption in visible region of 380e780 nm and very wide absorption peak. However, comparing these both magnetic states, wefind that because of the left shift of absorption edge, the increase of magnetization can lead to the relative weak but wider absorption peaks. While the tensile strain is applied, the absorption spectra will move toward low-energy area for that no matter FI or FM state, that is to say, the tensile strain can cause the optical absorption to red shift, while the compression strains can bring about

a blue shift of the optical absorption [11,16].

The optical band gaps obtained from the Tauc plots (seeFig. 6) are shown inTable 2, where the electronic band gaps also be given at the same time. It is found that although for the FI (FM) state the optical band gap under different strains is about 0.6 (1.0) eV bigger than corresponding electronic band gaps, they have the almost sameﬂuctuation trend in increasing compression or tensile strains.

For the FI (FM) case, weﬁnd that the optical band gaps have the maximum values 2.159 (1.822) eV when the LFOﬁlm is strain free, which is consistent with the experimental value [28], while both compressive and tensile strain will narrow this optical band gap.

The optical band gap is reduced to 2.004 (1.701) eV under 3%

strains in the FI (FM) state, while electronic band gap of LFOﬁlm narrows to 1.330 (0.610) eV.

The variation of band gap reflects the substantial effect of strain on the optical property of LFOfilm. For all our considered cases, we find that the3% compression strain cause the largest decrease of optical and electronic band gap of LFOfilms, especially in FM state.

Combining with the highest carriers concentration of LFOﬁlm in FM state under3% strain, we can deduce that as long as there’s no structural phase transition existed, the LFO ﬁlms with larger

Fig. 5.Absorption coefﬁcientsaof LFOﬁlms under different strains for (a) FI and (b) FM state.

Fig. 6.Tauc plots for LFOﬁlms with different strains in (a) FI and (b) FM state.

Table 2

Optical and electronic band gap (eV) of LFOﬁlm with different strains in FI and FM state.

Strain 3% 2% 1% 0 1% 2% 3%

Optical b and gap

FI 2.004 2.031 2.133 2.159 2.136 2.075 2.052

FM 1.701 1.724 1.781 1.822 1.780 1.751 1.733

Electronic band gap FI 1.330 1.390 1.430 1.471 1.461 1.451 1.431

FM 0.610 0.681 0.750 0.821 0.811 0.781 0.751

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compression strain in FM state can provide wider optical absorption, more carriers, and thus higher photoelectric conversion efficiency. Moreover, if allowing for the existed magnetoelectric coupling, the extensively application of the LFO film will display fully in ferroelectric photovoltaicfield.

4. Conclusion

In summary, the first-principles calculations of energy band structure and optical properties for LFO films with different magnetism and strains have been executed. Wefind that the lattice constant has a great change in FM state compared with in FI state, showing the giant magnetostrictive effect with the magnetostriction coefficient of 8300 ppm. Absorption coefficient curves show that LFOfilms have the wide and strong absorption in visible region, and magnetization may reduce slightly the absorption of visible light, and induces LFOfilm to vary from direct band gap to indirect band gap, however, the absorption peak become wider.

Although both compressive and tensile strains make the band gaps decrease and concentration of carriers of LFO ﬁlms increase, the effect of compressive strain is more obvious. Thus we think the biaxial compressive strain can provides the great help to promoting the optoelectronic application of magnetoelectric LFOﬁlms, especially in its FM state.

Author contribution statement

Hua Li: Writing - original draft.

Xin Wang: Investigation.

Pengxia Zhou: Methodology; Formal analysis.

Hua Wu: Conceptualization.

Chonggui Zhong: Writingereview&editing.

Zhengchao Dong: Project administration.

Junming Liu: Supervision.

Declaration of competing interest

The authors declare that they have no known competing ﬁnancial interests or personal relationships that could have appeared to inﬂuence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants No. 11604163 and No.11604164), the Natural Science Foundation of Jiangsu Province of China (Grant No.

BK2012655), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX18_2412), and the

Modern Education Technology Center of NTU.

References

[1] M. Ichiki, R. Maeda, Y. Morikawa, Appl. Phys. Lett. 30 (2004) 1831.

[2] L. Pintilie, V. Stancu, E. Vasile, J. Appl. Phys. 107 (2010) 114111.

[3] L. Pintilie, I. Vrejoiu, G. Le Rhun, J. Appl. Phys. 101 (2007) 064.

[4] R. Von Baltz, J. Phys. Status Solidi B 89 (1978) 419.

[5] S. Dunn, D. Tiwari, Appl. Phys. Lett. 93 (2008) 092905.

[6] J.F. Ihlefeld, N.J. Podraza, Z.K. Liu, Appl. Phys. Lett. 92 (2008) 475.

[7] P. Chen, X. Xu, C. Koenigsmann, J. Nano Lett. 10 (2010) 4526.

[8] W.C. Wang, H.W. Zheng, X.Y. Liu, Appl. Phys. Lett. 488 (2010) 50.

[9] B.Q. Song, X.J. Wang, C. Xin, L.L. Zhang, B. Song, Y. Zhang, Y. Wang, J. Wang, Z.G. Liu, Y. Sui, J.K. Tang, J. Alloy. Comp. 703 (2017) 67.

[10] A. Karaphun, S. Hunpratub, S. Phokha, T. Putjuso, E. Swatsitang, J. Mater. Sci.

Mater. Electron. 28 (2017) 8294.

[11] O.M. Sousa, R.S. Araujo, S.M. Freitas, Comput. Theor. Chem. 1159 (2019) 27.

[12] H.M. Widatallah, C. Johnson, A.M. Gismelseed, I.A. Al-Omari, S.J. Stewart, S.H. Al-Harthi, S. Thomas, H. Sitepu, J. Phys. D Appl. Phys. 41 (2008) 165006.

[13] A.V. Ramos, M.J. Guittet, J.B. Moussy, R. Mattana, C. Deranlot, F. Petroff, C. Gatel, Appl. Phys. Lett. 91 (2007) 122107.

[14] K.K. Kefeni, T.A.M. Msagati, B.B. Mamba, Mater. Sci. Eng. B 215 (2017) 37.

[15] K. Hayashi, R. Fujilkawa, W. Sakamoto, M. Inoue, T. Yogo, J. Phys. Chem. C 112 (2008) 14255.

[16] J. Li, D. Zhou, J. Alloy. Comp. 785 (2019) 13.

[17] R. Liu, L.L. Pan, S.L. Peng, J. Mater. Chem. C 7 (2019) 1999.

[18] V.N. Gridnev, V.V. Pavlov, R.V. Pisarev, J. Exp. Theor. Phys. Lett. 65 (1997) 68.

[19] Z.K. Heiba, M.B. Mohamed, Appl. Phys. A 124 (2018) 818.

[20] P. Thakur, P. Sharma, J.L. Mattei, P. Queffelec, A.V. Trukhanov, S.V. Trukhanov, L.V. Panina, A. Thakur, J. Mater. Sci. Mater. Electron. 29 (2018) 16507.

[21] P.H. Gomez, M.A. Valente, M.P.F. Graça, J.M. M~unoz, J. Alloy. Comp. 765 (2018) 186.

[22] M.N. Iliev, V.G. Ivanov, N.D. Todorov, Phys. Rev. B 83 (2011) 174111.

[23] C. Boyraz, D. Mazumdar, M. Iliev, V. Marinova, J. Ma, G. Srinivasan, A. Gupta, Appl. Phys. Lett. 98 (2011) 012507.

[24] S.E. Shabrawy, C. Bocker, D. Tzankov, J. Appl. Phys. 121 (2017) 133903.

[25] J.P. Perdew, K. Burke, M. Ernzerhoff, Phys. Rev. Lett. 77 (1996) 3865.

[26] P.E. Blochl, Phys. Rev. B 50 (1994) 17953.

[27] G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15.

[28] D. Zhang, L. Zhang, New J. Chem. 40 (2016) 7171.

[29] K. Wang, N. Si, Y.L. Zhang, F. Zhang, A.B. Guo, W. Jiang, Vacuum 165 (2019) 105.

[30] A. Stroppa, S. Picozzia, Phys. Chem. Chem. Phys. 12 (2010) 5405.

[31] P. Sarah, S.V. Suryanarayana, J. Magn. Magn. Mater. 260 (2003) 211.

[32] A.E. Clark, B. Desavage, W. Coleman, J. Appl. Phys. 34 (1963) 1296.

[33] R. Zhang, M. Liu, L. Lu, S. Mi, H. Wang, J. Mater. Chem. C 3 (2015) 5598.

[34] C. Gao, C. Cao, J. Zhao, Appl. Phys. A 125 (2019) 566.

[35] K. Jiang, R. Zhao, P. Zhang, Q.L. Deng, J.Z. Zhang, W.W. Li, Z.G. Hu, H. Yang, J.H. Chu, Phys. Chem. Chem. Phys. 17 (2015) 31618.

[36] X.Y. Wang, S.Q. Zhen, Y. Min, P.X. Zhou, Y.Y. Huang, C.G. Zhong, Z.C. Dong, J.M. Liu, J. Appl. Phys. 122 (2017) 194102.

[37] G. Tang, C. Yang, A. Stroppa, D. Fang, J.W. Hong, J. Chem. Phys. 146 (2017) 224702.

[38] Z. Liu, T. Zhang, Y.F. Wang, C.Y. Wang, P. Zhang, H. Sarvari, Z. Chen, S.B. Li, Nanoscale Res. Lett. 12 (2017) 232.

[39] Y.Z. Fang, T. Xu, Y.T. Zhang, X.J. Kong, J.H. Liu, S.X. Cui, D.T. Wang, J. Phys.

Chem. Solids 132 (2019) 121.

[40] C. Ambrosch-Draxl, J.O. Sofo, Comput. Phys. Commun. 175 (2006) 1.

[41] R.A. Smith, Semiconductors, Cambridge University Press, Cambridge, 1978.

[42] J. Torrent, V. Barron, Encyclopedia of Surface and Colloid Science, Marcel Dekker, Inc, NewYork, 2002.