- Email: [email protected]
TiO2 heterostructures under epitaxial strain and an electric field
Materials Chemistry and Physics 153 (2015) 405e409
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Photovoltaic and magnetic properties of BiFeO3/TiO2 heterostructures under epitaxial strain and an electric field Hong-Jian Feng School of Physics, Northwest University, Xi'an 710069, People's Republic of China
h i g h l i g h t s The photovoltaic effect in BiFeO3/TiO2 can be tuned by strain and an electric field. The magnetization in the interface is reversed by strain. There exists multi-field coupling in the interface.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 July 2014 Received in revised form 7 January 2015 Accepted 11 January 2015 Available online 13 January 2015
First-principles calculations show that the photovoltaic effect of the BiFeO3/TiO2 heterostructures in the visible-light region can be improved by applying epitaxial strain and an electric field. The multi-field coupling effect in the interface makes the heterojunction an intriguing candidate towards fabricating the multifunctional photoelectric devices, and the microscopic mechanism involved is attributed to the spin transfer and charge rearrangement between the Fe 3d and O 2p orbitals in the vicinity of the interface. © 2015 Elsevier B.V. All rights reserved.
Keywords: Interfaces Optical materials Magnetic materials Ab initio calculations Optical properties
1. Introduction BiFeO3(BFO) has attracted much interests due to its coexistence of antiferromagnetism and ferroelectricity at room temperature [1,2]. The G-type antiferromagnetic(AFM) plane is normal to the ferroelectric polarization along the eight pseudocubic [111] diagonal directions [3,4]. The spin cycloid arrangement in the crystal decreases the weak magnetization and it can be partially suppressed in BFO films. Moreover, BFO-based heterostructures have been proposed to increase the magnetization and it can be reversed by external electric field [5,6]. Meanwhile, it is worth mentioning that the photovoltaic(PV) properties observed in BFO makes it an excellent candidate for application in solar cells with a band gap of 2.67 eV [7]. The ferroelectric domain walls separating the electrons
E-mail addresses: [email protected], [email protected]. http://dx.doi.org/10.1016/j.matchemphys.2015.01.034 0254-0584/© 2015 Elsevier B.V. All rights reserved.
and holes have been proposed to be about 1e2 nm which is much smaller than the depletion layer of the silicon semiconductor [8]. As the photovoltaic effect was observed in pure BFO by Choi [9] and Yang [10], by preparing periodically ordered domain walls in BFO samples, Seidel and coworkers show that the photovoltages measured are additive and voltages are much larger than the band gap [11]. Ji and coworkers demonstrate that the bulk photovoltaic effect (BPVE) plays a crucial role in the PV response in BFO thin films [12]. The theoretical work by Young et al. indicates that shift current is the dominant mechanism of the BPVE in ferroelectrics [13]. The first-principles calculations show that the BPVE plays a role and interacts cooperatively with the domain-wall-driven voltages in polydomain BFO samples [14]. Anatase TiO2(TO) is well known as a promising candidate for photocatalyst, photovoltaic applications, and nanostructured solar cells due to its optical absorption in surface [15,16]. Ti plays an important role in stabilizing the ferroelectricity and insulating
406
H.-J. Feng / Materials Chemistry and Physics 153 (2015) 405e409
properties in BFO samples [17] as shown in our previous study [18]. Motivated by the enhanced PV properties in graphene/ polycrystalline BFO/Pt heterostructure [19], we suggest the BFO/ TO heterojunctions would possess an improved PV response due to the BPVE in BFO. Moreover, the PV effect and electronic properties in pure BFO can be engineered by electric field [20,21] and strain [22,23]. Therefore, a tunable PV effect by strain and electric field would be expected in the heterostructures. To our knowledge, there is no theoretical work done on the BFO/TO heterostructures until now. We used density functional theory(DFT) based first-principles calculations to investigate the optical and magnetic properties of the BFO/TO heterojunctions under strain as well as an external electric field. Indeed we found an increased optical absorption effect caused by the tensile stress and the external electric field. The remainder of this article is organized as follows: In section 2, we presented the computational details of our calculations. We provided the calculated results and discussions in section 3. In section 4, the conclusion were given.
!1=2 1=2 02 00 ε0 ðuÞ ε ðuÞ þ ε 2 ðuÞ IðuÞ ¼ 2u ; 2
(4)
where u is the angular frequency.
2. Computational details Calculations in this work have been done using the QuantumESPRESSO package [24], which is based on the DFT using the plane-wave pseudopotential formalism. The local spin density approximation(LSDA) to DFT scheme with an uniform energy cutoff of 500 eV was used as in our previous work [21]. Bi 5d, 6p, and 6s electrons, Fe 3s, 4s, 3p, and 3d electrons, Ti 3s, 4s, 3p, and 3d and O 2s and 2p electrons were considered as valence states. 6 6 1 Monkhorst-Pack sampling of the Brillouin zone was chosen for the relaxation process while it was increased to 20 20 1 to insure the convergence for the total energy calculation. The slab model was used to construct the heterostructure with a same vacuum thickness as the atomic layers. The relaxation was carried out with the forces on the ions less than 0.02 meV/Å. The AFM spins are perpendicular to the polarization direction to model the G-type AFM spin configuration without considering about the spin-orbit coupling(SOC) and noncollinear magnetism. A saw-tooth like external electric potential [21,25e27] has been used as
Vext ðrÞ ¼ 4pmðr=rm 1=2Þ; 0 < r < rm
(1)
where m is the surface dipole density of the slab, rm is the periodic length along the direction perpendicular to the slab. We used electric field of 0.1 V/Å for the bilayer film [21,25]. The imaginary part of the dielectric tensor is determined by the summation over the conduction band states [28]. 00
εij ðuÞ ¼
4p2 e2 1 X lim 2 2wk dðεck εvk uÞ U q/0 q c;v;k < uckþei q juvk > < uckþej q juvk > * ;
(2)
where c and v denote the conduction and valence band states, respectively. The real part of the dielectric tensor has the form
ε0ij ðuÞ ¼ 1 þ
2 P p
Z∞ 0
00
εij ðu0 Þu0 u02 u2 þ ih
du0 :
(3)
The optical absorption coefficient is obtained by the following expression:
Fig. 1. (a) The calculated optical absorption curves for BFO/TO heterostructures under different compressive and tensile strains, as well as the BFO and TO films. The planeaveraged electrostatic potential with (b) compressive strain of the order 4% and (c) tensile strain as great as 2%, respectively. The red lines denote the macroscopic average of potentials. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
H.-J. Feng / Materials Chemistry and Physics 153 (2015) 405e409
3. Results and discussion The absorption spectrum of BFO/TO heterostructures subject to different strains, as well as BFO and TO films, are reported in Fig. 1(a). In the visible-light region, it is clear that the optical absorption is increasing monotonically with the strains, leading to the highest performance with tensile strain of 2% and the lowest one for compressive strain of 4%. DFT þ U calculations predict a same trend as DFT. Therefore, only the DFT results are given in the following section. In comparison with the heterojunctions, BFO performs the best optical absorption activity while TO behaves the lowest absorption rate in the visible-light region. However, an opposite trend is found in the ultraviolet(UV)-light region. Anatase TO possesses the highest absorption activity in the UV-light region which is consistent with its photocatalytic activity [29e31] and absorption properties. Therefore, strain can be used to tune the PV effect for the BFO/TO heterostructures in the visible-light and UVlight region, respectively. In order to understand the strain driven mechanism in the PV effect, the plane-averaged electrostatic potential across the film for the heterostructures with different strains are shown in Fig. 1(b) and (c). Comparing with the case in the compressive strain, the distance between TiO2 and FeO2 layers in the interface is increased while that between FeO2 and BiO layers is decreased under tensile strain, leading to the decreased potential drop across the FeO2 and BiO layers. The macroscopically averaged potentials are also shown in Fig. 1(b) and (c) to shed light on the ability to separate the electronehole pairs for heterojunctions under different strains. It is clearly seen that the holes and electrons can be effectively separated by the potential drop across the interface under tensile strain in contrast to the potential drop subject to compressive strain, resulting in the large amount of charge carriers and the enhanced absorption in the visible-light region. In order to elucidate the large potential drop and the strong interaction between the adjacent layers in the interface, we constructed the cluster composed by TiO2eFeO2eBiO layers in the vacuum and computed the averaged potential along the normal direction as shown in Fig. 2. The potential drop between TiO2 and FeO2 layer is around 10 eV while the difference between TiO2 and BiO is only 3 eV, indicating the strong interaction between the atomic layers in the interface, and the potential drop is mainly determined by the fluctuation of average potential of interfacial
Fig. 2. The plane-averaged electrostatic potential for TiO2eFeO2eBiO layers along the normal direction.
407
layers. The electrons and holes can be effectively separated by this large potential drop to create novel PV effect with high efficiency. To demonstrate additional degree of control of PV effect in the heterojunction, a saw-tooth like potential has been applied across the film. We took into account the polarization along the electric field. A further enhancement of absorption in the visible light region is able to be found under an electric field. The corresponding optical absorption spectrum and plane-averaged electrostatic potentials are reported in Fig. 3(a) and (b), respectively. The absorption curve is lowered in the UV-light region while it is enhanced in the lower energy part of the visible-light region. Eventually, electric-field controlled PV properties can be achieved for BFO/TO heterostructure in visible-light region. The FeO2 and BiO layers move slightly along the ferroelectric polarization direction under the electric field. Moreover, the external electric field is able to induce charge carriers in the vicinity of the surface as shown in Fig. 3(b), leading to the increased optical absorption in the visiblelight region. The calculated differences in total energy for AFM configurations relative to that for ferromagnetic(FM) configurations under different strains are shown in Table 1. It is apparent that the FM
Fig. 3. (a) The optical absorption curves under tensile strain before and after applying an electric field. (b) The plane-averaged electrostatic potentials under tensile strain before and after applying an electric field, respectively.
408
H.-J. Feng / Materials Chemistry and Physics 153 (2015) 405e409
Table 1 Differences in total energy for AFM configurations relative to total energy for ferromagnetic(FM) configurations under different strains. ε(%) DE(eV)
4 0.199
2 0.161
0 0.001
2 0.076
spins change to AFM ones as the tensile strain is achieved to be 2%. The plane-averaged spin density for strains of the order 0% and 2% are reported in Fig. 4(a) and (b), respectively. The structure of the heterojunction is illustrated in Fig. 4(c). The spin density of Fe26 is bigger than Fe31 while O28 possesses a larger magnetization compared to O32, indicating there are spin carriers transfer in the vicinity of the interface between BFO and TO layers. Spin-up carriers tend to transport to the interface and result in the enhanced magnetization for Fe26 and O28. Meanwhile the occurrence of magnetization in O28 and O32 indicates the spin carriers are transferred along polarized direction. After applying tensile strain, magnetization of Fe26 and O28 are reversed to the opposite direction while the Fe31 and O32 still remain unchanged, leading to the AFM structure shown in Fig. 4(b). Combined with the enhancement of PV effect, this behavior further shows that there exists the interaction of photons with charges, spins, and lattice in the interface, and this may provide a new multi-field coupling mechanism in the interface. In order to demonstrate the charge transport along the Fe26eO28eFe31eO32 chain along the polarized direction, the
Fig. 5. The PDOS of (a) Fe26 3d, (b) O28 2p, (c) Fe31 3d, and (d) O32 2p for tensile strained BFO/TO bilayer film. The vertical dashed line indicates the Fermi level.
partial density of states(PDOS) for Fe 3d and O 2p under tensile strain are plotted in Fig. 5. Compared to O32, the manifold of O28 2p density of states are shifted down and positioned around 5 eV, hybridizing with Fe26 3d states in the energy range. The
Fig. 4. The distribution of magnetization across the bilayer film averaged over the plane parallel to the film (a) before and (b) after exerting tensile stress. The structure of the heterojunction is shown in (c). The red, blue, purple, and brown balls indicate the O, Ti, Bi, and Fe, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
H.-J. Feng / Materials Chemistry and Physics 153 (2015) 405e409
409
Fig. 6. The magnetic structures of BFO/TO heterojunction (a) before and (b) after applying tensile strain. The red, blue, purple, and brown balls indicate the O, Ti, Bi, and Fe, respectively. The arrow indicates the spin of Fe. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
hybridization and charge rearrangement between Fe26 3d and O28 2p orbitals present the photon-spin coupling mechanism associated with spin carrier transport in the BFO/TO interface, and the coupling effect is decreased gradually away from the interface. The charge transfer in the interface agrees well with the case in the well-studied LaAlO3/SrTiO3 heterostructure [32e34]. In addition, a half-metallic behavior is observed for Fe26 in the interface which can be used for designing novel photoelectric devices based on spintronics, and the half-metallic properties are caused by the spin carrier transfer in the interface. The ground state magnetic structures before and after applying tensile strain are illustrated in Fig. 6. It is clear that the ferromagnetic ordering changes to antiferromagnetic one with exerting tensile strain of 2%, indicating that the coupling among atoms in interface is strong and susceptible to the structural distortions. Under tensile strain, the occupied spin-up electrons are hopping to the spin-down states, leading to the flip of magnetization of Fe in the interface of the heterojunction. Moreover, this strain tunable magnetic property could be used in magnetic sensors and next-generation photovoltaics and multiferroics.
4. Conclusion DFT-based calculations predict that the optical absorption of BFO/TO heterojunction with tensile strain is enhanced in the visible-light region. A similar phenomenon is able to be observed in the bilayer film under an electric field. The transition from FM structure to AFM one under tensile strain implies the interaction of photons with charges, spins, and lattice. The coupling and the increased magnetization in the interface are caused by the charge rearrangement and orbital hybridization between Fe 3d and O 2p orbitals.
Acknowledgments This work was financially supported by the National Natural Science Foundation of China(NSFC) under Grants No. 11304248 and No. 11247230 (H.-J. F.), the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2014JM1014) (H.-J. F.), the Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 2013JK0624) (H.-J. F.), the Science Foundation of Northwest University (Grant No. 12NW12) (H.-J. F.), Bai-Ren (100 Talents Plan) Project in Shaanxi Province of China, and the scholarship under the State Scholarship Fund by China Scholarship Council (CSC).
References [1] J. Wang, J.B. Neaton, H. Zheng, V. Nagarajan, S.B. Ogale, B. Liu, D. Viehland, V. Vaithyanathan, D.G. Schlom, U.V. Waghmare, N.A. Spaldin, K.M. Rabe, M. Wuttig, R. Ramesh, Science 299 (2003) 1719. [2] I. Sosnowskat, T. Peterlin-Neumaier, E. Steichele, J. Phys. C Solid State Phys. 15 (1982) 4835. [3] G. Catalan, J.F. Scott, Adv. Mater. 21 (2009) 2463. [4] D. Lebeugle, D. Colson, A. Forget, M. Viret, A.M. Bataille, A. Gukasov, Phys. Rev. Lett. 100 (2008) 227602. [5] H. Bea, M. Bibes, F. Ott, B. Dupe, X.-H. Zhu, S. Petit, S. Fusil, C. Deranlot, K. Bouzehouane, A. Barthelemy, Phys. Rev. Lett. 100 (2008) 017204. [6] A.Y. Borisevich, H.J. Chang, M. Huijben, M.P. Oxley, S. Okamoto, M.K. Niranjan, J.D. Burton, E.Y. Tsymbal, Y.H. Chu, P. Yu, R. Ramesh, S.V. Kalinin, S.J. Pennycook, Phys. Rev. Lett. 105 (2010) 087204. [7] S.R. Basu, L.W. Martin, Y.-H. Chu, M. Gajek, R. Ramesh, R.C. Rai, X. Xu, J.L. Musfeldt, Appl. Phys. Lett. 92 (2008) 091905. [8] S.Y. Yang, J. Seidel, S.J. Byrnes, P. Shafer, C.-H. Yang, M.D. Rossell, P. Yu, Y.H. Chu, J.F. Scott, J.W. Ager III, L.W. Martin, R. Ramesh, Nat. Nanotechnol. 5 (2010) 143. [9] T. Choi, S. Lee, Y.J. Choi, V. Kiryukhin, S.W. Cheong, Science 324 (2009) 63. [10] S.Y. Yang, L.W. Martin, S.J. Byrnes, T.E. Conry, S.R. Basu, D. Paran, L. Reichertz, J. Ihlefeld, C. Adamo, A. Melville, Y.H. Chu, C.H. Yang, J.L. Musfeldt, D.G. Schlom, J.W. Ager, R. Ramesh, Appl. Phys. Lett. 95 (2009) 062909. [11] J. Seidel, D. Fu, S.Y. Yang, E. Alarcon-Llado, J. Wu, R. Ramesh, J.W. Ager III, Phys. Rev. Lett. 107 (2011) 126805. [12] W. Ji, K. Yao, Y.C. Liang, Phys. Rev. B 84 (2011) 094115. [13] S.M. Young, A.M. Rappe, Phys. Rev. Lett. 109 (2012) 116601. [14] S.M. Young, F. Zheng, A.M. Rappe, Phys. Rev. Lett. 109 (2012) 236601. [15] A. Fujishima, K. Honda, Nature 238 (1972) 37. [16] Joseph Muscat, Varghese Swamy, Nicholas M. Harrison, Phys. Rev. B 65 (2002) 224112. [17] Y. Wang, C.-W. Nan, Appl. Phys. Lett. 89 (2006) 052903. [18] H.-J. Feng, F. Liu, Phys. Lett. A 372 (2008) 1904e1909. [19] Y. Zang, D. Xie, X. Wu, Y. Chen, Y. Lin, M. Li, H. Tian, X. Li, Z. Li, H. Zhu, T. Ren, D. Plant, Appl. Phys. Lett. 99 (2011) 132904. [20] H.-J. Feng, Phys. B 412 (2013) 41. [21] H.-J. Feng, Europhys. Lett. 101 (2013) 67007. [22] R.J. Zeches, M.D. Rossell, J.X. Zhang, A.J. Hatt, Q. He, C.-H. Yang, A. Kumar, C.H. Wang, A. Melville, C. Adamo, G. Sheng, Y.-H. Chu, J.F. Ihlefeld, R. Erni, C. Ederer, V. Gopalan, L.Q. Chen, D.G. Schlom, N.A. Spaldin, L.W. Martin, R. Ramesh, Science 326 (2009) 977. [23] H. Dong, Z. Wu, S. Wang, W. Duan, J. Li, Appl. Phys. Lett. 102 (2013) 072905. [24] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. Fabris, G. Fratesi, S. de Gironcoli, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, J. Phys. Condens. Matter 21 (2009) 395502. [25] H.-J. Feng, J. Appl. Phys. 114 (2013) 123916. [26] L. Bengtsson, Phys. Rev. B 59 (1999) 12301. [27] B. Meyer, D. Vanderbilt, Phys. Rev. B 63 (2001) 205426. [28] M. Gajdos, K. Hummer, G. Kresse, J. Furthmüller, F. Bechstedt, Phys. Rev. B 73 (2006) 045112. [29] T.D. Beeson, D.W.C. MacMillan, J. Am. Chem. Soc. 127 (2005) 8826. [30] R. Asahi, T. Morikawa, T. Ohwaki, K. Aoki, Y. Taga, Science 293 (2001) 269. [31] L. Jia, C. Wu, Y. Li, S. Han, Z. Li, B. Chi, J. Pu, L. Jian, Appl. Phys. Lett. 98 (2011) 211903. [32] R. Pentcheva, W.E. Pickett, Phys. Rev. Lett. 102 (2009) 107602. [33] J. Lee, A.A. Demkov, Phys. Rev. B 78 (2008) 193104. [34] H. Chen, A. Kolpak, S. Ismail-Beigi, Phys. Rev. B 82 (2010) 085430.
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Photovoltaic and magnetic properties of BiFeO3/TiO2 heterostructures under epitaxial strain and an electric field Hong-Jian Feng School of Physics, Northwest University, Xi'an 710069, People's Republic of China
h i g h l i g h t s The photovoltaic effect in BiFeO3/TiO2 can be tuned by strain and an electric field. The magnetization in the interface is reversed by strain. There exists multi-field coupling in the interface.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 July 2014 Received in revised form 7 January 2015 Accepted 11 January 2015 Available online 13 January 2015
First-principles calculations show that the photovoltaic effect of the BiFeO3/TiO2 heterostructures in the visible-light region can be improved by applying epitaxial strain and an electric field. The multi-field coupling effect in the interface makes the heterojunction an intriguing candidate towards fabricating the multifunctional photoelectric devices, and the microscopic mechanism involved is attributed to the spin transfer and charge rearrangement between the Fe 3d and O 2p orbitals in the vicinity of the interface. © 2015 Elsevier B.V. All rights reserved.
Keywords: Interfaces Optical materials Magnetic materials Ab initio calculations Optical properties
1. Introduction BiFeO3(BFO) has attracted much interests due to its coexistence of antiferromagnetism and ferroelectricity at room temperature [1,2]. The G-type antiferromagnetic(AFM) plane is normal to the ferroelectric polarization along the eight pseudocubic [111] diagonal directions [3,4]. The spin cycloid arrangement in the crystal decreases the weak magnetization and it can be partially suppressed in BFO films. Moreover, BFO-based heterostructures have been proposed to increase the magnetization and it can be reversed by external electric field [5,6]. Meanwhile, it is worth mentioning that the photovoltaic(PV) properties observed in BFO makes it an excellent candidate for application in solar cells with a band gap of 2.67 eV [7]. The ferroelectric domain walls separating the electrons
E-mail addresses: [email protected], [email protected]. http://dx.doi.org/10.1016/j.matchemphys.2015.01.034 0254-0584/© 2015 Elsevier B.V. All rights reserved.
and holes have been proposed to be about 1e2 nm which is much smaller than the depletion layer of the silicon semiconductor [8]. As the photovoltaic effect was observed in pure BFO by Choi [9] and Yang [10], by preparing periodically ordered domain walls in BFO samples, Seidel and coworkers show that the photovoltages measured are additive and voltages are much larger than the band gap [11]. Ji and coworkers demonstrate that the bulk photovoltaic effect (BPVE) plays a crucial role in the PV response in BFO thin films [12]. The theoretical work by Young et al. indicates that shift current is the dominant mechanism of the BPVE in ferroelectrics [13]. The first-principles calculations show that the BPVE plays a role and interacts cooperatively with the domain-wall-driven voltages in polydomain BFO samples [14]. Anatase TiO2(TO) is well known as a promising candidate for photocatalyst, photovoltaic applications, and nanostructured solar cells due to its optical absorption in surface [15,16]. Ti plays an important role in stabilizing the ferroelectricity and insulating
406
H.-J. Feng / Materials Chemistry and Physics 153 (2015) 405e409
properties in BFO samples [17] as shown in our previous study [18]. Motivated by the enhanced PV properties in graphene/ polycrystalline BFO/Pt heterostructure [19], we suggest the BFO/ TO heterojunctions would possess an improved PV response due to the BPVE in BFO. Moreover, the PV effect and electronic properties in pure BFO can be engineered by electric field [20,21] and strain [22,23]. Therefore, a tunable PV effect by strain and electric field would be expected in the heterostructures. To our knowledge, there is no theoretical work done on the BFO/TO heterostructures until now. We used density functional theory(DFT) based first-principles calculations to investigate the optical and magnetic properties of the BFO/TO heterojunctions under strain as well as an external electric field. Indeed we found an increased optical absorption effect caused by the tensile stress and the external electric field. The remainder of this article is organized as follows: In section 2, we presented the computational details of our calculations. We provided the calculated results and discussions in section 3. In section 4, the conclusion were given.
!1=2 1=2 02 00 ε0 ðuÞ ε ðuÞ þ ε 2 ðuÞ IðuÞ ¼ 2u ; 2
(4)
where u is the angular frequency.
2. Computational details Calculations in this work have been done using the QuantumESPRESSO package [24], which is based on the DFT using the plane-wave pseudopotential formalism. The local spin density approximation(LSDA) to DFT scheme with an uniform energy cutoff of 500 eV was used as in our previous work [21]. Bi 5d, 6p, and 6s electrons, Fe 3s, 4s, 3p, and 3d electrons, Ti 3s, 4s, 3p, and 3d and O 2s and 2p electrons were considered as valence states. 6 6 1 Monkhorst-Pack sampling of the Brillouin zone was chosen for the relaxation process while it was increased to 20 20 1 to insure the convergence for the total energy calculation. The slab model was used to construct the heterostructure with a same vacuum thickness as the atomic layers. The relaxation was carried out with the forces on the ions less than 0.02 meV/Å. The AFM spins are perpendicular to the polarization direction to model the G-type AFM spin configuration without considering about the spin-orbit coupling(SOC) and noncollinear magnetism. A saw-tooth like external electric potential [21,25e27] has been used as
Vext ðrÞ ¼ 4pmðr=rm 1=2Þ; 0 < r < rm
(1)
where m is the surface dipole density of the slab, rm is the periodic length along the direction perpendicular to the slab. We used electric field of 0.1 V/Å for the bilayer film [21,25]. The imaginary part of the dielectric tensor is determined by the summation over the conduction band states [28]. 00
εij ðuÞ ¼
4p2 e2 1 X lim 2 2wk dðεck εvk uÞ U q/0 q c;v;k < uckþei q juvk > < uckþej q juvk > * ;
(2)
where c and v denote the conduction and valence band states, respectively. The real part of the dielectric tensor has the form
ε0ij ðuÞ ¼ 1 þ
2 P p
Z∞ 0
00
εij ðu0 Þu0 u02 u2 þ ih
du0 :
(3)
The optical absorption coefficient is obtained by the following expression:
Fig. 1. (a) The calculated optical absorption curves for BFO/TO heterostructures under different compressive and tensile strains, as well as the BFO and TO films. The planeaveraged electrostatic potential with (b) compressive strain of the order 4% and (c) tensile strain as great as 2%, respectively. The red lines denote the macroscopic average of potentials. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
H.-J. Feng / Materials Chemistry and Physics 153 (2015) 405e409
3. Results and discussion The absorption spectrum of BFO/TO heterostructures subject to different strains, as well as BFO and TO films, are reported in Fig. 1(a). In the visible-light region, it is clear that the optical absorption is increasing monotonically with the strains, leading to the highest performance with tensile strain of 2% and the lowest one for compressive strain of 4%. DFT þ U calculations predict a same trend as DFT. Therefore, only the DFT results are given in the following section. In comparison with the heterojunctions, BFO performs the best optical absorption activity while TO behaves the lowest absorption rate in the visible-light region. However, an opposite trend is found in the ultraviolet(UV)-light region. Anatase TO possesses the highest absorption activity in the UV-light region which is consistent with its photocatalytic activity [29e31] and absorption properties. Therefore, strain can be used to tune the PV effect for the BFO/TO heterostructures in the visible-light and UVlight region, respectively. In order to understand the strain driven mechanism in the PV effect, the plane-averaged electrostatic potential across the film for the heterostructures with different strains are shown in Fig. 1(b) and (c). Comparing with the case in the compressive strain, the distance between TiO2 and FeO2 layers in the interface is increased while that between FeO2 and BiO layers is decreased under tensile strain, leading to the decreased potential drop across the FeO2 and BiO layers. The macroscopically averaged potentials are also shown in Fig. 1(b) and (c) to shed light on the ability to separate the electronehole pairs for heterojunctions under different strains. It is clearly seen that the holes and electrons can be effectively separated by the potential drop across the interface under tensile strain in contrast to the potential drop subject to compressive strain, resulting in the large amount of charge carriers and the enhanced absorption in the visible-light region. In order to elucidate the large potential drop and the strong interaction between the adjacent layers in the interface, we constructed the cluster composed by TiO2eFeO2eBiO layers in the vacuum and computed the averaged potential along the normal direction as shown in Fig. 2. The potential drop between TiO2 and FeO2 layer is around 10 eV while the difference between TiO2 and BiO is only 3 eV, indicating the strong interaction between the atomic layers in the interface, and the potential drop is mainly determined by the fluctuation of average potential of interfacial
Fig. 2. The plane-averaged electrostatic potential for TiO2eFeO2eBiO layers along the normal direction.
407
layers. The electrons and holes can be effectively separated by this large potential drop to create novel PV effect with high efficiency. To demonstrate additional degree of control of PV effect in the heterojunction, a saw-tooth like potential has been applied across the film. We took into account the polarization along the electric field. A further enhancement of absorption in the visible light region is able to be found under an electric field. The corresponding optical absorption spectrum and plane-averaged electrostatic potentials are reported in Fig. 3(a) and (b), respectively. The absorption curve is lowered in the UV-light region while it is enhanced in the lower energy part of the visible-light region. Eventually, electric-field controlled PV properties can be achieved for BFO/TO heterostructure in visible-light region. The FeO2 and BiO layers move slightly along the ferroelectric polarization direction under the electric field. Moreover, the external electric field is able to induce charge carriers in the vicinity of the surface as shown in Fig. 3(b), leading to the increased optical absorption in the visiblelight region. The calculated differences in total energy for AFM configurations relative to that for ferromagnetic(FM) configurations under different strains are shown in Table 1. It is apparent that the FM
Fig. 3. (a) The optical absorption curves under tensile strain before and after applying an electric field. (b) The plane-averaged electrostatic potentials under tensile strain before and after applying an electric field, respectively.
408
H.-J. Feng / Materials Chemistry and Physics 153 (2015) 405e409
Table 1 Differences in total energy for AFM configurations relative to total energy for ferromagnetic(FM) configurations under different strains. ε(%) DE(eV)
4 0.199
2 0.161
0 0.001
2 0.076
spins change to AFM ones as the tensile strain is achieved to be 2%. The plane-averaged spin density for strains of the order 0% and 2% are reported in Fig. 4(a) and (b), respectively. The structure of the heterojunction is illustrated in Fig. 4(c). The spin density of Fe26 is bigger than Fe31 while O28 possesses a larger magnetization compared to O32, indicating there are spin carriers transfer in the vicinity of the interface between BFO and TO layers. Spin-up carriers tend to transport to the interface and result in the enhanced magnetization for Fe26 and O28. Meanwhile the occurrence of magnetization in O28 and O32 indicates the spin carriers are transferred along polarized direction. After applying tensile strain, magnetization of Fe26 and O28 are reversed to the opposite direction while the Fe31 and O32 still remain unchanged, leading to the AFM structure shown in Fig. 4(b). Combined with the enhancement of PV effect, this behavior further shows that there exists the interaction of photons with charges, spins, and lattice in the interface, and this may provide a new multi-field coupling mechanism in the interface. In order to demonstrate the charge transport along the Fe26eO28eFe31eO32 chain along the polarized direction, the
Fig. 5. The PDOS of (a) Fe26 3d, (b) O28 2p, (c) Fe31 3d, and (d) O32 2p for tensile strained BFO/TO bilayer film. The vertical dashed line indicates the Fermi level.
partial density of states(PDOS) for Fe 3d and O 2p under tensile strain are plotted in Fig. 5. Compared to O32, the manifold of O28 2p density of states are shifted down and positioned around 5 eV, hybridizing with Fe26 3d states in the energy range. The
Fig. 4. The distribution of magnetization across the bilayer film averaged over the plane parallel to the film (a) before and (b) after exerting tensile stress. The structure of the heterojunction is shown in (c). The red, blue, purple, and brown balls indicate the O, Ti, Bi, and Fe, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
H.-J. Feng / Materials Chemistry and Physics 153 (2015) 405e409
409
Fig. 6. The magnetic structures of BFO/TO heterojunction (a) before and (b) after applying tensile strain. The red, blue, purple, and brown balls indicate the O, Ti, Bi, and Fe, respectively. The arrow indicates the spin of Fe. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
hybridization and charge rearrangement between Fe26 3d and O28 2p orbitals present the photon-spin coupling mechanism associated with spin carrier transport in the BFO/TO interface, and the coupling effect is decreased gradually away from the interface. The charge transfer in the interface agrees well with the case in the well-studied LaAlO3/SrTiO3 heterostructure [32e34]. In addition, a half-metallic behavior is observed for Fe26 in the interface which can be used for designing novel photoelectric devices based on spintronics, and the half-metallic properties are caused by the spin carrier transfer in the interface. The ground state magnetic structures before and after applying tensile strain are illustrated in Fig. 6. It is clear that the ferromagnetic ordering changes to antiferromagnetic one with exerting tensile strain of 2%, indicating that the coupling among atoms in interface is strong and susceptible to the structural distortions. Under tensile strain, the occupied spin-up electrons are hopping to the spin-down states, leading to the flip of magnetization of Fe in the interface of the heterojunction. Moreover, this strain tunable magnetic property could be used in magnetic sensors and next-generation photovoltaics and multiferroics.
4. Conclusion DFT-based calculations predict that the optical absorption of BFO/TO heterojunction with tensile strain is enhanced in the visible-light region. A similar phenomenon is able to be observed in the bilayer film under an electric field. The transition from FM structure to AFM one under tensile strain implies the interaction of photons with charges, spins, and lattice. The coupling and the increased magnetization in the interface are caused by the charge rearrangement and orbital hybridization between Fe 3d and O 2p orbitals.
Acknowledgments This work was financially supported by the National Natural Science Foundation of China(NSFC) under Grants No. 11304248 and No. 11247230 (H.-J. F.), the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2014JM1014) (H.-J. F.), the Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 2013JK0624) (H.-J. F.), the Science Foundation of Northwest University (Grant No. 12NW12) (H.-J. F.), Bai-Ren (100 Talents Plan) Project in Shaanxi Province of China, and the scholarship under the State Scholarship Fund by China Scholarship Council (CSC).
References [1] J. Wang, J.B. Neaton, H. Zheng, V. Nagarajan, S.B. Ogale, B. Liu, D. Viehland, V. Vaithyanathan, D.G. Schlom, U.V. Waghmare, N.A. Spaldin, K.M. Rabe, M. Wuttig, R. Ramesh, Science 299 (2003) 1719. [2] I. Sosnowskat, T. Peterlin-Neumaier, E. Steichele, J. Phys. C Solid State Phys. 15 (1982) 4835. [3] G. Catalan, J.F. Scott, Adv. Mater. 21 (2009) 2463. [4] D. Lebeugle, D. Colson, A. Forget, M. Viret, A.M. Bataille, A. Gukasov, Phys. Rev. Lett. 100 (2008) 227602. [5] H. Bea, M. Bibes, F. Ott, B. Dupe, X.-H. Zhu, S. Petit, S. Fusil, C. Deranlot, K. Bouzehouane, A. Barthelemy, Phys. Rev. Lett. 100 (2008) 017204. [6] A.Y. Borisevich, H.J. Chang, M. Huijben, M.P. Oxley, S. Okamoto, M.K. Niranjan, J.D. Burton, E.Y. Tsymbal, Y.H. Chu, P. Yu, R. Ramesh, S.V. Kalinin, S.J. Pennycook, Phys. Rev. Lett. 105 (2010) 087204. [7] S.R. Basu, L.W. Martin, Y.-H. Chu, M. Gajek, R. Ramesh, R.C. Rai, X. Xu, J.L. Musfeldt, Appl. Phys. Lett. 92 (2008) 091905. [8] S.Y. Yang, J. Seidel, S.J. Byrnes, P. Shafer, C.-H. Yang, M.D. Rossell, P. Yu, Y.H. Chu, J.F. Scott, J.W. Ager III, L.W. Martin, R. Ramesh, Nat. Nanotechnol. 5 (2010) 143. [9] T. Choi, S. Lee, Y.J. Choi, V. Kiryukhin, S.W. Cheong, Science 324 (2009) 63. [10] S.Y. Yang, L.W. Martin, S.J. Byrnes, T.E. Conry, S.R. Basu, D. Paran, L. Reichertz, J. Ihlefeld, C. Adamo, A. Melville, Y.H. Chu, C.H. Yang, J.L. Musfeldt, D.G. Schlom, J.W. Ager, R. Ramesh, Appl. Phys. Lett. 95 (2009) 062909. [11] J. Seidel, D. Fu, S.Y. Yang, E. Alarcon-Llado, J. Wu, R. Ramesh, J.W. Ager III, Phys. Rev. Lett. 107 (2011) 126805. [12] W. Ji, K. Yao, Y.C. Liang, Phys. Rev. B 84 (2011) 094115. [13] S.M. Young, A.M. Rappe, Phys. Rev. Lett. 109 (2012) 116601. [14] S.M. Young, F. Zheng, A.M. Rappe, Phys. Rev. Lett. 109 (2012) 236601. [15] A. Fujishima, K. Honda, Nature 238 (1972) 37. [16] Joseph Muscat, Varghese Swamy, Nicholas M. Harrison, Phys. Rev. B 65 (2002) 224112. [17] Y. Wang, C.-W. Nan, Appl. Phys. Lett. 89 (2006) 052903. [18] H.-J. Feng, F. Liu, Phys. Lett. A 372 (2008) 1904e1909. [19] Y. Zang, D. Xie, X. Wu, Y. Chen, Y. Lin, M. Li, H. Tian, X. Li, Z. Li, H. Zhu, T. Ren, D. Plant, Appl. Phys. Lett. 99 (2011) 132904. [20] H.-J. Feng, Phys. B 412 (2013) 41. [21] H.-J. Feng, Europhys. Lett. 101 (2013) 67007. [22] R.J. Zeches, M.D. Rossell, J.X. Zhang, A.J. Hatt, Q. He, C.-H. Yang, A. Kumar, C.H. Wang, A. Melville, C. Adamo, G. Sheng, Y.-H. Chu, J.F. Ihlefeld, R. Erni, C. Ederer, V. Gopalan, L.Q. Chen, D.G. Schlom, N.A. Spaldin, L.W. Martin, R. Ramesh, Science 326 (2009) 977. [23] H. Dong, Z. Wu, S. Wang, W. Duan, J. Li, Appl. Phys. Lett. 102 (2013) 072905. [24] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. Fabris, G. Fratesi, S. de Gironcoli, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, J. Phys. Condens. Matter 21 (2009) 395502. [25] H.-J. Feng, J. Appl. Phys. 114 (2013) 123916. [26] L. Bengtsson, Phys. Rev. B 59 (1999) 12301. [27] B. Meyer, D. Vanderbilt, Phys. Rev. B 63 (2001) 205426. [28] M. Gajdos, K. Hummer, G. Kresse, J. Furthmüller, F. Bechstedt, Phys. Rev. B 73 (2006) 045112. [29] T.D. Beeson, D.W.C. MacMillan, J. Am. Chem. Soc. 127 (2005) 8826. [30] R. Asahi, T. Morikawa, T. Ohwaki, K. Aoki, Y. Taga, Science 293 (2001) 269. [31] L. Jia, C. Wu, Y. Li, S. Han, Z. Li, B. Chi, J. Pu, L. Jian, Appl. Phys. Lett. 98 (2011) 211903. [32] R. Pentcheva, W.E. Pickett, Phys. Rev. Lett. 102 (2009) 107602. [33] J. Lee, A.A. Demkov, Phys. Rev. B 78 (2008) 193104. [34] H. Chen, A. Kolpak, S. Ismail-Beigi, Phys. Rev. B 82 (2010) 085430.