Strain-induced phase transitions in multiferroic BiFeO3 (110)c epitaxial film

Physics Letters A 376 (2012) 3368–3371

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Strain-induced phase transitions in multiferroic BiFeO3 (110)c epitaxial film Takahiro Shimada ∗ , Kou Arisue, Takayuki Kitamura Department of Mechanical Engineering and Science, Kyoto University, Yoshida-hommachi, Sakyo-ku, Kyoto 606-8501, Japan

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Article history: Received 5 July 2012 Received in revised form 29 August 2012 Accepted 30 August 2012 Available online 3 September 2012 Communicated by R. Wu Keywords: Multiferroics Thin films Phase transition Strains First-principles

a b s t r a c t Intriguing rich phase transitions and multiferroic behavior in (110)-oriented BiFeO3 epitaxial films are studied by first-principles calculations. We demonstrate that a BiFeO3 (110)c film undergoes complicated monoclinic–monoclinic–orthorhombic (M a –M b –O ) phase transitions depending on the epitaxial strain conditions. During the phase transition, ferroelectric spontaneous polarization and a magnetic moment due to weak ferromagnetism rotate in different ways, leading to different anisotropies in the magnetoelectric response of the BiFeO3 (110)c film. Electronic structure analysis reveals that applying compression worsens the resistance to current leakage of the BiFeO3 film. © 2012 Elsevier B.V. All rights reserved.

1. Introduction In recent years, perovskite-structured bismuth ferrite, BiFeO3 , has attracted great interest and attention due to its large ferroelectric polarization and coexisting ferromagnetic/antiferromagnetic ordering at room temperature [1], namely multiferroic materials. Multiferroic materials exhibit an additional intriguing feature, namely that the coexisting ferroelectric and (anti-)ferromagnetic orderings strongly couple with each other; this coupling is known as magnetoelectric (ME) coupling. Because ME coupling enables ferroelectricity (ferromagnetism) to be controlled by applying a magnetic (electric) field [2], multiferroic materials have the potential to realize advanced technological devices, such as multiplestate memory elements and new functional sensors [3–6]. BiFeO3 thin films have been mainly synthesized by epitaxial growth on various perovskite-structured substrates. The intriguing characteristics of BiFeO3 films have been experimentally and theoretically investigated [7–13]. The epitaxial-stressinduced rhombohedral–monoclinic–monoclinic–tetragonal (R–M a – M c –T ) phase transitions accompanying a giant axial ratio and a large out-of-plane polarization [7–10], and a remarkable enhancement of magnetoelectric coefficients near the phase transitions [11,12]. Furthermore, it may be possible to obtain large piezoelectric responses by mixing nanodomains consisting of different phases [13]. These striking findings were all obtained for BiFeO3 thin films epitaxially grown on (001) substrates (BiFeO3 (001)c films). On the other hand, very few studies have investi-

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gated BiFeO3 thin films with different epitaxial orientations, especially BiFeO3 (110)c films [14–16] although distinctive phase transitions and resulting excellent multiferroicity are expected, just as in (001)c films. This Letter investigates the intriguing rich phase transitions in BiFeO3 (110)c films under a wide range of epitaxial strains as well as its multiferroic (ferroelectricity and ferromagnetism) and electronic properties by performing first-principles density-functional theory (DFT) calculations. These calculations successfully predict the phase transitions in BiFeO3 (001)c films [17]. Our results should provide fundamental insights into tunable multiferroicity and magnetoelectric responses in BiFeO3 (110)c films achieved by generating epitaxial strains through using different substrates. 2. Simulation models and procedure We perform first-principles DFT calculations within the local spin density approximation plus the Hubbard U (LSDA + U ) method with on-site Coulomb and exchange parameters of respectively U = 3.5 eV and J = 0.5 eV [18], as implemented in the Vienna Ab-initio Simulation Package (VASP) code [19]. The electronic wave functions are expanded in plane waves up to a cutoff energy of 500 eV. The electron–ion interaction is described by projectoraugmented wave (PAW) potentials [20] that explicitly include the Bi 5d, 6s, and 6p, the Fe 3p, 3d, and 4s, and the O 2s and 2p electrons in the valence states. A  -centered 5 × 3 × 5 Monkhorst–Pack k-point mesh is used for Brillouin zone integrations [21]. We perform fully unconstrained noncollinear magnetic calculations [22], which include spin–orbit coupling (SOC) to describe spin canting and the resulting weak ferromagnetism in BiFeO3 [23].

T. Shimada et al. / Physics Letters A 376 (2012) 3368–3371

Fig. 1. (a) Total energy E tot as a function of epitaxial strain εep for a BiFeO3 (110)c epitaxial film. M a –M b and M b –O phase transitions are indicated by the vertical dashed lines. (b) Ratio of out-of-plane a to in-plane c lattice parameters, a/c, as a function of epitaxial strain, εep .

We employ a simulation cell containing 20 atoms with Carte¯ ], [001], and [110], respectively, sian x, y, and z axes of [110 to simulate BiFeO3 (110)c pseudoepitaxy and the rock-salt antiferromagnetic (G-type AFM) order with a small spin canting. √ The simulation cell vectors√ are initially set to a = a0 (0, 0, 2 ), b = a0 (0, 2, 0), and c = a0 ( 2, 0, 0), respectively, where a0 is initially set to the lattice constant of bulk rhombohedral (R3c) BiFeO3 of 3.91 Å. A small increment of epitaxial (misfit) strain, εep (= εxx = ε y y ), is applied stepwise by stretching (or shrinking) the in-plane cell vectors of b and c. At each epitaxial strain, the internal atomic coordinates and the out-of-plane cell vector a are fully relaxed until all the Hellmann–Feynman forces and the stress components of σzz , τ yz , and τzx are less than 5.0 × 10−3 eV/Å and 5.0 × 10−3 GPa, respectively. 3. Results and discussion Fig. 1(a) shows the total energy E tot as a function of epitaxial strain εep for the BiFeO3 (110)c film. When strain free or under tension (εep  0.0), the BiFeO3 (110)c film belongs to a monoclinic (M a ) phase (space group Cc) [see also the crystal orientation in Fig. 1(a)]. In this phase, the spontaneous polarization (or ferroelectric structural distortion) P points between the symmetry axes of [111] and [001], which belong to the rhombohedral (R) and tetragonal (T ) phases, respectively. Under compression, on the other hand, the BiFeO3 (110)c film changes from M a to a different monoclinic M b phase (space group Cc), where the symmetry

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Fig. 2. (a) Spontaneous polarization P and (b) magnetic moment m as a function of epitaxial strain εep for BiFeO3 (110)c epitaxial film. The vertical dashed lines indicate M a –M b and M b –O phase transitions. The x, y, and z directions correspond ¯ ], [001], and [110], respectively. to [110

axis points between [111] and [110] (the R and orthorhombic (O ) phases, respectively). Note that M a and M b belong to the same space group (Cc), but the difference can be represented by the axial ratio of the out-of-plane a to the in-plane c lattice parameters; a/c < 1 for M a and a/c > 1 for M b [see Fig. 1(b)]. When the compression exceeds εep = −0.08, the orthorhombic (O ) phase (space group Amm2) becomes more energetically favorable than the M b phase. The sequent M a –M b –O phase transition of the BiFeO3 (110)c film clearly differs from the R–M a –M c –T transition previously reported for BiFeO3 (001)c films [17]. A synchrotron X-ray diffraction experiment identified the monoclinic M b phase for the BiFeO3 film epitaxially grown on a SrTiO3 (110) substrate with an in-plane lattice parameter of c = 3.88 Å [14]. The present results also give the M b phase at the corresponding strain of εep = −0.008. This good agreement demonstrates the reliability of the present calculations. Fig. 2(a) plots the spontaneous polarization P as a function of epitaxial strain εep , where the polarization is rigorously evaluated by the modern theory of polarization based on the Berry phase theory. Under tension (in M a ), the in-plane polarization P y tends to increase whereas the out-of-plane P z decreases, indicating that the polarization gradually rotates from [111] to [001] along the R–T line [see also Fig. 1(a)]. In contrast, the polarization changes in the opposite manner under compression (in M b ): it gradually rotates from [111] to [110] along the R–O line. In the O phase, the polarization lies along the purely out-of-plane [110]

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T. Shimada et al. / Physics Letters A 376 (2012) 3368–3371

direction and the polarization magnitude rapidly increases across the M b –O phase transition due to the rapid increase in the axial ratio a/c, as seen in Fig. 1(b). Similar enhancements of the axial ratio and spontaneous polarization have also been reported for various BiFeO3 (001)c films during the R–T phase transition [8,9]. We simultaneously investigate the change in the weak ferromagnetism in BiFeO3 originating from a local spin canting from the G-type AFM order [23]. Fig. 2(b) shows the total magnetic moment per unit cell m as a function of the epitaxial strain εep . The strain-free BiFeO3 film exhibits a magnetic moment of m = (0.00, −0.047, 0.033)μ B , which is almost in the [112¯ ] direction. Under tension (in M a ), the magnitude of m y decreases, finally becoming zero, whereas m z remains almost constant at about 0.04μ B . This indicates that the applied tension rotates the magnetic moment from [112¯ ] to [110]. On the other hand, the magnitudes of both m y and m z increase very slightly under compression (in M b ), suggesting that the magnetic moment direction remains almost constant at [112¯ ]. In the O phase, the total magnetic moment disappears because the magnetic ordering shifts to the pure G-type AFM order (no spin canting). This is because the oxygen octahedral tilting along [111], which induces the local spin canting [23], disappears in the O phase BiFeO3 (110)c film. As mentioned above, the ferroelectric polarization and magnetic moment in BiFeO3 (110)c films rotate in different ways depending on the applied epitaxial strain; this can lead to different anisotropies in the magnetoelectric response. Note that we considered the high-spin (HS) state of Fe in BiFeO3 for all the results shown above. The low-spin (LS) state of Fe in BiFeO3 , which was found in BiFeO3 under extremelyhigh hydrostatic pressure [24], is energetically unfavorable within the present strain region. Such difference may originate from the strain anisotropy applied in the present calculations: In the previous report [24], hydrostatic (isotropic) pressure was applied to BiFeO3 , while we imposed the epitaxial (110) strain, which leads to a strong anisotropy to not only the structure but also the magnetism in BiFeO3 , as shown in Fig. 2. Very recently, new oxygen octahedra tilting patterns were reported in complex perovskite oxdes [25]. The different oxygen octahedra tilting patterns may strongly affect the magnetic ordering (e.g., A-, F -, or G-type AFM states and/or a local spin canting) and the magnetoelectric coupling. Thus, it would be interesting to consider additional degrees of freedom for structural instabilities including these complex oxygen octahedra tilting patterns, especially, under high compression. This may, however, require an analysis of soft phonon modes and a systematic search for lowersymmetry structures considering increased structural degrees of freedom. It should be addressed as a future work. Finally, we briefly discuss the electronic properties of epitaxial BiFeO3 (110)c films. Fig. 3 shows the band gap energy E gap as a function of the epitaxial strain. Under tension, the band gap energy changes very slightly from 1.4 to 1.6 eV. On the other hand, the band gap energy tends to decrease when compression is applied. For the O phase under a relatively high compression, E gap drops to 0.5 eV, which is about 30% that of the strainfree BiFeO3 film. This suggests that compression could reduce the resistance to current leakage, which is often a critical problem in BiFeO3 films [4]. Note that, although these band gap energies are somewhat smaller than the experimental value (E gap = 2.5 eV [26]) due to a well-known problem within the framework of DFT, the trend should be qualitatively correct. 4. Conclusion In summary, intriguing rich phase transitions and multiferroic behavior in (110)-oriented BiFeO3 epitaxial films were studied by

Fig. 3. Band gap energy E gap as a function of epitaxial strain εep for BiFeO3 (110)c epitaxial film. The vertical dashed lines indicate M a –M b and M b –O phase transitions.

first-principles DFT calculations. The BiFeO3 (110)c film undergoes M a –M b –O phase transitions depending on the epitaxial strain conditions. This clearly differs from BiFeO3 (001)c films that exhibit a R–M a –M c –T transition [17]. During the phase transitions, ferroelectric spontaneous polarization and magnetic moment due to weak ferromagnetism rotate in different ways, leading to different anisotropies of the magnetoelectric response of the BiFeO3 (110)c film. Electronic structure calculations revealed that the applied compression reduces the resistance to current leakage of BiFeO3 . The results obtained here are promising for designing and applying BiFeO3 films to magnetoelectric devices. Acknowledgements This work was supported in part by a Grant-in-Aid for Scientific Research (S) (Grant No. 21226005) and a Grant-in-Aid for Young Scientists (A) (Grant No. 23686023) from the Japan Society of the Promotion of Science (JSPS). References [1] G. Catalan, J.F. Scott, Adv. Mater. 21 (2009) 2463. [2] H. Ohno, Science 281 (1998) 951. [3] M. Fiebig, T. Lottermoser, D. Frohlich, A.V. Goltsev, R.V. Pisarev, Nature 419 (2002) 818. [4] N.A. Spaldin, M. Fiebig, Science 309 (2005) 391. [5] M.Q. Cai, G.W. Yang, X. Tan, Y.L. Cao, L.L. Wang, W.Y. Hu, Y.G. Wang, Appl. Phys. Lett. 91 (2007) 101901. [6] J.F. Scott, Nature Mater. 6 (2007) 256. [7] H. Béa, B. Dupé, S. Fusil, R. Mattana, E. Jacquet, B. Warot-Fonrose, F. Wihelm, A. Rogalev, S. Petit, V. Cros, Phys. Rev. Lett. 102 (2009) 217603. [8] R.J. Zeches, M.D. Rosell, J.X. Zhang, A.J. Hatt, Q. He, C.-H. Yang, A. Kumar, C.H. Wang, A. Melville, C. Adamo, Science 326 (2009) 977. [9] A.J. Hatt, N.A. Spaldin, C. Ederer, Phys. Rev. B 81 (2010) 054109. [10] B. Dupé, I.C. Infante, G. Geneste, P.-E. Janolin, M. Bibes, A. Barthélémy, S. Lisenkov, L. Bellaiche, S. Ravy, B. Dkhil, Phys. Rev. B 81 (2010) 144128. [11] J.C. Wojdel, J. Iniguez, Phys. Rev. Lett. 105 (2010) 037208. [12] S. Prosandeev, I.A. Kornev, L. Bellaiche, Phys. Rev. B 83 (2011) 020102. [13] J.X. Zhang, B. Xiang, Q. He, J. Seidel, R.J. Zeches, P. Yu, S.Y. Yang, C.H. Wang, Y.-H. Chu, L.W. Martin, Nature Nanotech. 6 (2011) 98. [14] G. Xu, J. Li, D. Viehland, Appl. Phys. Lett. 89 (2006) 222901. [15] D. Kan, I. Takeuchi, J. Appl. Phys. 108 (2010) 014104. [16] J. Li, J. Wang, M. Wutting, R. Ramesh, N. Wnag, B. Ruette, A.P. Pyatakov, A.K. Zvezdin, D. Viehland, Appl. Phys. Lett. 84 (2004) 5261. [17] H.M. Christein, J.H. Nam, H.S. Kim, A.J. Hatt, N.A. Spaldin, Phys. Rev. B 83 (2011) 144107. [18] V.I. Anisimov, F. Aryasetiawan, A.I. Lichtenstein, J. Phys.: Condens. Matter 9 (1997) 767. [19] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558. [20] P.E. Blochl, Phys. Rev. B 50 (1994) 17953.

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[21] [22] [23] [24]

H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. D. Hobbs, G. Kresse, J. Hafner, Phys. Rev. B 62 (2000) 11556. C. Ederer, N.A. Spaldin, Phys. Rev. B 71 (2005) 060401(R). O.E. González-Vázquez, J. Íñiguez, Phys. Rev. B 79 (2009) 064102.

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[25] M.D. Peel, S.P. Thompson, A. Daoud-Aladine, S.E. Ashbrook, Ph. Lightfoot, Inorg. Chem. 51 (2012) 6876. [26] F. Gao, Y. Yuan, K.F. Wang, X.Y. Chen, F. Chen, J.-M. Liu, Z.F. Ren, Appl. Phys. Lett. 89 (2006) 102506.