Magnetism and ferroelectricity in BiFeO3 doped with Ga at Fe sites

Journal of Alloys and Compounds 797 (2019) 117e121

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Magnetism and ferroelectricity in BiFeO3 doped with Ga at Fe sites Qing-Yan Rong a, Wen-Zhi Xiao a, *, Chuan-Pin Cheng a, Ling-Ling Wang b a b

School of Science, Hunan Institute of Engineering, Xiangtan 411104, China School of Physics and Electronics, Hunan University, Changsha 410082, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 21 March 2019 Received in revised form 6 May 2019 Accepted 7 May 2019 Available online 9 May 2019

Theoretical calculations were performed to investigate the effect of isovalent substitution of Fe with Ga on the magnetic and ferroelectric properties in BiFeO3 doped with 16.6% and 8.3% Ga. Such substitution will break the G-type anti-ferromagnetic order and enhance the magnetism of BiFeO3 by forming a stable ferrimagnetic order. The doped system maintains robust spontaneous polarization that is sufficiently large for practical applications at room temperature. The findings explain experimentally observed magnetism. The coexistence of magnetism and ferroelectricity in the doped BiFeO3 render it a candidate material for application to information storage and spintronics devices. © 2019 Elsevier B.V. All rights reserved.

Keywords: BiFeO3 Magnetism Ferroelectricity Gallium Substitution

1. Introduction Bulk BiFeO3 is a well-known multifunctional material that has been widely applied to various fields, such as ferroelectrics [1,2], spintronics [3,4], and catalysis [5,6]. BiFeO3, in its ground state, possesses a distorted rhombohedral structure with R3c symmetry (space group #161). The arrangement of spins in Fe sites adopts a G
el temperature of type antiferromagnetic (AFM) order with a Ne approximately 643 K [7e9]. Moreover, weak ferromagnetism has been observed in the BiFeO3 thin films [10] and small nanoparticles [11] due to the non-compensated spins, that is, the size of thin film or nanoparticles were small enough to not close the cycloid spin structure period of approximately 62 nm along the [110] direction. Bulk BiFeO3 is ferroelectric and features a Curie temperature of approximately 1100 K [12]. Large spontaneous polarizations of 90e100 mC/cm2 have been observed in thin film forms of the material [13e15]. Although BiFeO3 simultaneously exhibits ferroelectric and ferromagnetic properties at room temperature as a multiferroic material [16,17], its weak ferromagnetism limits its practical applications. Introduction of other ions can effectively improve the ferromagnetic performance of this material [4,18e21]. We believe that substitution of Fe with Ga is a feasible and effective means to enhance the ferromagnetic performance of BiFeO3 and leave its

* Corresponding author. E-mail address: [email protected] (W.-Z. Xiao). https://doi.org/10.1016/j.jallcom.2019.05.082 0925-8388/© 2019 Elsevier B.V. All rights reserved.

ferroelectricity intact. For an ideal cubic perovskite-type structure, the Goldschmidt tolerance factor t ¼ 1 is defined as follows [22]:

rBi þ rO t ¼ pffiffiffi 2½ðð1  xÞrFe þ xrGa Þ þ rO  The estimated t of BiFeO3 is approximately 0.895. To form a stable, close-packed structure, BiFeO3 adopts a distorted perovskite-type structure through counter-rotations of adjacent FeO6 octahedra and relative ionic displacements along the [111] direction. Considering extreme cases, if trivalent Bi3þ/Fe3þ cations are wholly replaced by isovalent Ga3þ, t becomes 0.678 and 0.91 for Bi- and Fe-site doping, respectively. Substitution of Bi with Ga predictably leads to structural transition, whereas the substation of Ga for Fe t presents three advantages: (i) it maintains the initial structure of the material due to the similar ionic radii of Ga (0.62 Å) and Fe (0.64 Å), (ii) it breaks the G-type AFM network and enhances the magnetization of the BiFeO3 system, and (iii) it retains the ferroelectricity of the material due to the unspoiled sub-lattice of Bi and uninterrupted charge balance. Experiments have shown that Fe-site doping is feasible under Bi-rich conditions. Ga successfully occupies Fe sites in doped BiFeO3 systems, which crystallize as rhombohedral structures with the R3c space group at low doping concentrations [23e25]. A remarkable ferroelectric polarization of 230 mC cm2 was observed by Yan [23] but not by Cao [25]. Clearly, the exact perspective has not been deciphered. Thus, in this work,

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we conduct first-principles calculations to unlock the puzzle. 2. Computational methodology All structural optimizations and electronic structure calculations are carried out within the density functional theory as implemented in the Vienna Ab Initio Simulation Package [26]. The generalized gradient approximation (GGA) [27] in the form of the PerdeweBurkeeErnzernhof functional [28] is employed to calculate the exchange correlation potential. The projector augmented wave method is used to model electroneion interactions with a plane wave cutoff energy of 500 eV for all calculations [29], and all structures are fully optimized using the conjugate gradient method. The criteria for the total energy and maximum HellmanneFeynman force acting on each atom are less than 106 eV and 0.01 eV/Å, respectively. G-centered MonkhorstePack [30] k-point meshes of 13  13  3, 9  9  3, and 9  5  3 are adopted for the R3c/R-3c unit cells in the rhombohedral, hexagonal, and orthorhombic settings, respectively, as shown in Fig. 1. Due to the limitations presented by correlation effects in materials containing 3d transition metals, we carried out GGA þ U calculations as described by Dudarev et al. [31] throughout this paper. The Hubbard parameter U ¼ 4 eV and the exchange interaction J ¼ 1 eV are introduced to treat the strongly localized d orbital of Fe. The effective Hubbard parameter Ueff ¼ U  J (¼ 3 eV) yields a reasonable magnetic moment (~4.0 mB) on Fe sites and a bandgap (1.85 eV) that are close to the experimental observations of 3.75 mB [32] and 2.5 eV [33], respectively. Spontaneous polarization is estimated using the Berry phase approach based on modern theory of polarization [34]. 3. Results and discussion 3.1. Structure and magnetic property Bulk BiFeO3 possesses a rhombohedral structure with the space group R3c. Its structure can also be visualized in the hexagonal and orthorhombic settings, as shown in Fig. 1(b) and (c), respectively. The rhombohedral, hexagonal, and orthorhombic settings of the material contain one, three, and six primitive unit cells, respectively, and a unit cell contains two formula units (f.u.). Considering that a doping concentration of approximately 15% is expected to be feasible in the experiments [24], we utilize hexagonal and

orthorhombic unit cells to achieve minimum Ga doping concentrations of 16.6% (1/6) and 8.3% (1/12). The fully relaxed lattice parameters of BiFeO3 in the rhombohedral (ar, ar) and hexagonal settings (a ¼ b, ch) are tabulated in Table 1. The relaxed rhombohedral lattice parameters ar ¼ 5.71 Å and ar ¼ 59.06 agree with the experimental (ar ¼ 5.63 Å, ar ¼ 59.35 ) [35] and theoretical (ar ¼ 5.70 Å, ar ¼ 59.24 ) values [15]. Upon doping, the lattice constants demonstrate successive contraction as the Ga concentration increases, resulting in shrinkage of the ferrite structure (see Table 1). This structural contraction may be related to the substitution of large Fe3þ (0.65 Å) ions with smaller Ga3þ (0.62 Å) ions. The observed contraction may also be attributed to the lower electronegativity of Ga (1.81, Pauling electronegativity scale) compared with that of Fe (1.83), which indicates that the GaeO bond is stronger than the FeeO bond in the BiFeO3 host. This finding is verified by the bond lengths in Table 2. All of the details described above are obtained from the fundamental assumption that pure and doped systems are most energetically stable in the G-type AFM state with a ferroelectric phase. To verify this hypothesis, we conduct a series of calculations to determine the related ground states. Here, we consider five collinear magnetic configurations, including the non-magnetic (NM), ferromagnetic (FM), and A-, C-, and G-type AFM states. In the pure system, the G-type AFM state means the spins on two Fe sites are antiparallel in a primitive unit cell in the rhombohedral setting. In other words, the spins on Fe sites are ferromagnetically coupled within the pseudocubic (111) plane and antiferromagnetically coupled between adjacent planes. For other magnetic orders, a large supercell must be used to set the complex spin arrangement. The detailed spin arrangements of various AFM states are described elsewhere [15]. The calculated total energy and magnetic moments on the Fe sites of pure and doped BiFeO3 are provided in Tables 1 and 2. We do not consider the doping concentration of 16.6% Ga (1/12) because high Ga concentrations lead to structural phase transition. The AFM configuration is clearly and consistently energetically favored. As expected, the hypothetical ferroelectric phase in the G-type AFM state is the most stable among the various magnetic orders studied, which agrees well with previous reports [7e9]. More interestingly, the doped system shows the same order of energy as the pure system. Therefore, the doped BiFeO3 system with 8.33% Ga maintains a G-type AFM ground state. A structural transition from a rhombohedral phase with R3c symmetry to an orthorhombic one with Pbnm symmetry

Fig. 1. Crystal structure of BiFeO3 in the (a) R-3c and (b) R3c rhombohedral phases and the (c) R3c orthorhombic representation. (d) Spatial spin-density distribution of a BiFeO3 supercell with a substituted Ga atom. The yellow and blue isosurfaces correspond to the spin-up and spin-down components, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

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Table 1 Calculated lattice constants a/b in the hexagonal (ah/ch) and rhombohedral (ar/ar) frames, bond lengths (Å), volumes (Å3), polarizations (P, mC/cm2), local magnetic moments on Fe (MFe, mB), and band gaps (Eg, eV) of pure and doped BiFeO3 in the ferroelectric phase. ar/ar (Å)

ah/ch (Å)

Type

Bond length FeeO

Pure Pure [36] Pure [15] 16.6% 8.33%

5.631/14.089

5.71/59.06 5.63/59.35 5.70/59.24

5.619/14.028 5.616/14.058

1.984

1.981 1.977

is observed when the Ga content reaches 15% [23]. However, our test calculations show that the R3c structure is energetically favored over the Pbnm one in the G-type AFM state at a doping concentration of 25% Ga. Further theoretical and experimental studies are urgently needed to explain this phenomenon, which is beyond our scope of study in this work. The local magnetic moments (~4.0 mB) on Fe sites are nearly identical, thus indicating that substitution of Fe with Ga does not affect the local magnetic moments on Fe sites. In BiFeO3, Fe3þ [[ adopts a high spin electron configuration of t [[[ 2g e2g due to the crystal field effects exerted by distorted O octahedra. Hybridization interactions between O-2p and Fe-3d reduce the local magnetic moment on Fe and induce a slight parallel spin on its nearest neighboring O atom, as partly reflected in Fig. 1(d). Consequently, the local magnetic moment on Fe is not exactly 5.0 but approximately 4.0 mB. Considering the local magnetic moments (0.333mB) on the three nearest neighboring O atoms and the distribution of spins in the interstice, the total magnetic moment induced on a Fe3þ ion is expected to be 5.0 mB. The G-type AFM arrangement contributes to the strong AFM super-exchange via the Fe3þeO2eFe3þ pathway. Because Ga is a nominally trivalent metal, substitution does not introduce any additional electron or hole to the system, and the charge balance of the system is maintained. Thus, the local magnetic moments are immune to charge transfers. Substitution of Fe with Ga only breaks the AFM spin arrangement, thereby introducing ferrimagnetic ordering with a magnetic moment of 5.0 mB per dopant. To understand the related magnetic behaviors further, we plot the band structures of the G-type AFM phase of BiFeO3 in the ferroelectric R3c space group at doping concentrations of 0% and 16.6% Ga in Fig. 2(a) and (b), respectively; here, the band structure of doped BiFeO3 with 8.3% Ga is not provided due to its similarity with the case of BiFeO3 with 16.6% Ga. For pure BiFeO3, the conduction band minimum is derived mainly from Fe-3d anti-bonding states, whereas the valence band (Fermi level to 4.5 eV) forms by hybridization between O-2p, Bi-6p, and Fe-3d states. The orbitallike Fe-3d states are located at approximately 6.0 eV and feature a width of approximately 2 eV. Two well-dispersed bands in the range of 8.2 eV to 10 eV arise predominantly from Bi-6s electrons. More details are presented elsewhere [15]. Upon doping, five Fe-3d bands shift from the energy level at approximately 5.5 eV to around the valence band maximum in the spin-up channel, and electrons form Ga subsequently compensate for the shift. As a result, a net spontaneous moment of 5.0mB per dopant is introduced, consistent with our calculated values. The band emerges at

Table 2 Total energies (eV) of pure and doped BiFeO3 systems in the ferroelectric phase with different spin configurations: NM, FM, and A-, C-, and G-type AFM states. Type

NM

FM

A

C

G

Pure 1/12

59.969 58.916

63.815 62.675

64.019 62.994

64.171 63.116

64.391 63.240

Volume

P

MFe

Eg

128.94 124.60 128.48 127.87 128.05

99.3

4.07

1.878

88.7 92.1 89.5

3.789 4.08 4.08

0.97 1.860 1.820

GaeO

1.965 1.965

approximately 6.8 eV and mainly originates from the mixing of Ga-4s with Fe-3d states. 3.2. Spontaneous polarization and ferroelectricity As shown in Fig. 2 and Table 2, the Bi-6s states and band gaps of bulk BiFeO3 are not affected by Ga doping. The excellent ferroelectricity of BiFeO3 is mainly derived from the chemically inactive lone-pair of Bi-6s. Thus, Bi-6s does not participate in bonding but is sterically active [36]. The barely disturbed lone-pair electrons and semiconductor characteristics observed imply that Ga-doped BiFeO3 materials may retain the excellent ferroelectricity of the bulk material. To investigate this supposition, we evaluate the effect of Ga on the spontaneous polarization of the doped BiFeO3 systems. BiFeO3 in the R3c phase is a typical displacive-type ferroelectric material. The potential energy double-well curve, a standard feature of ferroelectric materials, results from the relative displacement between the center of positive and negative charges. To simulate the Bi ferroelectric displacement, we first move Bi from its equilibrium position along the [111] direction in a cell with a highly symmetric paraelectric R-3c phase. The lattice constants are then obtained from the corresponding optimized structures in the R3c phase. Thereafter, we fully relax the coordinates of O atoms and fix the coordinates of Fe and Bi atoms, as well as the lattice constants. The total energy obtained as a function of Bidisplacement is delineated in Fig. 3, which demonstrates that the pure and doped BiFeO3 systems possess well-defined ferroelectricity. The zero shift of Bi corresponds to the paraelectric R-3c phase, and the two minimum energy points found denote the þR3c or R3c phase. The ferroelectric Curie temperature of BiFeO3 depends on the well-depth defined by the energy difference between the paraelectric and ferroelectric phases. The well-depths of the pure and doped systems with 8.3% and 16.6% Ga are 410, 297, and 350 meV/f.u., respectively. The well-depth of the pure system qualitatively agrees with the values of 427 and 330 meV/f.u. reported by Ravindran [15] and Singh [37], respectively. This difference is mainly ascribed to the choice of exchange-correlation potential and Ueff. Such a well-depth is large enough to suppress the R3ceR-3c transition in BiFeO3 at room temperature. Considering that the observed ferroelectric Curie temperature of BiFeO3 is approximately 1000 K [12], we believe that the doped systems will restrain the ferroelectric phase at temperatures above room temperature. Spontaneous polarization can be estimated from Born effective charges and modern theory of polarization based on Berry phase theory. In general, the latter yields accurate quantitative results. Following the detailed procedures described in Refs. [14,38], we conduct calculations of the spontaneous polarization of pristine and doped BiFeO3 along the [111] direction. Here, the structure with R  3c symmetry is taken as the reference, so the polarization of ferroelectric BiFeO3 systems is defined as the difference in polarization between the structures in the R3c and R-3c phases. Fig. 4 illustrates the evolution of polarization along the transformation

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Fig. 2. Band structures projected on O, Fe, Bi, and Ga for (a) pure and (b, c) doped BiFeO3 in the G-type AFM state. The Fermi level is indicated by the dashed line. The black and red arrows denote the spin-down and spin-up channels, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

path from the paraelectric R-3c phase to the ferroelectric R3c phase in pure and doped BiFeO3. The predicted spontaneous polarization is 99.3 mC/cm2 for pure BiFeO3, which is consistent with the theo [39] values (range, 90e100 mC/ retical [14,15,38] and experimental  .  2 cm2). The polarization quantum e R =U obtained is 175.4 mC/cm , . where U is the unit cell volume, e is the electronic charge, and R is a    orientation of polarization. In the perfect case, lattice in the . pffiffiffi . vector .  ¼ 6a. The spontaneous polarizations of doped  R  ¼ . þ b þ c a     systems with 8.3% and 16.6% Ga are 89.5 and 92.1 mC/cm2, respectively, as shown in Table 2. These calculated spontaneous polarizations agree with the corresponding potential energy curves shown in Fig. 2. The effect of substitution of Fe with Ga on polarization is relatively weak because the stereochemically active Bi-6s lone pair is mainly responsible for the ferroelectricity of the bulk

Fig. 3. Potential energy double-well of pure and Ga-doped BiFeO3 at doping concentrations at 1/12 and 1/6. To compare well depths, the computed energy/unit cell is referred to that of pure BiFeO3. The off-center shift of Bi ions starts from its centrosymmetric position along the [111] direction in the R3c phase.

Fig. 4. Evolution of polarization P along the switching path from the centrosymmetric R-3c structure (0% distortion) to the ferroelectric R3c (or inverted eR3c) structure (100% distortion).

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material. Although polarization is slightly reduced by doping, the predicted values remain larger than those of well-known ferroelectrics, such as PbTiO3 (75 mC/cm2) [40] and PbZr0.52Ti0.48O3 (54 mC/cm2) [41]. These findings suggest that Ga-doped BiFeO3 is a promising candidate material for to ferroelectric devices. 4. Summary In conclusion, we theoretically predict the magnetic and ferroelectric properties of BiFeO3 with isovalent substitution of Fe with Ga using first-principles calculations. Considering that isovalent substitution does not introduce additional carriers to the bulk material, the doped BiFeO3 retains its semiconducting properties. Substitution destroys the initial G-type AFM order of BiFeO3 and establishes a stable ferrimagnetic order. More importantly, the doped system demonstrates robust spontaneous polarization, which is approximately 90% that of pristine BiFeO3. This finding suggests that the material is suitable for practical application at room temperature. The coexistence of magnetism and ferroelectricity renders Ga-doped BiFeO3 a candidate material for application to information storage and spintronics devices. Acknowledgements This work was supported by the Hunan Provincial Natural Science Foundation under Grant Nos. 2017JJ3049 and No. 2018JJ2080, and the Scientific Research Fund of Hunan Provincial Education Department (No. 16C0391). We acknowledge the computational support provided by the computing platform of the Network Information Center of Hunan Institute of Engineering. References [1] J.J. Steffes, R.A. Ristau, R. Ramesh, B.D. Huey, PNAS USA 116 (2019) 2413e2418. [2] M. Campanini, R. Erni, C.H. Yang, R. Ramesh, M.D. Rossell, Nano Lett. 18 (2018) 717e724. [3] J.H. Lee, I. Fina, X. Marti, Y.H. Kim, D. Hesse, M. Alexe, Spintronic functionality of BiFeO3 domain walls, Adv. Mater. 26 (41) (2014) 7078e7082. [4] I.S. Banu, S.D. Lakshmi, S. Kossar, N.A.A. Mundari, Substitution driven optical and magnetic properties of neodymium and nickel doped BiFeO3 ceramics for spintronics applications. Control and Communication (RTECC), IEEE 93e98 (2018). [5] Y.H. Si, Y. Xia, S.K. Shang, X.B. Xiong, X.R. Zeng, J. Zhou, Y.Y. Li, Enhanced visible light driven photocatalytic behavior of BiFeO3/reduced graphene oxide composites, Nanomaterials 8 (7) (2018) 526. [6] X.G. Zhang, B. Wang, X.Z. Wang, X.H. Xiao, Z.G. Dai, W. Wu, J.F. Zheng, F. Ren, C.Z. Jiang, Preparation of M@BiFeO3 nanocomposites (M ¼ Ag, Au) bowl arrays with enhanced visible light photocatalytic activity, J. Am. Ceram. Soc. 98 (7) (2015) 2255e2263. € ssbauer effect in ferroelectric-antiferromagnetic [7] V.G. Bhide, M.S. Multani, Mo BiFeO3, Solid State Commun. 3 (9) (1965) 271e274. [8] J.M. Moreau, C. Michel, R. Gerson, W.J. James, Ferroelectric BiFeO3 X-ray and neutron diffraction study, J. Phys. Chem. Solids 32 (6) (1971) 1315e1320. [9] D.P. Dutta, O.D. Jayakumar, A.K. Tyagi, K.G. Girija, C.G.S. Pillai, G. Sharma, Effect of doping on the morphology and multiferroic properties of BiFeO3 nanorods, Nanoscale 2 (7) (2010) 1149e1154. [10] C.Y. Kuo, Z. Hu, J.C. Yang, S.C. Liao, Y.L. Huang, R.K. Vasudevan, M.B. Okatan, Jesse Stephen, Sergei V. Kalinin, L. Li, Single-domain multiferroic BiFeO3 films, Nat. Commun. 7 (2016) 12712. [11] S. Kuila, S. Tiwary, M.R. Sahoo, A. Barik, P.D. Babu, V. Siruguri, B. Birajdar, P.N. Vishwakarma, Study of magnetization and magnetoelectricity in CoFe2O4/ BiFeO3 core-shell composites, J. Appl. Phys. 123 (2018), 064101. [12] J.R. Teague, R. Gerson, W.J. James, Dielectric hysteresis in single crystal BiFeO3, Solid State Commun. 8 (13) (1970) 1073e1074. [13] V.V. Shvartsman, W. Kleemann, R. Haumont, J. Kreisel, Large bulk polarization and regular domain structure in ceramic BiFeO3, Appl. Phys. Lett. 90 (17) (2007) 172115.

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