J. Appl. Phys. 114, 233912 (2013); https://doi.org/10.1063/1.4850975 114, 233912
© 2013 AIP Publishing LLC.
First-principles study on the magnetic properties in Mg doped BiFeO3 with and without oxygen vacancies
Cite as: J. Appl. Phys. 114, 233912 (2013); https://doi.org/10.1063/1.4850975
Submitted: 01 October 2013 . Accepted: 04 December 2013 . Published Online: 19 December 2013 Ruipeng Yang, Sixian Lin, Xiaogong Fang, Xingsen Gao, Min Zeng, and Junming Liu
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First-principles study on the magnetic properties in Mg doped BiFeO
3with and without oxygen vacancies
Ruipeng Yang,1Sixian Lin,1Xiaogong Fang,1Xingsen Gao,1Min Zeng,1,a) and Junming Liu2,b)
1Institute for Advanced Materials, South China Normal University, Guangzhou 510006, China
2Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
(Received 1 October 2013; accepted 4 December 2013; published online 19 December 2013) The magnetic properties of Mg-doped BiFeO3 (BFO) with and without oxygen vacancies are studied through first-principles calculations. The Mg-doping prefers to occupy the ferromagnetic planes and produces an obvious improved magnetization, and the magnetization is linearly enhanced with increasing Mg-doped content, which is consistent with the trend reported in experiment. However, our calculated result is significantly larger than the experimental one, and the reason is revealed that the relative energy differences of various spin-ordering configurations are small. Furthermore, oxygen vacancy in Mg-doped BFO can further enhance the magnetization, while keeping the insulating band gap character. The calculated results imply that the oxygen vacancy in Mg-doped BFO would be an effective way to improve the multiferroicity of BFO.
VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4850975]
I. INTRODUCTION
Multiferroics with magnetoelectric properties have recently become the focus of intensive research due to coex- istence of magnetic and electric ordering parameters, which is of interest for novel exciting applications like magnetic field sensors, tunable microwave devices, multiple state memory elements, and spintronic devices.1–3BiFeO3(BFO) is the known multiferroic oxide, which simultaneously proc- esses antiferromagnetic, ferroelectric, and ferroelastic prop- erties at room temperature as it has a ferroelectric Curie temperature of1100 K and a Neel temperature of640 K.4 The large spontaneous polarization P100lC/cm2, reported in thin film and single crystal forms, mainly origi- nates from the Bi atom off-center distortion.5–7However, its magnetism is very weak in the macroscopic size as it has an incommensurate sinusoidal spin arrangement with wave- length of 62 nm.8
Although BFO exhibits a large ferroelectric polarization, the magnetoelectric coupling effect is very small owing to its antiferromagnetic spin ordering, which further inhibits its extensive applications. In the past decades, people have tried many methods to improve the magnetism, in turn, magneto- electric coupling effect.9–18Among them, the substitution of A- and/or B-sites by other elements in BFO is extensively adopted as when these sites are occupied by different mag- netic/non-magnetic ions, the space-modulated antiferromag- netic state would be broken owing to the structural distortion so that the magnetism and even magnetoelectric coupling effect are enhanced. For examples, the enhanced ferromag- netism has been revealed in BFO ceramics with the partial substitution of Fe3þ ions by the Ca2þ, Mg2þ, Ti4þ, Mn4þ.9–13 The enhanced multiferroic properties of BFO ceramics have been reported in the partial substitution of
Bi3þ ions by the rare earth elements such as Nd4þ, La3þ, Dy3þ.14–19In addition, intrinsic lattice defects in BFO have been proposed to a possible source of magnetization. For instance, Ederer and Spaldin19 reported a slightly improved magnetization in BFO induced by oxygen vacancies in theory. Among those systems reported, the addition of Mg2þ ions to BFO was believed to maintain the structural stability as Mg2þhas a similar ion size with Fe3þ. In particular, it can suppress the antiferromagnetic spin ordering and introduce some oxygen vacancies through nonstoichiometric composi- tions. Wu et al.11 reported the enhanced magnetism in Mg-doped BFO ceramics and explained the reasons as the creation of unbalanced Fe3þspins and long range coupling among them mediated by localized charge carriers related to oxygen vacancies. However, the electronic mechanism for the enhanced magnetism in Mg-doped BFO is lack. Thus, a detailed investigation on the magnetic properties of Mg-doped BFO is needed. We hope the mechanism can sup- ply the guidance for further useful studies.
In this paper, we performed first-principles calculations on the magnetic properties of Mg-doped BFO with the con- sideration of doped contents, charge states, and oxygen vacancies. The calculated results were compared with the ex- perimental data. It was found that Mg-doping induces an obvious improvement in the magnetization, which is linearly enhanced with the increase of Mg-doped content. The trend is consistent with the one in experiment. However, the experi- mental results are significantly smaller than the theoretical values. The reason can be attributed to the very small relative energies differences of various spin-orderings configurations so that the Mg dopants in BFO do not have the energetic pref- erence to form a special spin ordering structure. Furthermore, we found that the oxygen vacancy in Mg-doped BFO can fur- ther enhance the magnetization and maintain the insulating band gap character. Our theoretical results imply that the mul- tiferroic behavior in BFO would be improved through com- bining Mg-doping and oxygen vacancies.
a)E-mail: [email protected]
b)E-mail: [email protected]
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II. COMPUTATION METHOD
We selected the projector augmented wave (PAW) method to perform our first-principles calculations with the local spin-density approximation plus the on-site repulsion (LSDAþU),20,21implemented in the Viennaab initiosimu- lation package (VASP).22,23 We used Ueff¼3 eV on Fe 3d states as other studies before for a better description of the localized transition.24 The basis was treated with Bi 5d106s26p3, Fe 3p63d64s2, O 2s22p4, and Mg 2p63s2. We used the energy cutoff of 400 eV for the plane wave expan- sion of the PAW, and the tetrahedron method for the Brillouin zone integrations. The convergence threshold for self-consistent iteration is set at 106eV. In order to model BFO crystal structures with doping and vacancy configura- tions, we built a 222 periodic supercell (80 atoms) based on the optimized primitive cell, see Figure1. In practi- cal calculations, antiferromagnetic (AFM) spin orderings are assumed for perfect BFO as it has a nearlyG-type AFM con- figuration observed in experiment. Doping and vacancy structures can be created by replacing Fe atom by Mg atom and removing oxygen atom, respectively. All calculated structures were relaxed in a 333 Monkhorst Pack grid of k points until all components of the residual forces are smaller than 1 meV/A˚ .
III. RESULTS AND DISCUSSION
To understand the origin of the magnetization in Mg doped BFO, we first studied one-Mg-atom-doped model, which is constructed by replacing one Fe atom at the 0 site using one Mg atom in the supercell, see Fig. 1 (the Mg- doping density is 6.25%). The calculated total density of states (TDOS) of Mg-doped BFO is shown in Fig.2along with the perfect BFO as a comparison. For perfect BFO, our calculated band gap is about 2.35 eV, which is in good agree- ment with the previous experimental data (2.5 eV)25and the theoretical values (2.22.8 eV).24,26 The significant differ- ences in TDOS are presented in the Mg-doped BFO due to the broken symmetry of originalR3cstructure, see Fig.2(b).
It is found that some electronic states are excited into the band gap, see the top of valence band in the minority and the bottom of conduction band in the majority, means that
Mg-doped BFO has a typicalp-type conducting character. It is noticed that the Mg-doped BFO generates a net magnetic moment of about 4.28lB compared with the no magnetic moment in the perfect BFO. Actually, the magnetic moment originates from the suppression of the spatially modulated AFM spin ordering. It is well-known that the magnetization in BFO mainly originates from the magnetic moment Fe atoms. Our calculated results show that the magnetic moment of Fe atom in the perfect BFO structure is about64.16lB. It is the Fe3þ-O-Fe3þAFM spin ordering that leads to a no net magnetic moment in perfect BFO. However, the AFM spin ordering network in one-Mg-atom-doped BFO is disrupted so that the spin ordering is changed from AFM to ferrimagnet- ism. The induced magnetic moment of 4.28lB is almost equal to the individual local magnetic moment of Fe atom (4.16lB).
Notice that the substitution in this one-Mg-atom-doped model is nonsymmetrical, i.e., a ferrimagnetism spin order- ing is established artificially without considering the ran- domly or nonsymmetrical distribution of the Mg dopants. To clarify the type of spin ordering distributions between the two Mg dopants, six different spin ordering configurations are modeled using the 80-atom 2 22 supercell, which are constructed by replacing two Fe atoms using two Mg atoms at positions (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), and (0, 6), respectively, as shown in Fig.1(the Mg-doping den- sity is 12.5%). For convenience, we use (i, j) to denote the structure in which the Fe atoms at the positions of (i, j) are replaced by Mg atoms. During the calculation, the spin ori- entation of other Fe atoms is the same with the perfect BFO.
In Table I, we summarized the calculated results for Mg- doped BFO. For each structure, the Mg-Mg distancedMg-Mg, relative energy DE, and total magnetic moment are listed.
For the (i, j) configuration, the relative energy is defined as the energy difference between the energy of the (0, j) and the total energy of the (0, 1) structure, i.e., DE¼E(i, j)-E(0, 1).
Clearly, the relative energyDEof (0, 6) structure is the low- est among six configurations, means that it is the most stable structure from the energy viewpoint. Correspondingly, the magnetic moment in (0, 6) structure is about 8.3lB, which is equivalent to the twice of one-Mg-atom-doped BFO.
However, we find that two Mg-dopants lying in two
FIG. 1. The 222 supercell of rhombohedral BFO containing 16 Bi (white), 16 Fe (blue), and 48 O (red) atoms with the labeled Mg-doped atomic sites. Here, two Fe atoms at different sites are replaced by two Mg atoms, which gives six distinct pairs of Mg atoms, such as (0, 1), (0, 2), (0, 3,), (0, 4), (0, 5), (0, 6), respectively.
FIG. 2. The total electronic density of states for (a) the perfect and (b) one- Mg-doped BFO.
233912-2 Yanget al. J. Appl. Phys.114, 233912 (2013)
antiferromagnetically aligned planes produce no net mag- netic moment, see the (0, 1), (0, 2), and (0, 4) structures.
It is also worthy noticing that the charge in this two-Mg- atom-doped model is non-neutral. To clarify the effect of charge on the magnetic property, we took into account with the consideration of possible charge states of q¼0,1, and 2 in (0, 6) structure. It is found that the calculated TDOS and magnetic moments are almost same among various charge states, indicating that the magnetism could be stabi- lized at charge states of 1and 2. However, the electronic structure in the two-Mg-atom-doped model, see Figure3(a) for the 2charge state as an example, is significantly differ- ent from that of the one-Mg-atom-doped BFO. It is found that the two-Mg-atom-doped structure has half-metallic char- acteristic with the spin-down DOS is metallic at Fermi level, while the spin-up DOS is insulating with a large band gap. In addition, the charge-neural state in the two-Mg-atom-doped model can be created by introducing one oxygen vacancy. In our calculation, the oxygen vacancy is created by removing the oxygen atom between two Mg atoms without considering the randomness and the calculated TDOS is presented in Figure3(b). The interesting feature is that the electronic state in Fermi level is absent, means that oxygen vacancy inhibits Mg-doped BFO to form half-metal band gap character.
Furthermore, the magnetic moment is further enhanced, and the value is up to 10lB. It should be noted that there do not have such apparent increase if oxygen vacancy is not in this specific. Thus, it can be expected that Mg-doped BFO with this special charge-neural oxygen state has an improved mul- tiferroicity due to the large magnetization and good insulat- ing band gap property (i.e., its ferroelectric polarization would not be degraded).
In order to further investigate the origin of magnetism in two-Mg-doped BFO, the spin density distributions are stud- ied, and the results are shown in Figure 4 for perfect and two-Mg-atoms-doped BFO in ð110Þ projected plane. The two axes are [110] and [001], respectively. The vertical axis is [111] direction. It is clearly observed that the spin moment is mainly originated from Fe atoms. Meanwhile, O atoms also generate weak local spin moments due to the strong hybridizations between Fe and O atoms, see Fig. 4(a). In Mg-doped system, the Mg sites (see the dotted cycles in Fig.
4(b)), corresponding to the center of positive charges induces Coulomb repulse and attraction with the neighbor’s Fe and O atoms, respectively. Consequently, a distortion is observed in the FeO6octahedrons near the Mg sites which make a set of three Fe-O bonds to be shorted and another set of three Fe-O bands to be elongated so that the spin moments are enhanced in the one end of shorter Fe-O bonds and disap- peared in the another end of longer Fe-O bonds, see the straight cycles. In addition, oxygen vacancy in two Mg-doped BFO further enhances the Fe-O hybridization near vacancy and generates an enhanced magnetism, and the spin density distribution is similar to the one in Fig.4(b).
Finally, a comparison of the magnetic moment between theoretical calculation and experimental results is presented in Figure5. It is found that the theoretical results (1lB per unit cell corresponds to150 emu/g) have the same tendency as experiment,11with increasing Mg-doped content, both of them increase linearly. However, it is worthy noticing that the experi- mental value is much smaller than the theoretical one (the result calculated in (0, 6) structure, see TableI). The difference can be explained that the six configurations have very close energies with one and another, and the difference between the lowest and highest ones is only 0.088 eV, suggesting that real materials certainly would be a mixture of the six configurations. In con- trast to this small energy difference, the magnetic moments of these configurations show a difference as big as8.9 emu, and in particular, the configurations (0, 1), (0, 2), and (0, 4) have zero effect moment. Therefore, one has reason to claim that the measured moment should be much smaller than the highest moment predicted from our first-principles calculation.
TABLE I. Calculated results for Mg-doped BFO: the optimized Mg…Mg distance (dMg-Mg) (A˚ ), the relative energies DE(eV), and total magnetic moment (M) (lB).
(i, j) (0, 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 6)
dMg-Mg 3.86 4.13 5.44 4.36 9.40 13.28
DE 0 0.0056 0.0504 0.0162 0.0644 0.0880
M 0.003 0.019 8.910 0.423 8.306 8.333
FIG. 3. The total electronic density of states for (a) the 2 charge state two-Mg-atom-doped BFO and (b) the charge-neural state two-Mg-atom- doped BFO created by introducing one oxygen vacancy.
FIG. 4. The spin density distributions of (a) perfect BFO, (b) two-Mg-doped BFO in the (110) plane. The Mg and O sites are labeled by dotted and straight circles, respectively.
It is well known that Mg2þhas a similar ion size with Fe3þ, the replacement of Fe3þ by Mg2þions would retain the structure stability. On the other hand, replacing the mag- netic ion with the nonmagnetic one would induce the imbal- ance of magnetic moment, which is the possible source of magnetism, see Fig.4. However, the large magnetization is few reported in experiment, which is attributed to the small energy difference in Mg-doped BFO with the ferromagnet- ism and AFM spin ordering configurations. In particular, the half metallic properties are also presented in Mg-doped BFO, which can degrade ferroelectric polarization. In con- trast, oxygen vacancy introduced in Mg-doped BFO can fur- ther enhance its magnetism and keep the insulating band gap character. Experimentally, a ferroelectric polarization is not reported, the reason may be that some impurity phases could be produced easily during in traditional fabrication pro- cess.11Thus, we hope that our theoretical results predict will inspire further experimental research in Mg-doped BFO with oxygen vacancies for multiferroics.
IV. CONCLUSIONS
In summary, the first-principles calculated results showed that Mg-substitution of Fe would induce the obvious increase of magnetic moment, which is linearly varied as the Mg content increases. The results were very different from the experiment those from the numerical view, but they had the same trend, and the reasons were caused by the small energy differences between spin-ordering configurations. In addition, the change of electrovalence induced by Mg2þ replacing Fe3þ would not seriously affect the magnetic moment. Finally, the multiferroic behaviors would be
improved in Mg-doped BFO through introducing some oxy- gen vacancies because the insulating property (the widen band gap) is not degraded when the magnetism is enhanced greatly. The theoretical results imply that the oxygen va- cancy in Mg-doped BFO would be an effective way to improve the multiferroicity of BFO.
ACKNOWLEDGMENTS
The authors gratefully acknowledge financial support from the National Science Foundation of China (Grant Nos.
51101063, 51272078, and 51332007), and the Natural Science Foundation of Guangdong Province of China (No.
S2011040003205).
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FIG. 5. The magnetic moment comparison among different Mg-doping con- centrations. The red and the blue lines represent the magnetic results in theo- retical calculation and experiment, respectively.
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