Intrinsic multiferroics in an individual single-crystalline Bi₅Fe_0.9Co_0.1Ti₃O₁₅ nanoplate†

Tong Chen ^a, Dechao Meng ^a, Zhiang Li ^a, Jifang Chen ^a, Zhiwei Lei ^a, Wen Ge ^a, Shujie Sun ^a, Dejuan Sun ^a, Min Liu *^abc and Yalin Lu *^abcde
aCAS Key Laboratory of Materials for Energy Conversion; Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, P. R. China. E-mail: liumin1106@ustc.edu.cn; yllu@ustc.edu.cn
^bSynergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, P. R. China
^cHefei Physical Sciences and Technology Center, CAS Hefei Institutes of Physical Sciences, Hefei 230031, P. R. China
^dHefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, P. R. China
^eNational Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230026, P. R. China

First published on 14th September 2017

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1. Introduction

Single phase multiferroic materials that are able to function well at RT, exhibiting simultaneously ferroelectric (FE) and ferromagnetic (FM) ordering, are gaining increasing attention in recent years. The availability of such crystals will not only offer the opportunity to explore interesting physics, but also have potential applications in advanced quantum devices, data storage, sensors, etc.^1–4 However, finding a new single phase multiferroic material is still very challenging, especially at RT, due to the competing electronic requirements for FE and FM.⁵ Empty d-orbitals are the requirement for FE in order to allow cation off-center displacement while FM necessitates an incomplete d-orbital electronic occupation with unpaired electrons. Layer-structured Bi-containing Aurivillius compounds, with a general formula of (Bi₂O₂)²⁺ (A_n−1B_nO_3n+1)²⁻, are formed by perovskite-type (A_n−1B_nO_3n+1)²⁻ blocks sandwiched between fluorite-type (Bi₂O₂)²⁺ slabs, where n is the number of ABO₃ perovskite units per half-cell. The layered structure of such materials allows for the incorporation of magnetic ions with +3 to +5 oxidation states within the nABO₃ perovskite unit,⁶e.g. Co³⁺, Mn³⁺ and Cr³⁺, and therefore the normally conflicting requirement for FM (partially filled d-orbitals, dⁿ) and FE (empty d-orbitals, d⁰) in a single phase can be circumvented. In the Bi₅FeTi₃O₁₅ compound, one such multiferroic material family, a large value of ∼55 μC cm⁻² for the spontaneous electric polarization was predicted by the first-principles electronic structure calculations,⁷ which was also validated by experiments.^8–14 Moreover, after Monte Carlo simulations, it is promising to obtain a magnetic order at higher temperature by increasing the concentration of magnetic cations within the perovskite-like layers.¹⁵ In cobalt (Co) doped Bi₅FeTi₃O₁₅ ceramics, Mao et al. found a magneto-dielectric constant of ∼10.5% at RT, a 2M_r of 51.2 memu g⁻¹ and a 2P_r of 15.4 μC cm⁻².⁸ Remarkably, Wang et al. reported a plausible intrinsic magnetoelectric (ME) coupling in five-layered Aurivillius ceramics, SrBi₅Fe_0.5Co_0.5Ti₄O₁₈, at a high temperature of 373 K, and a RT functioning device was also successfully demonstrated to convert an external magnetic field variation directly into an electric voltage output.⁹ Furthermore, by the nanoscale structural modulation, such ME coupling may be further enhanced due to the appearance of an analogous morphotropic transformation effect.¹⁰ Besides, magnetic-field-induced ferroelectric switching was also observed in the Mn doped Bi₆FeTi₃O₁₈ film,¹³ and a robust ME coupling of ∼400 mV Oe⁻¹ cm⁻¹ was yielded in a magnetically short-range ordered Bi₅FeTi₃O₁₅ film.¹⁴ This sheds light on both research and applications based on single phase multiferroic materials.

In fact, past research on Bi₄Bi_m−3Fe_m−3−xM_xTi₃O_3m+3 (BFMTO, M = Co, Mn, Ni) compounds was mainly focused on making them into ceramics and thin films,^16–26 However, BFMTO single crystals have not been synthesized, which should be the best choice of the material format for further scientific research on the corresponding intrinsic properties,^27–30e.g. multiferroic properties including remanent magnetization (M_r), magnetic coercive field (H_c), ferroelectric/ferromagnetic domains, etc., and also for future quantum device fabrication. Ulteriorly, the more profound physical issues, e.g. the origination of magnetism and magnetoelectric coupling mechanisms, may be elucidated. However, it has been a great challenge to grow high quality bulk BFMTO single crystals though Bi₄Ti₃O₁₂·nBiFeO₃ (n = 1, 2, 4, 5) single crystals without M magnetic ions were reported.³¹ The possible reasons are as follows: (i) BFMTO has a layered structure with a large c axis between fluorite-type (Bi₂O₂)²⁺ and perovskite-like (A_n−1B_nO_3n+1)²⁻, which induces much weaker chemical bonds between them; (ii) during the high temperature crystal growth process, the bismuth element will be much easier to volatilize and this induces the formation of Bi vacancies in the lattice accompanied by the appearance of O vacancies. This could induce the increasing number of stacking faults, and could further collapse the structure; (iii) the doping of M magnetic ions makes the synthesis of single crystals more difficult.

The hydrothermal method includes a one-pot synthesis of pure and uniform single-crystalline nanoparticles much suitably for complex compositions. With this advantage and here in this research, Bi₅Fe_0.9Co_0.1Ti₃O₁₅ (BFCTO) single-crystalline nanoplates were synthesized by the hydrothermal method for the first time: (i) Co(acac)₃ was chosen as the Co source allowing for the valence of the Co element in BFCTO and the reactivity of precursors; (ii) the reaction was performed in alkaline solution due to the strong oxidizability of Co³⁺ in acidic and neutral environments. Besides, electron holography and piezoresponse force microscopy (PFM) were chosen to detect the ferromagnetic and ferroelectric domains in an individual BFCTO nanoplate, respectively. The denser phase contours inside the plate than that outside, the closed magnetic flux lines between the neighboring nanoplates, and anti-parallel ferroelectric domains verify the intrinsic multiferroic properties of BFCTO compounds, very importantly all these were measured at RT. The results not only verified our former conclusions of the room temperature multiferroic behavior in these ceramic materials, but also indicate the first availability of such single crystals.

2. Experimental section

2.1. Synthesis of materials

All chemicals were of analytical grade and were directly used without any treatment. In a typical procedure, stoichiometric amounts of Bi(NO₃)₃·5H₂O, Fe(NO₃)₃·9H₂O and Ti(OC₄H₉)₄ were firstly dissolved in 10 mL diluted HNO₃ under vigorous stirring, and the solution was added dropwise into a concentrated NaOH solution under stirring until a yellow suspension formed. Then Co(acac)₃ dissolved in DMF was added dropwise into the above-mentioned suspension. The concentration of OH⁻ in the suspension was 1 mol L⁻¹. After being stirred vigorously for 40 min, the above-mentioned suspension was transferred into a 100 mL autoclave for hydrothermal treatment at 200 °C for 72 h. Subsequently, it was cooled to room temperature naturally, and the resultant samples were filtered and washed with deionized water and alcohol several times. The final products were obtained after drying at 70 °C for 6 h.

2.2. Characterization

The crystal structure of the synthesized plates was determined by using a powder X-ray diffractometer (XRD, TTR-III, Rigaku) with Cu-Kα (λ = 1.5405 Å) radiation. The morphology of the sample was observed using scanning electron microscopy (SEM, JSM-6700F) and transmission electron microscopy (TEM, JEM-2010). The high resolution transmission electron microscopy (HRTEM) images, selected area electron diffraction (SAED) patterns, scanning transmission electron microscopy-high-angle annular dark field (STEM-HAADF) images, energy dispersive X-ray (EDX) spectra and elemental mapping images were obtained using a TEM (JEM-ARM200F). The electron holography experiment was carried out using a TEM (JEM-2100F), and a biprism was installed to perform the holography experiment. The topography and domain images were investigated using a Bruker Multimode V scanning probe microscope in both atomic force microscopy (AFM) and piezoelectric force microscopy (PFM) modes, respectively. PFM was performed under a modulated sinusoid AC electrical field of 5 V with a SCM-PIT probe (Pt/Ir Coated Tips, 2.8 N m⁻¹, 75 kHz, Pt/Ir Reflective Coating). The corresponding ferromagnetic properties were determined using a Quantum-Design SQUID-VSM system. X-ray photoelectron spectroscopy (XPS) analyses were performed using an ESCALAB 250 system (Thermo Scientific). The Raman spectrum was recorded by using a SPEX-1403 Laser Raman spectrometer equipped with an Ar+ laser (514.5 nm), and the measurement was conducted in the frequency range of 50–1200 cm⁻¹ with a resolution of ∼1 cm⁻¹.

3. Results and discussion

Fig. 1(a) displays the XRD patterns of the obtained sample at room temperature. Strong and sharp diffraction peaks were observed, suggesting that the as-synthesized samples are well crystallized. All patterns indicate the BFCTO characteristic peaks with an orthorhombic structure (with a space group of A2₁am, JCPDS 38-1257). The XRD patterns of the BFCTO sample were also refined by using the Rietveld analysis, where no experimental background signal was deduced, as shown in Fig. 1(a). It can be observed that the fit between the experimental and calculated XRD patterns is relatively better based on the consideration of a lower R_P value of 5.85%. The lattice parameters turn out to be a = 5.4416 Å, b = 5.4361 Å and c = 41.5700 Å. The final refined parameters are shown in Table S1 (ESI†). Fig. S1–S6 in the ESI† show the optimizing process to synthesize BFCTO single-crystalline nanoplates.

The SEM image in Fig. S3 (ESI†) shows that the particles exhibit a uniform well-defined nanoplate morphology. TEM, HRTEM, STEM-HAADF and SAED were also adopted to characterize the microstructures of an individual BFCTO nanoplate. The HAADF images in Fig. 1(b) and (c) show the microstructure of the BFCTO nanoplate along the [100] direction. By measuring the enlarged HAADF image in Fig. 1(b), four perovskite layers can be observed, where three Ti–O layers and one Fe/Co–O layer are sandwiched by two (Bi₂O₂)²⁺ layers, and the lattice parameter c is 4.133 nm, consistent with the above-mentioned XRD result.^32,33 The SAED pattern in the inset of Fig. 1(b) shows regular and sharp diffraction spots, indicating a well-formulated and single-crystalline BFCTO nanoplate. Besides, SAED patterns were also recorded from four corners of the BFCTO plate (the inset of Fig. 1(d)), which exhibited almost identical diffraction spots, corresponding to the (200) and (020) planes. Such results confirm the single-crystalline nature of the BFCTO nanoplate. A typical HAADF image in Fig. 1(e) recorded along the [001] axis of one nanoplate shows the lattice fringes with interplanar spacings of d₁ = 2.738 Å and d₂ = 2.719 Å, attributing to the (200) and (020) planes of the BFCTO orthorhombic phase, respectively. Furthermore, EDX analysis and element mappings were also conducted on one single nanoplate to ascertain the elemental constitution and distribution. As shown in Fig. 1(f), the nanoplate is composed of Bi, Fe, Co, Ti and O, and the metal elements distribute homogeneously in the plate. The atomic ratio of Bi, Fe, Co and Ti is approximately 5:0.9:0.1:3, consistent with the formula of Bi₅Fe_0.9Co_0.1Ti₃O₁₅. Besides, both the Raman spectrum and XPS also confirm the synthesis of pure phase Bi₅Fe_0.9Co_0.1Ti₃O₁₅ (ESI Fig. S8 and 9†).

Upon successfully synthesizing the pure phase BFCTO single-crystalline nanoplate, we are now in a position to verify the multiferroic nature. Electron holography analysis has been widely carried out on multi-layer thin films and magnetic nanocubes.^34,35 Here, it is adopted to confirm the intrinsic ferromagnetism of BFCTO compounds in an individual single-crystalline nanoplate. The object holograms were obtained by using the interference of the object wave passing through the nanoplate and the reference wave passing through a vacuum. The corresponding reference hologram was obtained in the vacuum area far from the plate for accurate reconstruction of the object hologram. The phase shift of the electron wave, which is caused by the integrated magnetic field and the inner potential field along the path of the electron wave, can be reconstructed for the electron hologram by applying Fourier and inverse Fourier transforms (Fig. 2(a)). Fig. 2(b)–(e) show the bright-field TEM image of the BFCTO sample and the corresponding phase reconstruction image. As shown in Fig. 2(c), the phase contours inside the nanoplate are denser than that outside, suggesting the ferromagnetic nature of the BFCTO compound. Besides, to illustrate the magnetic coupling character over tens of nanometers, the stray magnetic field outside the sample was examined. As shown in Fig. 2(e), the closed magnetic flux lines make a significant magnetic interaction between the neighboring nanoplates, which also strongly proves the intrinsic ferromagnetism of the BFCTO compound.

To represent the intrinsic ferroelectric properties of BFCTO compounds, the topography and domain images were also investigated in an individual BFCTO nanoplate by PFM. Fig. 3 shows the topographic image, line profiles and the domain images of an individual BFCTO nanoplate. Fig. 3(a) and (b) show that the BFCTO particle possesses a plate-shaped structure, and the height and the lateral size are determined to be ∼869 nm and ∼3.8 μm, respectively. Domain images were obtained from the white rectangular part with a lateral size of ∼1.1 μm and further topographic characterization shows that it has a smooth surface with a roughness (R_a) of 0.706 nm (ESI Fig. S7(a)†), suggesting that the noise signals from the sample can be ignored for domain imaging. For direct observation of the domain structure, the out-of-plane (OP) and in-plane (IP) piezoelectric signal of the BFCTO plate was detected through a vertical and lateral scanning under non-resonance conditions with a frequency of 50 kHz, respectively. From our mappings, as shown in Fig. 3(c) and (d), both OP and IP phase images show a phase contrast of 180°, indicating that anti-parallel domains exist along the c axis and on the a–b plane, and the BFCTO single-crystalline nanoplate possesses a multi-domain structure. Fig. 3(e) and (f) display the in-phase images of OP and IP, respectively. It can be observed that the piezoelectric signal in-plane is stronger than that out-of-plane, in accordance with the theoretical results.⁷ A spontaneous polarization of ∼55 μC cm⁻² has been predicted in the (001) plane of the Bi₅FeTi₃O₁₅ compound.⁷ Besides, the OP phase image also indicates that the ferroelectric domains’ sizes range from sub-μm to μm. For the IP phase image, the domain configuration seems to be messy, which might be attributed to the complexity of structural details on the ab plane. To acquire a more obvious domain image, the measurement was also performed with a frequency of 320 kHz, under near-resonance conditions, and anti-parallel domains with a phase contrast of 180° and a sharp domain wall further confirm the intrinsic ferroelectric properties of BFCTO (ESI Fig. S7(b) and (c)†). The intrinsic ferroelectricity of BFCTO derives from broken spatial inversion symmetry due to the space group transition from the paraelectric I4/mmm system to the ferroelectric A2₁am structure. There are three kinds of structure distortions included in such a space group transition: (i) an overall displacement of the ions in the (Bi₂O₂)²⁺ layer relative to the ions in the perovskite layer along the in-plane [010] direction and a strong displacement of the B-site cations in the inner perovskite layer relative to the center of their coordination octahedra (ESI Fig. S10(a)†); (ii) “tilts” of the oxygen octahedra within the oxygen octahedra within the perovskite-like layers around the [001] direction (ESI Fig. S10(b) and (c)†).⁷ The HADDF images along the [110] direction further prove such structure distortions, as shown in Fig. S10(d) and (e) (ESI†). Obviously, the B-site cations in perovskite layers are located off-center.

Furthermore, the magnetic hysteresis (M–H) measurements at 300 K and 10 K were also performed under a magnetic field of −1.5 T to 1.5 T, as shown in Fig. 4(a). The M–H curves at 300 K and 10 K exhibit similar hysteresis loops, verifying the ferromagnetic nature of the sample. At 10 K, the remnant magnetization 2M_r and coercive field 2H_c are 0.43μ_B per f.u. and 4.5 kOe, respectively, larger than 0.14μ_B per f.u. and 1.5 kOe of BFCTO at 300 K. Moreover, both magnetization M values increase continuously and slowly and do not saturate under a higher field, implying the appearance of a small amount of the AFM phase, i.e. a superposition of both FM and AFM in our sample. It was proposed that Fe and Co ions occupied Ti sites randomly in the BFCTO sample.³⁶ In our sample, the atom ratio of Co to Fe is very small, i.e. 1:9. Furthermore, a linear extrapolation of M–H to H = 0 at 300 K shows that the spontaneous magnetization is 0.13μ_B per f.u., smaller than the spin difference between the isolated Fe³⁺ (2.5μ_B) and Co³⁺ (2μ_B) ions. Therefore, all the Fe³⁺–O–Fe³⁺, Co³⁺–O–Co³⁺ and Fe³⁺–O–Co³⁺ superexchange interactions probably exist in BFCTO.¹¹ Besides, the observed ferromagnetism in BFCTO can also derive from Dzyaloshinsky–Moriya interactions, due to the spin canting of the Fe(Co) atoms resulting from the titled Fe(Co)O₆ octahedra.^37,38 The ferromagnetic properties resulting from the trace Co–Fe spinel could not be excluded.

To visualize ulteriorly the magnetic properties of the BFCTO sample, the temperature dependence of magnetization in the zero-field-cooled (ZFC) and the field-cooled (FC) modes was also considered in the temperature range of 300–800 K under an applied magnetic field of 500 Oe, as shown in Fig. 4(b). Both the ZFC magnetization (M_ZFC) and FC magnetization (M_FC) curves become divergent with decreasing temperatures. The curve of dM/dT vs. T suggests that the ferromagnetic Curie temperature (T_c) of the BFCTO compound is 730.2 K (see the inset of Fig. 4(b)), much higher than RT, indicating its application potential as multiferroic materials. The temperature dependence of inverse magnetic susceptibility χ_m (1/χ_m = H/M) of BFCTO is shown in Fig. 4(c). For a ferromagnet in the paramagnetic region, the relationship between the χ_m and temperature T should follow the Curie–Weiss law, i.e., χ_m = C_m/(T − θ_p), where C_m is the molar Curie constant, and θ_p is the paramagnetic Curie temperature. The red line is the calculated curve deduced from the Curie–Weiss equation. It is found that the experimental curve in the paramagnetic temperature range can be well described by using the Curie–Weiss law. The paramagnetic Curie temperature θ_p is obtained to be 746.3 K, which coincides with the value of T_c. The Curie constant C_m deduced from the fitting data is 1.19 K cm³ mol⁻¹ for BFCTO. Thus, the effective magnetic moment μ_eff is determined to be 0.573μ_B.³⁹

Conclusions

In conclusion, BFCTO single-crystalline nanoplates were successfully synthesized by the hydrothermal method. To verify the intrinsic ferromagnetic and ferroelectric properties of BFCTO compounds, electron holography and PFM were adopted to characterize the ferromagnetic and ferroelectric domains in an individual single-crystalline nanoplate. Using electron holography, denser phase contours are detected inside the nanoplate, and the closed magnetic flux lines create a significant magnetic interaction between the neighboring nanoplates, strongly proving the ferromagnetic nature of the BFCTO compounds. Furthermore, in an individual single-crystalline nanoplate, the ferroelectric domains are also observed by PFM. Besides, the M–H loops of the BFCTO plates were also investigated. At room temperature, 2M_r, 2H_c and T_c reached 0.43μ_B per f.u., ∼1.5 kOe and ∼730.2 K, respectively. Our research indicates the potential of BFCTO compounds as single phase multiferroic materials.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

The authors are grateful to Xianhui Xu and Weixing Xia from the Ningbo Institute of Industrial Technology, CAS; and Jinlan Peng from the USTC Center for Micro- and Nanoscale Research and Fabrication for the measurements and fruitful discussions in holography observation and PFM, respectively. This work was supported by the National Key Research and Development Program of China, the Ministry of Science and Technology (2016YFA0400904), the External Cooperation Program of BIC, Chinese Academy of Sciences, (211134KYSB20130017), Key Research Program of Chinese Academy of Sciences (KGZD-EW-T06), Hefei Science Center CAS (2015HSC-SRG052, 2015HSC-UE009, 2016HSC-IU004) and the State Key Laboratory of Solidification Processing in NWPU (SKLSP201610).

References

1. R. Ramesh and N. A. Spaldin, Nat. Mater., 2007, 6, 21–29 CrossRef CAS PubMed .
2. C. A. F. Vaz, J. Hoffman, C. H. Ahn and R. Ramesh, Adv. Mater., 2010, 22, 2900–2918 CrossRef CAS PubMed .
3. J. F. Scott, Nat. Mater., 2007, 6, 256–257 CrossRef CAS PubMed .
4. W. Eerenstein, N. D. Mathur and J. F. Scott, Nature, 2006, 442, 759–765 CrossRef CAS PubMed .
5. D. Lebeugle, D. Colson, A. Forget, M. Viret, P. Bonville, J. F. Marucco and S. Fusil, Phys. Rev. B: Condens. Matter, 2007, 76, 024116 CrossRef .
6. P. Boullay, G. Trolliard, D. Mercurio, J. M. Perez-Mato and L. Elcoro, J. Solid State Chem., 2002, 164, 252–260 CrossRef CAS .
7. A. Y. Birenbaum and C. Ederer, Phys. Rev. B: Condens. Matter, 2014, 90, 214109 CrossRef .
8. X. Y. Mao, H. Sun, W. Wang, X. B. Chen and Y. L. Lu, Appl. Phys. Lett., 2013, 102, 072904 CrossRef .
9. J. L. Wang, Z. P. Fu, R. R. Peng, M. Liu, S. J. Sun, H. L. Huang, L. Li, R. J. Knize and Y. L. Lu, Mater. Horiz., 2015, 2, 232–236 RSC .
10. S. J. Sun, Y. Huang, G. P. Wang, J. L. Wang, Z. P. Fu, R. R. Peng, R. J. Knize and Y. L. Lu, Nanoscale, 2014, 6, 13494–13500 RSC .
11. X. Y. Mao, W. Wang, X. B. Chen and Y. L. Lu, Appl. Phys. Lett., 2009, 95, 082901 CrossRef .
12. X. W. Dong, K. F. Wang, J. G. Wan, J. S. Zhu and J. M. Liu, J. Appl. Phys., 2008, 103, 094101 CrossRef .
13. L. Keeney, T. Maity, M. Schmidt, A. Amann, N. Deepak, N. Petkov, S. Roy, M. E. Pemble and R. Whatmore, J. Am. Ceram. Soc., 2013, 96, 2339–2357 CrossRef CAS .
14. H. Y. Zhao, H. Kimura, Z. X. Cheng, M. Osada, J. L. Wang, X. L. Wang, S. X. Dou, Y. Liu, J. D. Yu, T. Matsumoto, T. Tohei, N. Shibata and Y. Ikuhara, Sci. Rep., 2014, 4, 5255 CrossRef CAS PubMed .
15. A. Y. Birenbaum, A. Scaramucci and C. Ederer, Phys. Rev. B: Condens. Matter, 2017, 95, 104419 CrossRef .
16. W. P. Wang, X. Chen, W. Wang, X. X. Guan, Y. Yao, Y. G. Wang and R. C. Yu, Inorg. Chem., 2017, 56, 3207–3213 CrossRef CAS PubMed .
17. T. T. Jia, H. Kimura, Z. X. Cheng, H. Z. Zhao, Y. H. Kim, M. Osada, T. Matsumoto, N. Shibata and Y. Ikuhara, NPG Asia Mater., 2017, 9, e349 CrossRef CAS .
18. J. Yang, W. Tong, Z. Liu, X. B. Zhu, J. M. Dai, W. H. Song, Z. R. Yang and Y. P. Sun, Phys. Rev. B: Condens. Matter, 2012, 86, 104410 CrossRef .
19. J. B. Li, Y. P. Huang, G. H. Rao, G. Y. Liu, J. Luo, J. R. Chen and J. K. Liang, Appl. Phys. Lett., 2010, 96, 222903 CrossRef .
20. M. A. Zurbuchen, R. S. Freitas, M. J. Wilson, P. Schiffer, M. Roeckerath, J. Schubert, M. D. Biegalski, G. H. Mehta, D. J. Comstock, J. H. Lee, Y. Jia and D. G. Schlom, Appl. Phys. Lett., 2007, 91, 033113 CrossRef .
21. Z. W. Lei, Y. Huang, M. Liu, W. Ge, Y. H. Ling, R. R. Peng, X. Y. Mao, X. B. Chen and Y. L. Lu, J. Alloys Compd., 2014, 600, 168–171 CrossRef CAS .
22. Z. W. Lei, M. Liu, W. Ge, Z. A. Li, R. J. Knize and Y. L. Lu, Mater. Lett., 2015, 139, 348 CrossRef CAS .
23. Y. Huang, G. P. Wang, S. J. Sun, J. J. Wang, R. R. Peng, Y. Lin, X. F. Zhai, Z. P. Fu and Y. L. Lu, Sci. Rep., 2015, 5, 15261 CrossRef CAS PubMed .
24. F. X. Wu, Z. Chen, Y. B. Chen, S. T. Zhang, J. Zhou, Y. Y. Zhu and Y. F. Chen, Appl. Phys. Lett., 2011, 98, 212501 CrossRef .
25. W. Bai, C. Chen, J. Yang, Y. Y. Zhang, R. J. Qi, R. Huang, X. D. Tang, C. G. Duan and J. H. Chu, Sci. Rep., 2015, 5, 17846 CrossRef PubMed .
26. Z. Liu, J. Yang, X. W. Tang, L. H. Yin, X. B. Zhu, J. M. Dai and Y. P. Sun, Appl. Phys. Lett., 2012, 101, 122402 CrossRef .
27. T. J. Park, G. C. Papaefthymiou, A. J. Viescas, A. R. Moodenbaugh and S. S. Wong, Nano Lett., 2007, 7, 766–772 CrossRef CAS PubMed .
28. 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 and R. Ramesh, Science, 2003, 299, 1719–1722 CrossRef CAS PubMed .
29. S. H. Baek, et al. , Nat. Mater., 2010, 9, 309–314 CrossRef CAS PubMed .
30. D. Lebeugle, D. Colson, A. Forget and M. Viret, Appl. Phys. Lett., 2007, 91, 022907 CrossRef .
31. H. Y. Zhao, et al. , Adv. Electron. Mater., 2017, 3, 1600254 CrossRef .
32. M. Krzhizhanovskaya, S. Filatov, V. Gusarov, P. Paufler, R. Bubnova, M. Morozov and D. C. Z. Meyer, Anorg. Allg. Chem., 2005, 631, 1603 CrossRef CAS .
33. N. A. Lomanova, M. I. Morozov, V. L. Ugolkov and V. V. Gusarov, Neorg. Mater., 2006, 42, 225 CrossRef .
34. A. Marchewka, D. Cooper, C. Lenser, S. Menzel, H. C. Du, R. Dittmann, R. E. D. Borkowski and R. Waser, Sci. Rep., 2014, 4, 6975 CrossRef CAS PubMed .
35. C. Gatel and E. Snoeck, Nano Lett., 2008, 8, 4293–4298 CrossRef PubMed .
36. H. H. Charles, S. Alan, R. Richard, H. K. Susan, M. Pascal and L. Philip, J. Solid State Chem., 2002, 164, 280–284 CrossRef .
37. I. Dzyaloshinsky, J. Phys. Chem. Solids, 1958, 4, 241–243 CrossRef CAS .
38. T. Moriya, Phys. Rev., 1960, 120, 91 CrossRef CAS .
39. J. Yang, L. H. Yin, D. F. Shao, X. B. Zhu, J. M. Dai and Y. P. Sun, EPL, 2011, 96, 67006 CrossRef .

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7nr04141a

This journal is © The Royal Society of Chemistry 2017