多鐵性 (Bi, Ln)FeO3之結構、磁性及介電性研究

全文

(1)Structural, magnetic and dielectric properties in (Bi, Ln) FeO3 ( Ln = La, Dy) bulks and nanoparticles.. Presented by Yung-Hsiu Tang. Advisors: Jauyn Grace Lin and Hsiang-Lin Liu, Ph.D.. A Master Thesis Submitted for the Degree of Master of Science. Department of Physics. National Taiwan Normal University. June, 2009.

(2) Abstract. Multiferroic bismuth ferrite (BiFeO3 ) has gained a considerable attention from the aspects of technology and fundamental science due to the coexistence of (anti)ferromagnetic and ferroelectric properties (so called multiferroics),which allows an additional degree of freedom for the design of spintronic devices. Moreover, the high transition temperature of BiFeO3 is the most important advantage for application in practice. In this master thesis, we prepared series of Bi1−x Lnx FeO3 (Ln = La and Dy, x = 0 ∼ 0.40) polycrystals by solid state reaction method. Moreover, sol-gel method is used to synthesize pure Bi1−x Dyx FeO3 (x = 0 ∼ 0.40). Their structural, magnetic and dielectric properties are systematically investigated. The crystal structures start transforming from rhombohedral to cubic ones near x = 0.15 for La-series and to orthorhombic ones near x = 0.10 for Dy-series. For samples prepared by solid state method, it is interesting to find that the room temperature magnetization at 20 kOe (Mef f ) for Dy-doped samples are one-order larger compared with that of La-doped samples, which is ascribed to the suppression of cycloidal spin structure. Furthermore, the dielectric constant is enhanced greatly from 68 to 300 with Dy = 0.10 to 0.30, which should be associated with the structural instability during the transformation. Finally, the grain size of Dy- series prepared by sol-gel method is in nanoscale. Those nanoparticles show the possibility of superparamagnetic behavior due to the finite coercive field (Hc ) and exchange bias (He ). At low temperature (10 K), the anharmonic cycloidal spin structure is attributed to the larg Mef f . The restrained leakage problem in nanoscaled Dy- series proves the ability of sol-gel method to control the leakage problem..

(3) Contents 1 Introduction. 1. 1.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1. 1.2. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3. 2 Literatural Review. 7. 3 Experimental technique 3.1. 3.2. 18. Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.1.1. Solid state reaction method . . . . . . . . . . . . . . . . . . . . . . 18. 3.1.2. Sol-gel method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20. Sample characterizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.1. Structural analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 22. 3.2.2. Magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 24. 3.2.3. Dielectric properties . . . . . . . . . . . . . . . . . . . . . . . . . . 25. 4 Results and discussion 4.1. 37. BL(x)FO and BD(x)FO, x = 0 ∼ 0.40 (solid-state method) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37. 4.2. 4.1.1. Structures and morphologies . . . . . . . . . . . . . . . . . . . . . . 37. 4.1.2. Magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 39. 4.1.3. Dielectric properties . . . . . . . . . . . . . . . . . . . . . . . . . . 43. BD(x)FO, x = 0 ∼ 0.40 (Sol-gel method) . . . . . . . . . . . . . . . . . . . 51 4.2.1. Structures and morphologies . . . . . . . . . . . . . . . . . . . . . . 51. 4.2.2. Magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 52. 4.2.3. Dielectric properties . . . . . . . . . . . . . . . . . . . . . . . . . . 54. i.

(4) 5 Conclusion. 99. ii.

(5) List of Figures 1.1. Illustration of time-reversal and spatial-inversion symmetry in ferroics. . .. 6. 1.2. Illustration of relationship between multiferroic and magnetoelectric.. 6. 2.1. Structure of BFO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. 2.2. Neutron diffractions of BFO with wavelengths of neutron beams (a) 9.2. . . .. ˚ A (b) 4.7 ˚ A (c) 3.6 ˚ A. The full circles are the data points and the full curve represents the spectrum calculated for the proposed model of spin configuration [40]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3. Hexagonal arrangement of spin structure of BFO. . . . . . . . . . . . . . . 13. 2.4. A ferroelectric hysteresis loop of BFO thin film measured at a frequency of 15 kHz [45]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14. 2.5. Polarization hysteresis loops of BFO ceramics (a) prepared by sol-gel method at various applied voltages [29]; (b) prepared by sol-gel method and annealed in different gases [34]; (c) with quench process (upper) and without quench process (lower) [50]; and (d) prepared by the rapid liquid phase sintering process and sintered at different temperatures [51]. . . . . . . . . 15. 2.6. Room temperature magnetization hysteresis loops of (a) La-doped BFO, where BLFOx denotes Bi1−x Lax FeO3 (x = 0 ∼ 0.40) [19]; (b) Nd-doped BFO where BNFOx denotes Bi1−x Ndx FeO3 (x = 0 ∼ 0.20), and the inset is the remanet magnetization (Mr ) vs. doping content [10]; and (c) BFO and Bi0.875 Sm0.125 FeO3 [21]. . . . . . . . . . . . . . . . . . . . . . . . . . . 16. iii.

(6) 2.7. (a) Room temperature polarization hysteresis loops of La-doped BFO, where BLFOx denotes Bi1−x Lax FeO3 (x = 0 ∼ 0.40) [19]; (b) room temperature polarization hysteresis loops of Nd-doped BiFeO3 where BNFOx denotes Bi1−x Ndx FeO3 (x = 0 ∼ 0.20) [10]; and (c) frequency dependence of dielectric constant (ε) and loss tangent (tan δ) for BiFeO3 and Bi0.875 Sm0.125 FeO3 [21]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17. 3.1. Schematic experimental setup of this work. . . . . . . . . . . . . . . . . . . 27. 3.2. Flow chart of sample preparation for (a) BFO and (b) Bi1−x Lnx FeO3 , where Ln = La and Dy, by solid state reaction method.. 3.3. . . . . . . . . . . . . . . 28. Simplified chart of sol-gel processes, where ”Gel-Point” means a sol can be transformed into a colloidal (or polymeric) gel by going through what is called a gel-point [53]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29. 3.4. Flow chart of sample preparation for sol-gel method. . . . . . . . . . . . . 30. 3.5. X-ray powder diffraction system (XRD, Bruker D8 advance) at Center for Condensed Matter Sciences, CCMS. . . . . . . . . . . . . . . . . . . . . . . 31. 3.6. Scanning electron microscope (SEM, JSM-6700F) at CCMS. . . . . . . . . 31. 3.7. Superconducting quantum interference device (Quantum Design MPMSXL7) at CCMS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32. 3.8. PPMS system (Quantum design Model 6000) at our lab. . . . . . . . . . . 32. 3.9. Illustration of Josephson junction, where SL and SR are the superconductors at left-hand side and at right-hand side, respectively. The middle ”I” indicates an insulator between two superconductors. ΨL and ΨR are the wavefunctions of superconductors at left-hand side and of the one at right-hand side, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . 33. 3.10 Experimental trace of Jmax vs. magnetic field, showing interference and diffraction effects for two junctions A and B [55]. . . . . . . . . . . . . . . 33 3.11 Arrangement for experiment on macroscopic quantum interference. A magnetic flux Φ passes through the interior of the loop. . . . . . . . . . . . . . 34 3.12 LCR meter (Agilent 4294a) and the home-made probe at our lab. . . . . . 34 3.13 Simplified operation of the auto balancing bridge [54]. . . . . . . . . . . . . 35 3.14 Auto balancing bridge section block diagram [54]. . . . . . . . . . . . . . . 35 3.15 Vector ratio detector section block diagram [54]. . . . . . . . . . . . . . . . 36 iv.

(7) 4.1. XRD patterns of BFO and BL(x)FO where the down triangle are denoted as the impurities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62. 4.2. XRD patterns of BFO and BD(x)FO where the down triangle are denoted as the impurities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62. 4.3. XRD patterns of (102) and (b)(204) peaks. . . . . . . . . . . . . . . . . . . 63. 4.4. SEM graph of BFO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64. 4.5. SEM graph of BL(0.05)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . 65. 4.6. SEM graph of BL(0.10)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . 65. 4.7. SEM graph of BL(0.15)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . 66. 4.8. SEM graph of BL(0.20)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . 66. 4.9. SEM graph of BL(0.30)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . 67. 4.10 SEM graph of BL(0.40)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.11 SEM graph of BD(0.05)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.12 SEM graph of BD(0.10)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.13 SEM graph of BD(0.15)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.14 SEM graph of BD(0.20)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.15 SEM graph of BD(0.30)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.16 SEM graph of BD(0.40)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.17 Room temperature field-dependent magnetization (M-H) curves of BL(x)FO. 71 4.18 Room temperature field-dependent magnetization (M-H) curves of BD(x)FO. 71 4.19 (a) Magnetizations at 20 kOe vs. doping content (b) coercive field (Hc ) vs. doping content, and (c) exchange field (He ) vs. doping content of all samples. The measured magnetization at highest field is called effective magnetization (Mef f ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.20 Room temperature frequency dependent dielectric constant of BL(x)FO and BD(x)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.21 Room temperature dielectric constants measured at 1 MHz of BL(x)FO and BD(x)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.22 Illustration of four polarization mechanisms in a material.. . . . . . . . . . 74. 4.23 Illustration of the relationship between frequency and polarization mechanisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74. v.

(8) 4.24 Room temperature frequency dependent dissipation factor of BL(x)FO and BD(x)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.25 Cole-cole plot of BL(x)FO at 300 K. . . . . . . . . . . . . . . . . . . . . . 76 4.26 Cole-cole plot of BD(x)FO at 300 K. . . . . . . . . . . . . . . . . . . . . . 76 4.27 Illustration of the difference between ideal Debye relaxation and Debye-like relaxation. The solid line is the semicircle of ideal Debye relaxation and the dashed line indicates the Debye-like relaxation. . . . . . . . . . . . . . 77 4.28 Schematic diagram of a complex impedance plot showing arcs due to three different processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.29 Equivalent circuits used to represent the electrical properties of a ceramic sample that exhibits grain (Rg , Cg ) and grain-boundary effects (Rgb , Cgb ). . 78 4.30 α as a function of temperature for BL(x)FO with x = 0.05 ∼ 0.30 and BD(x)FO with x = 0.05 ∼ 0.30. . . . . . . . . . . . . . . . . . . . . . . . . 79 4.31 Frequency dependent dissipation factor at different temperature of BFO. . 80 4.32 Frequency dependent dissipation factor at different temperature of BL(0.05)FO. 81 4.33 Frequency dependent dissipation factor at different temperature of BL(0.10)FO. 81 4.34 Frequency dependent dissipation factor at different temperature of BL(0.15)FO. 82 4.35 Frequency dependent dissipation factor at different temperature of BL(0.20)FO. 82 4.36 Frequency dependent dissipation factor at different temperature of BL(0.30)FO. 83 4.37 Frequency dependent dissipation factor at different temperature of BL(0.40)FO. 83 4.38 Frequency dependent dissipation factor at different temperature of BD(0.05)FO. 84 4.39 Frequency dependent dissipation factor at different temperature of BD(0.10)FO. 84 4.40 Frequency dependent dissipation factor at different temperature of BD(0.15)FO. 85 4.41 Frequency dependent dissipation factor at different temperature of BD(0.20)FO. 85 4.42 Frequency dependent dissipation factor at different temperature of BD(0.30)FO. 86 4.43 Frequency dependent dissipation factor at different temperature of BD(0.40)FO. 86 4.44 Arrhenius plot of dielectric relaxation time τ . . . . . . . . . . . . . . . . . 87 4.45 XRD patterns of BFO and BD(x)FO with x = 0.05 ∼ 0.40. . . . . . . . . . 88 4.46 XRD patterns of rhombohedral (012), orthorhombic (101), and orthorhombic (111) for BFO and BD(x)FO with x = 0.05 ∼ 0.40. . . . . . . . . . . . 88 4.47 SEM graph of BFO-SG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.48 SEM graph of BD(0.05)FO-SG. . . . . . . . . . . . . . . . . . . . . . . . . 90. vi.

(9) 4.49 SEM graph of BD(0.10)FO-SG. . . . . . . . . . . . . . . . . . . . . . . . . 90 4.50 SEM graph of BD(0.15)FO-SG. . . . . . . . . . . . . . . . . . . . . . . . . 91 4.51 SEM graph of BD(0.20)FO-SG. . . . . . . . . . . . . . . . . . . . . . . . . 91 4.52 SEM graph of BD(0.30)FO-SG. . . . . . . . . . . . . . . . . . . . . . . . . 92 4.53 SEM graph of BD(0.40)FO-SG. . . . . . . . . . . . . . . . . . . . . . . . . 92 4.54 Room temperature field-dependent magnetization (M-H) curves of BFO-SS and BFO-SG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.55 Room temperature field-dependent magnetization (M-H) curves of BD(x)FOSG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.56 (a) Magnetizations vs. doping content, (b) coercive field (Hc ) vs. doping content, and (c) exchange field (He ) vs. doping content for BD(x)FO-SS and BD(x)FO-SG. The measured magnetization at highest field is called effective magnetization (Mef f ).. . . . . . . . . . . . . . . . . . . . . . . . . 94. 4.57 Magnetic field-dependent magnetization (M-H) curves of BD(0.40)FO-SG sintered at 550 ◦ C for 1 hour (the solid squares) and sintered at 600 ◦ C for 3 hours (the open squares). . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.58 Field-dependent magnetization (M-H) curves of BD(x)FO-SG at 10 K. . . 96 4.59 (a) Magnetizations vs. doping content, (b) coercive field (Hc ) vs. doping content, and (c) exchange field (He ) vs. doping content for BD(x)FO-SG. . 96 4.60 Room temperature frequency dependent dielectric constant for BD(x)FO-SG. 97 4.61 Room temperature dielectric constants at 1 MHz for BD(x)FO-SG. . . . . 97 4.62 Room temperature frequency dependent dissipation factor at different temperature for BD(x)FO-SG. . . . . . . . . . . . . . . . . . . . . . . . . . . . 98. vii.

(10) List of Tables 1.1. Transition temperatures of different multiferroics. . . . . . . . . . . . . . .. 4.1. Lattice parameters of BL(x)FO with x = 0 ∼ 0.15 and BD(x)FO with x =. 5. 0 ∼ 0.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2. The composition analysis of BL(x)FO. . . . . . . . . . . . . . . . . . . . . 56. 4.3. The composition analysis of BD(x)FO. . . . . . . . . . . . . . . . . . . . . 56. 4.4. The estimated magnetic moment per unit cell, coercive field, and exchange bias of BL(x)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57. 4.5. The estimated magnetic moment per unit cell, coercive field, and exchange bias of BD(x)FO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57. 4.6. The fitted α of grain and grain boundary of BL(x)FO. . . . . . . . . . . . 58. 4.7. The fitted α of grain and grain boundary of BD(x)FO. . . . . . . . . . . . 58. 4.8. Activation energies (Ea ) of grain and grain boundary of BL(x)FO. . . . . . 59. 4.9. Activation energies (Ea ) of grain and grain boundary of BD(x)FO. . . . . . 59. 4.10 Lattice parameters of BD(x)FO-SG with x = 0 ∼ 0.10 and x = 0.30 ∼ 0.40. 60 4.11 The composition analysis of all BD(x)FO-SG. . . . . . . . . . . . . . . . . 60 4.12 The estimated magnetic moment per unit cell, coercive field, and exchange bias of BD(x)FO-SG at room temperature. . . . . . . . . . . . . . . . . . . 61 4.13 The estimated magnetic moment per unit cell, coercive field, and exchange bias of BD(x)FO-SG at 10 K. . . . . . . . . . . . . . . . . . . . . . . . . . 61. viii.

(11) Chapter 1 Introduction 1.1. Overview. ”Multi-ferroics” was first coined to describe the materials with two or all of three ferroic properties: ferroelectricity (FE), ferromagnetism (FM), and ferroelasticity (FEL) in 1994 [1]. Multiferroic materials are very attractive due to their ability to couple either the magnetic or the electric polarization, an extra degree of freedom in applications, and the rare categories of them. It is difficult for ferroelectricity and ferromagnetism to coexist in a oxides [2]. For example, as we know that a magnetic moment (m) is spatial inversion invariant, and a electric moment (p) is time reversal invariant. Therefore, no such symmetries could exist in a multiferroic. Fig. 1.1 shows the different symmetries for general ferromagnetics, ferroelectrics, and multiferroics. However, the original definition was modified slightly by excluding the requirement for ferroelasticity, but including the ferrotoroidic order in recent years. Moreover, the classification of a multiferroic has been broadened to include the antiferroic order [3]. For details, ferroelectric materials possess a spontaneous polarization that is stable and can be switched hysteretically by an applied electric field. Antiferroelectric materials possess ordered dipole moments that cancel each other completely within each crystallographic unit cell. As for (anti)ferromagnetic mate-. 1.

(12) rials, they behave similarly as (anti)ferroelectric materials with the only difference being that the magnetization is switched by applied magnetic field. A special case is the ferrimagnetic materials, differing from antiferromagnets, in which the magnetic moment cancelation is incomplete in such a way that there is a net magnetization switchable by an applied magnetic field. Ferroelastic materials display a spontaneous deformation that is stable and can be switched hysteretically by an applied stress. Ferrotoroidic materials possess a stable and spontaneous order parameter that is taken to be the curl of a magnetization or polarization. By analogy with the above examples, it is anticipated that this order parameter may also be switchable. The difference between magnetoelectric material and multiferroics are shown in Fig. 1.2. Specific device applications that have been suggested for multiferroic materials include the multiplestate memory elements, the electric-field-controlled ferromagnetic resonance devices, and the transducers with magnetically modulated piezoelectricity [4]. Bismuth ferrite (BFO) was first discovered in 1960s [5] which is the most promising system in multiferroics from many aspects. For example, from the fundamental physics points, there has been a resurgence in researches of the multiferroics with identification of three different genres of multiferroic systems in recent years [6]: (1) systems where magnetism and ferroelectricity originate in different sublattices, such as in BFO; (2) systems where commensurate spiral magnetic structure breaks down the spatial inversion symmetry and thereby gives rise to ferroelectricity, such as in TbMnO3 ; and (3) systems where elastic interaction at the interface of ferroelectric-magnetic superlattice structure governs the multiferroicity, such as in BaTiO3 -CoFe2 O4 multilayers. Yet none of these systems exhibit strong coupling between electrical polarization (p) and magnetization (m) near room temperature. On the other hand, for most of multiferroics, either Curie temperature. 2.

(13) (TC ) or N´eel temperature is much lower than room temperature as shown in Tab. 1.1, for example, the TC and TN of HoMnO3 are 875 and 72 K, respectively. However, both the transition temperatures for BFO are much higher than room temperature, a great benefit for practical applications. Besides, the weak ferromagnetic moment coupled to the antiferromagnetic spin ordering is also an advantage making BFO even more attractive for applications. Application of the ferroelectric polarization of BFO in lead-free high-density commercial ferroelectric random access memories (FeRAM) [7, 8] has been demonstrated by Fujitsu [9].. 1.2. Motivation. Regardless of many extensive studies on BFO since 1960s, three obstacles hinder the practical applications in this system [10]: (1) the difficulty in synthesizing the single-phase sample, which is related to the metastable state of BFO and the volatilization of bismuth oxide; (2) the vacancy/impurity-induced conductivity of BFO prevents the FE ordering and reduces the piezoelectric effects; and (3) the weak signal of the weak ferromagnetism related to the space-modulated spin structure. Recent years, many different synthesis methods of forming single-phase BFO are proposed [11] − [15]. Some studies are focus on the synthesis of solid solution of BFO with other perovskite, such as PbTiO3 [16] and Ba(Fe0.5 Nb0.5 )O3 [17]. However, others report the cationic substitutions of various elements including transition metals and rare earth elements. Previous works on lanthanide element at Bi site, i.e. La [18, 19], Pr [20], Nd [10], Sm [21], Gd [22], Tb [23], Dy [24, 25], and Yb [26] have been carried out. It has been demonstrated that the A-site substitution of rare earth elements in BFO can stabilize perovskite phase [27], and suppress the cycloidal spin structure [28] which may leads to the enhancement of the magnetoelectric 3.

(14) (ME) effect. Nevertheless, the methods of substitutions at Bi site are not satisfied with the expectation of impurity-free. Therefore, we substitute the Bi-site with the rare earth elements, La and Dy, not only to stabilize the perovskite phase, but also to investigate the ion-dependency of substitution effects in BFO. Furthermore, the sample prepared with the sol-gel methods which derives from the fine powders is usually more homogeneous and reactive than those prepared by conventional solid-state reaction since the mixing of the reagents is at the atomic-level scale [6], [29] − [35]. The remaining text of this thesis is divided into four sections. Chapter 2 presents a literatural review of BiFeO3 and Bi1−x Lnx FeO3 . In chapter 3 the experimental techniques are described. Chapter 4 is about the experimental results and discussion. Finally, chapter 5 is the conclusion.. 4.

(15) Tab. 1.1: Transition temperatures of different multiferroics. BiF eO3. Y M nO3. HoM nO3. T bM nO3. T bM n2 O5. N i3 V2 O8. TC (K). 1103. 914. 875. 28. 38. 6.3. TN (K). 643. 76. 72. 41. 43. 9.1. 5.

(16) Ferromagnets M. Ferroelectrics P. -M. -P. +. -t. x. -. Spatial inversion invariant. +. Time reversal invariant -M. P +. -t M. -. -. Time reversal M switched P invariant. P +. Multiferroics. M -. -P -. x. +. Spatial inversion M invariant P switched. Fig. 1.1: Illustration of time-reversal and spatial-inversion symmetry in ferroics.. Multi-ferroic Magnetically polarization Ferromagnetism Electrically polarization Ferroelectricity Multiferroic Magnetoelectric. Fig. 1.2: Illustration of relationship between multiferroic and magnetoelectric.. 6.

(17) Chapter 2 Literatural Review In 1957, P. Royen et al. [5] first discovered BFO which is known to have two longrange order parameters: one is the spin ordering of G-type antiferromagnetism with N´eel temperature (TN −AF M ) of 643 K [36], and the other is the polarization ordering [37] with a high Curie temperature (TC−F E ) of 1103 K [38]. Due to the large difference of two transition temperatures, the spin and polarization orderings are believed to be driven by different mechanisms. The hybridization of 6s and 6p atomic orbitals with 6s2 electrons filling one of the resulting orbitals in Bi forms the lone pair in its oxides. The hybridization further causes the lone pair to lose its spherical symmetry and is projected out on one size of the cation, resulting in an asymmetry of the metal coordination and distorted crystal structures [39]. The structure of BFO is a rhombohedrally distorted perovskite structure (a = b = c = 5.63 ˚ A, α = β = γ = 59.4◦ ), belonging to the space group R3c, as shown in Fig. 2.1 with a bimolecular unit cell where the Bi3+ and Fe3+ cations are displaced from their centrosymmetric positions. The centrosymmetric distortion is polar, and results in a spontaneous polarization (Ps ) along [111]c direction, about which axis there is a threefold rotation. The canted G-type antiferromangetic ordering of Fe3+ means that Fe3+ in BFO. 7.

(18) are surrounded by six nearest Fe3+ neighbors, with spin antiparallel to the central ion spin, and gives rise to weak magnetism in BFO at room temperature. Microscopically, the antiferromagnetic spin order is not homogeneous; in fact, an incommensurately modulated spin structure, a cycloidal spin structure, was observed in neutron diffraction studies. Sosnowska et al. [40] derived features of the spin structure from different details in the neutron diffraction patterns as shown in Fig. 2.2. The length of the spiral is derived from the span of the (101) triplet, the orientation of the propagation vector of spin forms the shape of the magnetic peaks and the type of spiral from the intensities of (003) and (101) peaks. Their results revealed that the wavelength (λ) of space-modulated spin structure is about 620 ˚ A, along the [110]h propagation direction and (110)h spin rotation plane. In the incommensurate phase, the periodicity of the spin polarization is incommensurate with the crystallographic lattice parameters. The reason for the space-modulated spin ordering is the absence of inversion symmetry in the crystal and magnetic structure of BFO which also results in linear magnetoelectric effect in BFO. However, the ME effect is averaged to zero due to the fact that the average value of the projection of the antiferromagnetic vector in the cycloidal spin structure is zero. However, the cycloidal structure does not prevent the manifestation of the quadratic magnetoelectric effect [41]. For convenience, the hexagonal arrangement of spin structure is shown in Fig. 2.3, where the hexagonal [001]h direction is equivalent to the pseudocubic [111]c . In BFO, the magnetic moments of the Fe3+ ions turn with the plane perpendicular to the hexagonal basal plane along the propagation direction of the modulated wave. In addition, the spin profile is nearly sinusoidal and the phase of the modulation is a linear function of the space coordinate in the direction of the modulation [40, 42]. Nevertheless, the temperature-dependent NMR studies revealed that the spin profile became more anharmonic as the temperature is. 8.

(19) decreased [43]. The first observation on the ferroelectricity in BFO was from Teague et al. [37]. At room temperature the crystal was too conductive to give a hysteresis loop, such that the measurements were only carried out at around 80 K. The result showed a spontaneous polarization of 3.5 µC/cm2 along the (100) direction and of 6.1 µC/cm2 in the (111) direction, but the saturation of the loop was not observed even at fields as high as 55 kV/cm. The low resistivity makes BFO unsuitable for applications. However, a result of epitaxial BFO thin film, done by J. Wang et al. and grown by pulsed laser deposition (PLD), showed a greatly enhanced ferroelectric polarization at room temperature, about 60 µC/cm2 at 55 MV/m with a saturated hysteresis loop, as shown in Fig. 2.4 [45]. This value consists with the theoretical calculation [44] predicting a large ferroelectric polarization of 90 ∼ 100 µC/cm2 . Since then, much work has been reported on BFO thin films [46] − [49]. As for BFO ceramics, many various synthesis processes are carried out to improve the ferroelectric properties, such as tuning the sintering temperatures, with quench process or not, and different anneal conditions. The typical polarization hysteresis loops of BFO prepared by different processes are shown in Fig. 2.5 [29, 34, 50, 51]. However, the mechanisms of the effects on the enhancement of polarization in BFO for different synthesis methods are still unclear. According to the Figs. 2.5, obviously, the polarizations and the maxima of applied electric fields are still much lower than those of thin films due to the leakage problem in ceramics. Therefore, improving the quality of bulk BFO is still an challenging work for researchers. Due to the interesting magnetic behaviors of rare earth elements, it is attractive to use them as a substitute for bismuth. According to Popov’s theory [52], Kadomtseva et al. reported on the magnetoelectric effect in Rx Bi1−x FeO3 (R = La and Nd), revealing that. 9.

(20) the magnetic rare earth ion (Nd) helps to reduce the critical magnetic field for destroying the cycloidal spin structure [28]. A breakthrough made by Palkar et al. [23] showed the high values of dielectric constant and magnetoelectric coupling at room temperature in Bi0.9−x Tbx La0.1 FeO3 where small amount of La is added to stabilize the perovskite phase of BFO. The Palkar’s success agitates the fevers of researches on rare earth substitution at Bi site in BiFeO3 . Previous works on doping lanthanide element at Bi site have been carried out recently [10], [18] − [26]. It is interesting to note that, based on those observations, the magnetic and dielectric/ferroelectric properties of BFO can be improved in different degree, depending on the mode of structural transformation. For example, Zhang. et al. [19] showed that structures of Bi1−x Lax FeO3 with x ≥ 0.30 are close to the orthorhombic ones which results in the enhanced ME interaction at x = 0.30. Therefore, the structural transformation is the key factor for the great enhancements of magnetization (as shown in Fig. 2.6(a)) and of polarization for Bi0.70 La0.30 FeO3 (as shown in Fig. 2.7 (a)). On the other hand, Yuan et al. [10, 21] reported that Bi0.875 Sm0.125 FeO3 and Bi1−x Ndx FeO3 with 0.05 ≤ x ≤ 0.15 were triclinic structure while those of Bi1−x Ndx FeO3 with 0.175 ≤ x ≤ 0.20 were pseudotetragonal ones. According to Figs. 2.6 (b) and (c), the increasing magnetization in Bi0.875 Sm0.125 FeO3 and Bi1−x Ndx FeO3 is attributed to the collapse of the space-modulated spin structure in the continuing structural transformation. Figs. 2.7 (b) and (c) show the gradual changing polarization with structural transformation in Bi1−x Ndx FeO3 and larger dielectric constant in Bi0.875 Sm0.125 FeO3 . The stronger dipoles in the triclinic structure contributes the enhanced polarization in Bi1−x Ndx FeO3 with 0.05 ≤ x ≤ 0.15 and Bi0.875 Sm0.125 FeO3 . However, it is still not clear how the structural symmetry is related to the activity of Bi 6s2 lone pair.. 10.

(21) Fig. 2.1: Structure of BFO.. 11.

(22) (a). (b). (c). Fig. 2.2: Neutron diffractions of BFO with wavelengths of neutron beams (a) 9.2 ˚ A (b) 4.7 ˚ A (c) 3.6 ˚ A. The full circles are the data points and the full curve represents the spectrum calculated for the proposed model of spin configuration [40].. 12.

(23) Fig. 2.3: Hexagonal arrangement of spin structure of BFO.. 13.

(24) Fig. 2.4: A ferroelectric hysteresis loop of BFO thin film measured at a frequency of 15 kHz [45].. 14.

(25) (a). (c). (b). (d). Fig. 2.5: Polarization hysteresis loops of BFO ceramics (a) prepared by sol-gel method at various applied voltages [29]; (b) prepared by sol-gel method and annealed in different gases [34]; (c) with quench process (upper) and without quench process (lower) [50]; and (d) prepared by the rapid liquid phase sintering process and sintered at different temperatures [51].. 15.

(26) (a). (b). (c). Fig. 2.6: Room temperature magnetization hysteresis loops of (a) La-doped BFO, where BLFOx denotes Bi1−x Lax FeO3 (x = 0 ∼ 0.40) [19]; (b) Nd-doped BFO where BNFOx denotes Bi1−x Ndx FeO3 (x = 0 ∼ 0.20), and the inset is the remanet magnetization (Mr ) vs. doping content [10]; and (c) BFO and Bi0.875 Sm0.125 FeO3 [21].. 16.

(27) (a). (b). (c). Fig. 2.7: (a) Room temperature polarization hysteresis loops of La-doped BFO, where BLFOx denotes Bi1−x Lax FeO3 (x = 0 ∼ 0.40) [19]; (b) room temperature polarization hysteresis loops of Nd-doped BiFeO3 where BNFOx denotes Bi1−x Ndx FeO3 (x = 0 ∼ 0.20) [10]; and (c) frequency dependence of dielectric constant (ε) and loss tangent (tan δ) for BiFeO3 and Bi0.875 Sm0.125 FeO3 [21].. 17.

(28) Chapter 3 Experimental technique In this chapter, we introduce two synthesis methods and several experimental techniques for data analysis. Solid-state-reaction method and sol-gel method are used to prepare samples in micrometer scale and in nanometer scale, respectively. As for techniques, structures are identified by XRD and SEM, SQUID/PPMS is used for magnetic properties, and LCR meter is used to measure the dielectric properties of samples. The experimental flow chart is shown in Fig. 3.1.. 3.1 3.1.1. Sample preparation Solid state reaction method. Solid-state-reaction method is a conventional way to synthesize new materials mainly due to its simplicity, practical effectiveness, and the low cost. “The diffusion between ions” is the principle mechanism of solid state reaction. Standard processes for solid state reaction are as following: First, high purity reagents, such as metallic oxides, are weighted stoichiometrically in a agate motar. Second, those powders are well ground in order to. 18.

(29) reduce the volume of particles and to make the mixture become homogeneous. Third, the mixture is calcined and/or sintered at high temperature to allow the cations being distributed uniformly. After going through the above three steps, the new material is formed. According to this principle mechanism, the quality of sample prepared by solid state reaction is influenced significantly by the uniformities of composition, the particle sizes, and size distributions. Consequently, the crucial factors of solid state reaction method are the properties of reagents, the uniformity of the mixture, the heating/cooling rate, sintering temperature, and sintering time, etc. However, the drawbacks of it are the large grain sizes and the bad uniformity of grain size. Moreover, little alumina of alumina crucible may participate in the reaction during the calcinating which results in multiphase and no-stoichiometric compositions. Bi1−x Lnx FeO3 (Ln = La and Dy, x = 0 ∼ 0.40) polycrystals are prepared by solidstate-reaction method. First, the high purity bismuth oxide (Bi2 O3 ), iron oxide (Fe2 O3 ) and lanthanum/dysprosium oxide (La2 O3 /Dy2 O3 ) are mixed stoichiometrically with some pure alcohol in a mortar. Then, the mixed powders are dried at 50 ◦ C in the furnace for 5 hours. For undoped BiFeO3 , powders are calcined in air at 500 ◦ C for 1 hour and at 850 ◦ C for 2 hours. Finally, the powders are pressed to pellets and sintered at 850 ◦ C for 4 hours. On the other hand, for La-doped and Dy-doped series, all powders are calcined for 2 hours at 870 ◦ C for x = 0 ∼ 0.10 and at 890 ◦ C for x = 0.15 ∼ 0.40, respectively. After pellets are formed, all samples are sintered at 890 ◦ C [18]. The flow chart of sample preparation for solid state reaction method is shown in Fig. 3.2. The samples of Bi1−x Lax FeO3 and Bi1−x Dyx FeO3 are denoted as BL(x)FO, and BD(x)FO respectively in the following text.. 19.

(30) 3.1.2. Sol-gel method. Sol-gel processing offers the most outstanding advantages for mixed oxides systems in which the chemical homogeneity of the various elements can be controlled down to the atomic level. The general definition of sol-gel process is a colloidal route used to synthesize ceramics with an intermediate stage including a sol and/or a gel state [53]. Before knowing the sol-gel process, three important terminuses one must known: (1) sol: a stable suspersion of colloidal solid particles within a liquid is called a sol [54]; (2) gel: an porous 3-dimensionally interconnected solid network that expands in a stable fashion throughout a liquid medium and only limited by the size of the container is called a gel; (3) gelation: a gel forms when the homogenous dispersion presents in the initial sol rigifies. This process, called gelation, prevents the development of inhomogeneities within the material. Many variations can be brought to the sol-gel synthesis of ceramics. In fact, sol-gel processing does not only designate a unique technique, but a very broad type of procedures that centralizes around a single scheme as presented in Fig.3.3. The first step of sol-gel process always consists of selecting the precursors of the wanted materials. It is the precursor that, by its chemistry, lead the reaction towards the formation of either colloidal particles or polymeric gels. In the case that the material is composed of several components, the use of a combination of different precursors and procedures can enhance various types of chemical synthesis and hence various products. The colloidal particles obtained can then be precipitated and treated following the conventional processing techniques, such as sintering, in order to produce the desired ceramic. There are many advantages of sol-gel method, including: (1) very pure products are obtained by simply purifying the precursors either by distillation, crystallization, or electrolysis; (2) the kinetics of the. 20.

(31) various chemical reaction can be easily controlled by the low processing temperatures and by the often dilute conditions; (3) the nucleation and growth of the primary colloidal particles can also be controlled in order to give particles with a given shape, size and size distribution. However, the greatest limitation of sol-gel synthesis is that this process will never be suitable for the mass production. Therefore, sol-gel processing becomes much more interesting for highly advanced ceramics. Bi1−x Dyx FeO3 (x = 0 ∼ 0.40) nanoparticles are prepared by sol-gel method. Bismuth nitrate (Bi(NO3 )3 ·5H2 O), ferric nitrate (Fe(NO3 )3 ·9H2 O), citric acid monohydrate (COOHCH2 C(OH)(COOH)CH2 COOH·H2 O, and ethylene glycol (C2 H6 O2 ) are dissolved in distilled (DI) water stoichiometrically as the precursor solution, where the ratio of citric acid to ethylene is 7:3. The pellucid solution is heated at 50 ∼ 60 ◦ C with constant stirring to avoid precipitation and to obtain a homogeneous mixture. Then, temperature increases to 80 ∼ 90 ◦ C, a brown gel is formed after water evaporating. The brown gel is dried in furnace at 120 ◦ C. The dried powders are well ground and calcined in air at 550 ◦ C for 1 hour. To eliminate the unwanted impurity phases, the calcined powders are leached with diluted nitric acids (0.05 M), which is known to be an effective way to eliminate the impurity phases in BiFeO3 . The leached powders are dried at 120 ◦ C for 3 hours. Finally, the powders are pressed to pellets and sintered at 550 ◦ C for 1 hour. The flow chart of sample preparation for sol-gel method is shown in Fig. 3.4.. 21.

(32) 3.2 3.2.1. Sample characterizations Structural analysis. The crystalline structures of samples are determined by using the x-ray diffraction (XRD) (Bruker D8 advance, as shown in Fig. 3.5) with Cu Kα1 radiation (λ = 1.56056 ˚ A). To get the data efficiently, the detector of XRD is set for high speed and high sensitivity with a PSD detector of which resolution is about 0.03 ◦ . The operating voltage is 40 kV and the operating current is 40 mA. The scanning range (2θ) is from 20◦ to 80. ◦. with a. scanning rate of 1.5 ◦ /min (scanning increment is 0.01◦ ; scanning speed is 0.4 s/step). XRD patterns vary with different materials, just like our fingerprints. Therefore, they are used for determining the structures of materials. The operating principle of XRD is based on Bragg law, which will be described as following. Assuming that the incident radiation is reflected specularly from parallel planes of atom in a crystal, the diffraction beams are found when the reflections interfere constructively. For the occurrence of constructive inference, two conditions have to be satisfied: one is the same phase of the reflections from the successive planes, and the other is that the path difference is an integral number n of wavelength λ, so that. 2d sin θ = nλ,. (3.1). This is the Bragg law, which can be satisfied only for wavelength λ ≤ 2d, where θ is measured as the angle from the plane, and d the spacing of successive plane [55]. The constraints on observing diffraction patterns are not only the requirements for Bragg’s law but also those for extinction conditions. For unit cells containing more than one atom, 22.

(33) the symmetry of the atoms determine the specific positions of diffraction peaks, called extinction conditions. Therefore, when a monochromatic light is incident in a crystal, the diffraction peaks can only be found at several specific incident angles which is determined by the shape and the volume of the unit cell as well as the symmetry. In addition, the different crossection for scattering x-ray at different atomic site lead to different intensity of diffraction peaks. Hence, even for the materials with single structure, the intensity distributions at different angles are different from each other. In conclusion, two factors provided in XRD, the positions of diffraction peaks and the intensities of diffraction peaks, reveal different information. The former one tells us the structure and the volume of a unit cell. On the other hand, the later one prevails the types of atoms and the positions of atoms. Scanning electron microscopy (SEM) micrograph is taken with a filed emission scanning electron microscope (FESEM) (JSM-6700F, as shown in Fig. 3.6). SEM is a type of electron microscope capable of producing high-resolution images of a sample surface. Due to the manner in which the image is created, SEM images have a characteristic of three-dimensional image and are useful for judging the surface structure of the sample. The range of accelerating voltages and magnifications of our SEM images are 5 ∼ 10 kV and 3,000 ∼ 10,000 times, respectively. In a typical SEM, the most common imaging mode monitors low energy (<50 eV) secondary electrons. Due to their low energy, these electrons originate from a few nanometers depth from a surface. The electrons are detected by a scintillator-photomultiplier device and can be viewed and saved as a digital image. This process relies on a raster-scanned primary beam. The brightness of the signal depends on the number of secondary electrons reaching the detector. If the beam enters the samples perpendicular to the surface, then. 23.

(34) the activated region is uniform about the axis of the beam and a certain number of electrons “escape” from within the sample. As the angle of incidence increases, the “escape” distance of one side of the beam decreases, and more secondary electrons are emitted. Thus steep surfaces and edges tend to be brighter than the flat surfaces, which results in images with a well-defined, three-dimensional appearance. Using this technique, resolutions less than 1 nm are possible. The spatial resolution of the SEM depends on the size of the electron spot which in turn depends on the magnetic electron-optical system which produces the scanning beam. The resolution is also limited by the size of the interaction volume, or the extent to which the material interacts with the electron beam. The spot size and the interaction volume are both very large compared to the distances between atoms, such that the resolution of the SEM is not high enough to image down to the atomic scale. However, the SEM has compensating advantages including the ability to image a comparatively large area of the specimen; the ability to image bulk material, and the variety of analytical modes available for measuring the composition and the nature of the specimen. Depending on the instrument, the resolution can fall somewhere between 1 and 20 nm.. 3.2.2. Magnetic properties. Magnetic measurements are carried out with the superconducting quantum interference device (SQUID, MPMS-XL7, Quantum Design, as shown in Fig. 3.7) and physical property measurement system (PPMS, Quantum Design Model 6000, as shown in Fig. 3.8). Several specifications of SQUID and PPMS are: the maximum of applied magnetic field is ± 7.0 T, the measuring temperature range is 2 ∼ 400 K, and the sensitivity is 10−8 emu. In this work, the magnetization are measured at 10 K and 300 K in field ±50 and. 24.

(35) ±20 kOe, respectively. SQUID is a very sensitive magnetometers based on superconducting loops containing Josephson junctions. A Josephson junction is a weak link between two individual superconductors separated by a insulator, as shown in Fig. 3.9. According to Quantum mechanism, if the potential barrier between two separated superconductors is finite, the cooper pairs can go through the barrier, resulting in a tunneling current. The effects of pair tunneling include [55] (1) dc Josephson effect: a dc current flows through the junction without electric or magnetic field; (2) ac Josephson effect: a dc voltage applied through the junction causes a rf current oscillation through the junction. Moreover, applying both a rf voltage and a dc current simultaneously cause a dc current through the junction; and (3) macroscopic long-range quantum interference: a dc magnetic applied in the superconducting circuit containing two junctions results in the maximum of current intensity with an interference effect as a function of magnetic field, as shown in Fig. 3.10. This effect can be utilized in a sensitive magnetometer, as shown in Fig. 3.11.. 3.2.3. Dielectric properties. Dielectric properties are measured by LCR-Meter (Agilent 4294A) with a homemade probe, as shown in Fig. 3.12. In the beginning, the samples are coated with a layer of silver about 30-nm thick on the top and bottom surfaces by a manual high resolution sputter. The conditions for coating silver on surfaces are as following: pressure = 4 × 10−2 mbar, operating voltage = 2 kV, current = 20 mA, time = 7 min. The as-prepared samples agglutinate with copper leads by silver paint. Finally, pellets are fixed on the home-made probe. The measured frequency range is from 40 Hz to 1 MHz and the oscillation level is 0.5 V.. 25.

(36) The impedance measurement methods of 4294 a is “auto balancing bridge method” [54]. The auto balancing bridge balances the range resistor current with the device under test (DUT) current to maintain a zero potential at the low terminal. Figure 3.13 shows a simplified block diagram of the bridge section. The detector D detects potential at the low terminal and controls both magnitude and phase of the OSC2 output, so that the detected potential becomes zero. The actual balancing operation is shown in Fig. 3.14. When the bridge is “unbalanced”, the null detector detects an error current and the phase detectors, at the next stage, separate it into 0◦ and 90◦ vector components. The output signals of the phase detectors go through loop filters (integrators) and are applied to the modulator to drive the 0◦ and 90◦ component signals. The resultant signal is amplified and fed back through range resistor Rr to cancel the current through the DUT, therefore no error current flows into the null detector. This balancing operation is performed automatically over the full frequency range of 40 Hz to 110 MHz. The section responses for the data analysis in 4294 is the vector ratio detector section. The vector ratio detector measures two vector voltages across the DUT (Edut) and range resistor Rr (Err) series circuit (as shown in Fig. 3.15). Since the range resistor value is known, measuring two voltages will give the impedance vector Zx of the DUT by Zx = Rr × (Edut/Err). Selector S1 selects either the Edut or Err signal so that these signals alternately flow identical paths to eliminate tracking errors between the two signals. Each vector voltage is measured using an A to D converter and separated into its 0X and 90X components by digital processing. We figure out the capacitance of DUT by Cp mode (R parallel to C) because of the rather high resistance of DUT.. 26.

(37) Sample preparation. Structure Identification XRD. Morphology SEM. Magnetic Properties SQUID, PPMS. Dielectric Properties LCR meter. Fig. 3.1: Schematic experimental setup of this work.. 27.

(38) (a). (b). BiFeO3. Bi1-xLnxFeO3 Bi2O3 ﹢ Fe2O3 ﹢Ln2O3. Bi2O3 ﹢ Fe2O3. (Dried at 50 ℃ for 5 h). (Dried at 50 ℃ for 5 h) 5 ℃/min. 500 ℃ for 1 h. 5 ℃/min. 5 ℃/min. 850 ℃ for 2 h. 5 ℃/min. 5 ℃/min. (Pellet). (Pellet) 5 ℃/min. 850 ℃ for 4 h. 870 ℃ (2h) for x<0.15 890 ℃ (2h) for x≧0.15. 5 ℃/min. 5 ℃/min. 890 ℃ for 4 h 5 ℃/min. 5 ℃/min. Ln = La and Dy. Fig. 3.2: Flow chart of sample preparation for (a) BFO and (b) Bi1−x Lnx FeO3 , where Ln = La and Dy, by solid state reaction method.. 28.

(39) Fig. 3.3: Simplified chart of sol-gel processes, where ”Gel-Point” means a sol can be transformed into a colloidal (or polymeric) gel by going through what is called a gel-point [53].. 29.

(40) Bi(NO3)3‧5H2O ＋ Dy(NO3)3‧5H2O ＋ Fe(NO3)3‧9H2O Citric acid ＋Ethylene glycol Transparent solution 50 ~ 60 ℃. Gel. 80~90 ℃. (dehydrated at 120 ℃) (sintered at 550 ℃ for 1 hr) (leached with NHO3 0.05 M) (pellet) (sintered at 550 ℃ for 1hr) Fig. 3.4: Flow chart of sample preparation for sol-gel method.. 30.

(41) Fig. 3.5: X-ray powder diffraction system (XRD, Bruker D8 advance) at Center for Condensed Matter Sciences, CCMS.. Fig. 3.6: Scanning electron microscope (SEM, JSM-6700F) at CCMS.. 31.

(42) Fig. 3.7: Superconducting quantum interference device (Quantum Design MPMS-XL7) at CCMS.. Fig. 3.8: PPMS system (Quantum design Model 6000) at our lab.. 32.

(43) SL. I. SR. ΨL. ΨR Z. Fig. 3.9: Illustration of Josephson junction, where SL and SR are the superconductors at left-hand side and at right-hand side, respectively. The middle ”I” indicates an insulator between two superconductors. ΨL and ΨR are the wavefunctions of superconductors at left-hand side and of the one at right-hand side, respectively.. Fig. 3.10: Experimental trace of Jmax vs. magnetic field, showing interference and diffraction effects for two junctions A and B [55].. 33.

(44) Insulator a. Ja. Jtotal. B. 2. 1. Jb Insulator b Fig. 3.11: Arrangement for experiment on macroscopic quantum interference. A magnetic flux Φ passes through the interior of the loop.. (a). (b). Fig. 3.12: LCR meter (Agilent 4294a) and the home-made probe at our lab.. 34.

(45) Fig. 3.13: Simplified operation of the auto balancing bridge [54].. Fig. 3.14: Auto balancing bridge section block diagram [54].. 35.

(46) Fig. 3.15: Vector ratio detector section block diagram [54].. 36.

(47) Chapter 4 Results and discussion. 4.1. BL(x)FO and BD(x)FO, x = 0 ∼ 0.40 (solid-state method). In this section, we discuss the data of the x-ray powder diffraction (XRD), morphology, magnetic, and dielectric measurements for BL(x)FO and BD(x)FO which are prepared by the solid-state method.. 4.1.1. Structures and morphologies. Figures 4.1 and 4.2 show the XRD patterns of BL(x)FO and BD(x)FO samples, respectively. All diffraction peaks are indexed on the basis of the rhombohedral structure. By doping the lanthanide element up to 10 %, the impurities marked by down triangles in Figs. 4.1 and 4.2 are eliminated. Figures 4.3 (a) and (b) present the splitting of XRD peaks (012) and (024) for both BL(0.20)FO and BD(0.10)FO. It indicates a structural transformation starting from x = 0.15 for BL(x)FO while from x = 0.10 for BD(x)FO. With examining all the XRD patterns carefully, it is found that the structures transform 37.

(48) to different symmetries for BL(x)FO and BD(x)FO: BL(x)FO with x ≥ 0.20 transform to higher symmetries, closer to the cubic structure, of which the space group is I¯43d. In contrary, those of BD(x)FO with 0.10 ≤ x ≤ 0.20 transform to lower symmetry with R3 group. With further increasing of Dy content, the structures transform to orthorhombic ones at x ≥ 0.30. Our results reveal that the doping level to induce the structural transformation is lower for Dy (rDy3+ = 0.912 ˚ A) than that for La (rLa3+ = 1.032 ˚ A). This phenomenon may be associated with the smaller ion radii of Dy, which is consistent with previous reports [10, 20, 21, 26]. We refine the crystal structures of low doped (x ≤ 0.15) samples with a space group of R3c by using the program of general structure analysis system (GSAS). Lattice parameters are shown in Tab. 4.1 for BL(x)FO with x = 0 ∼ 0.15 and BD(x)FO with x = 0 ∼ 0.10, revealing that the lattice constants reduce slightly with increasing the doping concentration while the bond angles show an opposite tendency, indicating that the doping of rare earth element enhances the structural distortion. Scanning electron microscopy (SEM) images of all samples are shown in Figs. 4.4 to 4.16. Based on these pictures, the average grain size of BFO is the largest among all, about 40 µm, suggesting that the doping of La and Dy reduce the grain sizes. The sizes are about 2 ∼ 10 µm for BL(x)FO, while only 2 ∼ 5 µm for BD(x)FO. For the same doping concentration, average grain size of Dy-doped sample is smaller than that of La-doped samples. Moreover, the grain shapes of La-doped samples are hexagons-like, but those for Dy-doped samples change to pebble-like shapes. The energy dispersive spectrometer (EDS) data provide the atomic compositions of each samples as shown in Tabs. 4.2 and 4.3, revealing that the ratio of A-site and B-site atoms in this ABO3 -system is close to 1:1. In addition, the resultant doping concentration is consistent with the nominal composition.. 38.

(49) 4.1.2. Magnetic properties. Figures 4.17 and 4.18 are the room temperature magnetic field-dependent magnetization (M-H) curves with a maximum magnetic field of 20 kOe for BL(x)FO and BD(x)FO samples. The undoped BFO shows the linear magnetic behavior, consistent with previous reports [10, 19, 21]. However, all doped samples present the weak ferromagnetic behaviors. The estimated magnetic moment per unit cell of BFO is 0.01 µB per unit cell, while those of BL(x)FO are 0.0017, 0.0086, 0.0105, 0.0116, 0.0228, and 0.0234 µB for x = 0.05, 0.10, 0.15, 0.20, 0.30, and 0.40, respectively. For BD(x)FO samples with x = 0.05, 0.10, 0.15, 0.20, 0.30, and 0.40, the magnetic moments are 0.0209, 0.0285, 0.0537, 0.0767, 0.1114, and 0.1608 µB , respectively. The magnetization versus x is shown in Fig. 4.19 (a). Worth noticing is that the doping of Dy enhances the magnetizations more effectively than La. It is wildly believed that the latent magnetization locked within the cycloidal spin structure would be released and a significant enhancement of magnetization could be observed when the cycloidal spin structure is suppressed or destroyed [10, 19, 21, 22, 56]. It was also reported that breaking of translational symmetry of the spiral spin modulation might be achieved by the substituent effect in perovskites [57]. To understand the mechanism of doping enhanced magnetization, the Landau-Ginzburg(LG) formalism for the free energy, is considered as following:. F = FL + Fexch + Fan + Fm ,. (4.1). where FL is the magnetoelectric coupling that is linear in gradient, in which the Lifshitz invariant is responsible for the creation of the spatially modulated spin structure, Fexch is the inhomogeneous exchange energy, Fan is the anisotropy energy, and Fm is the magnetic. 39.

(50) energy. In the expression of the long-range ordering, the contributions of the linear term in the derivatives of the order parameter are of great importance. Such kind of term has been recognized to be fundamental in governing the spatially modulated spin structures in magnetic materials. In BFO, the space-modulated spin structure is due to the coupling of the spontaneous electric polarization with the magnetic order parameter, taking the form of a Lifshitz invariant. The magnetic order can be characterized by the antiferromagnetic vector [58]:. L = v0−1. X (−1)i Mi ,. (4.2). i. where Mi are the magnetic moments of the six Fe ions of a unit cell, and v0 is the unit-cell volume. The sum index is running over all Fe ions of the unit volume. The vector L is the principal order parameter of BFO, the antimagnetic vector, and thus the free-energy density of the system, assumed as continuously distributed, is written as. f =A. X. (∇Li )2 + α ˜ Pz. i=x,y,z. X. Lj − Lz,j − Kµ L2z ,. (4.3). j=x,y. where A is the exchange stiffness of magnetic material and α ˜ is the nonhomogeneous relativistic constant. Pz is the polarization and Kµ the constant of uniaxial anisotropy. The notation Li,j indicates the derivatives of the i component with respect to the j variable. The second term of Eq. 4.3 is a Lifshitz-type invariant responsible for the modulated structure in this material. The leading contribution to the free energy is given by the exchange energy. A. X. (∇Li )2 = A. i. X (∇Li,j )2 . i,j. 40. (4.4).

(51) In a material without the inversion center in the crystal structure, such as BFO, the major contribution to the free energy, linear on the first derivatives of the order parameter, comes from the Lifshitz invariant term. Therefore, the second term in Eq. 4.3, the Lifshitz invariant, is responsible for the existing of the modulate spin structure in BFO. The components of the antiferromagnetic vector, in a polar reference frame, can be written as. Lx = L sin θ cos φ,. (4.5a). Ly = L sin θ sin φ,. (4.5b). Lz = L cos θ,. (4.5c). where θ and φ are the polar and azimuthal angles, defined in the usual way in the coordinate system. Therefore, the free-energy density of the cycloid structure of BFO is in the following form:. f = A[(∇θ)2 + sin2 θ(∇φ)2 ] + α ˜ Pz sin2 θ(θx0 cos φ + θy0 sin φ) + Kµ sin2 θ.. (4.6). The spin-density-wave solution is given by θ = q · r where q is the spiral propagation vector. Minimizing the free energy of the crystal and taking the Lifshitz invariant into account, it is found that the space-modulated spin structure (SSMS) to be expressed as. θ = qx X + qy Y, φ = arctan(. 41. qx ), qy. (4.7).

(52) To describe the homogeneous antiferromagnetic state (HAFS), which minimizes the free energy, the solutions are θ = const., and φ = const.. Averaging over the volume, one obtains. FSSM S. 1 = V. Z. dV A(∇θ)2 + sin2 θ(∇φ)2 + α ˜ Pz sin2 θ(θx0 cos φ + θy0 sin φ) + Kµ sin2 θ (4.8). = Aq 2 −. Kµ α q+ , 2 2. (4.9). where α = α ˜ Pz which is the nonhomogeneous relativistic exchange constant, assumed to be proportional to Pz . The value of q, minimizing the free energy, is then obtained as. q0 =. α . 4A. (4.10). The energy gain in the SSMS is. ∆F (q0 ) = F (q0 ) − F (0) = −Aq 2 +. Kµ < 0. 2. (4.11). Because the stable SSMS is realized in the BFO, relation in 4.11 imposes a finite wave vector q0 to the SSMS. Based on previous report, the doping of rare elements can reduce the value of Aq2 ; moreover, doping the magnetic ions reduces Aq2 greater than doping the non-magnetic ions [28]. In addition, Kµ can be tuned by the changing of structure. The phase transition to the homogenous state takes place when the modulated structure becomes energetically unfavorable. Therefore, the magnetizations of doped samples are larger than that of pure. 42.

(53) BFO. Different from La3+ which is a non magnetic ion, the magnetic moment of Dy3+ is the largest among the rare earth ions. According to XRD results, it is known that the structures of La-doped samples are more symmetric than those of Dy-doped samples; thus Kµ of La-doped sample is smaller than that of Dy-doped sample. Consequently, Dydoping suppresses or destroys the cycloidal spin structure more effectively than La-doping. The collapse of cycloidal spin structure enhances the ME interaction [41, 57], leading to the significant enhancements of magnetization for BL(x)FO with x ≥ 0.30 and BD(x)FO with x ≥ 0.15. Figures 4.19 (b) and (c) show the coercive field (Hc ) and the exchange field (He ) as the functions of x, respectively. The BFO, BL(x)FO, and BD(x)FO with x ≤ 0.15 all present large Hc at the order of kOe. While BD(x)FO with x ≥ 0.20 present small coercive field for only several Oe. On the other hand, only BD(x)FO with x ≥ 0.20 reveal positive He while others reveal negative He . The values of magnetization (at 20 kOe), coercive field, and exchange bias of BL(x)FO and BD(x)FO are presented in Tabs. 4.4 and 4.5. The negative He was first observed in 1956 [59], and was associated with the existence of ferromagnet/antiferromagnet interface. The reason of observing positive exchange biases in the BD(x)FO with x ≥ 0.20 may be the freezing of canting spins at the temperature close to TN [60]. Until now, the mechanisms of unusual positive exchange bias are still under debate.. 4.1.3. Dielectric properties. Figure 4.20 shows the room temperature frequency-dependent dielectric constants. The strong frequency-dependent dielectric constant, considerably high value at low frequency and low value at high frequency, may be due to the Maxwell-Wagner (M-W) polarization effect. M-W polarization effect often occurs in the heterogeneous systems in which the. 43.

(54) component dielectrics have different conductivities. Both of a depletion layer between a sample and electrode, and the interfacial layer of a grain boundary and/or domain boundary can produce the effect [61, 62]. When an electric current passes through the interface between different dielectric media, the surface charges piling up at the interface result in increasing the dielectric constant at low frequency and give rise to a Debye-like relaxation under an external applied field. For this reason, the large dielectric constant at low frequency is considered as the contribution of the inability of these surface charges to be in step with the frequency of the applied field. On the other hand, the dielectric constants at high frequency are regarded as the intrinsic dielectric constants. Figure 4.21 shows x-dependent dielectric constants at 1 MHz. The dielectric constant at 1 MHz for BFO is about 68, and for BL(x)FO is at the range of 89 ∼ 111. Particularly, the large structural distortion due to the large different radius between Bi3+ (rBi3+ = 1.030 ˚ A) and Dy3+ (rDy3+ = 0.912 ˚ A) induces more dipoles and results in the large dielectric constants observed, about 300, for BD(x)FO with x = 0.15 ∼ 0.30. For dielectric materials, the value of dielectric constant is determined by the polarized ability of a material. When one applies the electric field on a parallel capacitor, the stored charges(Q) can be presented as Q = CV where C is the capacitance of a capacitor, and V is the voltage (V). Two factors influence the capacitance: material and the geometry of a capacitor. In vacuum, the capacitance of a parallel capacitor is defined as. A C 0 = ε0 , d. (4.12). where A is the area of a capacitor, d is the thickness of the capacitor, and ε0 is the permittivity in vacuum and is a constant of 8.854×10−12 (F/m). If we put a dielectric material. 44.

(55) with permittivity ε into the parallel capacitor, the new capacitance can be calculated as. C = C0. ε = C0 κ, ε0. (4.13). where κ is the dielectric constance of a material. There are four kinds of polarized mechanisms contributing to the dielectric properties of a material: space charges polarization, dipolar polarization, ionic polarization, and electric polarization. Space charge polarization is the gathering and distribution of space charges on interfaces along the direction of applied electric field. Dipolar polarization (also called orientation polarization) is due to the electric dipoles aligning along the direction of the applied field when the filed is applied on a polarized molecular. Ionic polarization is the stretch of positive and negative ions in the crystal. Electric polarization occurring in every material is attributed to the electron cloud elongate along the direction of applied electric field. In principle, the measured polarization in a material is the sum of those four mechanisms as shown in Fig. 4.22. The cut-off frequency, the critical frequency for each mechanism to activate, is different from each other. For electric polarization, it is about 1014 ∼ 1018 Hz; while it is 1010 ∼ 1014 Hz for ionic polarization. The one for dipolar polarization is about 108 Hz, and the spaces charge dominates at low frequency about 102 Hz. According to Fig. 4.23, we know that in our measurement range, 40 Hz to 1 MHz, the electric response is the combination of space charge and dipolar mechanisms. Figure 4.24 shows the room temperature frequency-dependent dissipation factor of all samples. BL(x)FO with x = 0.05 ∼ 0.30, and BD(x)FO with x = 0.05 ∼ 0.30 show two resonance peaks in this measured frequency range. The two observed relaxations suggest two different conductivities components coexisting in these samples, referred to as Maxwell-Wagner relaxations. Particularly, BL(0.40)FO and BD(0.30)FO show tails 45.

(56) at low frequency indicating the leakage problem in those two samples. The dissipation factor (also called loss tangent, tanδ) and the dielectric quality factor (Q) are the other two important dielectric parameters. When the flipping rate of the dipolar can’t follow the changing rate of applied electric field, the total energy of electric field could not be transferred for the polarization effect, that is, the energy loss. Therefore, the energy loss is called loss tangent. In other words, a electric displacement (D) is behind a phase δ resulting in a dielectric loss when the AC electric field (E) is applied on a material. For dielectric materials, the complex permittivity is defined as ε∗ = ε0 - iε00 . Furthermore, the loss tangent is defined as. tanδ =. ε00 , ε0. (4.14). where ε0 and ε00 are the real part and imaginary part of complex permittivity, respectively. Hence, the tanδ can be regarding as the ratio of dissipative energy to the stored energy for a period in a material. There are two factors influencing tanδ: one is the conductivity which transfers the electromagnetic energy into heat, and the other is the dielectric loss which is due to the damping effect occurred when dipoles rotates with electric field. In practice, the dielectric loss can be divided into two part: intrinsic loss and extrinsic loss. Intrinsic loss is caused by the factors of intrinsic properties in a material, such as ion migration losses, ion vibration and deformation losses, electron polarization losses, density, pores, etc. On the other hand, extrinsic loss could be the errors caused by improper operations. In a homogeneous material, the dielectric quality factor (Q) is a reciprocal of tanδ and defined as. 46.

(57) Q=. 1 ω0 W ω0 = = , tanδ Pd σ. (4.15). where W is the maximum of stored magnetic and electric energy, Pd is the dielectric loss in the material, ω0 is the resonance angular frequency, and σ is the dc conductivity. Another way to see the different electrical responses is the Cole-Cole plot (ε0 v.s. ε00 ) [63]. The room temperature Cole-Cole plots for all the samples are shown in Figs. 4.25 and 4.26. As the plots form a distorted and incomplete semi-circle for each samples, with the center lying below rather than on the ε0 -axis, the process does not exhibit a unique relaxation time. In addition, the nonzero intercepts of ε0 of those arcs indicating the present of an arc with ωmax higher than the maximum frequency measured, here 106 Hz, or the resistance of bulk is not zero. For a homogeneous system revealing only one ideal Debye relaxation, its Cole-Cole plot is a full semicircle centering on the ε0 axis, and passing through the origin. In case many defects present in a system, it can’t present an ideal Debye relaxation. There will be three changes in the shape of the Cole-Cole plot [64]. One, the arc does not pass through the origin as shown in Fig. 4.27, either because there are other arcs appearing at higher frequencies and/or because resistance of bulk is not zero. Another, the center of an experimental arc is frequently displaced below the real axis because of the presence of distributed elements in the heterogenous system. The relaxation time τ is then not single-valued but is distributed continuously. The angle α as indicated in Fig. 4.27, by which such a semicircular is depressed below the real axis and is related to the width of the relaxation time distribution. The other, arcs can be substantially distorted by other relaxations whose mean time constants are within two orders of magnitude or less of that for the arc under consideration. Often, RC elements 47.

(58) have ωmax values that lie outside the available frequency range, especially if they represent either insulating regions with high R or semiconducting regions with low R. In such case, only parts of arcs may be observed. The difference of two peak frequencies in Fig. 4.24 can tell us the difference of resistances and capacitances of grain and grain boundary. BL(0.30)FO presents the largest difference of peak frequencies among all the samples; that is, the resistance and capacitance of grain are larger than those of grain boundary in it. According to M-W effect, for a heterogeneous system, there are more than one dielectric element showing the semicircles; for example, either the interface between grain and grain boundary or the one between the electrode and the grain can produce their own semicircles as shown in Fig. 4.28. Based on this figure, the response of electrode dominates at rather low frequency; while that of grain appears at high frequency regime. The distributions suggest the resistance (R) and capacitance (C) of grain are much larger than those equivalent R and C of grain boundaries and electrodes. Moreover, different form Fig. 4.28, the arcs of several systems may not separate from each other; therefore, we may observe a distorted arc that is the overlap of two or more semicircles. In the case of Figs. 4.25 and 4.26, the classical parallel combination of a resistor and capacitor, often used to model the relaxation process, can be replaced by a parallel combination of a resistor, a capacitance and a constant phase element (CPE). The equivalent circuit of M-W relaxation composes two parallel CPE connected in series where the CPE is a capacitor-like element determined by the value of α as shown in Fig. 4.27. For those samples showing two relaxations, the equivalent circuit is represented in Fig. 4.29. Furthermore, the complex permittivity of the equivalent circuit is calculated as [64]. 48.

(59) ε∗ (ω) = ε0∞ +. X. ε0s − ε0∞ σ0 , − i 1 + (iωτ )1−α ω. (4.16). where ε0s and ε0∞ are the static and high-frequency permittivity, respectively. σ is Ohmic conductivity, and τ is the relaxation time. α is a temperature dependent parameter describing the degree of homogeneity and it ranges between 0 and 1. Different α means different CPE in the equivalent circuit or different relaxation mechanisms from the ideal Debye relaxation. For an ideal Debye relaxation, α = 0, which indicates that the CPE is a capacitor. Meanwhile, 0 < α < 1 implies that the relaxation has a distribution of relaxation times, leading to a broader peak shape than a Debye peak, or it may form nonuniform diffusion whose electrical analog is an inhomogeneously distributed RC transmission line [64]. On the other hand, α = 1 means that the CPE is a resistor. In this case, it is difficult to define the position of the relaxation peak. Eq. 4.16 is expressed in the form of a Debye relaxation with a conduction term. Even without any dipole involved, the equivalent circuit in Fig. 4.29 gives rise to a relaxation spectrum similar to that of the Debye relaxation [61]. The fitted τ value for grain and grain boundary in all samples are around 10−2 ∼ 10−3 s and 10−5 ∼ 10−6 s, respectively. The fitted conductivities lie in the range of semiconductivity; hence, we use semiconductor model to explain our data. The fitted α for grain and grain-boundary responses at 290 K are shown in Tabs. 4.6 and 4.7. The larger the α, the broader the relaxation peak is, indicating that BD(0.40)FO has the widest relaxation peak contributed from the grain response. The α of grain boundary (αgb ) of all samples are larger than those of grain (αg ). That is, there are many more different conducting pathes in the interfaces of grain boundary and grain than in grains. Figure 4.30 shows the temperature dependent αg for BL(x)FO with 49.

(60) x = 0.05 ∼ 0.20 and BD(x)FO with x = 0.05 ∼ 0.30. BL(0.05)FO, BL(0.10)FO, and BD(x)FO with x = 0.05 ∼ 0.30 show a strong decrease in α with increasing temperature, which is a characteristic of a transition from a diffusion-like process towards a relaxation mechanism or from local to long-range charge transport. The temperature independent αg for BL(0.15)FO and BL(0.20)FO show that the mechanisms of charges transport are closer to Debye relaxations, instead of thermal activated. Figures. 4.31 to 4.43 show the frequency dependent dissipation factor at different temperatures. From Figs. 4.32 to 4.36, and from Figs. 4.38 to 4.42, we find that as temperature decreases, the positions of two peaks shift to lower frequencies, suggesting that both electric responses are thermal activated. The shifts of frequencies with decreasing temperature are due to the enhancement of the resistance and capacitance for grain and grain boundary. Further detailed analysis reveals that the relaxation times of grain and grain boundary at different temperature follow the Arrhenius law:. ( kEaT ). τ = τ0 e. B. ,. (4.17). where τ0 is the prefactor, Ea is the activation energy, kB is Boltzmann constant, and T is temperature. For convenience, we plot ln τ v.s 1/T in Fig. 4.44, in which the solid lines are fitting result using Eq. 4.17. From the slope of the fitted straight line one obtains the activation energy for the dielectric relaxation. All the activation energies are shown in Tabs. 4.8 and 4.9 for BL(x)FO and BD(x)FO, respectively. The nearly same value of activation energies for grain and grain boundary suggest that the associated relaxation processes originate from the same sources, the dipolar motion. It suggests that the activation energies of grain response of doped samples decrease with increasing the 50.