Chapter 1 Introduction
1.2.1 Magnetism
The origin of magnetism lies in the orbital and spin motions of electrons and how the electrons interact with one another. The best way to introduce the different types of magnetism is to describe a net magnetization corresponding to the alignment of magnetic moments under an applied magnetic field [5].
“Ferromagnetism" describes the property only when all magnetic moments are strongly coupled and add a positive contribution to the net magnetization after setting the external magnetic field to zero. If some of the magnetic moments are partially anti-aligned and add a net magnetization, then the material is "ferrimagnetic". If the identical moments anti-align completely so as to have zero net magnetization, despite the magnetic ordering, then it is antiferromagnetism. All of the above alignment effects only occur at temperatures below a certain critical temperature, called the Curie temperature (for ferromagnets and ferrimagnets) or the Neel temperature (for antiferromagnets). Paramagnetism happens when the magnetic moments are very loosely coupled so that thermal energy randomizes their orientation. All atoms, including magnetic ones, exhibit diamagnetism, which is a small current induced to oppose the external magnetic field by Lenz’s law [5].
Figure 1-4 Ferromagnetism: (a) Ferromagnetic materials exists a strong coupling between magnetic
atoms and the spins align in the same direction even at zero field. (b) An opposite coupled spins in antiferromagnetic materials (NiO, CoO) makes the net moment is zero. (c) Ferrimagnetism such as TbFe and Fe3O4 possesses unequal magnetic moments and hence nonzero moments.
1.2.2 Ferromagnetism and Hysteresis Loop
Ferromagnetic (ferrimagnetic) materials have a large and positive susceptibility to an external magnetic field. They exhibit a strong attraction to magnetic fields and are able to retain their magnetic properties after the external field has been removed. When the individual moments of the atoms are aligned with one another, a uniform magnetized region within a material forms and is called as domain. In these domains, large numbers of atom's moments (1012 to 1015) are aligned parallel so that the magnetic force within the domain is strong. When a ferromagnetic material is in the demagnetized state, the domains are nearly randomly organized and the net magnetic field for the part as a whole is zero. When a magnetizing force is applied, the domains become aligned to produce a strong magnetic field within the part. Iron, nickel, and cobalt are examples of ferromagnetic materials [6].
Figure 1-5 is a typical magnetization curve for ferromagnetic materials [6].
Magnetization (emu/cc) is plotted as a function of magnetic field intensity (Oe). In materials
science, the coercivity, also called the coercive field, of a ferromagnetic material is the intensity of the applied magnetic field required to reduce the magnetization of that material to zero after the magnetization of the sample has been driven to saturation. Coercivity is usually measured in oersted or ampere/meter units and is denoted HC. The saturation magnetization (Ms) means the magnetization M stays constant even when the applied field is increasing continuously. After saturation, the external field is set to zero and the residual magnetization was called Remnant magnetization (Mr) [5].
Figure 1-5 The Magnetization curves and hysteresis loops for ferromagnetic materials.
1.2.3 Magnetostriction
Magnetostriction is the name given to the changes of size and shape of structure which accompany the magnetization of a ferromagnetic. The phenomenon was discovered by Joule J.P. and published in Philosophical Magazine in 1847 [7]. Nearly all ferromagnetic
materials exhibit a change in shape resulting from magnetization change. The fact that magnetization causes mechanical strain implies that mechanical stress will affect the magnetization. It is this inverse effect that gives magnetostriction phenomena, the chief importance, for causing external or internal mechanical stresses to have a profound influence on the magnetic properties of a body [6].
In describing anisotropic magnetostriction in a material one can refer to its magnetostrictive constants, λs, the strains produced at magnetic saturation, or to its magnetoelastic coupling coefficients, Bij, the magnetic stresses causing λs [6]. In most common materials, nickel, iron, and cobalt, the change in length is on the order of 10 parts per million. The highest room temperature magnetostriction of a pure element is that of Co which saturates at 60 microstrain. Fortunately, by alloying elements one can achieve "giant"
magnetostriction under relatively small fields. The engineering era of magnetostrictive materials began with the discovery of giant (1000’s of ppm) magnetostriction in rare earth alloys during the 1960’s by A.E. Clark and others [8]. The culmination of research into a engineering alloy incorporating rare earth materials was Terfenol-D, a specially formulated alloy of Terbium, Dysprosium, and Iron that exhibits large magnetostriction at room temperature and relatively small applied fields [9].
Table 1-1 Magnetostriction Constrants λ100 and λ111 (×106) at 4.2K and Room Temperature for several materials
1.3 Multiferroic Materials
1.3.1 Origin of Multiferroics
Materials in which ferromagnetism and ferroelectricity occur simultaneously in the same composite and allow coupling between the two order-parameters are known as multiferroics [10]. As a consequence, they have a spontaneous magnetization that can be switched by an applied electric field and a spontaneous electrical polarization that can be switched by an applied magnetic field. This is the famous magnetoelectric effect (ME effect) [11]. The figure below shows the definitions of multiferroics and magnetoelectrics. Although initially with different meanings, they have been widely used and interchangeable now.
Figure 1-6 Schematic illustration of multiferroics. (a) Relationship between multiferroic and magnetoelectric materials illustrates the requirements to achieve both in a material. (b) Schematic illustrating different types of coupling present in materials. Much attention has been given to materials where electric and magnetic order are coupled known as magnetoelectric materials.
Hitherto, there have been very few multiferroics existing in nature or synthesized in the
laboratory. The first discovered multiferroic material was nickel iodine boracite, (Ni3B2O13I) [12]. This discovery was followed by the synthesis of several multiferroic boracites compounds, all of which have complex structures with many atoms per formula unit and more than one formula unit per unit cell. The large number of inter-ionic interactions in these materials prevented isolation of the essential factors causing multiferroicity and the nature of the coupling between the magnetic and electric polarization, and structural order parameters.
The search for other multiferroics began in Russia as early as the 1950s, with the replacement of some of the B cations contenting zero d-orbital electrons in ferroelectric perovskite oxides by magnetic dn cations [13]. The first synthetic multiferroic material, (1−x)PbFe0.66W0.33O3 – xPbMg0.5W0.5O3 [14], was produced at the beginning of the 1960s.
In this case, Mg2+ and W6+ ions were diamagnetic and caused ferroelectricity whereas d5 Fe3+
ions are responsible for the magnetic ordering. As a result of the dilution of the magnetic ions, these materials all have rather low Curie or Neel temperatures.
In the past few years, there has been renewed interest in studying the perovskite-based multiferroic materials, such as rare earth manganates TbMn2O5, YMnO3, BiMnO3, which have higher Curie temperatures and large magnetoelectric effects. Furthermore, recently efforts have been made to synthesize the new multiferroic in the form of thin film, by employing ferroelectric and ferromagnetic compounds to make a nanocomposite, a superlattice, or a multilayer structure [18].
However the single-phase ME materials show weak ME coupling due to the basic problem that the electric configurations favoring magnetization are antagonistic to those that favor polarization [19]. Van Suchtelen proposed the concept of a product property in two-phase composite materials in 1972, arising from an elastic coupling between two phases of different properties. The ME effect in a composite material having one magnetostrictive and one piezoelectric phase is one such product tensor property. Scientists in Philips Laboratory experimentally found that large ME effect could be produced in such composites [7]. The ME effect obtained in this way can reach about hundred times larger than that in single-phase multiferroic one.
A milestone in the development of ME bulk composites was the appearance of one containing giant magnetostrictive rare-earth-iron alloy Tb1-xDyxFe2 (Terfenol-D) in 2001.
The Terfenol-D/PZT and Terfenol-D/PVDF composites have been experimentally found to exhibit a giant ME effect [20]. In 2004, Zheng et al. reported a pioneering experiment on nanostructured films of the BaTiO3-CoFe2O4 system with 1-3 connectivity schemes [11]. In the last two years, a series of experimental and theoretical work on such multiferroic oxides has been reported. Such multiferroic nanostructures have become the topic of the day in the multiferroic composites field, and they promise potential applications of ME composites in microelectronic devices.
1.3.2 Classification of multiferroic materials
Magnetoelectric materials with coexistence of at least two ferroic orders are divided into single-phase and multiphase multiferroics by their composition and phase connectivity.
1.3.2.1 Single-phase multiferroics
Single-phase multiferroics contains only one component but posses both ferroelectric and ferromagnetic properties. However, there is a contra-indication between the conventional mechanism for cation off-centering in ferroelectrics (which require formally empty d orbitals), and the formation of magnetic moments (which usually results from partially filled d orbitals). This is the main challenge in studying single-phase multiferroics since 1960s. For ferroelectricity and magnetism to coexist in a single phase, the atoms that move off center to form the electric dipole moment should be different from those that carry the magnetic moment. Different mechanisms to single-phase multiferroics were studied and the most common routes were listed [18].
In the magnetic perovskite-structure oxides and related materials, multiferroism is most commonly achieved by making use of the stereochemical activity of the lone pair on the large (A-site) cation to provide the ferroelectricity, while keeping the small (B-site) cation magnetic.
This is the mechanism for ferroelectricity in the Bi-based magnetic ferroelectrics, the most widely studied of which is bismuth ferrite, BiFeO3. A second route to multiferroism is provided by “geometrically driven” ferroelectricity, which is compatible with the coexistence of magnetism; the antiferromagnetic ferroelectrics YMnO3 and BaNiF4 fall into this class [21].
To be ferroelectric, a material must be insulating otherwise the mobile charges would screen out the electric polarization. This is a common problem in the case of magnetic ferroelectrics, because magnetic transition metal ions are often able to accommodate a wider range of valence states than their diamagnetic counterparts, leading in turn to non-stoichiometry and hopping conductivity. Clearly many potential combinations of lone pairs and transition metals remain to be explored, but in all cases, the stoichiometry must be carefully controlled so that the transition metal d electrons provide magnetism without also contributing to electronic transport. Therefore, detailed characterization of the domain structure, dynamics for improving magnetoelectric coupling, and reduction of the leakage current density and the coercive field, are critical challenges that need to be addressed before BiFeO3-based films will be candidates for integrated microelectronic devices such as storage elements in non-volatile ferroelectric memories [7].
1.3.2.2 Multiphase multiferroics
Multiphase multiferroics are investigated as an alternative approach using bonded magnetostrictive and piezoelectric materials to overcome the low ME coupling and low-temperature problems of single-phase multiferroics. The classification of multiphase multiferroics is based on the phase connectivity. They are divided into the following types:
As for piezoelectric composites, the ME composites could have various connectivity schemes, but the common connectivity schemes are 0-3–type particulate composites of piezoelectric
and magnetic oxide grains, 2-2–type laminate ceramic composites consisting of piezoelectric and magnetic oxide layers, and 1-3–type fiber composites with fibers of one phase embedded in the matrix of another phase, as shown in Fig. 1-7. BaTiO3, PZT, PbMgNbO3-PbTiO3, etc., are usually chosen as the piezoelectric ceramic phase, and ferrites usually as the magnetic phase. [7]
Figure 1-7. Schematic illustration of three bulk composites with the three common connectivity schemes: (a) 0–3 particulate composite, (b) 2–2 laminate composite, and (c) 1–3 fiber/rod composite.
1.3.3 Applications of multiferroics
Multiferroics are of interest for memory and logic device applications, as the coupling between ferroelectric and magnetic properties enables the dynamic interaction between these order parameters. Recently, Ying-Hao Chu performed an experiment of using electric-field to control local ferromagnetism by making the magnetoelectric multiferroic structure. Their work reveals the possibility to locally manipulate ferromagnetism with an electric field for ultra-thin device-scale uses [22].
Besides, promising applications include magnetic field sensors, transducers, filters, oscillators, phase shifters, memory devices, and so on. At the resonance frequency the ME composite can be used as a transducer which converts the microwave magnetic field into a microwave electric field. Because of the shift in the resonance frequency in a static
magnetic or electric bias field the composite materials hold promise in electrically tunable microwave applications such as filters, oscillators, and phase shifters. Due to the hysteretic nature of the ME effect, the composites may find applications in memory devices. This coupling could, in principle, permit data to be written electrically and read magnetically in memory technologies. [7]
1.4 Motivation
1.4.1 Why multiphase magnetoelectric materials
In a single-phase compound, the magnetoelectric effect requires long range atomic moments and electric dipoles. For this reason, the effect is often very weak. On the other hand, the ME coupling of multi-phase multiferroic mediated by mechanical stress at the interface between two phases in a composite has greatly enhanced the magnetoelectric coupling in thin films based on either nanocomposites or superlattices. In this case, by matching a suitable piezomagnetic and an electrostrictive, it can be a suitable way to obtain a large value of the magnetoelectric coefficient and hold great potential for future applications.
1.4.2 Why micro-Raman system
To obtain a fundamental understanding of multiferroics, the experimental observation of the coupling mechanism between the ferroelectric and ferromagnetic orders is of great importance. For multiphase multiferroics, the physical properties at the interfaces is an important aspect to achieve functional multiferroics as the ME interaction happens here.
With a scale of single atomic boundary, the polarization and magnetization will reconstruct by chemical bonding, exchange interactions, and strain effects. On the other hand, one can
directly obtain the information about the polarization states and the variation of structure from the phonons in Raman spectra. Phonons at the interface are sensitive to strain induced by lattice mismatch and the broken symmetries. However, very little is known about the behavior of phonons in magnetoelectric multiferroics, even though investigations of phonons have in the past played a crucial role in the understanding of classic ferroelectrics.
Recently, some studies on behaviors of phonons in multiferroics, the variation of phonon energy in spectrum is not obvious and relations between phonon shifting and coupling mechanism are not investigated [23-25]. In our work, we proposed a micro-Raman detection method in which the micro-focused light is employed to measure the coupled interactions across micro hetero-interfaces. Not only the stress dependence of phonon shifting at the interface was observed in Raman spectrum but also the distinct magnetic properties in M-H hysteresis is studying and discussed in three different geometrical CoFe2O4-PbTiO3
multiferroic systems.
1.5 Organization of the thesis
There are five chapters in this thesis. In Chapter 2, we will introduce the theory of phonon modes in Raman spectra, hysteresis loop of ferromagnetic materials, and X-ray diffraction. Chapter 3 describes the experimental details of sol-gel methods and spin-coating process. We will present the results and discussion about multiphase multiferroics of three geometric structure on the subjects including structure analysis, coupling mechanism induced
phonon modes shifting, and unsaturated magnetization and coercivity. In the last chapter, we conclude the investigations on multiphase multiferroics thin film and proposed several topics worthy of further studying.
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Chapter 2 Theoretical Background
2.1 Magnetoelectric Effect
[1]The magnetoelectric response is the appearance of an electric polarization upon applying a magnetic field and the appearance of magnetization upon applying an electric field. The coupling interaction between ferroelectric and ferromagnetic materials in multiphase multiferroics has been found to be due to elastic interaction as was the case in bulk composites.
Magnetic-field-induced electric polarization (MIEP) in nanostructured multiphase multiferroic composite films was studied by using the Green’s function approach. As the coupled interaction between ferroelectric and ferromagnetic phases in the multiferroic nanostructures is an elastic interaction, the constitutive equations for the coupling magnetic-mechanical-electric interactions in the nanostructured films can be expressed by direct notation for tensors as
where σ, ε, D, E, B, and H are the stress, strain, electric displacement, electric field, magnetic induction, and magnetic field, respectively; c and к are, respectively, the stiffness at constant fields and the dielectric constant at constant strain; the permeability μ strongly depends on ε and electric and magnetic fields; e (eT being the transpose of e) is the piezoelectric coefficient;
21
and εms is the magnetostrictively induced strain related with the magnetic field dependent magnetostriction constants (e.g., λ001 and λ111) of the ferromagnetic phase; α is the magnetoelectric coefficient. These are the same as the case for bulk multiferroic composites.
However, in comparison to the bulk composites, there exist remarkable residual stress σs (or residual strain εs), spontaneous polarization Ps and magnetization Ms in the multiferroic films.
The effective properties (denoted by the starred quantities below) of the multiferroic films can still be defined as the averaged fields (denoted by < >), e.g., <D> = e*<ε> + к*<E> + α*<H> + Ps. We considered the ME effect of such nanostructured films. Under only applied magnetic field, the effective polarization in the mechanically clamped films is
22
P
sP = α * H < > +
(2.1-2)In a state of static equilibrium,
( ) ( ) ( )
By solving the equilibrium equations (2.1-3) under the homogeneous magnetic-mechanical-electric (H0-ε0-E0) boundary conditions in terms of the Green’s function approach [2], the local fields within the composite films can be obtained as
0
where, c0, к0, and μ0 represent the constitutive constants of a homogeneous reference medium;
Gu, GФ, and GΨ are the modified displacement, electric and magnetic potential Green’s functions for the homogeneous medium [2, 3]. Substitution of Eq. (2.1-4) into (2.1-1) directly gives explicit solutions for the local σ, D, and B, also as a function of ε0, E0, and H0. By averaging these solutions for local field quantities and eliminating ε0, E0, and H0 from them, one can get the effective polarization in the mechanically clamped films as
23
where T66 and T33 are two so-called t-matrix tensors. This equation is quite general and independent of the models assumed for the topology of the phases in the composite film.
For the (00l)-oriented multiferroic nanostructure, only the volume average is necessary in Eq.
(2.1-5). Ferroelectric phase is taken as the homogeneous reference medium, since the ferroelectric phase with high volume fraction is a matrix phase. Furthermore due to the fact that e = 0 and Ps = 0 for the ferromagnetic phase, εms = 0 and Ms = 0 for the ferroelectric phase,
Fig. 2-1 Schematic illustration of the nanostructured multiferroic BaTiO3-CoFe2O4 films in (a) the 1-3 type where the CoFe2O4 nanopillars (shaded) are embedded in the BaTiO3 matrix, and in (b) the 2-2 type where the BaTiO3 layer is first deposited on the substrate SrRuO3 and then the CoFe2O4 layer (shaded) on the piezoelectric layer.
For the 1-3 type (using the terminology introduced by L. E. Cross and co-workers) nanostructured composite films with (00l) ferromagnetic nanopillars embedded in a ferroelectric matrix, the effective electric polarization P along the symmetric direction is easily
For the 1-3 type (using the terminology introduced by L. E. Cross and co-workers) nanostructured composite films with (00l) ferromagnetic nanopillars embedded in a ferroelectric matrix, the effective electric polarization P along the symmetric direction is easily