Chapter 1 Introduction
1.3 Multiferroic materials
Multiferroics displaying both ferroelectric and ferromagnetic properties is
known possessing the magnetoelectric (ME) effect between the two parameters [12].
The ME effect in multiferroics possesses not only simultaneous magnetic and electric ordering but also interconversion of energies stored in electric and magnetic fields.
It is also an important mechanism in applications of transducers, actuators, and sensors [13, 14]. There are some theoretical studies [15-17] on calculating the coupling effect of different geometric structures and many experimental reports [13, 18] of ME effect in various types of materials, different geometric shapes, and
operational modes. The coexistence of magnetic and electric subsystems engenders the material with the “product” property (i.e., the composite exhibits responses that are not available in the individual component phases), thus allowing an additional degree of freedom in the design of actuators, transducers, and storage devices.
However, the choice of single-phase materials exhibiting coexistence of strong ferro/ferrimagnetism and ferroelectricity is limited [19, 20]. Van Suchtelen et al. [21]
proposed that composites of piezoelectric and magnetostrictive phases can be electromagnetically coupled via stress mediation (see Fig. 1.4). The ME coupling Figure 1.4: Schematic illustration of multiferroic material.
results from the elastic bonding at the interface and is transmitted through the stress/strain exerted by a magnetized magnetostrictive phase on a piezoelectric phase or vice versa along their boundary, hence it induces a net polarization or magnetization [12, 22, 23].
1.4 Motive
To develop a solution for integrated modulable devices, study on not only the emission properties of rare-earth (RE)-doped ferroelectric materials but also the various properties of host materials is strongly motivated.
1.4.1 Dependence of crystal structure on substitution, size, and shape
The physical properties of complex oxide perovskites have been dramatically influenced by various effects, such as temperature [24-26], pressure [25, 27], substitution [28], size, and shape [29-33]. With the development of miniaturization of electronics, recent advances in solid-state science have resulted in ferroelectric materials and devices with nanostructures with length scales less than 200 nm. The size dependence of Curie temperature and tetragonal distortion of the ferroelectric phase has been investigated theoretically based on the Landau-Ginsburg-Devonshire (LGD) theory in the case of isolated particles.[34-37] The change of the ferroelectric phase in isolated particles is mainly the consequence of the surface effect and a transition from the ferroelectric phase to a cubic paraelectric phase at room
temperature for a critical particle size from a few nanometers to a few tens of nanometers is predicted. However, it is often difficult in experiment to separate true size effects from other factors that change with the size. The fixity of the ferroelectric phase can be determined by additional factors like defect chemistry, incorporation of foreign atoms and bulk hydroxyl groups, aggregation level of the particles, porosity level, and residual stresses.[38-43] To avoid the disturbance of other causes, powders with uniform size therefore seems a more convenient system to study size effects. In this part, we synthesize BaTiO3 nanocrystals with uniform crystal size less than 200 nm by using glycothermal synthesis method. We probe the size dependence of structure characterization with crystal size ranging from ~μm to
~10 nm by using the x-ray diffraction (XRD), scanning Electron microscope (SEM) and Raman scattering. The research topic will focused on the behavior of phonon modes, including the displacement of B cation and the coupling of phonon, as the crystal size decreases from ~μm to ~10 nm. We also attempt to synthesize BaTiO3
nano-wires (nano-rods) by using molten-salt synthesis method.
1.4.2 Dependence of mechanism of luminescence on crystal structure in rare-earth ions doped materials
The different crystal field caused by structure symmetry of the host material would contribute to different perturbation terms for the rare-earth ions inner shell
transitions. Therefore, the crystal structure is a more important mechanism for not only emission efficiency in erbium-doped Pb0.8La0.2TiO3 system, but also converting up-conversion (UC) green radiation to red radiation due to the EBT process in Er-Yb codoped ferroelectrics. In this part, we have studied the dependence of emission mechanism on the crystal structure of perovskites doped with rare-earth ions.
1.4.3 Dependence of coupling of electricity and magnetism on lattice mismatch Multiferroics displaying both ferroelectric and ferromagnetic properties is known possessing the ME effect between the two parameters. Van Suchtelen et al. [21]
proposed that composites of piezoelectric and magnetostrictive phases can be electromagnetically coupled via stress mediation. The ME coupling results from the elastic bonding at the interface and is transmitted through the stress/strain exerted by magnetized magnetostrictive phase on piezoelectric phase or vice versa along their boundary and hence it induces a net spontaneous polarization or magnetization [12, 22, 23]. Moreover, it is well known that the behavior of interfacial phonon is sensitive
to the giant residual stress/strain resulting from the lattice misfit between the different media [44]. It is interesting and important to investigate the relationship between the ME effect and the behavior of interfacial phonon. Recent studies on phonon behavior of multiferroics were reported [45-47], but the results are inconclusive. In this part, we report on the stress dependence of the behavior of interfacial phonon and
the magnetic properties in three multiferroics consisting of the different geometric shapes of ferromagnetic CoFe2O4 (CFO) embedded in ferroelectrics PbTiO3 (PTO) by using the micro-Raman spectroscopy and superconducting quantum interference device (SQUID).
1.5 Organization of this dissertation
In this thesis, I present investigations of the influence of perovskite structure on luminescence and characteristics of ferroics. The dissertation is organized as follows.
I first describe the related theoretic background in Chapter 2, including a general concept of crystal structures, lattice dynamics, fundamental optical transitions, and magnetoelectric (ME) effect. In Chapter 3, I present the synthesis of the samples with different processes and also show the brief illustrations of characterization techniques. In Chapter 4, I discuss the dominant mechanisms on visible emission of the Er3+ doped Pb0.8La0.2TiO3 polycrystalline films. Combining with examining the disappearance of Raman modes, I show destruction to a displacement of Ti in the short-range structure for doping concentration exceeding 7 mol%. The diminishing of symmetry breaking causes quench of Er3+ emission. As increasing Yb3+ co-doped concentrations in 6 mol% Er3+ doped PbTiO3, BaTiO3, and SrTiO3 polycrystalline powder samples, the dominant mechanisms of visible upconversion emissions in Er-Yb codoped ferroelectrics are discussed in Chapter 5. In Chapter 6, I discuss the
attractive LO-TO splitting behavior and depict the low frequency TO spectral peak along with change of the tetragonal phase toward the cubic one for reducing diameter of BaTiO3 nanocrystals from 140 nm to 30 nm. In Chapter 7, I discuss the characteristics of three different geometric forms of the PbTiO3-CoFe2O4
multiferroics. The analysis of the magnetic and Raman measurements under different geometric forms indicates the dependence of magnetic property and interfacial phonon behavior on stress/strain due to the lattice misfit and the strongest chemical bonding at the interface between CoFe2O4 and PbTiO3 matrices. In the final Chapter 8, I conclude the studies on the ferroics and propose the several topics worthy of the future work.
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Chapter 2 Theoretical Background
In this chapter, lattice vibration in crystals, optical transitions of rare earth, and multiferroic magnetoelectrics are reviewed. Lattice dynamics corresponding to lattice vibrational properties, the behavior of coupled phonon and, the mechanism of LO-TO splitting are discussed. Optical transitions in rare earth doped materials have been described, including the mechanism of fundamental optical transitions and upconversion.
2.1 Vibrational spectroscopy
2.1.1 IR absorption
For infra-red (IR) wavelengths, absorption must in some way be related to a variation in the charge distribution. This arises due to a change in the dipole moment associated with molecule. After bonding, one atom of the molecules has a local charge q then the rest of atoms have charge q and the dipole moment , is given by
l q
, (2-1) where l is the separation of the charges (see Figure 2.1).Electromagnetic wave can be absorbed or emitted by a medium if during its interaction there is a change in the charge distribution within the medium. During the interaction with photon, the dipole moment will change, thus one can rewrite the dipole moment as
In order to describe the excitation of a molecule from vibrational level, v to i f
v , as shown in Figure 2.2, an interaction Hamiltonian Hint E that expresses the interaction of an atom with a photon is added to the unperturbed Hamiltonian H0to describe the total Hamiltonian,
Hint Figure 2.1: Diagram of dipole moment.
q q
IR absorption occurs as the transition R0, in other words, there must be a change in the dipole moment due to vibration of the molecule which is induced by the applied field E, since the transition probability P is equal to| |R 2. The condition that an IR absorption or emission must be associated with a change in dipole moment is known as the dipole selection rule. The dipole selection rule plays an important role in IR spectroscopy because it tells us whether a molecule will be IR active or not.
2.1.2 Raman scattering
When light passes through a medium, most of the light is reflected, transmitted, absorbed, elastic or inelastic scattered. Raman scattering is an inelastic scattering process. When the light encounters the medium, it interacts inelastically with phonon (vibration) modes and produces outgoing photons whose frequencies are relatively shifted by an amount of energy correspondent to phonon energy from that of the incoming light. The scattered outgoing photons are called the Raman-scattered photons. If the light of frequencyv0 is scattered by some media, the spectrum of the scattered light contains a strong line of frequencyv0 and much Figure 2.2: Transition from level i to f.
f
i
weaker lines of frequenciesv0 v1, v0 v2, ………, v0 v2,v0 v1, etc. Those lines on the low frequency side of the exciting lines (i.e., v0 vi,i1,2,...) are always matched by lines on the high frequency side (i.e., v0 vi,i1,2,...) but the latter are much weaker when the scattering medium is at room temperature. Raman scattering is inherently a weak process, but laser provides enough intensity that the spectra can be routinely measured. In analogy with terms used in the discussion of fluorescence spectra, lines on the low frequency side of the exciting line are known as Stokes lines and those on the high frequency side as anti-Stokes lines.
The incident photon loses its energy by producing a phonon (Stokes shifted), or gain energy and momentum by absorbing a phonon (anti-Stokes shifted), according to the energy conservation rules： the energy of the molecule before and after the interaction, respectively.
Assuming that the scattering medium is in temperature equilibrium at temperature T, the distribution of the molecules over the energy states will be Boltzmann and the ratio of the number of molecules N1 in a state of energy W to the 1 if degeneracy is neglected. If one includes the fact that scattered intensity is proportional to the fourth power of the frequency then the relative intensities of
Stokes to anti-Stokes lines and their temperature dependence be consistent with the All the Raman mode frequencies, intensities, line-shape, and line-width, as well as polarization behavior can be used to characterize the lattice and impurities. The intensity gives information on crystallinity. The line-width increases when a material is damaged or disordered, because damage or disorder occurs in a material will increase the phonon damping rate or relax the rules for momentum conservation in Raman process. All these capabilities can be used as a judgment for layered microstructure as well as bulk materials, subject only to the limitation that the penetration depth of the exciting radiation ranges from a few hundred nanometers to few micrometers.
2.2 Coupled phonon model
The Hamiltonian of an isolated system can always be brought to a diagonal form, which means that any coupling of the quantum states is reducible. Under this assumption, the reflectivity of the crystal with more than one infrared active mode is often quite well reproduced by a formula involving the sum of contributions from independent classical oscillators. However, no system above the temperature 0K is isolated, for that we have least the blackbody radiation connecting it with the environment. In some notable cases, the Hamiltonian of the system is intrinsically
non-diagonal. The profile of the energy spectrum of such system is not composed of a set of Lorentzian peaks, but contains asymmetric interfering features.
Since the occurrence of coupling in the lattice modes was recognized by Barker and Hopield to explain the infrared reflectivity of some perovskites, a handful of spectral anomalies in data on Raman. Brillouin and neutron scattering were observed and associated with phonon-phonon coupling. Because the coupling phenomenon is a temperature-induced effect, it seems probable that its occurrence will be more frequent in crystal showing other thermal anomalies in the phonon behavior. In fact, most of the crystals undergo a structural phase transition at some temperature not far from where the interference starts to be observable. BaTiO3
presents three structural phase transitions, at -80, 0, and 130℃. In the tetragonal phase between 0 and 130℃ the dynamics of the crystal is complicated. All the three A1 modes of vibration are strongly coupled and two of them are heavily damped.
Because the three A1(TO) modes are strongly coupled and two of them are heavily damped in the tetragonal phase of ABO3, Sood, [1] and Chaves, et al. [2] have considered three coupled A1(TO) modes to describe the complicated coupling phenomenon. The Raman intensity of the three coupled modes can be expressed by
) (
I
A [n()1]Im[T*GT], (2-10) where A is a constant, ( )n is Bose-Einstein factor, T is a vector involving Ramanscattering amplitudes, and the inverse matrix response is parameters; this is a reasonable approximation because they are too far from each other, having no spectral superimposition.
2.3 Born effective charges and LO-TO splitting
The total polarization in the crystal can be expressed as a sum of contribution from the displacements of the charged ions and from the displacements of electrons relative to their ionic nuclei
electron
where i is the label of Cartesian coordinate, N is the number of primitive cells in the crystal volume V and e is the charge of the
th ions in a primitive cell, all ions of the same label suffering the same displacementU.It is convenient to express the ionic polarization in terms of the normal coordinates. The polarization is a vector, and the vibrational modes that contribute to the polarization are limited to those with the same symmetry character as a polar vector. These polar modes can be chosen so that their contributions to the polarization are parallel to principal axes of the susceptibility tensor. Let be a unit vector parallel to the polarization contributed by the displacement of normal coordinatesW. Then one of the Cartesian componentsi is unity and the other two are zero. The ionic polarization can be written as
where the transformation coefficients can be chosen to satisfy the orthonormality relations The presence of an electric field E modifies the harmonic oscillator equation of the normal modes toi The applied electric field of frequency
, therefore, produces a steady-state normal-mode amplitude, and the ionic polarization can be written in a form proportional to the electric-field components. We assume that
is in the vicinity of the vibrational frequencies and well below the frequencies of all electric transitions. The relative permittivity is then
where is a constant electric contribution to the relative permittivity, so that i
i i
i
electron E
P 0( 1) . (2-22) The electric field and polarization of any electromagnetic wave frequency
and wavevector q will satisfy the Maxwell’s equation :
2 2 2 2 2
0c q q E( ) 0(c q )E P.
(2-23) This equation is unfortunately very complicated in its most general form, but simplification can be made for most applications. The most striking simplification occurs when the frequency and wavevector satisfy cq. We obtained
2 0 By combining the equation for the divergence of the electrical displacement,
, with Eqs. (2.23) and (2.24), we can obtain the general representation
)
where
is summed over all the polar modes. In cubic symmetry crystal, the polar-vector representation is threefold degenerate. The crystals are optically isotropic and the principal axes are not restricted to lie in any particular directions. For any direction of the wavevector of a threefold polar mode, it is permissible to choose two of the polarization vectors perpendicular to q and the third parallel to q. The two transverse polar modes have a frequency determined by the standard lattice dynamics calculation. The longitudinal polar mode has the associated macroscopic electric field, and its frequency is determined by the equation above, which reduces to0
(2-27) in the cubic case. The simplest cases to consider first are the cubic crystals that have a single threefold polar mode. The relative permittivity has the isotropic form
/ ,
where the mode frequency is replaced by0 to emphasize its transverse nature T and redundant subscripts and superscripts are omitted. The longitudinal frequency obtained from the equation mentioned above with the damping removed is
,
where is the zero-frequency value of the relative permittivity 0
2.
This expression for the longitudinal frequency is the Lyddane-Sachs-Teller relation. The equation of motion for the longitudinal mode takes the form
,
and leading to Resta et al. [3] have shown that polarization is linear in the change of the position vector of the basis atom to a good approximation. The Born effective charge tensorZ*m is rewritten through
The Born effective charge tensor reflects the effects of the Coulomb interactions and is directly related to the LO-TO splitting. The general representation of the dynamical material for LO and TO modes at q =0 are the related by
0
where D represents the dynamical matrix and is proportional to the square of the vibration frequency. Zhong, et al.[4] and Waghmare, et al. [5] have calculated that the softest TO mode is most associated with the hardest LO mode via Coulomb interaction to give rise to giant LO-TO splitting in ABO3 compounds, especially for the ferroelectric phonon modes.
2.4 Optical transitions of rare earth doped materials and upconversion
2.4.1 Fundamental optical transitions
Trivalent rare-earth (RE) ions are well known for their special optical properties, which result from the fact that the electrons of the partially filled 4f-shell are shielded from the surrounding completely filled 5s and 5p shells. The energy levels of the 4f-shell have equal parity, and hence electric dipole transitions are forbidden. In a solid, the slight mixing with odd-parity wavefunctions makes the transition slightly
Trivalent rare-earth (RE) ions are well known for their special optical properties, which result from the fact that the electrons of the partially filled 4f-shell are shielded from the surrounding completely filled 5s and 5p shells. The energy levels of the 4f-shell have equal parity, and hence electric dipole transitions are forbidden. In a solid, the slight mixing with odd-parity wavefunctions makes the transition slightly