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Figure 3.5: color wheel - A sample absorbs visible light of color of the specific wavelength and reflects the rest, in appears the complementary color of light. Find the color that is absorbed, then move directly across the wheel to the other side to get the complement.
3.5 Jahn-Teller Theorem
The Jahn-Teller theorem (named after Hermann Arthur Jahn and Edward Teller), also called Jahn-Teller distortion often, was published in 1937 [18]. The crystal distortion occur due to the asymmetry of distribution of electrons in the system, which mostly be observed in octahedral system. In the octahedral d9case (nine electrons occupy the d-orbitals), the ninth electron may occupy either dz2 or dx2−y2 orbitals. If it occupies the dz2 orbital, there will be more Coulomb repulsion along the z-axis so that the compound tends to elongate along the z-axis. Conversely, elongation along x and y axes if the ninth electron occupies the dx2−y2 orbital. Likewise, the distortion can occur theoretically in almost all cases except d3, d8, d10, high-spin d5 and low-spin d6, since the distributions of electrons of these cases are symmetric. Considerable distortion are usually observed in high spin d4 , low spin d7 and d9 cases, since the unpaired electron occupies the orbital of egset, the more Coulomb repulsion lead to the more distortion.
3.6 Colors of Transition Metal Complexes
Here we discuss the colors of some complexes that can be explained by CFT in this section.
As we know, if a sample absorbs all wavelength of visible light, none reflects and reaches our eyes from that sample, it appears black. Conversely, if the sample do not absorb any wavelength of visible light, it appears white. Since the sample absorbs visible light of color of the specific wavelength and reflects the rest, in appears the complementary color of light. The color wheel shown in Figure 3.5 can demonstrate which color a sample will appear. Find the color that is absorbed, then move directly across the wheel to the other side to get the complement. For example, if the sample absorbs the red-light, it appears cyan, and if the sample absorbs the blue-light, it appears yellow. Now we get back to the subject, as mentioned before, energy of the d-orbitals of the transition metal atom will split into two or more levels in the presence of ligands.
An electron occupies the lower energy d-orbital would jump to the higher unoccupied d-orbital as it absorbs light of wavelength correspond to the certain energy ( the crystal field splitting).
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Fortunately, the energy (the crystal field splitting) often corresponds to the visible region of the spectrum. Therefore, we can explain or predict colors of the transition metal complexes. In Table 3.2, a number of cobalt (III) complexes are listed [19], various ligands (including the strong-field
Table 3.2: Cobalt (III) complexes, colors and corresponding absorbed lights are listed.
Co3+ complex absorbed light color seen
[CoF6]3− red green
[Co(H2O)6]3+ orange blue [Co(NH3)5Cl]2+ yellow violet [Co(NH3)5H2O]3+ blue-green red
[Co(NH3)6]3+ blue yellow-orange [Co(CN)6]3− ultraviolet pale yellow
and weak-field ligands) combine with the cobalt ion and present different colors. The results agree with CFT well. Take [Co(CN)6]3−for example, CN−is a strong-field ligand so that it will lead to a large crystal-field splitting. Thus the energy an electron needs for transition must be high enough (ultraviolet light). Conversely, F−is a weak-field ligand, which will lead to a small splitting. The energy of red light is large enough to excite the transition.
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Chapter 4 Multiferroics
4.1 Introduction
Multiferroics is a material simultaneously having more than one ferroic order parameter in a phase. These parameters are ferromagnetism, ferroelectricity and ferroelasticity (Nowadays what most people mean by multiferroic material predominantly applies to the coexistence of magnetism and ferroelectricity). Some coexistent order parameters in the material has the cross coupling. Take a material involving the coexistance of ferromagnetism and ferroelectricity with cross coupling for example, it means that we can control the electric order in the system by applying a magnetic field and vice versa. This behavior is called the magnetoelectric effect [20].
Such material has the potential of technological applications that it provides opportinities for designing the better electronic devices in the future. As is known, the common data storage device like the hard disk drive is devised using the ferromagnetism of the material. And also the common data storage device, the flash memory, devised using the ferroelectricity of the material.
The two storage devices have their respective pros and cons. If the cross coupling of a discovered multiferroic material can be strong enough, the large degrees of freedom of its properties can probably be used to devise some better electronic devices including the advantages of both hardisk and flash memory, or to create some multifunctional electronic components like a new types of 4-state logic (i.e., with both up and down polarization and up and down magnetization).
The studies of multiferroic material can be traced back to 1960s [21]. However, it has been considered that the strong enough coupling between ferromagnetism and ferroelectricity is im-possible. The early studies represent that the conditions to cause the ferromagnetism and fer-roelectricity usually interfere each other. For example, a condition for causing ferfer-roelectricity requires empty d-orbitals (diamagnetic ions), while a condition for ferromagnetism requires par-tially filled d-orbitals (paramagnetic ions). Therefore, the interesting field has been forgotten for a while. Since the precursory works on thin films of BiFeO3[22], TbMnO3[24] and TbMn2O5 [23] in 2003, multiferroic materials attract much attention once again. Considerable effort has been devoted to search for new compounds with good multiferroic properties and even strong
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enough magnetoelectric coupling. The advancements of the ab initio calculation and experi-mental techniques make it possible to predict or design the system, and to realize the mechanics of the coexistence of the order parameters and the cross coupling of them.
There are generally two types of the multiferroic materials distinguished by considering the microscopic source of the ferroelectricity. The first type, called the type-I multiferroics, contains those materials with weak or no cross coupling of ferromagnetism and ferroelectricity.
Conversely, the type-II multiferroics appears the strong cross coupling between ferromagnetism and ferroelectricity. The two types of multiferroics will be discussed in the following.