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Chapter I Introduction to Multiferroics

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Chapter I

Introduction to Multiferroics

This chapter presents a brief account of the history of multiferroics, Progress in the area of multiferroic materials is traced, and the different pathways to achieve multiferroic order in materials are explained. Requirements for magnetoelectric effects are emphasized, and present state of art in the field of multiferroics in relation to the developments in single phase and composite materials is highlighted.


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1.1. Introduction Advances in modern electronics and the development of new generation devices have necessitated the use of smart materials with multifunctional properties. Magnetoelectric multiferroics are a special class of materials possessing magnetic and ferroelectric ordering together with coupling between them over a certain range of temperature. Many oxide materials exhibiting miscellaneous behaviors such as dielectric, ferroelectric, magnetic and multiferroic properties have been investigated. Recently, there has been an upsurge in the research activity on multiferroic systems due to the observation of interesting magnetoelectric coupling in thin films of some of the transition metal oxides (Ramesh, et al., 2007, Gajek, et al., 2007; Nan, et al., 2008). This envisages the potential applications of multiferroic systems for magnetoelectric sensors, magnetocapacitive devices and electrically driven magnetic data storage and recording devices (Nan, et al., 2008). As ferroelectric polarization and magnetization are used to encode binary information in ferroelectric random access memories (FeRAMs) and magnetic random access memories (MRAMs), respectively, the coexistence of magnetization and polarization in a multiferroic material allows the realization of four-state logic in a single device (Gajek, et al., 2007, Scott, 2007). Magnetoelectric property originates from the coupled action of charge as well as spin nature of electrons that leads to an alliance of electrical and magnetic properties in the same material. The recent advancements in the characterization techniques and materials processing techniques have expanded the realm of materials functionality. One of such new generation materials used to realize smart materials possessing multifunctional properties, is the multiferroic materials, with sufficient amount of coupling among elasticity, charge and spin degree of freedoms. Unlike the natural multiferroics having weak magnetoelectric coupling, newly developed multiferroic composites yield giant magnetoelectric coupling response near to the room temperature, enabling their use for wider technological applications (Nan, et al., 2008; Ramesh, et al., 2007). 1.2. Multiferroic Materials

Multiferroic materials showing the coexistence of at least two ferroic orders (ferroelectric, antiferromagnetic or ferromagnetic, and ferroelasticity) are expected to


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find potential applications in many devices. Amongst these properties the co-existence of ferroelectricity and ferromagnetism is highly desired. Besides their coexistence, of utmost importance is a strong coupling between the two ferroic orders. In multiferroic materials, the coupling interaction between the different order parameters can produce additional functionalities, such as a magnetoelectric (ME) effect (Ma, et al., 2011) In recent years, however, the term (magnetoelectric) multiferroics has become more popular, this term comprises not only ferroelctromagnets but also all the materials in which any two of the following ferroic orders co-exist (Eerenstein, et al., 2006):

(i) Ferroelectric materials: possess a spontaneous electrical polarization which can be switched by an applied electric field.

(ii) Antiferroelectric materials: possess ordered dipole moments that cancel each other completely within each crystallographic unit cell.

(iii) Ferromagnetic materials: possess a spontaneous magnetization that is stable and can be switched hysteretically by an applied magnetic field.

(iv) Antiferromagnetic materials: possess ordered magnetic moments that cancel each other completely within each magnetic unit cell.

(v) Ferrimagnetic materials: These materials differ from antiferromagnets because the magnetic moment cancellation is incomplete in such a way that there is a net magnetization that can be switched by an applied magnetic field.

(vi) Ferroelastic materials: display a spontaneous deformation that is stable and can be switched hysteretically by an applied external stress.

(vii) Ferrotoroidic materials: possess a stable and spontaneous order parameter that is taken to be the curl of a magnetization or polarization. It is anticipated that this order parameter may be switchable.

The multiferroic behavior involves two or more of the following materials, and describe the following order parameter coupling (Eerenstein, et al., 2006): (a) Magnetoelectric coupling describes the influence of a magnetic (or electric)

field on the polarization (or magnetization) respectively. (b) Piezoelectricity describes a change in strain as a function of applied electric

field, or a change in polarization as a function of applied stress.


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(c) Piezomagnetism describes a change in strain as a function of applied magnetic field, or a change in magnetization as a function of applied stress.

(d) Electrostriction describes a change in strain as a quadratic function of applied electric field.

(e) Magnetostriction describes a change in strain as a quadratic function of applied magnetic field.

Although the magnetoelectric effect and magnetoelectric multiferroics have been studied for more than four decades, the temperature scale for ferroelectric order is much larger than for magnetic order (Table 1.1), and the origin of these orders are quite different and do not strongly interfere with each other in most of the multiferroics. This leads to only a weak coupling between magnetism and ferroelectricity. Fig. 1.1 schematically represents a relationship between multiferroic and magnetoelectric materials and Table 1.1 lists important multiferroic oxides and their ferroelectric and magnetic transition temperatures.

Relationship Between Multiferroic and Magnetoelectric Materials

MagneticallyPolarizable

ElectricallyPolarizable

Ferromagnetic Ferroelectric

Multiferroic

Magnetoelectric

Spin ChargeH E

M P

Fig. 1.1: Relationship between multiferroic and magnetoelectric materials. Ferromagnetic form a subset of magnetically polarizable materials such as paramagnets and antiferromagnets and ferroelectric are a subset of electrical polarizable materials. The overlapping zone (shown by green hatching) represents materials that are multiferroic. Magnetoelectric coupling shown by (black hatching) is an independent phenomenon involving the combination of (ferro-/piezoelectric and magnetostrictive) properties in composite material systems and the coupling in such systems arises either directly or via strain. [Adapted from Ref: Martin, et al., (2012), and Eerenstein, et al., (2006)]


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Table 1.1: Multiferroic materials and their transition temperatures:

Compounds Ferroelectric transition

(Anti) Ferromagnetic/ Ferrimagnetic

transition

Reference & Year

BiFeO3 1103 K 647 K Teague, et al., (1970) Ni3B7O13I 64 K 64 K Ascher, et al. (1996) LuMnO3 900 K 90 K Tomuta, et al., (2001) Ni3V2O8 6 K 9 K Rogado, et al., (2002) GdMn2O5 30 K 40 K Golovenchits, et al., (2004) YCrO3 440 K 140 K Fu, et al., (2005) HoMnO3 875 K 72 K Vajk, et al., (2005) LuFe2O4 330 K 250 K Ikeda, et al., (2005) Bi1-xSrxMnO3 103-105 K 155 K Trokiner, et al., (2005);

Chiba, et al., (1997) TbMn2O5 39 K 42 K Aguilar, et al., (2006) GaFeO3 220 K 225 K Sun, et al., (2006) CoCr2O4 26 K 93 K Yamasaki, et al., (2006) Pr0.6Ca0.4MnO3 240 K 170 K Serrao, et al., (2007) BiMnO3 750 K 105 K Ramesha, et al., (2007) La0.25Nd0.25Ca0.5MnO3 240 K 150 K Serrao, et al., (2007) BiCrO3 440 K 114 K Ramesha, et al., (2007) Nd0.5Ca0.5MnO3 240 K 140 K Serrao, et al., (2007) YMnO3 950 K 80 K Fukumura, et al., (2007) DyMnO3 19 K 39 K Strempfer, et al., (2007) Pr0.7Ca0.3MnO3 225 K 130 K Serrao, et al., (2007) Cd0.5Fe0.5Cr2S4 137 K 137 K Yan, et al., (2007) TbMnO3 28 K 43 K Abe, et al., (2007) ErMnO3 830 K 80 K Vermette, et al., (2008) BiMn2O5 35 K 39 K Shukla, et al., (2008) ErMnO3 830 K 80 K Vermette, et al., (2008) Bi0.1Co1.9MnO4 366 K 184 K Rajeevan, et al., (2008) K3Fe5F15 490 K 123 K Blinc, et al., (2009)


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1.3. History of Multiferroics Electricity and magnetism were combined into one common discipline in the 19th century, culminating in the Maxwell equations. But electric and magnetic ordering in solids is most often considered separately and usually with two good reasons: (a) the electric charges of electrons and ions are responsible for the charge effects, whereas (b) the electron spins govern the magnetic properties. There are, however, cases where these degrees of freedom couple strongly. Attempts to couple both the magnetic and ferroelectric properties in one material started in 1970’s, (Boomgaard, et al., 1976) at Phillips Research labs, Eindhoven, and predominantly by two groups in the Soviet Union: the group of Smolenskii in St. Petersburg (Smolenskii et al., 1971 & 1982) and by Venevtsev et al., (1994) in Moscow. For example, in the new field of spintronics, the effects of spins on the transport properties of solids (and vice versa) allow the possibility to control one by the other. The finding of a strong coupling of magnetic and electric degrees of freedom in insulators can be traced back to Pierre Curie at the end of the nineteenth century, but the real beginning of this field started with a short remark in 1959, “The magnetoelectric effect is odd with respect to time reversal and vanishes in materials without magnetic structure” by Landau, et al., (1959). Initially, such effects were observed experimentally by Dzyaloshinskii in 1959 in his studies on Cr2O3, and Astrov in 1960 and are now known as the linear magnetoelectric effect. In the most general sense, the field of multiferroics was born from studies on magnetoelectric systems (Smolenskii et al., 1959). There have been a number of studies on multiferroics, especially in the 1960s and 1970s, particularly in the former Soviet Union (Loidl, et al., 2008; Smolenskii et al., 1971 & 1974), but these activities faded away, most probably due to the lack of materials with strong magnetoelectric coupling and high ordering temperature, although the enormous potential of multiferroics for technological important applications was recognized early on (Wood, et al., 1974). Despite the original explosion of interest, research on multiferroics remained almost untouched until early 2000. In 2003, the discovery of large ferroelectric polarization in epitaxially grown thin films of BiFeO3 (Wang, et al., 2003) and the discovery of strong magnetic and electric coupling in orthorhombic TbMnO3 (Kimura et al.,


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2003) and TbMn2O5 (Hur, et al., 2004) re-stimulated the activity in the field of multiferroics. In last few years many interesting review articles have been published (Kimura, et al., 2007; Nan et al., 2008; Khomskii, 2009; Wang et al., 2010; Ma et al., 2011), and summarize the rapid progress in this field.

To understand the basic phenomena in the field of multiferroics, and appreciate the main achievements in this field, it is necessary to classify multiferroics on the basis of microscopic mechanisms that determine the coupled effects. 1.4. Different Types of Multiferroics The microscopic origin of magnetism is basically the same in all magnets: it is the presence of localized electrons, mostly in the partially filled d or f shells of transition-metal or rare-earth ions, which have a corresponding localized spin, or magnetic moment. Exchange interactions between the localized moments lead to magnetic order. The situation with ferroelectrics is quite different. There are several different microscopic sources of ferroelectricity, and accordingly lead to different types of multiferroic properties. Generally speaking, there are two groups of multiferroics (Khomskii, 2009).

1.4.1. Type-I Multiferroics The first group, called type-I multiferroics, contains those materials in which ferroelectricity and magnetism have different sources and appear largely independently of one another, though there is some coupling between them. In these materials, ferroelectricity typically appears at higher temperatures than magnetism, and the spontaneous polarization P is often rather large (of order 10 - 100 µC/cm2). Examples are BiFeO3 (TFE ~ 1100K, TN = 643 K, P ~ 90µC/cm2) and YMnO3 (TFE ~ 914K, TN = 76 K, P ~ 6 µC/cm2). These are often good ferroelectrics, and the critical temperatures of the magnetic and ferroelectric transitions can be well above room temperature. Unfortunately, the coupling between magnetism and ferroelectricity in these materials is usually rather weak. There are several different subclasses of type-I multiferroics such as:


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(i) Multiferroic perovskites: In this class of multiferroic materials, ferroelectricity is caused by the off-center shifts of transition metal ion, which forms strong covalent bonds with one (or three) oxygens, using their empty d states.

Fig. 1.2(a): In “mixed” perovskites with ferroelectrically active “d0” ions (green circles) and magnetic “dn” ions (red), shifts of d0 ions from the centers of O6 octahedra (yellow plaquettes) lead to polarization (green arrows), coexisting with magnetic order (red arrows). For example BaTiO3 or Pb(ZrTi)O3 (Khomskii, 2009).

(ii) Ferroelectricity due to lone pairs: In these multiferroic Bi3+ and Pb2+ play the major role in the origin of ferroelectricity. In these ions, there are two outer 6s electrons that do not participate in chemical bonds. They are called lone pairs, or sometimes dangling bonds, and lead to high polarizability, a condition required for ferroelectricity in the classical description. More microscopically one can explain the origin of ferroelectricity in these compounds by ordering of these lone pairs (with certain admixture of p orbitals) in one direction.

Fig. 1.2(b): In Bi and Pb based materials the ordering of lone pairs (yellow “lobes”) of Bi3+ and Pb2+ ions (orange), contributes to the polarization (green arrow). For examples BiFeO3, BiMnO3 and PbVO3 (Khomskii, 2009).


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(iii) Ferroelectricity due to charge ordering: Ferroelectricity and type-I multiferroicity can be due to charge ordering, often observed in transition metal compounds, especially those formally containing transition metal ions with different valence. If, after charge ordering, both sites and bonds turn out to be in-equivalent, this can lead to ferroelectricity (Brink, et al., 2008).

Fig. 1.2(c): In charge ordered systems, the coexistence of in-equivalent sites with different

charges, and in-equivalent (long and short) bonds, leads to ferroelectricity. e.g., Pr1/2Ca1/2MnO3 (Efremov, et al., 2004,) or RNiO3 nickelates (Cheong, et al., 2007).

(iv) Geometric ferroelectricity: Ferroelectricity in YMnO3 has nothing to do with the magnetic Mn3+, but is caused by the tilting of the practically rigid MnO5 block. This tilting occurs just to provide closer packing, and as a result the oxygen ions move closer to the rather small Y ions.

Fig. 1.2(d): The “geometric” mechanism of generation of polarization in YMnO3 describes the

tilting of a rigid MnO5 block with a magnetic Mn remaining at the center. Because of the tilting, the Y-O bonds form dipoles (green arrows), and there appears two “up” dipoles per one “down” dipole so that the system becomes ferroelectric (and multiferroic when Mn spins order at lower temperatures) (Aken, et al., 2004).


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1.4.2. Type-II Multiferroics: Magnetic Multiferroics The second group classified as type-II multiferroics, includes the more recent materials (Kao, 2004; Jonscher, 1983), in which magnetism causes ferroelectricity, implying a strong coupling between the two. However, the polarization in these materials is usually much smaller (10-2 µC/cm2). From the point of view of the mechanism of multiferroic behavior, one can divide type-II multiferroics into two groups: those multiferroics in which ferroelectricity is caused by a particular type of magnetic spiral are called Spiral type-II multiferroics, like TbMnO3, Ni3V2O6, and MnWO4, and those multiferroics in which ferroelectricity appears even for collinear magnetic structures like Ca3CoMnO6 are called Type-II multiferroics.

Different types of spin structures relevant for type-II multiferroics are shown in below figure.

Fig. 1.3(a): Sinusoidal spin density wave, in which spins point along one direction but vary in magnitude. This structure is centro-symmetic and consequently not ferroelectric (Arima, 2007).

Fig. 1.3(b): The cycloidal spiral with the wave vector Q = Qx and spins rotating in the (x,z)-plane. In

this case where one finds nonzero polarization, Pz is not zero (Katsura, et al., 2005).

Fig. 1.3(c): In a so-called “proper screw” the spins rotate in a plane perpendicular to Q. Here the

inversion symmetry is broken, but most often it does not produce polarization, although in certain cases it might (Arima, 2007).


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1.5. Requirement for Magneto-electric Multiferroicity By definition, for a material to be a magnetoelectric multiferroic it must be simultaneously ferromagnetic and ferroelectric. Therefore it’s allowed structural, physical and electronic properties are restricted to those which occur both in ferromagnetic and in ferroelectric materials as follows (Hill, 2000):

(i) Symmetry A primary requirement for the existence of ferroelectricity is a structural distortion from the prototypical high symmetry phase which removes the center of symmetry and allows an electric polarization. There are 31 point groups which allow a spontaneous electric polarization, P, and 31 which allow a spontaneous magnetic polarization. 13 point groups are found in both sets, allowing both properties to exist in the same phase. Although this represents a considerable reduction from the total number of possible crystal structures (the total number of Shubnikov point groups is 122), it is not an insignificant number, and many candidate materials which are not in fact ferromagnetic and ferroelectric exist in one of the allowed symmetries. Therefore it is unlikely that symmetry considerations are responsible for the scarcity of ferromagnetic ferroelectric materials.

(ii) Electrical Properties A ferroelectric material must be an insulator (otherwise an applied electric field would induce an electric current to flow, rather than causing an electrical polarization.) Ferromagnets, although not required to have specific electrical properties, are often metals. Therefore one could assume that the lack of simultaneous occurrence of magnetic and ferroelectric ordering is simply the result of a dearth of magnetic insulators.

However if we include ferrimagnets or weak ferromagnets (which have canted antiferromagnetic ordering, resulting in a weak magnetic moment in the direction of the canting) this argument no longer holds, since most ferrimagnets, or weak ferromagnets are in fact insulators. In addition, there are also very few antiferromagnetic ferroelectrics, even though antiferromagnets are usually insulating materials.


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(iii) Chemistry - “d0-ness” Most common ferroelectric perovskite oxide materials have a formal charge corresponding to the d0 electron configuration on the B cation. Clearly if there are no d electrons creating localized magnetic moments, then there can be no magnetic ordering of any type, either ferro-, ferri-, or antiferromagnetic. It appears however that, in most cases, as soon as the d shell on the small cation is partially occupied, the tendency for it to make a distortion which removes the center of symmetry is eliminated. This could be the result of a number of effects, like size of the small cation, structural distortions, magnetism versus d orbital occupancy etc. 1.6. Magneto-electric Coupling The magnetoelectric (ME) effect in its most general definition denominates the coupling between electric and magnetic fields in materials (Fiebig, 2005). The magneto-electric effect in a single-phase crystal is described (Schmid, 1994; Rivera,1994) by writing the free energy F of the system in terms of an applied magnetic field H and an applied electric field E, their ith components are denoted as Hi, and Ei respectively. Let us consider a non-ferroic material, where both the temperature-dependent electrical polarization Pi(T) (µC/cm2) and the magnetization Mi(T) (µB /formula unit, where µB is the Bohr magneton) are zero in the absence of applied electric and magnetic fields, and there is no hysteresis. It may be represented as an infinite, homogeneous and stress-free medium by writing F under the Einstein summation convention in S.I. units as (Eerenstein, et al., 2006):

........21

21),( 00 +++=− jiijjiijjiij HEHHEEHEF αµµεε (1.1)

The first term on the right hand side describes the contribution resulting from the electrical response to an electric field, where the permittivity of free space is denoted by 0ε , and the relative permittivity ijε is a second-rank tensor that is typically independent of Ei in non-ferroic materials. The second term describes the contribution resulting from the magnetic response to a magnetic field, where 0µ is the permeability


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of free space and ijµ (T) is the relative permeability. The third term describes linear magnetoelectric coupling via ijα (T). In the present scheme, magnetoelectric

coefficient incorporates the field independent material response functions ijε (T) and

ijµ (T). The magnetoelectric effects can then easily be established in the form Pi (Hj) or Mi (Ej). The former is obtained by differentiating F with respect to Ei, and then setting Ei = 0.

A multiferroic that is ferromagnetic and ferroelectric is liable to display large linear magnetoelectric effects. This follows because ferroelectric and ferromagnetic materials often (but not always) possess a large permittivity and permeability respectively, and ijα is bounded by the geometric mean of the diagonalized tensors

ijε and ijµ such as

jjiiij µεµεα 002 ≤ ---- (1.2)

The ME response can be written as in terms of electric and magnetic susceptibilities (Fiebig, 2005);

mjj

eiiij χχα ≤2 ---- (1.3)

According to these relations the ME response can only be large in ferroelectric and (or) ferromagnetic materials. 1.7. Single Phase and Composite Multiferroic Materials In the case of single phase materials, the intense research activity in the field of multiferroic has not yet yielded the desired single phase material, although new materials like TbMnO3 showed great promise, it does not compare favourably with the boracite Ni3B7O13 identified long ago, and above all electrically induced magnetic reversal has been scarcely investigated which is of great interest for applications (Erenstein, et al., 2006). BiFeO3 emerged as a strong candidate, with a large ferroelectric polarisation (Tc ~1100 K) and magnetisation (Néel temperature of 640K)


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and strong magneto electric coupling was demonstrated by reversing the polarisation by an electric field which rotates the anti-ferromagnetic spins (Chu, et al., 2008). However, many issues still remain and need to be addressed that relate to the reduction of high leakage currents, need for lowering the writing voltages and high frequency (GHz) operation in nano scale device structures (Bibes, et al., 2007).

In contrast to the single phase materials, composites which are very easy to make and incorporate ferroelectric and ferri-/ ferromagnetic phases typically yield giant magneto electric coupling (MEC) response above room temperature. Ferrite-piezo ceramic composites (e.g., with PZT), (magnetic alloy Terefenol D - PZT), ceramic-alloy (FeBSiC/PZT-fiber) and polymer based composites (Terefenol-D in epoxy/PZT) have shown excellent magneto-electric conversion (Ma et al., 2011). A wide variety of composite materials (ferrite and piezoelectrics) with different connectivity and material combinations have been investigated, and both direct and converse ME effects have been demonstrated which are very attractive for a variety of device applications. In this area now the focus is more towards the development of magneto electric (ME) nanostructures especially in the form of thin films for direct integration with IC chips, and the emphasis is more towards the understanding of the timescale of the coupling process (Nan et al., 2008). 1.8. Focus in the Present Thesis From the literature it is still hard to find a single phase material exhibiting strong magneto-electric properties with coexistence of ferroelectricity and ferromagnetism at practically useful temperatures. Crystal symmetry in spinel oxides has attracted our attention as if offers sufficient opportunities for tailoring the composition for new functional properties, and numerous permutations and combinations are possible at A and B sites. In the Co-based spinel oxides the substituted trivalent metal ion occupies the octahedral sites, while cobalt ions are distributed over both octahedral (Co3+ ions, non-magnetic) and tetrahedral sites (magnetic Co2+ ions, magnetic). Mixed valence states of this spinel oxide play a key role in determining the electrical and magnetic characteristics and require further investigations to understand the intriguing nature of spin state distribution and hybridization states.


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Mixed oxides known as spinels with the general formula AB2O4 where A = Mg, Cr, Mn, Fe, Co, Ni, Zn, Cd, and B = Al, Cr, Mn, Fe, Co, Ga represent divalent and trivalent transition metal cations respectively. They form a special class of compounds with interesting electronic, magnetic, optical, and catalytic properties, and have been extensively investigated by introducing a variety of dopants (Tian et al., 2012; Rios et al., 2004; Philip, et al., 1999; Dormann, et al., 1990). In recent years Co3O4 has also been identified as a magnetic semiconductor (Zeng et al., 2011). Earlier studies on the magnetic properties of Co3-xMnxO4 (x = 0.1 to 1.0) have revealed its ordered ferrimagnetic behaviour, and a phase transition from para- to ferrimagnetic below 191 K (Wickham, et al., 1958). From the substitution point of view, it appears a lot of scope exists to substitute various trivalent cations by replacing a fraction of Co3+ ions by Al, Mn, Ni, Cr, Ti etc (Suzuki et al., 2007; Yamasaki et al., 2006; Wickham, et al., 1958).

In the present thesis the focus is on the substitution of Mn3+ ions having larger ionic radii to look into the possibility of developing a new class of single phase multiferroic materials with the expectation that Mn can induce non-centro-symmetric charge ordering and consequent polarization.

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