**3.1 Multiferroic systems of BaTiO3**

#### *3.1.1 X-ray diffraction for BaTiO3 and BaTM0.01Ti0.99O3 nanoparticles*

The sol-gel method is used to prepare pure BaTiO3 and BaTM0.01Ti0.99O [TM = Cr (BTO:Cr), Mn (BTO:Mn), Fe (BTO:Fe), Co (BTO:Co), Ni (BTO:Ni), Cu (BTO:Cu)] nanoparticles [4]. The TM ions in perovskite BTO structure highly influenced lattice constants to induce lattice strain and unit cell expansion, which responsible into defects vacancies formation. **Figure 3** shows the Rietveld refinement (Full-Prof program) of X-ray diffraction (XRD) patterns for pure and BaTM0.01Ti0.99O nanoparticles measured at room temperature. A polycrystalline with tetragonal BTO phase (space group:P4*mm*) is detected. The fitting parameters, Rp(%) = 6.7, 7.1, 6.7, 4.9, 9.1, 8.2 and 9.8, Rwp(%) = 3.2, 9.9, 9.2, 10.0, 12.5, 1.2 and 14.6, χ<sup>2</sup> = 1.1, 1.4, 0.81, 1.4, 3.3, 3.3 and 0.9 and distortion ratio, (*c*/*a*) = 1.00959, 1.00932, 1.00688, 1.00909, 1.00776, 1.00625 and 1.00508, respectively, refined for pure BTO and BTO with Cr, Mn, Fe, Co, Ni, Cu doping. Also, **Figure 3(a)** shows the tetragonal splitting of (200) diffraction peak at 2θ = 44.3–45.7°. The diffraction peak of pure BTO has shifted towards a lower diffraction angle with TM doping which supports the lattice strain in BTO. Such splitting of (200) peak might be confirmed the tetragonal phase formation. It is due to electrostatic repulsions between 3d electrons of Ti4+ ions and 2p electrons of O2<sup>−</sup> ions, the structure becomes distorted. It is also reported in Ref. [4] that the average particles size, from TEM, DTEM (nm) = 20 ± 3, 13 ± 1, 33 ± 5, 35 ± 3, 17 ± 1 and 47 ± 7, the value of saturation magnetization, Ms (emu g<sup>−</sup><sup>1</sup> ) = 0.056, 0.042, 0.066, 0.035, 0.013 and 0.021, and the ME coupling constant, αME (mV cm<sup>−</sup><sup>1</sup> Oe<sup>−</sup><sup>1</sup> ) = 25.91, 11.27, 31.15, 16.58, 11.61 and 16.48, respectively, measured with Cr, Mn, Fe, Co, Ni, Cu doping into BTO.

**Figure 3.**

*XRD pattern for pure BaTiO3 and BaTM0.01Ti0.99O3 nanoparticles. (a) Showing the splitting of the (200) peak. Adopted from Verma and Kotnala [4].*

### *3.1.2 Nanostructure of BaTiO3 (BTO) and BaFe0.01Ti0.99O3 (BFTO) multiferroic*

The BTO and BFTO were prepared by a hydrothermal method of processing temperature 180°C/48 h [5]. The XRD pattern shows the coexistence of cubic/tetragonal/ hexagonal phases of BTO and cubic/tetragonal of BFTO. **Figure 4(a** and **b)** reveals the TEM images of BTO and BFTO nanostructure. It shown that BTO (**Figure 4(a)**) is the product that consist of nanorods structure having hexagonal like face of average diameter 50 nm and length 75 nm. However, **Figure 4(b)** shows the nanowires formation of BFTO with average diameter ~45 nm and the length >1.5 μm. It is also reported in Ref. [5] that the room temperature *M*-*H* hysteresis shows diamagnetism in BTO and ferromagnetism in BFTO with Ms ~ 82.23 memu g<sup>−</sup><sup>1</sup> , Mr ~ 31.91 memu g<sup>−</sup><sup>1</sup> with Hc ~ 122.68 Oe and ME coupling coefficient, αME = 16 mV Oe<sup>−</sup><sup>1</sup> cm<sup>−</sup><sup>1</sup> .

### *3.1.3 Ferromagnetism/ferroelectricity in Ce,La:BaFe0.01Ti0.99O3 nanostructures*

The nano-aggregation type Ba(Fe0.67Ce0.33)0.01Ti0.99O3 (BFTO:Ce) and Ba(Fe0.67La0.33)0.01Ti0.99O3 (BFTO:La) product is synthesized by a hydrothermal process [2]. Rietveld refinement of XRD pattern indicates polycrystalline phase with tetragonal BFTO. It is reported that the Ce and La ions in BFTO improved lattice distortion, c/a ratio. These dopant Ce and La in BFTO forms nano-aggregation type product with average value of aggregation diameter, D = 40 and 22 nm, respectively, for BFTO:Ce and BFTO:La. The formation of tetragonal BTO phase and lattice defects due to vacancies is attributed by Raman active modes. These defects and vacancies are also confirmed with photoluminescence measurement that might be altered due to higher surface-tovolume ratio in nano-aggregation. **Figure 4(d** and **e)** shows the ferromagnetic behavior of Ce, La doped BFTO, respectively, by magnetization versus field (M-Hdc hysteresis) measured at room temperature [2]. The values of Ms (emu g<sup>−</sup><sup>1</sup> ) = 0.15 and 0.08, and Mr (emu g<sup>−</sup><sup>1</sup> ) = 0.039 and 0.015 with Hc (Oe) = 242 and 201, respectively, for BFTO:Ce and BFTO:La. It is well predicted that the formation of Fe4+–O2<sup>−</sup> –Fe4+ interaction is ferromagnetic, which dominate in BFTO over the antiferromagnetic Fe3+–O2<sup>−</sup> –Fe4+

**99**

and Fe3+–O2<sup>−</sup>

**Figure 4.**

expects *Fe*3+

Pr (μC cm<sup>−</sup><sup>2</sup>

doping, Ps (μC cm<sup>−</sup><sup>2</sup>

–*VO* 2− –*Fe*3+

2

value of spontaneous polarization, Ps (μC cm<sup>−</sup><sup>2</sup>

polarization-induced surface charges [29].

*3.1.4 Magnetization at low temperature measurement*

) = 5.45 with electric coercivity, Ec (kV cm<sup>−</sup><sup>1</sup>

*following ZFC/FC at H = 500 Oe for Ce, La doped BFTO. Adopted from Refs. [2, 5].*

) = 8.28, and Pr (μC cm<sup>−</sup><sup>2</sup>

orbital, pz that overlaps *dz*

*Ferromagnetism in Multiferroic BaTiO3, Spinel MFe2O4 (M = Mn, Co, Ni, Zn) Ferrite…*

–Fe3+ interactions, producing weak ferromagnetism. Generally, the

*Transmission electron microscopy (TEM) of (a) pure BaTiO3 (b) Ba(Fe0.01Ti0.99)O3. (c) ME voltage coefficient (αME), (d and e) M-Hdc hysteresis at room temperature, (d*′ *and e*′*) P-E hysteresis, and (d*″ *and e*″*) M(T)* 

transition that generally exists in the structure where an electron

) = 13.83 and remanent polarization,

) = 2.46, with Ec (kV cm<sup>−</sup><sup>1</sup>

) = 9.53. However, with La

electronic

) = 6.14. These

of d shells in iron neighbors. The Fe3+ ions have 3d5

ferromagnetism in Fe-doped BaTiO3 is explained into two ways: the partially filled inner shells (d- or f-levels) and formation of nanostructures. An F-centre exchange (FCE) mechanism describes the required ferromagnetism [24, 25]. Such a mechanism

trapped in oxygen vacancies, VO to form F-centre. For this, the electron occupies an

values of polarization have an improvement over reported work [26–28]. This is due to nano-aggregation formation and lattice distortion enhancement in BTO lattice. The smaller polarization in BFTO:La is the nano-size effect that involved compensation of

The origin of observed ferromagnetism at room temperature in Ce- and La-doped BFTO is described by measuring their magnetization from zero-field cooling (ZFC) and field cooling (FC) at 500 Oe (**Figure 4**(**d″** and **e″**)). A clear separation between FC and ZFC retains up to low temperature without blocking temperature is observed. This is an indication of weak antiferromagnetic interactions.

configurations for which spin down trapped electron and spin up in two iron Neighbors. Therefore, the F-centre has the exchange interaction among two iron ions that would leads to ferromagnetism. The insets of **Figure 4(d′** and **e′)** show the polarizationelectric field (P-E) hysteresis at room temperature. With Ce doping into BFTO, the

*DOI: http://dx.doi.org/10.5772/intechopen.82437*

*Ferromagnetism in Multiferroic BaTiO3, Spinel MFe2O4 (M = Mn, Co, Ni, Zn) Ferrite… DOI: http://dx.doi.org/10.5772/intechopen.82437*

**Figure 4.**

*Electromagnetic Materials and Devices*

*3.1.2 Nanostructure of BaTiO3 (BTO) and BaFe0.01Ti0.99O3 (BFTO) multiferroic*

*3.1.3 Ferromagnetism/ferroelectricity in Ce,La:BaFe0.01Ti0.99O3 nanostructures*

The nano-aggregation type Ba(Fe0.67Ce0.33)0.01Ti0.99O3 (BFTO:Ce) and

Ba(Fe0.67La0.33)0.01Ti0.99O3 (BFTO:La) product is synthesized by a hydrothermal process [2]. Rietveld refinement of XRD pattern indicates polycrystalline phase with tetragonal BFTO. It is reported that the Ce and La ions in BFTO improved lattice distortion, c/a ratio. These dopant Ce and La in BFTO forms nano-aggregation type product with average value of aggregation diameter, D = 40 and 22 nm, respectively, for BFTO:Ce and BFTO:La. The formation of tetragonal BTO phase and lattice defects due to vacancies is attributed by Raman active modes. These defects and vacancies are also confirmed with photoluminescence measurement that might be altered due to higher surface-tovolume ratio in nano-aggregation. **Figure 4(d** and **e)** shows the ferromagnetic behavior of Ce, La doped BFTO, respectively, by magnetization versus field (M-Hdc hysteresis)

) = 0.039 and 0.015 with Hc (Oe) = 242 and 201, respectively, for BFTO:Ce

and ferromagnetism in BFTO with Ms ~ 82.23 memu g<sup>−</sup><sup>1</sup>

~ 122.68 Oe and ME coupling coefficient, αME = 16 mV Oe<sup>−</sup><sup>1</sup>

measured at room temperature [2]. The values of Ms (emu g<sup>−</sup><sup>1</sup>

and BFTO:La. It is well predicted that the formation of Fe4+–O2<sup>−</sup>

ferromagnetic, which dominate in BFTO over the antiferromagnetic Fe3+–O2<sup>−</sup>

The BTO and BFTO were prepared by a hydrothermal method of processing temperature 180°C/48 h [5]. The XRD pattern shows the coexistence of cubic/tetragonal/ hexagonal phases of BTO and cubic/tetragonal of BFTO. **Figure 4(a** and **b)** reveals the TEM images of BTO and BFTO nanostructure. It shown that BTO (**Figure 4(a)**) is the product that consist of nanorods structure having hexagonal like face of average diameter 50 nm and length 75 nm. However, **Figure 4(b)** shows the nanowires formation of BFTO with average diameter ~45 nm and the length >1.5 μm. It is also reported in Ref. [5] that the room temperature *M*-*H* hysteresis shows diamagnetism in BTO

*XRD pattern for pure BaTiO3 and BaTM0.01Ti0.99O3 nanoparticles. (a) Showing the splitting of the (200) peak.* 

, Mr ~ 31.91 memu g<sup>−</sup><sup>1</sup>

) = 0.15 and 0.08, and

–Fe4+ interaction is

–Fe4+

 cm<sup>−</sup><sup>1</sup> . with Hc

**98**

Mr (emu g<sup>−</sup><sup>1</sup>

**Figure 3.**

*Adopted from Verma and Kotnala [4].*

*Transmission electron microscopy (TEM) of (a) pure BaTiO3 (b) Ba(Fe0.01Ti0.99)O3. (c) ME voltage coefficient (αME), (d and e) M-Hdc hysteresis at room temperature, (d*′ *and e*′*) P-E hysteresis, and (d*″ *and e*″*) M(T) following ZFC/FC at H = 500 Oe for Ce, La doped BFTO. Adopted from Refs. [2, 5].*

and Fe3+–O2<sup>−</sup> –Fe3+ interactions, producing weak ferromagnetism. Generally, the ferromagnetism in Fe-doped BaTiO3 is explained into two ways: the partially filled inner shells (d- or f-levels) and formation of nanostructures. An F-centre exchange (FCE) mechanism describes the required ferromagnetism [24, 25]. Such a mechanism expects *Fe*3+ –*VO* 2− –*Fe*3+ transition that generally exists in the structure where an electron trapped in oxygen vacancies, VO to form F-centre. For this, the electron occupies an orbital, pz that overlaps *dz* 2 of d shells in iron neighbors. The Fe3+ ions have 3d5 electronic configurations for which spin down trapped electron and spin up in two iron Neighbors. Therefore, the F-centre has the exchange interaction among two iron ions that would leads to ferromagnetism. The insets of **Figure 4(d′** and **e′)** show the polarizationelectric field (P-E) hysteresis at room temperature. With Ce doping into BFTO, the value of spontaneous polarization, Ps (μC cm<sup>−</sup><sup>2</sup> ) = 13.83 and remanent polarization, Pr (μC cm<sup>−</sup><sup>2</sup> ) = 5.45 with electric coercivity, Ec (kV cm<sup>−</sup><sup>1</sup> ) = 9.53. However, with La doping, Ps (μC cm<sup>−</sup><sup>2</sup> ) = 8.28, and Pr (μC cm<sup>−</sup><sup>2</sup> ) = 2.46, with Ec (kV cm<sup>−</sup><sup>1</sup> ) = 6.14. These values of polarization have an improvement over reported work [26–28]. This is due to nano-aggregation formation and lattice distortion enhancement in BTO lattice. The smaller polarization in BFTO:La is the nano-size effect that involved compensation of polarization-induced surface charges [29].

#### *3.1.4 Magnetization at low temperature measurement*

The origin of observed ferromagnetism at room temperature in Ce- and La-doped BFTO is described by measuring their magnetization from zero-field cooling (ZFC) and field cooling (FC) at 500 Oe (**Figure 4**(**d″** and **e″**)). A clear separation between FC and ZFC retains up to low temperature without blocking temperature is observed. This is an indication of weak antiferromagnetic interactions.

An upward curvature observed in M-T curve suggests a Curie-Weiss like behavior. It is attributed with short-range ferromagnetism, or a spin-cluster within a matrix of spin disorder [30]. Li et al*.* [31] suggested that the oxygen vacancy might be mediate antiferromagnetic-ferromagnetic interactions in multiferroics.
