International Journal of Thermophysics

, Volume 34, Issue 4, pp 567–574 | Cite as

Effect of Previous Milling of Precursors on Magnetoelectric Effect in Multiferroic \({\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}}\) Ceramic

  • J. Dercz
  • J. Bartkowska
  • G. Dercz
  • P. Stoch
  • M. Łukasik


\(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) magnetoelectric (ME) ceramics have been synthesized and investigated. The ME effect can be described as an induced electric polarization under an external magnetic field or an induced magnetization under an external electric field. The materials in the ME effect are called ME materials, and they are considered to be a kind of new promising materials for sensors, processors, actuators, and memory systems. Multiferroics, the materials in which both ferromagnetism and ferroelectricity can coexist, are the prospective candidates which can potentially host the gigantic ME effect. \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\), an Aurivillius compound, was synthesized by sintering a mixture of \(\mathrm{Bi}_{2}\mathrm{O}_{3}, \mathrm{Fe}_{2}\mathrm{O}_{3}\), and \(\mathrm{TiO}_{2}\) oxides. The precursor materials were prepared in a high-energy attritorial mill for (1, 5, and 10) h. The orthorhombic \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) ceramics were obtained by a solid-state reaction process at 1313 K. The ME voltage coefficient (\(\alpha _\mathrm{ME}\)) was measured using the dynamic lock-in method. The highest ME voltage coefficient (\(\alpha _\mathrm{ME} = 8.28\,\text{ mV }{\cdot }\text{ cm }^{-1}{\cdot }\text{ Oe }^{-1})\) is obtained for the sample milled for 1 h at \(H_\mathrm{DC }= 4\) Oe (1 Oe = 79.58 \(\text{ A }{\cdot }\text{ m }^{-1})\).


\(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) Dielectric properties Ferroelectric High-energy ball milling Magnetoelectric (ME) effect Sintering 

1 Introduction

The magnetoelectric (ME) effect, i.e., the induction of ferroelectric polarization by a magnetic field and magnetization by an electric field can be achieved in multiferroic materials that show the coexistence of ferroelectricity and ferromagnetism [1, 2, 3, 4, 5, 6, 7]. The ME effect can be observed in some chemical compounds and solid solutions with different crystal structures including perovskites, \(\mathrm{BiFeO}_{3}\) [8] bismuth oxides with a layered structure, boracites, orthorhombic manganites of the \(\mathrm{RMnO}_{3}\) (R = Eu, Gd, Tb) type [9], hexagonal fluorites of the \(\text{ Ba-MeF }_{4}\) type, and some compounds with the \(\mathrm{BaTiO}_{3}\) and \(\mathrm{GdFe}_{3}(\mathrm{BO}_{3})_{4}\) structure [10]. In most of these materials, the ME effect is observed in an \(H > 10\) Oe (1 Oe = 79.58 A \({\cdot }\text{ m }^{-1})\) magnetic field [11] or at low temperatures. \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) ceramics with their bismuth-layered perovskite-like structure are characterized by the ME effect in an \(H = 4\) Oe magnetic field at room temperature.

The ME effect, in its most general definition, describes the coupling between electric and magnetic fields in matter, i.e., the induction of magnetization by an electric field or polarization generated by a magnetic field. Thermodynamically, the ME effect can be understood within the framework of Landau’s theory, approached by the expansion of the free energy for the ME system, i.e.,
$$\begin{aligned} F({E,H})&= F_0 -P_i^\mathrm{s} E_i -M_i^\mathrm{s} H_i -(1/2)\varepsilon _0 \varepsilon _{1{k}} E_i E_k \nonumber \\&-({1/2})\mu _0 \mu _{1{k}} H_i H_k -\alpha _{ik} E_i H_k \nonumber \\&-({1/2})\beta _{ijk} E_i H_j H_k -({1/2})\gamma _{ijk} H_i E_j E_k +\cdots , \end{aligned}$$
where \(F_{0}\) is the ground state free energy, subscripts (\(i, j,k\)) refer to the three components of a variable in spatial coordinates, \(E_{i}\) and \(H_{i}\) are the components of the electric field \(E\) and magnetic field \(H\), respectively, \(P_{i}^\mathrm{s}\) and \(M_{i}^\mathrm{s}\) are the components of spontaneous polarization \(P^\mathrm{s}\) and magnetization \(M^\mathrm{s}, \varepsilon _{0}\) and \(\mu _{0}\) are the dielectric and magnetic susceptibilities of vacuum, \(\varepsilon _{ij}\) and \(\mu _{ij}\) are the second-order tensors of dielectric and magnetic susceptibilities, \(\beta _{ijk}\) and \(y_{ijk}\) are the third-order tensor coefficients and, most importantly, \(\alpha _{ij}\) is the component of tensor \(\alpha \) which is designated as the linear ME effect and corresponds to the induction of polarization by a magnetic field or magnetization by an electric field. The remaining terms in the preceding equations correspond to the high-order ME effects parameterization by tensors \(\beta \) and \(\gamma \) [12]. Then the polarization is as follows:
$$\begin{aligned} P_i \left( {E,H} \right) \!=\!-\frac{\partial F}{\partial E_i}=P_i^\mathrm{s} +\varepsilon _0 \varepsilon _{ik} E_k \!+\!\alpha _{ik} H_k +\left( {1/2} \right) \beta _{ijk} H_j H_k +\gamma _{ijk} H_i E_j +\cdots \nonumber \\ \end{aligned}$$
and the magnetization is as follows:
$$\begin{aligned} M_i \left( {E,H} \right) \!=\!-\frac{\partial F}{\partial H_i}=M_i^\mathrm{s} \!+\!\mu _0 \mu _{ik} H_k \!+\!\alpha _{ik} E_k \!+\!\beta _{ijk} H_j E_k +\left( {1/2} \right) \gamma _{ijk} E_j E_k +\cdots \nonumber \\ \end{aligned}$$
Equation 2 can be also written as (neglecting the higher-order terms):
$$\begin{aligned} P_k =const+\alpha H+\left( {1/2} \right) \beta H^2 . \end{aligned}$$
The electric output voltage is measured across the sample by applying the magnetic field. From the value of the obtained voltage, the electric field \((E)\) can be calculated taking the thickness of the sample into consideration.

2 Measurements

2.1 Specimens

The \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) synthesis proceeds according to the following reaction:
$$\begin{aligned} \mathrm{5Bi}_2\mathrm{O}_3 +\mathrm{6TiO}_2 +\mathrm{Fe}_2\mathrm{O}_3 \rightarrow \mathrm{2Bi}_5\mathrm{Ti}_3\mathrm{FeO}_{15}. \end{aligned}$$
The high-energy ball milling process was carried out in a vibratory mill (SPEX 8000 CertiPrep Mixer/Mill type) for (1, 5, and 10) h in an argon atmosphere. The balls to powder mass ratio was 5:1 [13]. The free sintering process was conducted for 5 h at 1313 K. Then, in order to obtain parallelepiped surfaces, the material was ground off and polished. The pellets with a diameter of 10 mm and a thickness of 1 mm prepared in this way underwent 20 min stress relief annealing in order to remove the stresses that had appeared during grinding. Electrodes were placed on the ceramic material prepared in this way.

2.2 Procedures

ME measurements were performed using the lock-in method based on a lock-in amplifier (Stanford Research SR830m). In order to measure the ME voltage coefficient, a disk shaped sinter of 1 mm in height and 10 mm in diameter was placed into a static magnetic field \(H_\mathrm{DC}\), created by an electromagnet with additional modulation of the \(H_\mathrm{AC}\) magnetic field produced by Helmholtz coils. Both magnetic fields were oriented perpendicular to the surface of the sinter. An electric signal \((U)\) from the sample was detected using a lock-in amplifier. The \(U\) voltage was measured for different magnitudes of the static magnetic field and the frequencies of the modulation field in the range of 200 Hz to 20 kHz. The magnetoelectric voltage coefficient (ME) was derived using the following formula [14]:
$$\begin{aligned} \alpha _\mathrm{ME} =\frac{U}{Hd}, \end{aligned}$$
where \(d\) is the height of the investigated sample.

The measurements of \(^{57}\)Fe Mössbauer spectra were performed in transmission geometry by means of a constant spectrometer of the standard design. The 14.4 keV gamma rays were provided by a 50 mCi source of \(^{57}\)Co/Rh. The spectra of the samples were measured at room temperature. Hyperfine parameters of the investigated spectra were related to the \(\alpha \)-Fe standard. The experimental spectrum shape was described with a transmission integral calculated according to the numerical Gauss–Legendre procedure.

X-ray analysis was carried out using the X-Pert Philips diffractometer equipped with a curved graphite monochromator on a diffracted beam and a tube provided with a copper anode. It was supplied by a current intensity of 30 mA and voltage of 40 kV. The length of radiation (\(\lambda _{\mathrm{CuK}\!\upalpha }\)) was 1.54178 Å. The diffraction lines were recorded by the “step-scanning” method in the range of 2\(\theta \) from \(15^{\circ }\) to \(140^{\circ }\) with a \(0.05^{\circ }\) step. The Rietveld analysis was performed applying the DBWS-9807 program that is an updated version of the DBWS programs for Rietveld refinement with PC and mainframe computers. The pseudo-Voigt function was used in the description of diffraction line profiles at Rietveld refinement [13, 15, 16, 17, 18]. The phase abundance was determined using the relation proposed by Hill and Howard [16].

3 Results

Qualitative analysis (\(Y\)-axis is formatted as a square root) shows that ceramics sintered from the substrates after preliminary (1 and 5) h high-energy ball milling is a one-phase material containing the \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) (ICDD PDF 82-0063) phase (Fig. 1). However, in the case of a ceramic sample obtained from the substrate milled for 10 h, the phase analysis showed that the material was a two-phase one and contained the \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) (ICDD PDF 82-0063) and \(\mathrm{Bi}_{12}\mathrm{TiO}_{20}\) (ICDD PDF 34-0097) phases (Fig. 1). The appearance of the \(\mathrm{Bi}_{12}\mathrm{TiO}_{20}\) phase is probably caused by the formation of agglomerates during the process of high-energy ball milling. With the use of the Rietveld analysis, the qualitative composition of individual phases was determined. The calculations showed that the content of the \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) phase is 97.6 mass%, whereas for \(\mathrm{Bi}_{12}\mathrm{TiO}_{20}\), the phase share is 2.4 mass% [15].
Fig. 1

Diffraction pattern for the \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) ceramics obtained after sintering from the substrates milled for (1, 5, and 10) h

Based on the share of the components that were being adjusted, the qualitative phase composition of the investigated material was estimated. Table 1 presents hyperfine parameters characteristic of individual components obtained during calculations. The spectrum of the \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) ceramics has been described with the use of two components—\(Z_{1}\) and \(Z_{2}\). The process of preliminary milling of ceramic samples results in an average increase in the value of the hyperfine magnetic field, which ranges from \(14.1 \times 10^{4}\) Gs (1 Gs = 10\(^{-4}\,T)\) for 1 h BTFO milling up to \(21.9 \times 10^{4}\) Gs for 10 h BTFO. The observed increase in the value of the hyperfine magnetic field is caused by the increase in Fe concentration in the matrix phase.
Table 1

Hyperfine parameters for the \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) ceramics



QS (\(\text{ mm }{\cdot }\text{ s }^{-1}\))

SD (\(\text{ mm }{\cdot }\text{ s }^{-1}\))

IS (\(\text{ mm }{\cdot }\text{ s }^{-1}\))

SD (\(\text{ mm }{\cdot }\text{ s }^{-1}\))

\(A\) (%)

SD (%)

\(B_\mathrm{hf}\) (\(10^{4}\) Gs)

SD (\(10^{4}\) Gs)

1 h BTFO


















5 h BTFO


















10 h BTFO


















The isometric shift (IS) characteristic of the \(Z_{1}, Z_{2}\) component confirms that this layer contains both the Fe and Ti atoms and that their mutual redistribution is caused by the milling process. Low quadrupole splitting (QS) values—of the parameter which describes the symmetry of the set—calculated for the \(Z_{1}\) component prove that the set of elements is homogeneous (Table 1).

The differences in the values of the IS demonstrate that the local environment of the Mössbauer nuclide changes. High QS values calculated for the \(Z_{2}\) component are a sign of some disturbances in the homogeneous set of elements in both the perovskite and bismuth oxide layers. The values of the isometric shift determined for all components clearly show that Fe atoms in the perovskite layer are surrounded by Ti and Bi atoms [16, 17, 18].

In Fig. 2, the dependence of the ME effect on frequency can be observed. The strongest dependence of \(\alpha _\mathrm{ME}\) and frequency has been observed for 1 h BTFO, whereas the weakest one—in case of 10 h BTFO ceramics. However, in both cases it is the linear dependence.
Fig. 2

Magnetoelectric coefficient for the \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) ceramics as a function of frequency

Figure 3a, b shows the ME coefficient for \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\). The experiment was performed at room temperature under an alternating magnetic field of 4 Oe amplitude. The ME effect in the studied material is weak, but measurable at room temperature. The differences that have been observed in the ME effect (Fig. 3a) probably result from the way the grains in the ceramics are arranged. In previous research, the authors showed the correlation between the precursor’s milling time and the arrangement of the grains in the synthesized ceramics [13, 15]. It was found that the longer is the precursors’ milling time and the bigger is the grains’ dispersion, the larger is the number of similarly oriented grains and the fewer is the number of pores in the ceramics. An example of an enlarged part of the hysteresis from the BTFO 1 h sample is presented in Fig. 3b. The value of the ME coefficient and its changes depend on the milling time. The highest value is obtained for the 1 h BTFO \((\alpha _\mathrm{ME} = 8.2\,\text{ mV }{\cdot }\text{ cm }^{-1}{\cdot }\text{ Oe }^{-1})\) ceramics, whereas the lowest one appears with 10 h BTFO \((\alpha _\mathrm{ME} = 0.8\,\text{ mV }{\cdot }\text{ cm }^{-1}{\cdot }\text{ Oe }^{-1})\). The plot indicates that the ME coupling parameter increases nonlinearly with increasing magnetic field. But when reversing the field, it does not retrace its path either, and shows a hysteresis behavior [19, 20, 21, 22].
Fig. 3

Magnetoelectric coefficient for the \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) ceramics as a function of (a) the bias magnetic field and (b) example of an enlarged part of the hysteresis

The realization of the ME coupling parameter in the multiferroic material is due to the product’s property, which is the ferroelectric and piezoelectric phase and the ferromagnetic phase. The coupling nature depends on the mechanical coupling between (\(\mathrm{Bi}_{2}\mathrm{O}_{2})^{2+}\) and (\(\mathrm{A}_{\mathrm{m}-1}\mathrm{B}_\mathrm{m}\mathrm{O}_{3\mathrm{m}+1})^{2-}\) phases, where A = Bi, B = Ti, Fe, and m = 4 phases. If the transfer of stress from the (\(\mathrm{A}_{\mathrm{m}-1}\mathrm{B}_\mathrm{m}\mathrm{O}_{3\mathrm{m}+1})^{2-}\) magnetostrictive phase to the (\(\mathrm{Bi}_{2}\mathrm{O}_{2})^{2+ }\) ferroelectric and piezoelectric phase is strong enough, a high value of the ME coupling parameter can be obtained [20].

The ME hysteresis loops are observed for the multiferroic material at room temperature; a strictly induced polarization takes place. The presence of Fe in the lattice can induce bulk magnetization in such perovskites. The observed phenomenon may arise due to the slight canting of the Fe–O–Fe chain of spins in the regular octahedra, which is slightly tilted. The addition of (\(\mathrm{Bi}_{2}\mathrm{O}_{2})^{2+}\) to (\(\mathrm{A}_{\mathrm{m}-1}\mathrm{B}_\mathrm{m}\mathrm{O}_{3\mathrm{m}+1})^{2-}\) reduces the degree of incommensurate structure, but preserves the nonlinearity [21].

Magnetic properties of the studied \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) ceramics were also confirmed with the use of magnetic scales. The initial magnetization curve (Fig. 4) was determined by simultaneous measurement of the magnetic induction and the strength of the external \(H\) field which causes the ordering of domains. Examples of curves for the two bordering samples of 1 h BTFO and 10 h BTFO are presented in Fig. 4. \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) ceramics exhibit weak magnetic properties. However, these values are measurable. The strongest relation between the magnetic induction and the field strength has been observed for the material marked as 1 h BTFO, and the lowest for 10 h BTFO. The lowering of magnetic properties for 10 h BTFO is probably the result of the fact that the extension of the high-grinding process causes significant de-ordering of magnetic domains.
Fig. 4

Dependence of the magnetic induction on the strength of the external \(H\) field for BTFO 1 h and 10 h

4 Conclusions

  1. 1.

    Mössbauer studies performed with the use of conversion electron Mössbauer spectroscopy (CEMS) technique confirmed the magnetic properties of the \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) ceramic.

  2. 2.

    The ME effect in the \(\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}\) ceramics is weak, yet measurable at room temperature.

  3. 3.

    The fastest growth of the ME effect is obtained for the 1 h BTFO sample.

  4. 4.

    The highest values of the ME coefficient were obtained for the 1 h BTFO sample.



  1. 1.
    C.W. Nan, Phys. Rev. B 50, 6082 (1994)ADSCrossRefGoogle Scholar
  2. 2.
    N. Cai, J. Zhai, L. Liu, Y. Lin, C. Nan, Mater. Sci. Eng. B 99, 21 (2003)CrossRefGoogle Scholar
  3. 3.
    P. Curie, J. Phys. 3, 393 (1894)MATHGoogle Scholar
  4. 4.
    D.N. Astrov, Sov. Phys. JETP 11, 708 (1960)Google Scholar
  5. 5.
    D.N. Astrov, Sov. Phys. JETP 13, 729 (1961)Google Scholar
  6. 6.
    G.T. Rado, V.J. Folen, Phys. Rev. Lett. 7, 310 (1961)ADSCrossRefGoogle Scholar
  7. 7.
    V.J. Folen, G.T. Rado, E.W. Stalder, Phys. Rev. Lett. 6, 607 (1961)ADSCrossRefGoogle Scholar
  8. 8.
    X.Y. Zhang, J.Y. Dai, C.W. Lai, Prog. Solid State Chem. 33, 147 (2005)CrossRefGoogle Scholar
  9. 9.
    K. Noda, M. Akaki, F. Nakamura, D. Akahoshi, H. Kuwahara, J. Magn. Magn. Mater. 310, 1162 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    A.K. Zvezdin, A.M. Kadomtseva, S.S. Krotov, A.P. Pyatakov, YuF Popov, G.P. Vorob’ev, J. Magn. Magn. Mater. 300, 224 (2006)ADSCrossRefGoogle Scholar
  11. 11.
    R. Grössinger, G.V. Duong, R. Sato-Turtelli, J. Magn. Magn. Mater. 320, 1972 (2008)CrossRefGoogle Scholar
  12. 12.
    M. Fiebig, J. Phys. D Appl. Phys. 38, 123 (2005)ADSCrossRefGoogle Scholar
  13. 13.
    G. Dercz, J. Dercz, K. Prusik, A. Hanc, L. Pająk, J. Ilczuk, Arch. Metall. Mater. 54, 741 (2009)Google Scholar
  14. 14.
    J.A. Bartkowska, J. Ilczuk, Int. J. Thermophys. 31, 1 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    J. Dercz, A. Starczewska, G. Dercz, Int. J. Thermophys. 32, 746 (2011)Google Scholar
  16. 16.
    R.J. Hill, C.J. Howard, J. Appl. Cryst. 20, 467 (1987)Google Scholar
  17. 17.
    J. Dercz, G. Dercz, K. Prusik, B. Solecka, A. Starczewska, J. Ilczuk, Int. J. Thermophys. 31, 42 (2010)Google Scholar
  18. 18.
    G. Dercz, J. Rymarczyk, A. Hanc, K. Prusik, R. Babilas, L. Pająk, J. Ilczuk, Acta Phys. Pol. A 114, 1623 (2008)ADSGoogle Scholar
  19. 19.
    L. Fuentes, M. Garcia, J. Matutes-Aquino, D. Rios-Jara, J. Alloys Compd. 369, 1 (2004)CrossRefGoogle Scholar
  20. 20.
    G.A. Gehring, Ferroelectrics 161, 275 (1994)CrossRefGoogle Scholar
  21. 21.
    S.A. Kizaev, G.D. Sultanov, F.A. Mirshili, Sov. Phys. Solid State 15, 214 (1973)Google Scholar
  22. 22.
    A. Srinivas, S.V. Suryanarayana, G.S. Kumar, Kumar M. Mahesh, J. Phys. Condens. Matter 11, 3335 (1999)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • J. Dercz
    • 1
  • J. Bartkowska
    • 1
  • G. Dercz
    • 2
  • P. Stoch
    • 3
  • M. Łukasik
    • 3
  1. 1.Department of Material ScienceUniversity of SilesiaSosnowiecPoland
  2. 2.Institute of Material ScienceUniversity of SilesiaChorzówPoland
  3. 3.Faculty of Materials Science and Ceramics, Academy of Mining and MetallurgyCracowPoland

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