Grain size dependent magnetoelectric coupling of BaTiO₃ nanoparticles

Abstract

We report the magnetoelectric (ME) coupling properties of BaTiO₃ nanoparticles of different grain sizes ranging from 16–26 nm synthesized using a modified Pechini method. Nanostructured multiferroic BaTiO₃ shows good ferroelectric and magnetic properties at room temperature, which is confirmed using temperature dependent dielectric spectroscopy and a magnetometer. A quantitative magnetoelectric coefficient measurement of BaTiO₃ samples at room temperature was performed using the dynamic lock-in amplifier technique. The obtained magnetoelectric coefficient values of all the samples indicate the occurrence of strong magnetoelectric coupling and the maximum recorded at an AC magnetic field of 77 Oe is 32 mV cm⁻¹ Oe⁻¹ and exhibits size-dependent magnetoelectric coupling. This enhanced room temperature ME voltage coefficient with perfect ME anisotropy provides the possibility for using such a material in low energy consumption or miniaturized device applications in the area of sensors and memory devices.

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1. Introduction

The coexistence of several order parameters in MF brings out novel physical phenomena and offers the possibility for new device functionalities.^1–4 The current surge of interest in MF materials showing magnetoelectric (ME) coupling due to the presence of both magnetic and ferroelectric ordering is fuelled by both the potential technological applications and the underlying new physics.^5–8 The coexistence of magnetic and ferroelectric ordering only is not enough; it is most important to acquire a strong coupling interaction between two ferroic (FM and FE) orders,^9–11 because of the possibility of controlling the magnetization or magnetic order with an electric field,^12–16 and the ferroelectric polarization with a magnetic field.¹⁵ Magnetization and polarization could independently encode information in a single MF bit, and the coupling of them in principle could permit data to be written electrically, and read magnetically.⁷

Ferroelectric or antiferromagnetic/ferromagnetic properties are the general prerequisites for compounds to induce ME coupling. However, there are few^17,18 MF systems existing in nature at room temperature because transition metal d electrons reduce the tendency for an off-centering FE distortion.¹⁹ The rareness of a single phase MF material that exhibits the coupling of ferroelectricity with ferromagnetism has led many researchers to combine ferroelectric materials with ferromagnetic phases at nanoscopic scales.^12,16,20 For example, the spin-polarization of Fe/ and Co/BaTiO₃ interfaces was controlled by the direction of the ferroelectric polarization in BaTiO₃, and for both cases a spontaneous and hysteresis magnetic moment in BaTiO₃ was detected.^21,22 So far, only hexaferrites have shown a sizable control of ferroelectric polarization using a magnetic field.²³

Recent reports confirm the occurrence of magnetoelectric coupling in single phase hexagonal nanocrystalline YMnO₃ at low temperature.²⁴ BaTiO₃ has been a widely used indispensable compound as a composite multiferroic material. To achieve atomic level ME coupling in ferromagnetic BaTiO₃, chemical synthesis would be a good choice in order to obtain the pure phase rather than the conventional solid state reaction method.²⁵ The extraction of the multiferroic and magnetoelectric effect of nanocrystalline BaTiO₃ motivated us to investigate the magnetoelectric coupling effect of different samples of nanocrystalline BaTiO₃ prepared using a polymer precursor method. A total of ten samples of BaTiO₃ nanoparticles were synthesized by varying the citric acid to ethylene glycol ratio in citrate solutions from 10–50% under the same heat treatment. In this paper, we explore the magnetoelectric effect of different nanocrystalline BaTiO₃ samples employing the dynamic lock-in amplifier technique.

2. Experimental

2.1 Materials

Barium titanate powder was prepared using a complex method based on the Pechini type reaction route²⁶ by mixing barium and titanium citrates. The chemicals used are barium acetate Ba[C₂H₃O₂]₂ (Sigma Aldrich 99%), titanium-tetra isopropoxide Ti[OCH(CH₃)]₄ (Sigma Aldrich, ≥97%), citric acid C₆H₈O₇ (Merck) and ethylene glycol C₂H₆O₂ (Merck).

2.2 Synthesis

A barium citrate solution was prepared by dissolving barium acetate Ba[C₂H₃O₂]₂ (Sigma Aldrich 99%) in citric acid C₆H₈O₇ solution then the solution was heated at 90 °C and when it became transparent, ethylene glycol C₂H₆O₂ (Merck) was added. Parallel to this a titanium citrate solution was prepared by dissolving titanium-tetra isopropoxide Ti[OCH(CH₃)]₄ (Sigma Aldrich, ≥97%) in a solution of ethylene glycol at T > 60 °C with constant stirring for 10 min. Then citric acid solution was added. The solutions of barium citrate and titanium citrate were mixed, at 90 °C with constant stirring, until a clear transparent yellow solution formed. The temperature was maintained in the range of 120–140 °C, to promote polymerization and remove solvents. The solution became more viscous and its color changed from light yellow to brown and finally it solidified into a dark brown glassy resin. Decomposition of most of the organic part was performed in an oven at 250 °C for 1 h, and then at 300 °C for 4 h. The resin became a bulk solid mass, and then the material was pulverized, using an agate mortar and pestle, before further treatment. Thermal treatment was performed at 500 °C for 4 h, 700 °C for 3 h, and 750 °C for 2 h. The agglomerates were broken in an agate mortar, and then BTO powder was obtained. Finally, further heat treatment was carried out at a temperature of 850 °C, 950 °C, 1050 °C, and 1150 °C for the sample synthesized using 25% CA. After drying the samples at room-temperature, the agglomerates were broken in an agate mortar and finally BTO powder was obtained. More details of the experimental procedure are described elsewhere.²⁶ The measurement values of each sample were recorded and they are listed in Table 1.

Table 1 Sample code, CA percentage, calcination temperature, average grain size and linear magnetoelectric coupling coefficient (α) of respective BaTiO₃ samples

Sample code	CA percentage	Calcination temp. (°C)	Average grain size (nm)	α (mV cm^−1 Oe^−1)
BT-1	10	750	25	15
BT-2	20	750	18	23
BT-3	25	750	16	32
BT-4	30	750	21	16
BT-5	40	750	24	16
BT-6	50	750	26	12
BT-A	25	850	20	18
BT-B	25	950	21	14
BT-C	25	1050	22	13
BT-D	25	1150	23	11

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3. Results and discussion

3.1 Structural and morphological characterization

The structural characterization of the samples was carried out using an X-ray diffractometer (PANalytical, X’Pert PRO) with monochromatized CuK_α radiation. Fig. 1 shows the XRD patterns of six samples obtained by heating/calcining all samples at 750 °C, which were prepared with varying CA concentrations of 10–50%. The XRD patterns obtained for all the samples are in correlation with the diffraction peak positions and intensities and in agreement with the structure reported in JCPDS files no. 31-0174 of known BaTiO₃ crystalline phases with a cubic structure. The grain size of each sample was estimated from four higher intensity averaged XRD peaks using the Scherrer formula and was found to be in the range of 16–26 nm and is listed in Table 1.

Fig. 1 XRD patterns of BaTiO₃ samples obtained by varying the CA percentage.

Fig. 2(a) shows the XRD patterns of samples prepared using the same CA concentration (25%), but calcined at different temperatures ranging from 750–1150 °C. The XRD patterns of BT-3, BT-A, and BT-B samples reveal crystalline phase BaTiO₃ with a cubic structure, but the XRD patterns obtained for BT-C, and BT-D samples, peak (110) and (101) around 2θ = 31.5° and peak (200) and (002) around 2θ = 45°, show splitting. Fig. 2(b) shows the split of peak (200) and (002) at around 2θ = 45°, which reveals the formation of tetragonal phase BaTiO₃ as the peaks correspond to tetragonal planes of BaTiO₃ in correlation with the structure reported in JCPDS file no. 5-0626. Fig. 2(b) provides evidence of the transformation of the unit cell of BaTiO₃ from cubic to tetragonal. Increasing the calcination temperature from 1050–1150 °C is accompanied by a cubic to tetragonal phase transition. The estimated grain sizes using the same technique carried out above were found to be in the range of 16–23 nm and are listed in Table 1.

Fig. 2 XRD patterns of BaTiO₃ samples (a) with heat-treatment at different temperatures, and (b) XRD pattern of BT-3 split peak (200) and (002) at around 2θ = 45°.

Fig. 3(a) shows the grain size versus CA% of the BT-1 to BT-6 samples. The grain size of each sample was estimated from four higher intensity averaged XRD peaks using the Scherer formula and was found to be in the range of 16–26 nm. The smallest grain size obtained was 16 nm; this is because of stronger bonding which is due to good polymerization. Below or above 25% CA, the grain size increased. The time taken for the polymerization of samples prepared using less than 25% CA was longer and shorter for samples prepared above 25% CA. The variation of the polymerization time may account for the occurrence of this weak bonding that resulted for a bigger grain size. Fig. 3(b) shows the temperature dependence of the grain size, as the calcination temperature increases the grain size increases, for samples synthesized using the same CA to EG ratio.

Fig. 3 (a) Grain size versus citric acid percentage and (b) grain size vs. temperature.

The microstructure, particle size and morphology were investigated using images recorded on a high resolution transmission electron microscope (HRTEM), JEOL-JEM 2100 operating at 200 kV. The TEM image in Fig. 4(a) shows some agglomerates of BaTiO₃ nanoparticles in sample BT-C and the particles shown in the inset are spherical nanoparticles of size 20 nm. The sizes of the synthesized BaTiO₃ nanoparticles are 10–35 nm and they are spherical in shape, whereas the estimated average grain size of the BaTiO₃ samples from the XRD results are in the range of 16–26 nm. This varying size of the individual particles suggests that the synthesized samples are polycrystalline. Fig. 4(b) shows a typical lattice image of a 20 nm nanocrystalline grain with clear lattice fringes with a d-spacing of 0.25 nm and reveals the formation of well-crystalline BT nanoparticles. The inset in Fig. 4(b) shows an image of the selected area electron diffraction (SAED) pattern. The circular bright rings in the SAED pattern indicate that the particles of barium titanate are nanocrystalline in nature.

Fig. 4 (a) TEM image of sample BT-3, the inset shows 20 nm BaTiO₃ nanoparticles, and (b) lattice image and the inset is a SAED pattern.

To study the phase transitions, Raman measurements were performed at room temperature using a Jobin-Yvon T64000 triple spectrometer system. Raman spectroscopy is a powerful tool to investigate the cubic-tetragonal phase transition by probing the structure of the BaTiO₃ samples. Fig. 5(a) shows the Raman spectra of BaTiO₃ samples synthesized using different CA concentrations while the calcination temperature remained the same, and Fig. 5(b) shows the spectra of samples synthesized using the same concentration of CA but with different calcination temperatures. The Raman spectra for these samples have been plotted for wavenumbers ranging from 100 cm⁻¹ to 800 cm⁻¹. In tetragonal BaTiO₃, there are Raman active lattice vibration modes, but there are no Raman active modes in cubic BaTiO₃.²⁷ The Raman spectra of the samples calcined at 1050 °C and 1150 °C exhibit the characteristic features of the BaTiO₃ tetragonal phase: a broad peak at about 264 cm⁻¹ corresponding to [A₁(TO)], a sharp peak at 308 cm⁻¹ corresponding to [B₁ and E(TO + LO)], an asymmetric peak at 516 cm⁻¹ corresponding to [A₁(TO), and E(TO)] and a peak at 715 cm⁻¹ related to [A₁(LO) and E(LO)] phonon modes.²² A small dip at 180 cm⁻¹ and 183 cm⁻¹ in the respective spectra of BT-C and BT-D is attributed to the anharmonic coupling among three A₁(TO) phonons.^28–30 For the samples calcined below 850 °C the peaks at 518 cm⁻¹ and 718 cm⁻¹ are broadened. This broadening and reduction in the intensity of the peaks and disappearance of the peak at 715 cm⁻¹ reveal a distorted cubic structure. Fig. 5(b) shows the broadening of those peaks as the grain size decreases.

Fig. 5 Raman spectra of (a) BT-1 to BT-6 samples, and (b) BT-3 to BT-D samples.

3.2 Ferroelectric properties

In order to confirm the ferroelectric properties of the BTO samples, the real dielectric constant ε′ variation with temperature at 20 test frequencies has been measured and is shown in Fig. 6. The value of ε′ shows dispersion behavior with decreasing test frequencies.³¹ It is observed that the dielectric constant is found to increase with temperature, reach a maximum value at the Curie temperature (T_C) and after that follow a decreasing trend indicating a phase transition. However, the observed peak temperature, the Curie temperature (T_C), is in the range of 120–150 °C, which is a clear indication of the ferroelectricity of the samples. As the temperature increases the mobility of the charge carriers increases which results in an increase in the polarization and conductivity of the samples, thus the dielectric constant increases. The enhanced value of ε′ may be ascribed to the space charge polarization effect at the interface of the ferrite/ferroelectric phases,³² and the hopping conduction mechanism which is a thermally activated process. As the temperature increases, the hopping of holes between Ba³⁺/Ba²⁺ in the ferroelectric phase gives rise to p-type charge carriers.^33–36 However, the contribution of p-type carriers is negligible compared to n-type carriers because their contribution decreases rapidly at low frequency. Further increase in the temperature beyond the critical temperature causes the dielectric constant of the composites to decline.

Fig. 6 Temperature dependence of the dielectric constant (ε′) of sample BT-D.

3.3 Magnetic properties

In an effort to get a thorough understanding of the magnetic properties, VSM measurement was performed at room temperature for a bias field of 15 kOe. Fig. 7 shows the magnetization versus magnetic field measurement of the nanocrystalline BaTiO₃ of sample BT-D. The sample shows ferromagnetic behavior with a coercive field of 159 Oe, remnant magnetization of 28 × 10⁻⁴ emu g⁻¹ and saturation magnetization of 1.89 × 10⁻² emu g⁻¹. This shows the occurrence of ferromagnetism in BaTiO₃ nanoparticles, which shows that point defects such as cation/anion vacancies in an insulator can create magnetic moments.^37,38 BaTiO₃ is a ferroelectric material but from the obtained result, one can understand that ferromagnetism is intrinsic to nanocrystalline BaTiO₃.¹

Fig. 7 Room-temperature magnetic hysteresis of sample BT-D.

3.4 ME coupling of nanocrystalline BaTiO₃

The magnetoelectric (ME) effect is the dielectric polarization of a material in an applied magnetic field or an induced magnetization in an applied external electric field. The coexistence of the ferroelectric and ferromagnetic phases in BaTiO₃ samples gives rise to a magnetoelectric effect, which is analyzed using the linear magnetoelectric coupling coefficient, α = dE/dH.³⁹ To confirm the magnetic and electric dipole interaction at the atomic level, the ME coupling coefficient of the BaTiO₃ samples has been determined using the dynamic lock-in amplifier method since there are no methodical reviews on a way of measuring the polarization difference of a ME nanostructured material under a magnetic field. The linear ME coupling coefficient α can be written either electrically as α_E = dM/dH or magnetically as α_H = dP/dH. The magnetoelectric output voltage across the BaTiO₃ samples was measured by applying an external magnetic field. In this dynamic measurement the linear ME coupling coefficient (α) is determined at a fixed DC magnetic field along with simultaneous sweeping of the AC magnetic field. Similarly, the magnetoelectric output voltage across the BaTiO₃ samples was recorded at a fixed bias AC magnetic field along with simultaneous sweeping of the DC magnetic field.⁴⁰

Fig. 8 shows the dependence of the ME voltage on the AC magnetic field at room temperature. The measurements have been performed by coupling a 500 Oe DC magnetic field of frequency 850 Hz collinearly with sweeping the AC magnetic field from 0 to 80 Oe. The magnetoelectric voltage response of all the BaTiO₃ samples shows a linear path. The ME coupling coefficient (α) value of each sample was calculated from the slope of the respective ME voltage versus AC magnetic field plot and is recorded in Table 1. All samples show a magnetoelectric effect and the maximum calculated value of the linear ME coefficient was α ∼32 mV Oe⁻¹ cm⁻¹. This is the highest value of the linear ME coefficient, compared to the reported values of the same material.^41,42 This is highly significant from a technological point of view, as a high value from a single phase polycrystalline compound is a promising finding for application in new generation devices.

Fig. 8 ME voltage vs. AC magnetic field at a constant DC (500 Oe) bias magnetic field for BaTiO₃ samples.

Fig. 9 shows the ME voltage versus DC magnetic field plot at room temperature. In this measurement, a 5 Oe AC magnetic field of 850 Hz frequency was applied collinearly with sweeping the DC magnetic field from 0 to 5000 Oe. The ME coupling coefficient values of the BaTiO₃ samples were calculated from the ratio of the output ME voltage to the applied DC magnetic field of the respective samples.⁴¹ It is well known that the strain due to magnetostriction increases with the DC magnetic field and saturates at a certain field.⁴³ The values obtained in this measurement are in line with the values obtained for the AC magnetic field sweeping measurements.

Fig. 9 ME voltage vs. DC magnetic field at a constant AC (5 Oe) bias magnetic field for BaTiO₃ samples.

Fig. 10 shows the linear ME coefficient versus grain size of all the BaTiO₃ samples ranging from 16–26 nm. As is seen from the plot, the linear ME coupling coefficient decreases with increasing grain size, which shows the dependence of the magnetization of nanoparticles on grain size. When the grain size gets smaller and smaller, the lattice size diminishes, then the surface strain⁴³ introduces coordinated distortion and in turn disorder permeates throughout the entire particle, as opposed to being confined only at the surface.⁴⁴ Consequently, different frustrated spin structures are produced. In addition, the particle’s magnetization increases and inter-particle interactions become stronger. This may be the reason for the increase in linear ME coupling with decreasing grain size.

Fig. 10 Linear ME coefficient vs. grain size of BaTiO₃ samples.

4. Conclusion

Nanocrystalline BaTiO₃ samples have been synthesized using a polymer precursor method by varying the citric acid to metal ion ratio and calcination temperatures. The structural properties of the synthesized samples were characterized using XRD, TEM and Raman spectroscopy. The XRD and Raman spectroscopy analysis confirmed the formation of pure BaTiO₃ nanoparticles of cubic and tetragonal phases. The ordered ferroelectric and ferromagnetic behavior of the samples at room temperature was confirmed by the variation of the dielectric constant as a function of temperature and M–H hysteresis loops, respectively. All the nanocrystalline BaTiO₃ samples show the co-existence of ferromagnetism and ferroelectricity at room temperature. The linear ME coupling coefficient values range from 10.7 to 32 mV cm⁻¹ Oe⁻¹ and show the dependence of the ME coupling coefficient values on the grain size of the BaTiO₃ samples. The values are found to increase with the reduction in grain size. The present investigations confirm nanosized BaTiO₃ as a single phase ferroelectric based magnetoelectric coupling material, which makes it a significant material for a variety of next generation device applications in the areas of spintronics, sensors, memory devices, and actuators.

Acknowledgements

The author (TW) is thankful to the Government of Ethiopia for the financial support through Osmania University, University foreign relation office (UFRO) program, Hyderabad, TS, and India. NK also acknowledges the financial support from DST-Govt. of India through the Nano Mission, PURSE, FIST Programs, and UGC-Govt. of India for the SAP program. MVR also acknowledges UGC-UPE-FAR, OU New Delhi for providing financial assistance.

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