Dielectric relaxation and anti-ferromagnetic coupling of BiEuO3 and BiGdO3

Journal of Magnetism and Magnetic Materials 360 (2014) 80–86

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Dielectric relaxation and anti-ferromagnetic coupling of BiEuO3 and BiGdO3 Sujoy Saha a,n, Sadhan Chanda a, Alo Dutta a, Uday Kumar b, Rajeev Ranjan c, T.P. Sinha a a

Department of Physics, Bose Institute, 93/1 Acharya Prafulla Chandra Road, Kolkata 700009, India Department of Physical Sciences, Indian Institute of Science Education and Research, Kolkata, Mohanpur 741252, India c Department of Materials Engineering, Indian Institute of Science, Bangalore 560012, India b

art ic l e i nf o

a b s t r a c t

Article history: Received 28 October 2013 Received in revised form 29 January 2014 Available online 8 February 2014

BiEuO3 (BE) and BiGdO3 (BG) are synthesized by the solid-state reaction technique. Rietveld refinement of the X-ray diffraction data shows that the samples are crystallized in cubic phase at room temperature having Fm3m symmetry with the lattice parameters of 5.4925(2) and 5.4712(2) Å for BE and BG, respectively. Raman spectra of the samples are investigated to obtain the phonon modes of the samples. The dielectric properties of the samples are investigated in the frequency range from 42 Hz to 1.1 MHz and in the temperature range from 303 K to 673 K. An analysis of the real and imaginary parts of impedance is performed assuming a distribution of relaxation times as confirmed by the Cole–Cole plots. The frequency-dependent maxima in the loss tangent are found to obey an Arrhenius law with activation energy
1 eV for both the samples. The frequency-dependent electrical data are also analyzed in the framework of conductivity formalism. Magnetization of the samples are measured under the field cooled (FC) and zero field cooled (ZFC) modes in the temperature range from 5 K to 300 K applying a magnetic field of 500 Oe. The FC and ZFC susceptibilities show that BE is a Van Vleck paramagnetic material with antiferromagnetic coupling at low temperature whereas BG is an anti-ferromagnetic system. The results are substantiated by the M–H loops of the materials taken at 5 K in the ZFC mode. & 2014 Elsevier B.V. All rights reserved.

Keywords: Rietveld refinement Raman spectroscopy Van Vleck paramagnetism

1. Introduction The crystal structure of bismuth europium oxide, BiEuO3 (BE) and bismuth gadolinium oxide, BiGdO3 (BG) has been investigated by Nasonova et al. [1]. They observed that both BE and BG crystallize in cubic Fm3m phase having lattice parameters of 5.483 Å [2] and 5.462 Å [3] respectively. BE and BG appear to be of perovskite ABO3 structure but the values of their lattice parameters do not support the perovskite (cubic) structure with Fm3m symmetry and hence making these systems very interesting for investigation. Unfortunately, there exists no report in the literature related to the electrical, magnetic and vibrational properties of these materials. In the present work we have synthesized the materials by the solid state reaction technique. The Raman spectroscopy is used to investigate the vibrational modes of the materials. The frequency dependence of dielectric constant,

n Corresponding author. Tel.: þ 91 33 2303 194; fax: þ91 33 2350 6790. E-mail addresses: [email protected], [email protected] (S. Saha).

http://dx.doi.org/10.1016/j.jmmm.2014.01.075 0304-8853 & 2014 Elsevier B.V. All rights reserved.

dielectric loss and ac conductivity is investigated by impedance spectroscopy at various temperatures. The magnetic behaviour of the samples is studied under the field cooled (FC) and zero field cooled (ZFC) modes in a temperature range from 5 K to 300 K.

2. Material and methods Bi2O3 (Loba Chemie, 99% pure), Eu2O3 (Sigma Aldrich, 99.9% pure) and Gd2O3 (Sigma Aldrich, 99.9% pure) powders are taken in stoichiometric ratio and mixed in the acetone medium for 8 h. The mixture is calcined at 930 1C in air for 8 h for BE and 950 1C for 10 h for BG and cooled down to room temperature at a rate of 100 1C/h. The calcined samples are pelletized into discs using polyvinyl alcohol as binder. Finally, the discs are sintered at 980 1C for 8 h for BE and at 1000 1C for 8 h for BG and cooled down to room temperature at a rate of 1 1C/min. The X-ray diffraction pattern of the samples is obtained by a powder X-ray diffractometer (Rigaku Miniflex II) in the 2θ range from 201 to 1201 by step scanning at 0.021 per step using CuKα radiation. The determination of lattice parameters and the identification of the phase of the samples are performed by the Rietveld refinement of

S. Saha et al. / Journal of Magnetism and Magnetic Materials 360 (2014) 80–86

the XRD profiles using the Fullprof program [4]. A sixth order polynomial function is taken to refine the background of the XRD profile for both the samples. The peak shapes are described by pseudo-Voigt profiles. In all the refinements, scale factor, zero correction, background, half width parameters, lattice parameters, fractional positional coordinates and isotropic thermal parameter (Biso) of the cations [5] are varied. Occupancy parameters of all the ions are kept fixed during refinement. To get a better understanding of the crystal structure and its consequence on the vibrational features of the sample, the Raman spectra of the samples are obtained in the frequency range from 50 cm  1 to 800 cm  1 at an excitation wavelength of 488 nm using a Lab-RAM HR 800 (Jobin Yvon) Raman spectrometer. Magnetic susceptibility measurements are made using a SQUID magnetometer (Quantum Design MPMS). The data are collected after cooling the sample in the absence of an applied magnetic field (zero field cooled (ZFC)) and after cooling in the magnetic field (field cooled (FC)) of 500 Oe in a temperature range from 5 K to 300 K. In the ZFC mode, the field dependent magnetization of the samples is measured at 5 K in the magnetic field range of 7 40 kOe.

3. Results and discussion 3.1. Structural and vibrational analysis The room temperature X-ray diffraction (XRD) patterns of BE and BG are shown in Fig. 1(a) and (b) respectively, where the open circles represent the experimental data and the solid lines represent the calculated data obtained from Rietveld refinement. The curve at the bottom represents the difference between experimental pattern and the calculated one. Good agreement between the observed and calculated interplanar spacings (d-values) suggests that the compounds crystallize in cubic Fm3m phase with the following distribution of ions in crystallographic positions: Bi3 þ /Eu3 þ /Gd3 þ ions at 4a site, and O2  ions at 8c and 32f sites. O2  ions at 8c and 32f positions are henceforth referred as OI and OII respectively. A schematic presentation of the BiEuO3/ BiGdO3 unit cell is shown in Fig. 2. It has been observed from Fig. 1 that in both the samples there is a trace of another phase. This phase is recognized to be Eu2O3 (space group Ia3 #206) for BE and Gd2O3 (space group Ia3 #206) for BG respectively. The appearance of these oxide peaks may be due to the slight evaporation of Bi2O3 at high calcination temperatures. We have calculated the weight percentage of BiEuO3/Eu2O3 for BE and

531 442 600

440

422

333 511

331 420

400

BiGdO 3

20

30

40

50

80

90

100

531 442 600

440

422

70

333 511

60

331 420

311

400

10

222

200

220

111

Intensity (arb. unit)

222

311

220

200

111

BiEuO 3 Observed Calculated (Obs-Cal) Bragg positions

110

120

2θ (degrees) Fig. 1. Room temperature refined powder X-ray diffraction pattern of BE and BG. Open circles represent the experimental data and the solid lines represent the calculated data obtained from Rietveld refinement.

81

Fig. 2. Crystal structure of BiRO3 (R ¼ Eu/Gd). (Bi3 þ /Eu3 þ /Gd3 þ ) ions occupy the 4a lattice sites. Oxygen (O2  ) ions occupy 8c and 32f lattice sites.

Table 1 Details of the structure refinement of BE and BG. y

z

Biso (Å2)

wt%

BiEuO3 (Fm3m# 225) a ¼b ¼c ¼ 5.4925(2) Å Bi/Eu 4a 0 OI 8c 0.25 OII 32f 0.306(3)

0 0.25 0.306(3)

0 0.25 0.306(3)

2.983 1.000 1.000

96.30

Eu2O3 (Ia3# 206) a ¼b ¼c ¼ 10.85909(66) EuI 8a 0 EuII 24d 0.254(8) O 48e 0.083(4)

0 0 0

0 0.25 0.147(3)

1.436 2.932 1.000

3.70

Site

x

Reliability factors Rp ¼ 4.93, Rwp ¼ 6.80, Rexp ¼ 3.99, χ2 ¼ 2.91 BiGdO3 (Fm3m# 225) a ¼b ¼c ¼ 5.4712(2) Å Bi/Gd 4a 0 OI 8c 0.25 OII 32f 0.302(3)

0 0.25 0.302(3)

0 0.25 0.302(3)

2.822 1.000 1.000

Gd2O3 (Ia3# 206) a ¼b ¼c ¼ 10.81042(64) GdI 8a 0 GdII 24d 0.254(1) O 48e 0.083(2)

0 0 0

0 0.25 0.147(3)

7.202 3.136 1.000

93.55

6.45

Reliability factors Rp ¼ 4.32, Rwp ¼ 6.00, Rexp ¼ 3.97, χ2 ¼ 2.29

BiGdO3/Gd2O3 for BG from the structural refinement analysis and the results are listed in Table 1. The lattice parameters for BE and BG are found to be 5.4925(2) Å and 5.4712(2) Å respectively. These values of the lattice parameters are in good agreement with earlier reported results [2,3]. Fig. 3 shows the Raman spectra of BE and BG. The sum of five Lorentizan peaks is used to fit each of the Raman spectra. Since BE and BG have adopted the cubic crystal structure with Fm3m (O5h ) symmetry, the irreducible representation of the O5h point group [6] is given by Γ ¼5T1u þA1g þ Eg þ 3T2g, with five Raman-active modes (one A1g, one Eg, and three T2g), four IR active modes (4T1u) and one triply degenerate acoustical mode (T1u). These phonon modes correspond to vibrations of the Bi3 þ /Eu3 þ /Gd3 þ cations (5T1u) and oxygen anions (4T1u þA1g þEg þ3T2g). The Raman spectra of BE and BG show two strong peaks at 97 and 625 cm  1 and three weaker features at 137, 316 and 570 cm  1. Following the technique of Denisov et al. [7], the weak intense peak at 570 cm  1 may be assigned as A1g mode of the systems. It is well known that there is only one T2g Raman active mode at the center of the Brillouin zone for fluorite structure having Fm3m symmetry [8]. BE and BG show a wide and asymmetric band at 625 cm  1 which may be

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BiEuO3

BiGdO3 10000

ε'

303 K 473 K 523 K 573 K 623 K 673 K

Intensity (arb. unit)

1000

BiGdO3

tanδ

0.4

0.2

100

200

300

400

500

600

700

800

0.0

-1

2

Raman shift (cm )

3

4

5

7

6

-1

logω (rad s )

Fig. 3. Room temperature micro Raman spectra of BE and BG.

Fig. 5. Frequency dependence of the (a) ε0 and (b) tan δ of BG at various temperatures.

BiEuO3

7 BiEuO3 BiGdO3 Linear Fitting

10000

6 1000

-1

log ωmax(rad s )

ε'

303 K 473 K 523 K 573 K 623 K 673 K

5

100

4

0.4

3

1.5

1.8 3

2.1 -1

tanδ

10 /T (K ) Fig. 6. The Arrhenius plot of ωmax corresponding to tan δ for BE and BG. 0.2

0.0 2

3

4

5

6

7

-1

logω (rad s ) Fig. 4. Frequency dependence of the (a) ε0 and (b) tan δ of BE at various temperatures.

assigned as T2g mode. Hence one can conclude that both BE and BG have fluorite structure like δ-Bi2O3 [9,10] with Fm3m symmetry having oxygen ions sitting at 32f sites. 3.2. Dielectric relaxation and ac conductivity The angular frequency ω( ¼2πυ) dependence of the real (ε0 ) part of the complex dielectric constant (εn) and the dielectric loss tangent (tan δ) of BE and BG at several temperatures between 303 and 673 K are plotted in Figs. 4 and 5 respectively. A relaxation is observed in the entire temperature range as a gradual decrease in ε0 (ω) and a broad peak in tan δ(ω). Relaxation phenomena in these dielectric materials are associated with a frequency-dependent

orientational polarization. At low frequency, the permanent dipoles align themselves along the field and contribute fully to the total polarization of the dielectric. At higher frequency, the variation in the field is too rapid for the dipoles to align themselves, so their contribution to the polarization and, hence, to the dielectric permittivity can become negligible. Therefore, the dielectric constant ε0 (ω) decreases with increasing frequency. It is evident from Figs. 4(b) and 5(b) that the position of loss peak, tan δmax centered at the dispersion region of ε0 (ω) shifts to higher frequency with increasing temperature and that a strong dispersion of tan δ exists in both the materials. It seems clear that the width of the loss peaks in Figs. 4(b) and 5(b) cannot be accounted for in terms of a monodispersive relaxation process but points towards the possibility of a distribution of relaxation times. At a temperature T, the most probable relaxation time corresponding to the peak position in tan δ vs. logω curve is proportional to exp(  Ea/kBT) (Arrhenius law) with activation energies 1.11 and 0.99 eV for BE and BG respectively, as shown in Fig. 6. Such a value of activation energy indicates that the conduction mechanism for both the materials is due to ion hopping. In Fig. 7 we have scaled each tan δ by tan δmax and each frequency by ωmax for both the materials. It is observed that the

S. Saha et al. / Journal of Magnetism and Magnetic Materials 360 (2014) 80–86

1.0

Table 2 Hopping frequencies at different temperatures obtained from fitting with Eq. (1).

BiEuO3

tanδ/tanδmax

0.5

0.0 1.0

BiGdO3

0.5

0.0 -4

-2

2

0

4

log(ω/ωmax) Fig. 7. Scaling behaviour of tan δ at various temperatures for BE and BG.

-2

673 K 623 K

-4

BiEuO3

523 K 473 K -1

logσ (S m )

-6 373 K 303 K 673 K 623 K 573 K

BiGdO3

523 K 473 K -6

373 K 303 K 2

6

4

Sample

Temperature (K)

ωH (kHz)

BE

473 523 573 623

6.05 32 175.1 955

BG

473 523 573 623

6.05 47.7 650 398

frequency region the electric field cannot perturb the hopping conduction mechanism of charged particles and hence the conductance is approximately equal to the dc value. As the temperature is increased, the dc part of the conductivity spectra shifts to higher frequency side. The large value of dc conductivity at 673 K with respect to the value at 303 K indicates the generation of large number of thermally activated charge carriers in the materials at higher temperatures. The conductivity begins to increase nonlinearly after the frequency exceeds the critical frequency called hopping frequency (ωH). The frequency dependence of the ac-conductivity is explained by the universal power law [11], defined as 
n  ω ð1Þ sac ¼ sdc 1 þ ωH where n is a dimensionless frequency exponent. The experimental conductivity data were fitted to Eq. (1) with sdc and ωH as variables, keeping in mind that the values of parameter n are weakly temperature dependent. The values of n varies from 0.90 to 0.98 for BE and from 0.91 to 0.98 for BG. The values of ωH at different temperatures are listed in Table 2. The temperature dependence of sdc, as obtained from the fitting of experimental data of BE and BG by Eq. (1), obeys the Arrhenius law defined as   E ð2Þ sdc ¼ s0 exp  kB T

573 K

-4

83

8

-1

logω (rad s ) Fig. 8. Frequency (angular) dependence of the ac conductivity (s) of (a) BE and (b) BG at various temperatures where the symbols are the experimental points and the solid lines represent the fitting to experimental data using Eq. (1). In the insets the Arrhenius plot of sdc obtained from the fitting of the conductivity spectra by Eq. (2) is shown.

scaling spectra collapse into a single master curve indicating that the relaxation mechanism is temperature independent for both the materials. Fig. 8 shows the frequency dependence of the real part of the ac conductivity sac(ω) for BE and BG at different temperatures. The conductivity shows a dispersion which shifts to higher frequency side with an increase in temperature. At low frequency, the extrapolation of the conductivity spectrum at a particular temperature gives dc conductivity (sdc) which is attributed to the long range translational motion of the charge carriers. In this low

where s0 is the pre exponent factor, kB is the Boltzmann constant, T is the temperature in K and E is the activation energy. The values of E are found to be 1.10 and 1.01 eV for BE and BG respectively. The linear fit to the experimental data is shown in the inset of Fig. 8 by the solid line. The high value of activation energy may be attributed to the ionic conduction [12] in the materials. Since the BE and BG belong to fluorite (δ-Bi2O3) structure [13], there exists one fourth vacancy of the 8c oxygen sites which creates energetically allowed hopping sites for the oxide ions taking part in conduction mechanism. 3.3. Complex impedance analysis We have adopted the impedance formalism to study the relaxation mechanism in BE and BG. Figs. 9 and 10 show the complex impedance plane plots (Zn-plots) of BE and BG respectively, plotting the imaginary part Z″ against the real part Z0 at some selected temperatures. It is well known that Zn-plots for polycrystalline dielectric materials do not always yield perfect circular or semicircular arcs, even they become asymmetric. Similar behaviour is observed in Figs. 9 and 10 for BE and BG respectively. The arcs in Zn-plots are depressed with its center below the real axis (Z0 ) which deviates from ideal Debye like behaviour (where a set of two parallel RC elements one for grain and another for grain-boundary connected in series is considered as the electrical equivalent circuit). It is observed from the insets of

84

S. Saha et al. / Journal of Magnetism and Magnetic Materials 360 (2014) 80–86

BiEuO3

303 K

0

5

10

0

0

5

Zn ¼

10

80

40

3.4. Magnetic study

Z' (kΩ) Fig. 9. Complex plane impedance plot at various temperatures for BE (solid line is the fitting data of the RC equivalent circuit).

623 K 643 K

303 K

20 300

20

40

0 0

20

Table 3 Fitting parameters of Zn-plots obtained using Eq. (4).

80

40

0

0

40

80

120

Sample name

Temperature (K)

BE

573 593 603 613 623 643

BG

573 593 603 613 623 643

160

Z' (kΩ)

5.6

Cgb (pF)

Fitting factor (α)

73 36.5 26.9 16.5 9 6.7

593.59 568.13 533.28 499.74 527.69 589.80

0.62 0.62 0.62 0.62 0.61 0.61

179 88 62 45 35 16.9

505.79 492.41 484.89 460.81 491.83 489.19

0.61 0.61 0.61 0.61 0.6 0.6

χ

Curie-Weiss fitting

150

120

χ

-1

4.9 4.2

0

Z ¼

1 1 Rgb þ jωC gb

ð3Þ

where Rgb and Cgb are the resistance and capacitance of grainboundary respectively. Based on Eq. (3), the response peaks of the grain-boundary arcs are positioned at 1/(2πRgbCgb), and the peak values are proportional to the associated resistances. Due to the depressed nature of the semicircular arcs of Zn-plots as seen in Figs. 9 and 10, the experimental data cannot be well described by

200

300

3.5 2.8

FC at 500 Oe ZFC at 500 Oe

BiGdO 3

300

200

40

χ

Curie-Weiss fitting

30 20 10 0

n

100

T (K) -1

Figs. 9 and 10 that at 303 K the Zn-plot consists of two depressed semicircular arcs. The high frequency arc at 303 K for both materials is attributed to the grain effect whereas the lower frequency arc represents the grain-boundary contribution. With increasing temperature, the arc due to grain effect shifts to the higher frequency side, and grain-boundary contribution plays the major role in the measuring frequency window as seen in Figs. 9 and 10. Above 573 K a single depressed semicircular arc is observed at lower frequency side at each temperature for both the samples. This indicates that for both the materials grain boundary effect plays the significant role for conduction mechanism at higher temperatures. For BG above 573 K, another arc appears at lowest frequency side. This arc corresponds to the electrode effect. The effect of grain and grain-boundary contributions in the materials can be separated by fitting the experimental response to that of an electrical equivalent circuit, which is usually considered to comprise a series of parallel resistor–capacitor (R–C) elements. In our case we have fitted only for those temperatures at which grain boundary effect is significant. If the circuit consists of a series array of one sub–circuit of parallel R–C element, representing the grain-boundary, the complex impedance can be defined as

M (emu mol )

Fig. 10. Complex plane impedance plot at various temperatures for BG (solid line is the fitting data of the RC equivalent circuit).

Rgb (kΩ)

-1

Z'' (kΩ)

0 0

(mol emu )

573 K 593 K 603 K 613 K

Fig. 11(a and c) shows the FC and ZFC magnetization (M) as a function of temperature (T) for BE and BG, respectively. For both the systems, magnetization increases with decreasing the temperature. The value of magnetization for BE increases almost linearly (Fig. 11a) as the temperature decreases, and there is a sharp increase of magnetization below 30 K. This increase of the magnetization may be supposed to have a ferromagnetic/antiferromagnetic transition in the material. To support this assumption we have carried out

m

600

160

120

ð4Þ

where τgb ¼RgbCgb and the parameter α is constant (0 oαr1). The solid lines in Figs. 9 and 10 show the fitting of the experimental data using Eq. (4). The fitted parameters at different temperatures are listed in Table 3.

0

BiGdO3

Rgb 1 þ ðjτgb Þ 1  α

-1

0

0

(mol emu )

40

5

m

573 K 593 K 603 K 613 K

the Eq. (3). However, we find that the complex plane plot is better described by the Cole–Cole equation [14,15] which is commonly used for polycrystalline ceramic samples [16] and which modifies the Eq. (3) as follows:

623 K 643 K

-1

Z'' (kΩ)

200

10

χ

80

0

100

200

300

T (K)

100

FC at 500 Oe ZFC at 500 Oe

0

0

100 200 Temperature (K)

300

Fig. 11. (a) Magnetization (M) vs. temperature (T) curve of BE. (b) Curie–Weiss fitting of the 1/χm vs. T curve for BE. (c) Magnetization (M) vs. temperature (T) curve of BG. (c) Curie–Weiss fitting of the 1/χm vs. T curve for BG.

S. Saha et al. / Journal of Magnetism and Magnetic Materials 360 (2014) 80–86

360

excited state of Eu3 þ . Since the ground state is extremely sensitive to the external field, the final expression for the susceptibility for Eu3 þ may be given by [19], 
 6 NA μ0 g 2 JðJ þ 1Þμ2B N A μ2B f ðJÞ f ðJ þ 1Þ þ χ Eu3 þ ¼ ∑ þ 3kB T 6ð2J þ 1Þh νðJ  1; JÞ νðJ þ 1; JÞ J¼0

BE-ZFC Hyst. at 5K

180 0



-180

N A μ0 e2 _2 ∑r 6m

ð6Þ

where, NA ¼6.023  1023 mol  1, μ0 ¼8.854  10  12 F m  1, μB ¼ 9.274  10  24 J T  1, e¼1.602  10  19 C and m ¼9.31  10  31 kg. The above equation is called the Van Vleck paramagnetic equation. The function f(J) is given by

-1

M (emu mol )

85

-360 26000 BG-ZFC Hyst. at 5K

1 f ðJÞ ¼ ½ðS þ L þ 1Þ2 J 2 ½ J 2  ðS LÞ2 : J

13000

ð7Þ

The first and last terms in the Eq. (6) are the Curie and diamagnetic contribution to the total susceptibility respectively for Eu3 þ . υ is the frequency of transition. Using Eq. (7) in Eq. (6) we get the explicit form of susceptibility for Eu3 þ as

0 -13000

χ Eu3 þ ¼

-26000 0 H (kOe )

ð8Þ

20

40

where γ¼λ/T ¼1/21 is the ratio of the over-all multiplet width (ΔW) to kBT [19]. λ is the spin orbit coupling constant [19]. For Eu3 þ the value of λ is
300 [19]. Thus the magnetic susceptibility of BE may be defined as

Fig. 12. ZFC hysteresis curves for Be and BG at 5 K.

the magnetization vs. magnetic field (hysteresis) measurement at 5 K which is shown in Fig. 12(a). The absence of any retentivity and coercivity does not support any ferromagnetic transition in the material below 30 K. For an anti-ferromagnetic transition a cusp like discontinuity should be present in the M–T curve [17]. No cusp like discontinuity is observed down to 5 K in the M–T curve for BE indicating the absence of the antiferromagnetic transition below 30 K. The temperature (T) dependence of the inverse molar magnetic susceptibility (1/χm) of BE in the field of 500 Oe is plotted in Fig. 11(b). A linear fit to the experimental data at higher temperatures by Curie– Weiss law yields a Curie–Weiss constant Θ ¼  344.86 K which is negative. The effective Bohr magneton number is found to be 5.49 μB which does not match with the experimental value reported for Eu based materials [18]. We observe an unconventional behaviour of the magnetic properties of BE. They cannot be explained only by using the Curie or Curie–Weiss law which is based on the assumption of infinite multiplet width of an element [19]. It is to be mentioned that the multiplet intervals of Eu3 þ are very small compared to kBT [20]. Van Vleck [19] has shown that the various components of the multiplet of Eu3 þ are not evenly spaced, and instead crowd together for small values of J. The overall multiplet width ΔW is given by [19], ΔW ¼ W Jmax –W Jmin ¼ ð1=2ÞA½ðL þ SÞðL þ S þ 1Þ–jL–SjðjL–Sjþ 1Þ

ð5Þ

where L and S are the orbital and spin angular momenta respectively. WJmax (WJmin) is the energy of the upper most (lower most) multiplet component. A is a constant for a particular element. The ground state of Eu3 þ is 7F0. Hence the total angular momentum J for the ground state is zero indicating no paramagnetic effect [18]. The relative muliplet separation between the ground (J¼ 0) state and the first excited (J ¼1) state for Eu3 þ is also very small (¼ 1/21) [19]. This may be the reason of failure of the Curie or Curie–Weiss law to BE. To calculate the correct susceptibility (χm) for BE, we have incorporated the second order perturbation theory to the expression for susceptibility considering the finite population in the first

χm ¼

C þ χ 0 þ χ Eu3 þ ðΔW; TÞ T Θ

ð9Þ

where, the first term denotes the Curie–Weiss contribution. The sharp growth of the susceptibility in BE at low temperatures allows one to assume the presence of a paramagnetic contribution. According to local moment model, Bi3 þ ions have completely filled subshells and they are diamagnetic. Again paramagnetic behaviour of Eu3 þ ions is saturated below 100 K [19] so the paramagnetic contribution to the susceptibility in BE at low temperatures may be attributed to the presence of a small impurity of Bi2 þ ions. The second term in Eq. (9) is a temperature-independent contribution due to the diamagnetism of the Bi3 þ ions and the last term indicates the Van Vleck susceptibility for the Eu3 þ ions. In the first term the constant Θ stands for the Weiss constant, typically accounts for the magnetic ordering of the elctronic moments below the Curie or Néel temperature for uncorrelated spins. We have fitted the experimental data of susceptibility of BE using Eq. (9). The solid line in Fig. 13 represents the fitted data. The

0.012 BiEuO3 ZFC at 500 Oe fitting 0.010 -1

-20

χm (emu mol )

-40

0:12506 24 þ ð13:5γ  1:5Þe  γ þ ð67:5γ  2:5Þe  3γ þ ð189γ  3:5Þe  6γ γT 1 þ 3e  γ þ 5e  3γ þ 7e  6γ

0.008

0.006 0

100

200

300

T (K) Fig. 13. A non-linear fitting of ZFC inverse molar magnetic susceptibility using Eq. (9) of BE is shown.

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S. Saha et al. / Journal of Magnetism and Magnetic Materials 360 (2014) 80–86

values of C, χ0, λ and Θ are found to be 0.025 emu K mol  1, 0.00098 emu mol  1, 300 and  1 K respectively. From the negative value of Weiss constant (Θ), one can conclude that there exists antiferromagnetic coupling [21] in BE. Thus due to the presence of several additive contributions to the susceptibility (and especially the paramagnetic contribution from an impurity), it is hardly possible to determine reliably a parameter of effective magnetic interaction in BE. Fig. 11(c) shows the FC and ZFC magnetizations of BG. In the temperature range from 5 K to 300 K there is no deviation 1 between FC and ZFC data. The inverse of susceptibility (χm ) vs. T curve for BG is shown in Fig. 11(d), where the solid line is the fitting to Curie–Weiss law. We have obtained the effective magnetic moment (peff) of Gd3 þ as 8.3 μB per formula unit using the following relation [18]: pffiffiffiffi ð10Þ pef f ¼ 2:827 C

673 K for the first time. The increasing dielectric constant with decreasing frequency is associated with a frequency-dependent orientational polarization. The frequency-dependent maxima of the loss tangent are found to obey Arrhenius law with activation energy of 1.11 and 0.99 eV for BE and BG respectively. Analysis of the real and imaginary part of complex impedance with frequency are performed assuming a distribution of relaxation times as confirmed by Cole–Cole plot. The frequency-dependent electrical data are also analyzed in the framework of the conductivity. The magnetic behaviour of the samples are studied under field cooled (FC) and zero field cooled (ZFC) modes in a temperature range from 5 K to 300 K. BE shows a typical Van Vleck paramagnetism. On the other hand BG shows an antiferromagnetic nature.

where C is the Curie constant. This value is very close to the theoretically predicted value of 7.94 μB per formula unit [18]. Similar value (8 μB per formula unit) of magnetic moment is also observed for other compounds containing Gd3 þ ion [22]. The Weiss constant (Θ) is found to be  15.3 K which indicates antiferromagnetic nature of BG. The hysteresis loops of BE and BG taken at 5 K are shown in Fig. 12. Typical antiferromagnetic hysteresis loops are observed for both materials as there are no retentivity and coercivity. Magnetization at the highest field for BG is seventy times larger than that of BE. At low temperature the susceptibility for BG varies as
1/T obeying Curie–Weiss law and hence magnetization of BG will be linearly increasing with magnetic field but for BE magnetization does not obey Curie–Weiss law rather follows Eq. (9) which offers a lower value of susceptibility at lower temperature and hence giving less magnetization with the increase of magnetic field.

Sujoy Saha acknowledges the financial support provided by the UGC New Delhi in the form of SRF. Alo Dutta thanks to Department of Science & Technology of India for providing the financial support through DST Fast Track Project under Grant no. SR/FTP/ PS–032/2010.

4. Conclusions The Rietveld refinement of the room temperature powder XRD profiles of BE and BG, synthesized by solid state reaction technique, confirms that both the materials crystallize in cubic Fm3m symmetry having lattice parameters of 5.4925 (2) and 5.4712 (2) Å respectively. Raman spectra also confirm the validation of the crystal structures of the synthesized materials. From the analysis of the phonon modes it has been concluded that both BE and BG have fluorite structure with Fm3m symmetry having oxygen ions sitting at 32f sites. The frequency-dependent dielectric dispersion of the samples is investigated in the temperature range from 303 K to

Acknowledgments

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