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Journal of Magnetism and Magnetic Materials 320 (2008) 1657–1665

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Complex permittivity and complex permeability ofSr ions substituted Ba ferrite at X-band

Charanjeet Singha, S. Bindra Naranga,�, I.S. Hudiaraa, K. Sudheendranb, K.C. James Rajub

aDepartment of Electronics Technology, Guru Nanak Dev University, Amritsar, Punjab, IndiabSchool of Physics, Central University Hyderabad, Andhra Pradesh, India

Received 8 August 2007; received in revised form 17 October 2007

Available online 12 November 2007

Abstract

M-type hexagonal ferrite composition, Ba(1�x)SrxFe12O19 (x ¼ 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0), was prepared by a two route ceramic

method. Complex permittivity (e0�je00) and complex permeability (m0�jm00) have been measured using a network analyzer from 8.2 to

12.4GHz X-ray diffraction confirmed the M-type hexagonal structure and a scanned electron micrograph was used to analyze the grain

size distribution of ferrite. Substitution of Sr2+ ions causes an increase in porosity that deteriorates the electromagnetic and

microstructural properties in the doped samples. Both dielectric constant and dielectric loss are enhanced in comparison to the

permeability and magnetic loss over the entire frequency region. This is due to a resistivity variation and the formation of Fe2+ ions,

which increases the hopping mechanism between Fe2+ and Fe3+ ions.

r 2007 Elsevier B.V. All rights reserved.

Keywords: Ferrites; Permeability; Permittivity

1. Introduction

Fast development in wireless systems has led to anotherkind of environmental pollution. This pollution is asso-ciated with an electromagnetic interference (EMI) and anelectromagnetic compatibility (EMC) problem. Ferriteshave been used as a shield/absorber to tackle the EMI/EMC problem [1,2]. High dielectric loss and magnetic lossare the prime factors to attenuate the unwanted microwavesignal. Magnetic losses become low in the microwaveregion due to a number of reasons. Another option is toincrease dielectric losses through appropriate substitutionas well as sintering temperature. On the contrary, dielectricand magnetic losses should be low for high frequencyapplications.

Electromagnetic properties of Sr2+ ions substitutedM-type Ba hexagonal ferrite are reported here. Composi-tions for high frequency applications have also beenproposed.

- see front matter r 2007 Elsevier B.V. All rights reserved.

/j.jmmm.2007.11.002

onding author. Tel.: +91183 2256203; fax: +91 183 2258820.

ddress: sukhleen2@yahoo.com (S. Bindra Narang).

2. Experimental

Samples of M-type hexagonal ferrite, Ba(1�x)SrxFe12O19

(x=0.0, 0.2, 0.4, 0.6, 0.8, 1.0), were prepared by a tworoute ceramic method. The required ratio of chemicals(BaCO3, SrCO3 and Fe2O3) was calculated from thefollowing chemical reaction:

ð1� xÞBaCO3 þ ðxÞSrCO3 þ 6Fe2O3

! Bað1�xÞSrxFe12O19þCO2.

Powders were grounded in an agate pestle and mortarwith distilled water for 8 h. Pre-sintering was carried out inan electric furnace at 1000 1C for 8 h, grinding was repeatedunder the same conditions. Post-sintering was performed at1250 1C for 20 h. Powders were granulated through sievingafter adding polyvinyl alcohol as a binder. Mixtures wereshaped into pellets using hydraulic press under uniaxialpressure of 75 kNm�2.Complex permeability and complex permittivity of the

samples were studied by a network analyzer (Agilent8722ES) at 8.2–12.4GHz using the Nicholson and Rossmethod. Calibration of the analyzer was made in air before

ARTICLE IN PRESSC. Singh et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 1657–16651658

taking the final measurements. X-band was divided into201 points i.e. successive increment of 0.021GHz. Theanisotropic field was measured by a vibrating samplemagnetometer (Lake Shore VSM 7307) at an appliedexternal field of 10 kOe. The phase structure was identi-fied using X-ray diffraction (XRD) (Philips ExpertDiffractometer) with CuKa radiation (l=1.54 A) and themicrostructure was studied with an scanning electronmicroscopy (SEM) instrument (Hitachi S-4700 FESEM).Resistivity was measured by a two-probe method (Keithleysetup 6517A).

3. Results and discussion

3.1. XRD

XRD of the samples (Fig. 1) exhibit magnetoplumbitestructure. With increasing substitution of Sr2+ ions, latticeconstant ‘a’ is almost constant and lattice constant ‘c’ goesthrough fast reduction. This follows the fact that hexago-nal ferrites exhibit constant lattice parameter ‘a’ and

1200

1000

800

500

400

200

0

20 30 40

[cou

nts]

2θ

(11

0)

(00

8)

(11

2)

(10

7)

(11

4)

(20

1)

(10

8)

(20

3)

(20

5)

(20

6)

Fig. 1. X-ray diffractograms of Ba(1�x)SrxFe

variable parameter ‘c’ [3]. It also indicates that morechange in the easy magnetized c-axis will occur than ata-axis with Sr2+ ions substitution. This is implied to smallionic radii of Sr2+ ions (1.12 A) than Ba2+ ions (1.34 A) [4].

3.2. SEM

SEM photomicrographs (Fig. 2) of Ba(1�x)SrxFe12O19

particles indicate poor grain connectivity with Sr2+ ionssubstitution. Grains get agglomerate in Ba-ferrite (x ¼ 0.0),all the grains in this ferrite are of multidomain nature.Average grain size in the ferrite samples decreases(9.8–2.5mm) with Sr2+ ions substitution (Table 1). Singledomain grains require size less than 1mm [5]. Grain sizedecreases at lower substitution (x ¼ 0.2) but the grains stillremain in multi domain state. Some single domain grains,along with multi domain grains, are observed at x ¼ 0.4.Increase in single domain grains takes place at highersubstitution and Sr ferrite (x ¼ 1.0) contains the maximumnumber of single domain grains. These small grains have aprofound effect on microstructure and hysteresis properties.

50 60 [2T] 70-Scale

x = 1.0

x = 0.8

x = 0.6

x = 0.4

x = 0.2

x = 0.2

(30

0)

(21

7)

(22

0)

(20

12

)

(21

8)

(20

11

)

(20

14

)

12O19 ferrite sintered at 1250 1C for 20 h.

ARTICLE IN PRESS

Fig. 2. SEM micrographs of ferrite samples: (a) BaFe12O19, (b) Ba0.8Sr0.2Fe12O19, (c) Ba0.6Sr0.4Fe12O19, (d) Ba0.4Sr0.6Fe12O19, (e) Ba0.2Sr0.8Fe12O19, and

(f) SrFe12O19.

Table 1

Lattice constants a and c, cell volume, X-ray density, bulk density, porosity, anisotropy field and resistivity of Ba(1�x)SrxFe12O19 ferrite

x a (A) c (A) v (A) T.D

(g cm�3)

B.D

(g cm�3)

Porosity

(%)

Average grain

size (mm)

Ha (kOe) r (kO cm�1)

0.0 5.8882 23.135 694.64 5.3137 4.9191 7.43 9.8 15.04 41.35

0.2 5.8707 23.085 689.01 5.3092 4.8416 8.81 7.2 14.43 31.50

0.4 5.871 23.068 688.58 5.2646 4.8169 8.50 5.0 13.94 39.90

0.6 5.871 23.063 688.42 5.2178 4.7413 9.13 4.0 14.46 23.54

0.8 5.8557 23.038 684.09 5.2026 4.7312 9.06 3.5 14.07 43.68

1.0 5.8466 22.968 679.89 5.1862 4.5962 11.38 2.5 14.24 25.20

C. Singh et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 1657–1665 1659

ARTICLE IN PRESSC. Singh et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 1657–16651660

The cell volume variation (theoretical) corresponds to change(Table 1) in bulk density (experimental). The increase incalculated porosity is in accordance with the observed porosityrise in the microstructure (grain separation). Maximumobtained bulk density is 93% of theoretical value in the sample0.0 (Ba ferrite) and minimum is 87% in the sample 1.0 (Srferrite). Thus, Ba2+ ions promote densification of the ferrite.

3.3. Complex permittivity complex permeability

Dielectric constant and dielectric loss (Fig. 3) of allsamples exhibit non-linear behavior with frequency, this

0

2

4

6

8

10

12

14

16

18

20

8 8.5 9 10

0

2

4

6

8

10

12

14

16

18

20

x=0.6

x=0.8

x=1.0

ε'

Frequen

9.5 1

8 8.5 9 10

Freque

9.5 1

ε'

Fig. 3. Dielectric constant (e0) and dielectric loss (e00) of Ba(1�x)S

behavior is neither resonance nor relaxation type. Sample0.8 reflects maximum e0 (19) at 11.9GHz, while theundoped sample 0.0 shows the lowest e0 (0.4) at 12GHz.Microstructure is an important factor in influencing thestatic and dynamic properties of the ferrite. Sample 0.0 haslarge e0 in spite of having high resistivity of 41.35 kO cm�1

(Table 1). This is related to the microstructure, large grainsize is present in sample 0.0 (Ba ferrite) than doped samples.Grain enlargement is due to the large ionic radius of Ba2+

ions (1.34 A) than Sr2+ ions (1.12 A). Large grain size offersless hindrance to the applied field, thus polarization isenhanced leading to increase of both e0 and e00.

11 11.5 12 12.5

x=0.0

x=0.2

x=0.4

(x=0.0)

cy (GHz)

0.5 13

11 11.5 12 12.5

ncy (GHz)

0.5 13

(x=0.2)

(x0.4)

(x=0.8)

(x=0.6)

(x=1.0)

rxFe12O19 ferrite as a function of frequency and substitution.

ARTICLE IN PRESSC. Singh et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 1657–1665 1661

Dielectric loss; decreases (linear trend) non-linearly(Fig. 4) with frequency in samples 0.0, 0.4 and 0.8; remainsoscillatory or constant in samples 0.2 and 1.0; increaseswith frequency in sample 0.6. Dielectric loss mechanism ofsamples 0.0, 0.4 and 0.8 agrees with contributions from DCand AC conductivity or ion jump and dipole relaxationbased on expression e00 ¼ [(sDC/oeo)+e00AC], [6,7] wheresDC is the DC conductivity, o is the angular frequency, eo

is the permittivity of free space and e00AC is the ac losscontribution at high frequencies. According to aboveexpression, DC conduction loss varies inversely withfrequency, thus e00 increases at low frequency region.

0

2

4

6

8

10

12

14

16

18

8 8.5 9 10

0

2

4

6

8

10

12

14

8 9 10

ε"ε"

9.5 1

Freque

8.5 9.5 1

Freque

Fig. 4. Dielectric constant (e0) and dielectric loss (e00) of Ba(1�x)S

e00 in samples 0.2 and 1.0 (Sr-ferrite) remains constant(linear trend). Porosity is maximum (Table 1) in sample 1.0causing polarization decrement, hence e00 will decrease. Onother side, it owes low resistivity (25.20� 103O cm�1)which will increase e00. Competition between two factorskeeps e00 constant or oscillatory over entire frequencyregion. Similar reasons can be attributed to sample 0.2which possess high resistivity (31.50� 103O cm�1) andlowest porosity among the doped samples. Sample 0.0has significant dielectric loss at all frequencies, unlikemagnetic loss, which is nearly zero except in the highfrequency region.

11

x=0.0

x=0.2

x=0.4

11

x=0.8

x=1.0

(x=1.0)

0.5 11.5 12 12.5 13

ncy (GHz)

0.5 11.5 12 12.5 13

ncy (GHz)

x=0.6

(x=0.6)

(x=0.8)

(x=0.2)

(x=0.0)

(x=0.4)

rxFe12O19 ferrite as a function of frequency and substitution.

ARTICLE IN PRESSC. Singh et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 1657–16651662

In this composition, high temperature sintering (1250 1C)for a long duration of 20 h will result in formation of Fe2+

ions by the reduction of Fe3+ ions. Additional d electronsin Fe2+ ions can jump to neighboring Fe3+ ions accordingto following mechanism:

Fe2þ þ Fe3þ2Fe3þ þ Fe2þ:

This hopping of electrons will also result in the increase indielectric loss. These Fe2+ ions are easily polarized thanFe3+ ions causing an increase in e0 and e00.

Permeability and magnetic loss also exhibit non-linearvariation while encompassing low to high frequencyregimes in all the samples. Dispersion in m0 is large

0

0.5

1

1.5

2

2.5

3

3.5

8 9 9.5 10

x=0.0

x=0.2

x=0.4

x=0.6

x=0.8

x=1.0

μ'

0

0.5

1

1.5

2

2.5

3

3.5

μ'

8.5 1

Freque

8 9 9.5 108.5

Freque

(x=0.2)

Fig. 5. Permeability (m0) and magnetic loss (m00)of Ba(1�x)SrxF

(Fig. 5) in the undoped sample 0.0 at the high frequencyregion, exhibiting maximum 3.15 at 11.85GHz m0 stays at ahigh value for most of the frequencies in the undopedsample 0.0 (Ba-ferrite) among all the samples and increaseswith frequency; is neither increasing nor decreasing withfrequency in doped samples over the entire frequencyregime. m0 (linear trend) decreases with the substitution ofSr2+ ions from sample 0.2 to sample 0.6 (Fig. 5), while it isminimum at higher substitution (sample 0.8). Low m0 insubstituted samples can be ascribed to high porosity; theundoped sample 0.0 is less porous than the sample 1.0.Pores act as an impediment to domain wall motion andinduce local demagnetizing fields, resulting in reduction of

110.5

ncy (GHz)

11.5 12 12.5 13

1110.5

ncy (GHz)

11.5 12 12.5 13

(x=0.0)

(x=0.4)

(x=0.8)

(x=0.6) (x=1.0)

e12O19 ferrite as a function of frequency and substitution.

ARTICLE IN PRESSC. Singh et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 1657–1665 1663

m0 in the doped samples [8,9]. High density in sample 0.0improves grain-to-grain connectivity which eases magneticflux flow, thus m0 is kept high over the doped samples(Table 1).

Magnetic loss arises due to lag between magnetizationand applied field. m00 is maximum (1.02) in sample 0.0 at10.59GHz (Fig. 6). All the samples (except 0.4) exhibitnearly zero m00 from 8.2 to 10GHz, sample 0.8 stays atminimum m00 throughout the frequency region. Sample 0.4shows a different behavior with m00 increases withfrequency. Low magnetic loss in all the samples can beascribed to strong uniaxial anisotropy (Table 1) [10]. Smallgrain size in doped samples (Fig. 2) causes a reduction in

-2

-1.5

-1

-0.5

0

0.5

1

1.5

8 8.5 9 10

x=0.0

x=0.2

x=0.4

-1

-0.5

0

0.5

1

x=0.6

x=0.8

x=1.0

μ"

9.5

Freque

8 8.5 9 109.5

Freque

μ" (x=0.6)

(x=1.0)

x=0.8

Fig. 6. Permeability (m0) and magnetic loss (m00)of Ba(1�x)SrxF

domain wall damping and offers more hindrance to thevarying field that causes a reduction in m00 [8].Domain wall resonance is absent in all samples due to its

occurrence at the lower side of X-band. Ferrimagneticresonance (FMR) is also absent over the entire frequencyregime in the ferrite. Ba hexagonal ferrite has an anisotropyfield (Ha) of 17.09 kOe with a resonance frequency of47.6GHz [10]. In our composition, Ha of Ba ferrite comesout to be 15.04 kOe (Table 1) indicating that FMR will notbe observed at X-band. More specifically, anisotropy mustbe reduced through substitution of Fe3+ ions to obtainFMR at X-band, as Fe3+ ions decide anisotropy of ferritein spin-up and spin-down state. Since Fe3+ ions are not

11 12 13

(x=0.2)

ncy (GHz)

10.5 11.5 12.5

11 12 13

ncy (GHz)

10.5 11.5 12.5

(x=0.4)

(x=0.0)

e12O19 ferrite as a function of frequency and substitution.

ARTICLE IN PRESSC. Singh et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 1657–16651664

substituted, the anisotropy field is not reduced forresonance to occur at frequencies of our interest. Although,there is some variation of Ha with substitution (Table 1)which is presumably due to movement of Fe3+ ions fromlattice sites to accommodate substituted Sr2+ ions. Thismovement converts some of the Fe3+ ions to Fe2+ ions,consequently, partial reduction of Ha in doped samples isobserved in comparison with the undoped sample 0.0.

Frequency dependence of imaginary permeability ex-hibits anti-phase oscillations with imaginary permittivity(Fig. 7) from 8.2 to 12.4GHz. Thus total loss (dielec-tric+magnetic) does not oscillate with frequency, conclud-ing that oscillations in m00 and e00 are due to measurement

-40

-30

-20

-10

0

10

20

8 9 10

0.0e"

0.4e"

0.8e"

0.0u"

0.4u"

0.8u"

ε"

8.5 9.5

Frequency

10.5

u”=Magnetic Loss

e”=Dielectric Loss

Fig. 7. Anti-phase oscillations of m00 a

-3

-2

-1

0

1

2

3

4

5

8 9 10

x=0.2

x=0.4

x=0.6

x=0.8

x=1.0

x=0.0

tan

δ ε

8.5 9.5 10.5

Frequency

Fig. 8. Loss tangent (tan de) variation with frequenc

uncertainty and apparent splitting is ascribed to measure-ment error. Similar variation in complex permeability,complex permittivity and total loss (dielectric+magnetic)was observed by Meshram et al. [11] in Mn–Ti andCo–Mn–Ti substituted Ba-ferrite. Negative values in m0

(X-band) and tan de (0–40GHz) have also been reported inthe Refs. [12–14].The oscillatory behavior of sample 0.0 gives rise to high

tan de (23) at the high frequency region (Fig. 8), tan de isnearly 5 (linear trend) at 12GHz. Samples 0.6 and 0.8 alsohave low tan de at some frequencies. Sample 0.0 exhibitslarge tan dm 0.55 at 10.6GHz than other doped samples(Fig. 9), while sample 0.8 remains at low tan dm at most

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0.2e"

06e"

1.0e"

0.2u"

0.6u"

1.0u"

(GHz)

11 11.5 12 12.5 13μ"

nd e00 in Ba(1�x)SrxFe12O19 ferrite.

0

5

10

15

20

25

(GHz)

11.511 12.512 13

tan

δ ε

y and substitution in Ba(1�x)SrxFe12O19 ferrite.

ARTICLE IN PRESS

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

8 9 10 11 11.5 12 12.5 13

x=0.0

x=0.2

x=0.4

x=0.6

x=0.8

x=1.0

tan

δ μ

8.5 9.5 10.5

Frequency (GHz)

Fig. 9. Loss tangent (tan dm) variation with frequency and substitution in Ba(1�x)SrxFe12O19 ferrite.

C. Singh et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 1657–1665 1665

frequencies. The tan dm of all the samples is maximum atthe high frequency region than at the low frequency region.

The above mentioned concludes for large dielectric loss(e00), tan de than magnetic loss (m00) and tan dm. Therefore,dielectric properties are enhanced in comparison tomagnetic properties.

4. Conclusions

Complex permeability and permittivity of synthesizedBa(1�x)SrxFe12O19 ferrite varies with frequency and sub-stitution of Sr2+ ions. Ba ferrite is appreciated forimproved microstructural properties, dielectric loss andmagnetic loss, whereas, incorporation of Sr2+ ionsdiscourages these material parameters. Dielectric loss isdecided by hopping mechanism, resistivity and grain size,and magnetic loss depends on anisotropy field and grainsize. Ba-ferrite can be useful for lossy dielectric and EMIsuppression applications due to large tan de. Sample 0.6 haspotential for high frequency dielectric applications, whilesample 0.8 shows significance in both high frequencymagnetic and dielectric applications.

References

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[11] M.R. Meshram, N.K. Agrawal, B. Sinha, P.S. Misra, J. Magn.

Magn. Mater. 271 (2004) 207.

[12] F. Brown, C.L. Gravel, J. Phys. Rev. 97 (1955) 55.

[13] W.H. Von Aulock, Handbook of Microwave Ferrite Materials,

Academic Press, London, 1965, p. 385.

[14] M.D. Janezic, D.F. Williams, IEEE International Microwave

Symposium Digest (1997) 1343.