silicone composites

Journal of Magnetism and Magnetic Materials 325 (2013) 82–86

Contents lists available at SciVerse ScienceDirect

Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm

High-frequency magnetic properties at K and Ka bands for barium-ferrite/silicone composites Z.W. Li a,n, Z.H. Yang a, L.B. Kong a, Y.J. Zhang b a b

Temasek Laboratories, National University of Singapore, 5A Engineering Drive 1, Singapore 117411, Singapore DSO National Laboratories, 20 Science Park Drive, Singapore 118230, Singapore

a r t i c l e i n f o

a b s t r a c t

Article history: Received 22 February 2012 Received in revised form 27 June 2012 Available online 9 August 2012

High-frequency magnetic properties at K and Ka bands (18–40 GHz) have been studied for M-type barium ferrite BaMnxTixFe12  2xO19 (x ¼0.4–1.0) composites. The results show that complex permeability of the composites has a resonancelike-type dispersion. Although (m00 1) is rather small (about 0.2), m00max achieves 0.53–0.78, due to small effective damping coefficient. The composites also exhibit relatively high resonance frequencies fR covering 20–33 GHz, which are proportional to anisotropy fields Ha of the barium ferrites. These properties will be beneficial to the design of electromagnetic composites at a desired working frequency. & 2012 Elsevier B.V. All rights reserved.

Keywords: Superhigh-frequency magnetic property Complex permeability The relationship between dynamic and static magnetic property

1. Introduction With the developments of electronic and telecommunication technology, the high-frequency magnetic properties of materials, not only from UHF (ultrahigh frequency, from 300 MHz to 3 GHz) to SHF (superhigh frequency, from 3 to 30 GHz) but also from SHF to EHF (extremely high frequency, namely millimeter-wave), have abstracted much attention [1–5]. At UHF and low SHF bands, spinel ferrite composites and barium ferrite composites with c-plane anisotropy are often used, while high SHF band (Ku to Ka), barium ferrite composites with c-axis anisotropy are good candidates due to their high resonance frequency [2,3]. Further, complex permeability at millimeter-wave bands has also been reported in recent years [4,5]. In general, when an EM wave is irradiated into magnetic materials, a natural resonance (ferromagnetic resonance without an applied magnetic field) occurs. The resonance frequency fR is determined by the magnitude in anisotropy fields, Ha, of materials by [6,7] f R ¼ gH a

ð1Þ

for c-axis anisotropy, where g  2:83:0 GHz=kOe is the gyromagnetic factor. For example, Ha of BaFe12O19 is about 16 kOe, which leads to a high fR of about 45–48 GHz. On the other hand, it is known that the magnitude of anisotropy fields are closely

n

Corresponding author. Tel.: þ65 65164035; fax: þ 65 68726840. E-mail address: [email protected] (Z.W. Li).

0304-8853/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmmm.2012.07.040

related to the composition of substituted ions, which can decrease or increase the anisotropy fields [8]. Using the two properties, we prepared a series of MnTi substituted barium ferrite composites with resonance frequency as high as 20–30 GHz. This paper reports on their SHF (K and Ka bands) magnetic properties and the correlation between the dynamic and static magnetic properties.

2. Experimental Samples of BaMnxTixFe12  2xO19 with x ¼0.4, 0.6, 0.8 and 1.0 were synthesized using the conventional ceramic technique. A mixture of BaCO3, Fe2O3, MnO2 and TiO2 in the appropriate ratio required for the barium ferrite was calcined at 1080 1C for 4 h. The calcined samples were then crushed and ball-milled. Finally, the powders were shaped and sintered at 1350 1C for 16 h. Three types of samples were prepared for various measurements: (1) The sintered samples were prepared into cylinders with diameter of about 4 mm and thickness of about 1.5 mm; they were used in the measurements of magnetization curves and M–H loops. (2) The aligned samples were prepared by mixing the fine powders with silicone in a mould, followed by placing the mould in applied fields of about 3 kOe. The powders can freely rotate in silicone. After the silicone was solidified, the magnetic field was removed and all particles were aligned along a crystallographic direction. The plane of the aligned samples is normal to the alignment direction. The aligned samples were used in X-ray diffraction (XRD) and magnetic anisotropy measurements. (3) The composite samples were prepared by mixing fine powders of

Z.W. Li et al. / Journal of Magnetism and Magnetic Materials 325 (2013) 82–86

BaMnxTixFe12  2xO19 with silicone for microwave measurements; the volume concentration of the powders is 30%. X-ray diffraction (XRD) was performed for powder samples and aligned samples using a ULTIMA IV diffractometer with Cu Ka radiation. Magnetization curves and M–H loops were measured with applied fields of 0–22 kOe, and between  22 and þ 22 kOe, respectively, at room temperature for all sintered samples, using EV9-VSM (vibrating sample magnetometer). The demagnetizing corrections have been considered. Coercivity Hc was obtained from the M–H loops. Saturation magnetization Ms was deduced from a numerical analysis of the magnetization curves for sintered samples, based on the law of approach to saturation with the first and third terms retained,   B MðHÞ ¼ Ms 1 þ 2 ð2Þ H where H¼H0 Hd, H0 is the applied field, Hd is the demagnetization field of the samples, and B is a parameter relative to a magnetic anisotropy field Ha. The values of anisotropy fields were determined by two methods: the magnetization curves parallel and perpendicular to the alignment direction for the aligned samples, and the law of approach to saturation for the sintered samples. Magnetic permeability spectra of the samples were measured by a reflection–transmission method using a Anritsu vector network analyzer 37 369A. K and Ka band waveguides were used to measure the reflection and transmission between 18 and 40 GHz. Then the Nicolson and Ross algorithm is used to compute the permeability of the samples from the measured reflection and transmission. The measured permeability spectra are curve-fitted using the model of resonance-frequency distributions with the Kittel equation [9]

mðf Þ ¼

n X

i

wi0

i¼1

1 þ jlf =f r i i 1þ jðlf =f r Þ2 ðf =f r Þ2

þ1

ð3Þ

where n is the number of resonance frequency, wi0 and f ir are the static susceptibility and intrinsic resonance frequency of the i subspectrum, respectively, and l is the damping coefficient of composites. fr is determined by the effective magnetic field, including the anisotropy field and demagnetizing field.

3. Results

83

Table 1 Structural and magnetic parameters, where a and c are the lattice parameters, Haa and Hba are anisotropy fields obtained from law of approach to the saturation and the aligned samples, respectively. x

a (nm)

c (nm)

Haa (kOe)

Hba (kOe)

0.4 0.6 0.8 1.0

0.5908(4) 0.5913(3) 0.5916(3) 0.5923(10)

2.323(4) 2.325(3) 2.326(3) 2.328(9)

12.1 10.8 8.6 7.9

11.7 10.2 9.1 7.8

Fig. 2. The saturation magnetization Ms (open circles) and coercivity Hc (solid squares) for BaMnxTixFe12  2xO19 with x¼ 0.4–1.0.

parameters are listed in Table 1. The lattice parameters a and c increase gradually from 0.5908(4) nm to 0.5923(10) nm, and from 2.3230(4) nm to 2.3276(9) nm, respectively, as x varies from 0.4 to 1.0. The increase is attributed to the large Mn2 þ and Ti4 þ ion radius of 0.083 and 0.061 nm, respectively, as compared to the Fe3 þ ion radius of 0.051 nm. Fig. 1(a)–(d) also shows the XRD patterns of the aligned samples. The strong lines are found at 2y angles of 23.01, 30.81 and 55.41, which correspond to the (0 0 6), (0 0 8) and (0 0 14) crystal planes. Besides, some weak lines can be indexed as (0 0 10), (0 0 12) and (0 0 16). Further, as compared to the powder samples, many strong lines, such as line (1 0 7) at 32.11 and line (1 1 4) at 34.01, completely disappear. These imply that the grains are aligned along c-axis ([0 0 1] direction). For aligned samples, the easy magnetization directions should be along the applied magnetic field (normal to the surface of samples), due to free rotation of the particles during the preparation. Therefore, XRD patterns of the aligned samples show that the easy magnetization directions are along the c-axis.

3.1. X-ray diffraction XRD patterns confirm that all samples are single phase with M-type hexagonal structure. A typical pattern is shown is Fig. 1(e) for the powder sample with x ¼1.0. The structural

Fig. 1. Some typical X-ray diffraction patterns for BaMnxTixFe12  2xO19, aligned samples with (a) x¼ 0.4, (b) x¼ 0.6, (c) x¼ 0.8, and (d) x ¼1.0, and for (e) powder sample with x¼ 1.0.

3.2. Static magnetic properties Fig. 2 shows the dependence of saturation magnetization Ms and coercivity Hc on MnTi substitution. With MnTi substitution from 0.4 to 1.0, Ms decreases from 56 to 48 emu/g and Hc reduces rapidly from 64 Oe to 32 Oe. The decrease in Hc is attributed to a decrease in anisotropy field Ha. The anisotropy fields of BaMnxTixFe12  2xO19 are determined by two methods; one is for aligned samples and the other is using the law of approach to saturation. The reduced initial magnetization curves (starting from demagnetized samples) parallel and perpendicular to the alignment direction, ðMðHÞ=M s ÞJ and ðMðHÞ=M s Þ? , are respectively shown in Fig. 3 for the aligned samples. At magnetic fields H from 0 to about 8 kOe, ðMðHÞ=M s Þ? is approximately linear to H. The field corresponding to the intersection of the straight line and ðMðHÞ=M s ÞJ is just the anisotropy field Ha, as shown in the inset of Fig. 2. Using the method, Ha ¼ 11:7, 10.2, 9.1 and 7.8 kOe is obtained for BaMnxTixFe12 2xO19 with x¼0.4, 0.6, 0.8 and 1.0, respectively. At higher fields, ðMðHÞ=M s Þ? deviates from the straight line. The deviation is attributed to the higher order magnetocrystalline anisotropy or incomplete orientation of part of the particles.

84

Z.W. Li et al. / Journal of Magnetism and Magnetic Materials 325 (2013) 82–86

2.0

1.0

1.6

μ ' and μ ''

x=0.8

0.8 0.6

M/Ms

M/Ms

1.2 x=1.0

x=0.6

0.4

0.8

Ha

0.4 x=0.6

x=0.4

0

5

10

15

20

H (kOe) 0.0

0

4

8

12

16

24

μ ' and μ ''

0.0 16

μ ' and μ ''

56

0

4

20

24

28

32

36

40

0.8 0.4 0.0 16

48 0.004

0.006

8

12

16

20

24

28

32

36

f (GHz)

0.008

1/H2 (kOe-2) 0

40

52

0.002

10

36

x=1.0

1.2

20

32

0.4

50

30

28

0.8

1.6

40

24

1.2

60

M (emu/g)

M (emu/g)

x=0.8,

20

1.6

Fig. 3. The magnetization curves parallel and perpendicular to the alignment direction for aligned samples BaMnxTixFe12  2xO19. (in inset) The anisotropy field Ha is determined by the intersection between the linear extrapolation of ðMðHÞ=M s Þ? and ðMðHÞ=M s ÞJ .

x=0.6,

0.4

2.0

20

H (kOe)

x=0.4,

0.8

0.0 16

0.0

0.2

1.2

Fig. 5. Real and imaginary permeability spectra for BaMnxTixFe12  2xO19 composites with (a) x ¼ 0.4, (b) x ¼0.6 and (c) x¼ 1.0, where symbols represent the experimental data and solid lines represent the fitted curve.

20

H (kOe) Fig. 4. The magnetization curves M(H) for BaMnxTixFe12  2xO19 powder samples and (inset) the dependence of M on 1/H2, where B can be obtained from the slope of the lines.

Table 2 Fitted static permeability m00 , the maximum m0max , the maximum imaginary permeability m00max , effective damping coefficient leff and resonance frequency fR, where w2 is the standard deviation of fit.

On the other hand, anisotropy fields Ha are also obtained from the law of approach to saturation for powder samples with c-axis anisotropy. The B=H2 term in Eq. (2) is related to the magnetocrystalline anisotropy. Based on domain rotation model and the condition of K 1 bK 2 , where K1 and K2 are the first and second order magnetocrystalline anisotropy constants, respectively, B can be expressed as [10] 1 2 B ¼ 15 Ha

x

w2

m00

m0max

m00max

leff

fR

0.4 0.6 1.0

0.86 1.07 0.90

1.13 1.16 1.20

1.53 1.66 1.73

0.74 0.65 0.53

0.09 0.12 0.19

33.1 28.2 20.2

ð4Þ

The magnetization curves of BaMnxTixFe12  2xO19 powder samples are shown in Fig. 4. It is found a good linear relationship between M(H) and 1=H2 in H¼12–20 kOe, as shown in the inset of Fig. 3. The value of B can be derived from the slope of the straight line, and thus obtaining the anisotropy fields Ha from Eq. (4). The values of Ha are 12.1, 10.8, 8.6 and 7.9 kOe, respectively, for x¼ 0.4, 0.6, 0.8 and 1.0. Ha obtained from the above two different methods, as listed in Table 1, is well consistent. 3.3. Dynamic magnetic properties The measured and curve-fitted permeability spectra are shown, respectively, in the symbols and solid lines of Fig. 5 for BaMnxTixFe12  2xO19 composites with x ¼0.4, 0.6 and 1.0. The fitted dynamic parameters are listed in Table 2 and shown in Fig. 6, where m00 is the quasi-static permeability that is defined as the real permeability away from resonance, m00max is the maximum in m00 ðf Þ2f curves, and fR is the resonance frequency that is defined as the corresponding frequency for m00max . As the substitution x increases from 0.4 to 1.0, m00 slightly increases from 1.13 to

Fig. 6. The fitted dynamic parameters for BaMnxTixFe12  2xO19 composites: (a) m00 and m00max , (b) resonance frequency fR, and (c) effective damping coefficient leff .

Z.W. Li et al. / Journal of Magnetism and Magnetic Materials 325 (2013) 82–86

1.24, m00max decreases from 0.74 to 0.53, while fR is significantly shifted to low frequency, from 33.1 to 20.2 GHz. The fitted effective damping coefficients leff are very small; as x varies from 0.4 to 1.0, leff increases from 0.09 to 0.19. It is also noted that, in Fig. 5, besides the main absorption peak, a tail extended with a wide frequency range also exists in m00 2f curves. The main absorption peak has its origin in the natural resonance associated with anisotropy fields. The tail can be understood by the influence of demagnetization and the formation of poles on the wall for unsaturation-magnetized samples, according to the suggestions of Polder and Smit [11]. The resonance can cover from f ¼ gHa to the maximum f ¼ gðHa þ 4pM s Þ. For BaMnxTixFe12  2xO19 composites, the real permeability, m00  1:2, is very small away from the resonance. However, m0 ðf Þ significantly increases to the maximum 1.5–1.7 near resonance, and then rapidly decreases. The imaginary permeability m00 ðf Þ has a relatively narrow absorption peak. These describe the main characteristics of resonancelike-type dispersion. Second, the fitted effective damping coefficients leff are very small; they are 0.09, 0.12 and 0.19 for composites with x¼0.4, 0.6 and 1.0, respectively. Finally, the fit to permeability spectra provides the information on the distribution of intrinsic resonance frequencies fr. For each fir, the corresponding wi0 is obtained. Therefore, the reduced wi0 , as a function of fir, is plotted in Fig. 7. From the reduced distribution of resonance frequencies (RDRF), the frequency bandwidth, Df , of the distribution is defined as Df ¼ f 2 f 1 , where f2 and f1 are the frequency limits for which the probability Pðf 1 Þ ¼Pðf 2 Þ ¼ 0:5. For BaMnxTixFe12  2xO19 composites with x ¼0.4, 0.6 and 1.0, Df is only 2.2, 2.4 and 2.8 GHz, respectively. The spectrum-shape of permeability, small effective damping coefficient and narrow RDRF reveal that the permeability spectra have resonancelike dispersion.

85

to (m00 1) is closely associated with leff by [3] sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 m00max ¼ ðm00 1Þ 1 þ 2 2 l

ð5Þ

eff

For general relaxationlike-type spectra, leff is rather large, which is experimentally 1–2 [3,12]. From Eq. (5), the ratio of m00max to (m00 1) is only 0.56–0.71. If m00 is 1.2, m00max only reaches 0.11–0.14. However, permeability spectra of the BaMnxTixFe12 2xO19 composites has resonancelike dispersion with very small leff of only 0.09–0.19 (see Table 2), and the ratio of m00max to (m00 1) can achieve as high as 5.3–11.3. Therefore, although (m00 1Þ  0:2 is very small, relatively large m00max of 0.74–0.53 can still be acquired. Further, if leff is sufficiently small, Eq. (5) is simplified as 2m00max 1 ¼ m00 1 leff

ð6Þ

Eq. (6) predicts an inverse function between 2m00max =ðm00 1Þ and leff , which is indeed found in Fig. 8. For electromagnetic attenuation applications, large imaginary permeability m00max is desired, especially in the case of small real permeability m00 . Another advantage is high resonance frequency fR, due to larger c-axis anisotropy field Ha for BaMnxTixFe12  2xO19. The dependence of fR on Ha is plotted in Fig. 9, which shows a good proportional correlation between fR and Ha. The correlation is just predicted by Eq. (1). The fitted slope of the straight line is 2.75 GHz/kOe, which is in a good agreement with the gyromagnetic factor of g ¼ 2:823:0. Fig. 10 shows the relationship between fR and MnTi substitution x for the BaMnxTixFe12  2xO19 composites. A fair good linear relation of fR to x is found. From the relationship, the desired fR of composites can be obtained from BaMnxTixFe12  2xO19 barium ferrites with various MnTi substitution. This property will be beneficial to the design of electromagnetic composites at a desired frequency.

4. Discussion In general, the permeability spectra of composites have two types, namely resonancelike and relaxationlike dispersions, which can be distinguished by the magnitude of effective damping coefficient leff . Most of the spinel ferrite composites and barium ferrite composites with c-plane anisotropy have relaxationlike dispersion with experimental leff of larger than 1 and theoretical leff of infinity [3]. As compared to the relaxationlike dispersion, the permeability spectra with resonancelike dispersion have two interesting characteristics: (1) relatively large m00max , in spite of small (m00 1) and (2) high resonance frequency fR. The imaginary permeability m00max is closely related to the magnitude of damping coefficient. For natural resonance, the ratio of m00max

2μ ''max/ (μ'0-1)

14 12 10 8 6 4 4

6

8

10

12

14

1/λeff Fig. 8. The correlation between 2m00max =ðm00 1Þ and effective damping coefficient leff .

40 1.2 x=1.0

x=0.6

x=0.4

0.8 0.6 0.4

20 10

0.2 0.0 16

k=2.7 GHz/kOe

30

fR (GHz)

Probability

1.0

0 20

24

28

32

36

40

44

fr (GHz) Fig. 7. The reduced distribution of intrinsic resonance frequencies fr for BaMnxTixFe12  2xO19 composites with x¼ 0.4 (dot line), x¼ 0.6 (dashed line) and x ¼1.0 (solid line).

0

3

6

9

12

15

Ha (kOe) Fig. 9. The dependence of resonance frequency fR on anisotropy fields Ha for BaMnxTixFe12  2xO19 composites with x ¼0.4–1.0, where the solid and open circles present the values of Ha from the powder samples (approach saturation law) and the aligned samples, respectively.

86

Z.W. Li et al. / Journal of Magnetism and Magnetic Materials 325 (2013) 82–86

depending on MnTi substitution x. The composites are potential candidates for EM applications in a frequency range from centimeter- to millimeter-wave bands (18–40 GHz).

40

fR (GHz)

30 20

Acknowledgments

10 0 0.0

0.5

1.0

1.5

2.0

2.5

The authors would like to acknowledge the Defence Research and Technology Office (DRTech), Singapore for financial support to this work.

MnTi substitution x Fig. 10. The dependence of resonance frequency fR on MnTi substitution x for BaMnxTixFe12  2xO19 composites, where the open circles denote this work and the solid circles are taken from Ref. [13].

5. Conclusions From the above results, main conclusions are obtained as follows: (1) BaMnxTixFe12  2xO19 with 0.4–1.0 has c-axis anisotropy with relatively large anisotropy fields Ha of 12–8 kOe. The resonance frequency fR of BaMnxTixFe12  2xO19 composites is proportional to Ha. (2) The permeability spectra of BaMnxTixFe12  2xO19 composites have resonancelike dispersions. m00 is rather small of about 1.1. However, due to small effective coefficient, the ratio of m00max to (m00 1) achieves 5.3–11.3, instead of general 0.5 for relaxation-type dispersion. Therefore, relatively large m00max of 0.53–0.74 is obtained. (3) The BaMnxTixFe12  2xO19 composites with x ¼0.4–1.0 have significant high resonance frequency fR of 20–33 GHz,

References [1] S. Sugimoto, S. Kondo, K. Okayama, H. Hakamura, D. Book, T. Kagotani, M. Homma, H. Ota, M. Kimura, R. Sato, IEEE Transactions on Magnetics 35 (1999) 3154. [2] Y.J. Kim, S.S. Kim, Journal of Electroceramics 24 (2010) 314. [3] Z.W. Li, Z.H. Yang, L.B. Kong, Journal of Applied Physics 109 (2011) 033916. [4] K.A. Korolev, L. Subramanian, M. Afsar, IEEE Transactions on Magnetics 42 (2006) 2864. [5] A. Namai, S. Sakurai, M. Nakajima, T. Suemoto, K. Matsumoto, M. Goto, S. Sasaki, S.I. Ohkoshi, Journal of the American Chemical Society 131 (2009) 1170. [6] J.L. Snoek, Physica XIV (1948) 207. [7] J. Nicolas, in: E.P. Wohlfarth (Ed.), Ferromagnetic Materials, vol. 2, NorthHolland Publishing Company, 1980, p. 243. [8] H. Kojima, in: E.P. Wohlfarth (Ed.), Ferromagnetic Materials, vol. 3, NorthHolland Publishing Company, 1982, p. 305. [9] Z.W. Li, in: H. Lim, M. Serguei, Y.B. Gan, L.B. Kong (Eds.), Proceedings of Symposium P: Electromagnetic Materials, International Conference on Materials for Advanced Technologies, World Scientific Publishing, 2007, p. 79. [10] Z. Yang, H.X. Zeng, D.H. Han, Z.J. Liu, S.L. Geng, Journal of Magnetism and Magnetic Materials 115 (1992) 77. [11] D. Polder, J. Smit, Reviews of Modern Physics 25 (1953) 89. [12] Z.W. Li, Y.P. Wu, G.Q. Lin, L. Chen, Journal of Magnetism and Magnetic Materials 310 (2007) 145. [13] Z.W. Li, unpublication.