Study of Voigttype magneto microwave Kerr effect in ferritesPrabhat K. Singh, P. K. Singh, and S. V. Bakre Citation: Journal of Applied Physics 57, 4186 (1985); doi: 10.1063/1.334606 View online: http://dx.doi.org/10.1063/1.334606 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/57/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Magnetite particles studied by Mössbauer and magneto-optical Kerr effect J. Appl. Phys. 95, 1343 (2004); 10.1063/1.1637134 Enhanced magneto-optical Kerr effects and decreased Curie temperature in Co–Mn ferrite thin films Appl. Phys. Lett. 79, 1849 (2001); 10.1063/1.1402656 A study of the magnetooptical Kerr effect in layered films J. Appl. Phys. 70, 7033 (1991); 10.1063/1.349805 A study of phase and losses in ferrites by the magnetomicrowave Kerr effect J. Appl. Phys. 53, 9180 (1982); 10.1063/1.330430 The Microwave MagnetoKerr Effect in Silicon and Germanium. II. Determination of Relaxation Time andEffective Mass J. Appl. Phys. 39, 4099 (1968); 10.1063/1.1656932

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study of Voogt-type magneto microwave Kerr effect hl ferrites Prabhat K. Singh, P. K. Singh,a) and S. V. Bakre Department of Physics, University of Delhi, Delhi-llOOO7, India

The magneto microwave Kerr effect (MMKE) in the Voigt configuration is observed, for the first time, on two poJ.ycrystaUine MgMn ferrite samples at x-band frequency. The experimental data are analyzed on the basis of the MMKE theory suitably modified for Voigt configuration Kerr effect. The values of effective linewidth have also been calculated.

I. INTRODUCTION

In our laboratory, the magneto microwave Kerr effect (MMKE) in a Faraday configuration has received much at­tention because of its application as a simple and convenient method to study magnetic properties particularly perme­ability tensor components 1.2 and effective linewidth3

,4 of fer­rimagnetic materials. However, this effect in Voigt configu­ration has not been reported so far in ferrites. In the Kerr effect, generally, a rotation in the plane of polarization in the reflected wave is observed but the difference between the Voigt and Faraday cases is that in the former, the dc magnet­ic field (H de) is applied to the direction of propagation while in the latter the field is in the transverse direction.

The purpose ofthe present paper is to give a preliminary report on the study of the Voigt type MMKE, observed for the first time in two polycrystalline ferrite samples at 9.44 GHz. The data have been analyzed on the basis of the Kerr effect theory suitably modified for the Voigt configuration and which takes into account the internal multiple reflec­tions and demagnetization effects within the sample.

II. EXPERIMENTAL DETAILS

The measurements were performed using a double-mi­crowave bridge operating at 9.44 GHz. This bridge has been used earlier lA for the studies of Faraday configuration MMKE. In the present measurements, the orientation of electromagnet was changed in order to apply the dc magnet­ic field transverse to the direction of propagation of the microwaves, i.e., H de is along the diameter of the sample. The room temperature measurements were made in terms of a parameter R, the amplitude ratio of the two orthogonal linearly polarized components of the reflected beam, as a function of applied dc field (up to 7 kOe) on two disk-shaped MgMn ferrite samples. The samples were prepared by stan­dard ceramic techniques and had good microwave proper­ties. In our samples no second crystalline phase was ob­served. The sample properties are given in Table I. After lapping, the samples were polished by using an alumina slur­ry. The samples then were subjected to thermal annealing for an hour at 900·C followed by slow cooling in an oxygen atmosphere to remove surface strains and high surface losses resulting from lapping and polishing.

alMaterials Division, National Physical Laboratory, Hillside Road, New Delhi-I 10012, India.

m. THEORY

The theory of the magneto microwave Kerr effect de­veloped for the Faraday configuration3 has suitably been modified for the Voigt configuration. In Voigt-type MMKE, the parameter R is related to the reflection and propagation constants in the similar way to the Faraday configuration Kerr effect. The propagation constants depend upon the ef­fective permeability iJ.teff) values which are different for the cases of longitudinally (i.e., Faraday configuration) and transversely (i.e., Voigt configuration) magnetized samples. 5

In both the cases, however,,ueff is related to the permeability tensor components (e.g.,,u and K J.

In the present theory the contribution of demagnetizing fields has been accounted by using internal magnetic field value instead of external field in the tensor components and the effects of internal mUltiple reflections have been incorpo­rated by considering effective reflection coefficients3 in place of reflection coefficients in the expression of R. Moreover, the theory is based on the guided wave propagation of microwaves.4

In order to calculate effective permeabilities and hence R in the saturated state of magnetization, the Polder'S ex­pressions for permeability tensor components5 have been used. The internal field was estimated by using demagnetiza­tion factors from the work of Sawad06 which are also valid for Voigt configuration. In the data analysis the damping constant a was taken as an adjustable fitting parameter. The best fit values of damping constant which gave the same maximum value of R as observed experimentally have been used to calculate effective linewidth J.Heff by using the fol­lowing relation

TABLE I. Sample parameters.

Parameter MgMn2000 MgMnl400

Nature Polycrystalline PolycrystaJline Saturation magnetization 2000± 5% 1750 ± 5%

(Gauss) Dielectric constant 11±5% 12±5% Loss tangent 0.0005 0.0005 Resistivity (il cm) ::::::107 ::::::107

A verage Grain Size (!.tm) ",,8 ::::::10 porosity 2% 3% Surface finish (eLA) 0.06 0.10 Thickness (cm) 0.11 0.10 r41TM,I(1l 0.59 0.41

4186 J. Appl. Phys. 57 (1),15 April 1985 0021-8979/85/014186-03$02.40 © 1985 American Institute of PhySiCS 4186 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

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2uJa AHeff =--, r (1)

where aJ is operational angular frequency and r is gyromag­netic ratio.

IV. RESULTS AND DISCUSSION

The theoretical and experimental variation of R with external magnetic field H up to 7 kOe have been studied in two disk-shaped samples of MgMn ferrites e.g., MgMn2000 and MgMnl400. In these samples the field region for a par­tially magnetized state is small and the peaks and data of interest are all in a region of saturation.

The experimental and theoretical results for R vs H for the MgMn2000 sample have been shown in Fig. 1. The pa­rameter R increases with H initially and a peak is observed at a magnetic field strength of approximately 3.5 kOe. Theore­tically, a pronounced maxima has been observed at 4.5 kOe. It has been found that a small variation in the value of damp­ing constant (a) produces a significant change in the magni­tude of R in the vicinity of the peak. This behavior has been shown in Fig. 2 where theoretical R vs H curves are plotted for three different values of a.It is to be pointed out here that a similar sensitivity of damping values has been found for Faraday configuration MMKE.3 The value of damping con­stant which gave the same maximum R value as observed experimentally for MgMn2000 was 0.033. However, as shown in Fig. 1, the positions of the experimental and theo­retical peaks were shifted somewhat. The value of AHeff cor­responding to this value of a is 220 Oe.

In the MgMnl400 sample one peak was also observed approximately at 3 kOe as shown in Fig. 3. In this sample the corresponding theoretical peak was also found to occur in a somewhat higher magnetic field. The value of damping con­stant which gave a match to the maximum experimental R value was 0.016, corresponding to a AHeff equal to 110 Oe.

The values of AHeff in these samples are high and are

0'"8

0·7

0·6

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o

o

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o

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(KOe)-MAGNETIC FIELD

FIG. \. The theoretical and experimental R vs H curves for sample MgMn2000. The experimental points are shown by circles and the theoreti­cal curve for (l = 0.033 is represented by the solid line.

4187 J. Appl. Phys., Vol. 57, No.1, 15 April 1985

2'0

c(-o·QfO 1·5

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05

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MAGNETIC FIELD (KOel-

FIG. 2. The theoretical R vs H curves for three different values of damping constant (i.e., (l = 0.01, 0.02, and 0.035).

comparable with the values obtained from Faraday orienta­tion MMKE experiment at dimensional resonance peaks.3.4

It has been found theoretically that the peaks observed in MgMn2000 and MgMnl400 are also due to the dimen­sional resonance. The phenomenon of dimensional reso­nance occurs when the wavelength of electromagnetic wave inside the material is smaller then twice the relevent dimen­sions of the specimen, standing waves which can result in high losses may be excited. The dimensional resonance max­imum and minimum can be excited when the well known interference condition3

Ck:

2k'd=mT

0·8

0·7

0·6

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0

o

o o

o

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(2)

FIG. 3. The theoretical and experimental R ys H curves for sample MgMn 1400. The experimental points are shown by circles and the theoreti­cal curve for (l = 0.016 is represented by the solid line.

Singh, Singh, and Bakre 4187

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is satisfied. Here k' and d stand for the real part ofpropaga­tion constant and sample thickness respectively and n is an integer. The dimensional resonance maximum is excited when n is an odd integer and in our samples the resonance condition is satisfied for n = 1 at peaks.

In the present configuration where the dc magnetic field is parallel to the air-sample interface, a normally inci­dent wave can be analyzed in terms of two linearly polarized waves one of which has its rf magnetic field parallel to H de

and the other of which has rf magnetic field perpendicular to the H de. In the former case, ferromagnetic resonance (FMR) can be observed while in the latter, the FMR is not possible. But for any general direction of H de' the perpendicular com­ponent will contribute to the FMR. In our measurements the samples are magnetized to saturation but may not be uni­formly magnetized which can result in some transverse mi­crowave coupling locally in the various parts where the in­ternal magnetic field is not collinear with external magnetic field. Thus, the observed values of R may be affected by the transverse coupling. The parameter R having contribution of transverse coupling is overlapped by the maximum of di­mensional resonance. We, therefore, observed only a resul­tant of all these effects. This overlapping can even shift the position of experimental peak from the usual position as pre­dicted by the theory. The magnitude of the shift will depend upon the magnitude of the transverse coupling. The shift in the theoretical and experimental peak positions in Figs. 1 and 3 can be attributed due to this effect at least partially. Moreover, these discrepancies may al,so be due to the demag­netizing inhomogenities which are not taken into account in the present theory and are discussed below.

As pointed out earlier that for calculation of internal fields, the demagnetizing fields should be known correctly. In nonellipsoidal bodies (e.g., disk or rectangular prisms) the demagnetizing fields are, in general, nonuniform. 7 For the determination of demagnetizing fields, the total magnetic field is expressed as a series of ascending powers of the ratio

4188 J. Appl. Phys., Vol. 57, NO.1, 15 April 1985

of saturation magnetization to the applied dc magnetic field. The first term (first-order demagnetizing field) of this series gives the demagnetizing field at large applied magnetic fields where the sample is uniformly magnetized and the higher­order terms (second-order demagnetizing field) provides an idea of nonuniformity. It has been shown by Joseph and Schlomann 7 that for a nonellipsoidaI sample magnetized transversely, the second-order correction to demagnetizing factors is about 20% of the first-order contribution. In the present analysis we have considered onl.y the first-order de­magnetizing field (by using Sawado's expression6

) because the second-order correction in demagnetizing field is diffi­cult to evaluate. Moreover, we have also neglected the spa­tial variation of demagnetizing field. If we could account for the spatial variation and second-order correction of the de­magnetizing field into our theory, the discrepancies between theoretical and experimental peak positions can definitely be reduced significantly.

The present paper deals with the report on the observa­tion of Voigt configuration MMKE in ferrites and the pre­liminary analysis of the data only, the rigorous analysis is in progress and will soon be published.

ACKNOWLEDGMENTS

The authors gratefully acknowledge Professor G. P. Srivastava, Dr. Shiva Prashad, Dr. Pran Kishan, and Dr. S. B. Singh for many helpful discussions.

's. Prasad and R. M. Mehra, J. Phys. Chern. Solids 39,353 (1978). 2S. Prasad, J. Magn. Magn. Mater. 5,353 (1977). 3p. K. Singh, S. Prasad, Prnbhat K. Singh, ancl S. 13, Singh, J. Appl. Phys. 53,9180 (1982).

'P. K, Singh and S. Prasad, IEEE Trans. Magn. MAG-IS, 1633 (1982). 'B. Lax and K. J. Button, Microwave Ferrites and Ferrimognetics (McGraw-Hill, New York, 1962), p. 304.

6E. Sawado, J. Appl. Phys. 40, 1860 (1969). 'R, I. Joseph and E. Schlornann, J. Appl. Phys. 36, 1579 (1965).

Singh, Singh, and Bakre 4188

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