Ferromagnetic relaxation processes in polycrystalline magnetic insulators

JOURNAL

OF MAGNETIC

RESONANCE

15,359-366

(1974)

FerromagneticRelaxation Processesin Polycrystalline Magnetic Insulators C. M. SRIVASTAVA AND M. J. PATNI Indian

Institute

of Technology,

Bombay-400

076, India

Presented at the Fifth International Symposium on Magnetic Resonance, Bombay, India, January, 1974 The ferromagnetic resonance linewidth in polycrystalline insulators contains contributions which arise from intrinsic and extrinsic properties of the material and also from the electromagnetic perturbations of the resonant cavity. Contribution to the relaxation frequency due to anisotropy, porosity, and surface pits are wellknown. Cavity measurements introduce two additional sources of electromagnetic nature which had not been hitherto analyzed satisfactorily. These arise from eddy currents induced in the cavity wall due to the proximity of the precessing dipoles and nonuniformity of the rf-field over the volume occupied by the sample. The analysis involving all these contributions leads to a diameter dependence of the relaxation frequency. This prediction of the theory has been satisfactorily verified by experiments on a number of samples with widely varying saturation magnetization. An attempt has also been made to obtain the intrinsic linewidth using this analysis and to compare it with the reported linewidths in single crystals. INTRODUCTION

The observed ferromagnetic linewidth, AH, in polycrystalline magnetic insulators is at present difficult to interpret as it contains contributions from a large number of sources. Apart from the uncertainties brought about in the intrinsic parameters through the preparation techniques for the samples, measurements employing cavity methods introduce additional problems of electromagnetic nature which give rise to size-dependent effects in lineshifts and linewidths in ferromagnetic resonance. We have already shown that the lineshifts can be explained satisfactorily through our analysis of the electromagnetic perturbations due to eddy currents and inhomogeneous demagnetization when the samples are located on the base of the cavity (1). In this study we show that the contribution to linewidthfrom relaxation processes arising from the polycrystallinity of the sample on the basis of the existing theories does not lead to a satisfactory explanation of the observed linewidth. This indicates the inadequacy of the oversimplified models on which the present calculations of relaxation frequencies are based. In polycrystalline magnetic insulators, the observed AH contains, in addition to the intrinsic single-crystal relaxation component, AHi, contributions from anisotropy, AH,, porosity, AH,, and scattering from surface pits, AHpi, (2). In resonance measurements, with samples located on the base of the cavity, significant contributions to lineshift also arise on account of wall eddy currents and inhomogeneous demagnetization fields, H, and Hid, respectively (1). Denoting the contributions to the linewidth due to Copyright 0 1974 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain

359

360

SRIVASTAVA

AND

PATNI

these fields by AH, and AHid, the observed linewidth, AH, assuming the variouscclntributions to be additive, can be written as AH= AHi + AHa + AH, + AH,,, + AH, + AH,,. In case the contributions from these effects can be properly estimated, it is possible to obtain AHi, which ideally should be the single-crystal linewidth. At present, large uncertainties exist in the analysis of the contributions from the different sources and hence the estimate of AHi by this method often yields unrealistic values (3). In Eq. [l J, the first three terms are independent of the sample size, while the remaining terms are diameter dependent. It will be shown in this paper that reasonably satisfactory analysis of the contributions from the latter three sourcescan be made andexperimentally verified through the diameter dependence of AH. This has been made possible by using the same sample and grinding it to different diameters keeping approximately the same surface finish. The analysis of the size-independent terms has been based on simplified models. The analysis of the dipole-narrowed anisotropy linewidth appears to be in reasonable agreement with experiment (4). On the other hand, several attempts to obtain line widths due to the pores have yielded results which at best are in agreement with experimental observations within a factor of 2 (5). Our results show that in Ni-Zn and Mg-Mn ferrite systems, this is overestimated by almost a factor of 10. This indicates that the simple models used in obtaining AH,, need further examination. In particular, the presence of canted angles and nonmagnetic cations in the system seems to considerably reduce the contribution from this source. THEORY

The linewidth contributions from anisotropy, porosity, and surface pits, for a spherical sample, are given by (6, 7):

Pal v 0.109(3 co? 0, + 1.4)2 0, .---> cos 8, Oi R 0.109(3 cos’ 8, + 1.4)’ o, .-, AHoi, = $4nMd cos 8, cc)i AH, = ;.4nMF

where 47cM is the saturation magnetization, K1 is the anisotropy constant, v/V is the pore to sample volume ratio, R is the mean radius of the surface pits, dis the diameter of the sample, CD,is the uniform precession resonant frequency, and wi is the internal frequency, oi = y(HO - (471M/3)). In our calculations we make use of the approximation that 1 -.0’=2/3 1+; ) where CY= ‘T) COSH, wi 0 ( 1 Ho being the value of the dc resonant field. Here we note that the proportionality of AH, to the factor (2KJM)‘. li4nhf has been experimentally verified (8). The linewidth expression [2b] explains the observed frequency dependence of AH, and is thus best equipped to explain experimental data (9). The expression for AHpi, has been verified by Dionne (IO).

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Our experimental study on the line shift due to eddy current and inhomogeneous demagnetization fields shows that the analysis carried out by us is on right lines and the fields H, and Hi, are given by (I): H, = - 0.321 4nM(l + &;);

Pa3

and

where 1 is the wavelength of the rf field, E is the dielectric constant, and t1 and t2 are functions of the effective rf permeability, p, (II) : 1 h+2)c71b+ 11) s1 = s [ (/I, - 1)(/k + 3) I ’ v

<* = ! (A + a2 (7/b + 11) 9 [ be- l)(Pe+3Y I .

Within the sample, the fields He and Hid are inhomogeneous and in phase. Using now the analysis of Geschwind and Clogston as modified by Sparks for the dipole-narrowed inhomogeneously broadened linewidth, we obtain (7): AH,

+

AHid

z

2”‘H;

LHidJ2

&

71

[41

2. u

I

Neglecting the small second-order term in Eq. [3b], we find that (AH, + A Hid) varies as d2, while AHpi, varies as d-l. Since the remaining terms in Eq. [l] are independent of the sample size, we may write AH = AH, + C, d-’ + Czd2,

[51

where AH0 = AHi + AH, + AH,, Cl = AHDi,d, c = (AHid + AHe) 2

d2

In the systems studied by us, the variation of AH with the diameter of the sample follows the dependence predicted by the theory. The constants C, and C, obtained experimentally also are in good agreement with the theoretical values. RESULTS

AND

DlSCUSSIONS

The diameter dependence of AH has been studied in the Ni-Zn and Mg-Mn ferrites and in YIG, i.e., on ferrites having widely varying 4nM and AH. The analysis has been done on the basis of Eq. [5]. As the resistivities of all the samples were high (greater than IO5 ohm-cm), the volume eddy current contribution to the linewidth was ignored. The constants C1 and C2 were obtained using Eqs. [2c] and [4], respectively, the values for He + Hid being obtained from Eq. [3]. This is justified on the basis of our experimental studies on the lineshift due to these fields on the systems reported here.

362

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The measurements were made at room temperature, using a TE,,, cylindrical cavity at a fixed frequency of 9950 MHz. Spherical samples were prepared with a mean surface pit size of about 25 pm. The ferrite sphere was located at the base of the cavity and the diameter dependence of AH was studied by progressively reducing the diameter of the same sample. The error in the measurement of AH was k5 Oe. In Table 1 are given the observed linewidths for different sphere diameters for the ferrite Mg0.25Mn0,75Fe204. Also listed are the calculated values of AHpi, and (AH, + AHid).

0

EXPERlMENi-AL

OBSERVATIONS

THEORY LOO - 1 YIC 2

NiO.s

Z~O.~

Fc20.,

N’o.25 Zno.75 Fe204 4 N;0.7sZ”o.2s Fe204 s MgO.*s%75F’2% 6 Mg0.,5M”0.2sF.20.,

3

320-

0

I

0

0.2

I

0.L

I

0.6

I

t

I

0.0

1.0

1 .2

d in

FIG.

1. Linewidth

1.L

1.6

mms

as a function

of diameter.

Using Eq. [5] and a constant value of AH,, the theoretical linewidth AHtheory was obtained, as shown in the last column. The observed and theoretical values show reasonably good agreement. Using this method, the observed diameter dependence of All can be accounted for satisfactorily as can be seen for six different ferrite compositions in Fig. 1. The diameterindependent value of the linewidth, AH,,, has been given in Table 2 for the Ni-Zn and Mg-Mn ferrites and for YIG. The error in AH, is 410%.

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Although the analysis of the diameter-dependent part of the linewidth yields results in agreement with the observed linewidths, attempts to explain the observed AH,] on the basis of Eqs. [2a] and [2b] for AH, and AH,, respectively, have not yielded realistic values of AHi. Table 2 contains the parameters related to the samples which have been used in the calculations of AH, and AH,. We find that in some of the cases, .4Hi is TABLE LINEWIDTHS

YIG NIFez04 Nio.7~Zno.&e~0~ Nio.5Zno.sFezOa Ni o.2Jno,&%04 MgFW, Mgo.~sMno.&e~04 Mgo.~Mno.&~O.+ M&.t~Mno.75Fe~04 MnFezOl

2

FROM

47cM (gauss)

2KJM 0)

1750 3270 5100 4800 2300 1600 2920 3285 4010 4850

80 440 300 200 20 460 260 240 200 160

negative and so large that it cannot measurements. As discussed above, general agreement with experiments, of AHi, its contribution happens to crepancy arises on account of the AH,, in these systems.

FMR

DATA

01 v --.0.01 0.03 0.07 0.07 0.02 0.02 0.03 0.07 0.04 0.09

AHo (04 ~~ ._~30 500

110 95 120 600 300 100 170 470

AH,, We) -.-31 157 340 393 81 58 149 378 237 428

AHa 03

AHi (Oe)

9 186 65 29 _-

-10 -t157 --295 -327 -t39 +205 +83 -332 -100 +2!

337 68 54 33 19

be accounted for on the basis of the errors in the the analysis of the anisotropy contribution is in and in cases where we obtain large negative values be small. We may conclude that most of the disincorrect analysis of the porosity contribution,

600 5 oog \ u 400-’ 0 .c

300-

z

zoo-

\

\\ ‘1

\

\ ‘\

loo0

\

0

, 0.2

I 0.4 x

FIG. 2. Linewidth

---+-------O

-o---

in

of polycrystalline

I 0.6

NilWx

Zn,

! 0.8

I.0

Feg04

Ni,-,Zn,Fe,O,

as a function of X.

To investigate the possible reasons for the inadequacy of the simple model used for the analysis of AH,, we have plotted AH, as a function of x for the Ni,-,Zn,Fe,O, and Mg,-,Mn,Fe,O, ferrites in Figs. 2 and 3, respectively.

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In the Ni-Zn system, we find that AH, drops suddenly as x is increased from 0 to 0.25 and is then essentially constant for any further increase in x. The spin ordering in this system shows that NiFe,O, is collinear but the other three ferrites studied, viz., x = 0.25, 0.5, and 0.75, have a canted spin arrangement (12). The analysis of the linewidth contributions dH, and AH, for canted systems is complicated and has not been attempted. It is possible that the narrowing occurs due to the presence of Yafet-Kittel angles in these systems. In the Mn,-,Mg,Fe,O, system, AIf,, as a function of composition shows a minimum at about x = 0.5. A similar observation has been reported by Belov et al. in single crystals of Mg-Mn ferrites (13). This reduction in linewidth is likely to occur on account

I’

500

1’

it 400 c I.- 300 0

‘\

\

\

\ \

\

\

200

i

IOOC 01 0

I 0.2

I 0.4

x

FIG. 3. Linewidth

in

of polycrystalline

I 0.6

I 0.8

Mnl~xM&Fo204

Mnl-xMgxFeZ04

as a function of x.

of the presence of the nonmagnetic cations in the system, which may cause a reduction in the density of degenerate magnon-modes due to the loss in translational invariance. The data on Mn,-,Zn,Fe,O, shows a similar order of magnitude as well as linewidth minimum at x = 0.5, indicating that the nature of the nonmagnetic cation is not of any major significance in the relaxation mechanism for these systems (14). The reported values of AH for single crystals of the same composition show a wide scatter although these are an order of magnitude smaller than the polycrystalline AH. The results of Makram on single-crystal NiZn ferrites show that AH lies between 20 and 50 Oe in this series (15). A linewidth of 15 Oe has been reported for single-crystal nickel ferrite (16, 17). Similar values have been reported for single-crystal MgMn ferrites although in this series heat treatment of the samples could change the linewidth by as much as an order of magnitude (13). The lowest linewidth of 8 Oe in this series has been obtained for Mn,,,,Mg0.53Fe,04 by Dixon and Leo (18). CONCLUSIONS

At present, there exist uncertainties in the evaluation of the intrinsic linewidth both for single-crystal and polycrystalline samples on account of the perturbation due to electromagnetic effects and ionic distribution between the crystallographic sites (19). Our present analysis shows that it is possible to account satisfactorily for the electromagnetic effects in ferromagnetic resonance. Using this method, it may be possible to

366

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the relaxation processes in single and polycrystalline samples originating the nature and distributions of ions between the crystallographic sites.

study

from

REFERENCES I. 2. 3. 4. 5. 6. 7. 8.

Y. f0. II.

12. 13. 14.

15. 16. 17.

18. 19.

M. J. PATNI AND C. M. SRIVASTAVA, “Ferrites” (Y. Hoshino, S. lida, and M. Sugimoto, Eds.). p. 551, University of Tokyo Press, Tokyo, 1971. McGraw-Hill Book Co., New York, 1964. M. SPARKS, “Ferromagnetic Relaxation Theory,” G. F. DIONNE, J. Appl. Phys. 40, 1839 (1969). E. SCHL~MANN, J. Phys. Chem. Solids 6,242 (1958). G. F. DIONNE, Mat. Res. BIJII. 5, 939 (1970). M. SPARKS, J. Appl. Phys. 36,157O (1965). P. E. SEIDEN AND M. SPARKS, Phys. Rev. A 137, 1278 (1965). R. KRISHNAN, IEEE Tram Magnetics MAC-6,618 (1970). A. S. RISLEY, E. G. JOHNSON, AND H. E. BUSSEY, J. Appl. Phys. 37, 656 (1966). G. F. DIONNE, J. Appl. Phys. 43, 1221 (1972). C. M. SRIVASTAVA, Indian J. Pure Appl. Phys. 9, 416 (1971). N. S. SATYA MURTHY, M. G. NATERA, S. 1. YOUSSEF, R. J. BEGUM, AND C. M. SRIVASTAVA, Phys. Rev. 181, 969 (1969). K. P. BELOV, V. F. BELOV, AND A. A. POPOVA, Sov. Phys. JETP l&l372 (1960). W. H. VON AULOCK, “Handbook of Microwave Materials,” p. 346, Academic Press, New York, 1965. H. MAKRAM, Czech. J. Phys. B17, 387 (1967). A. B. SMITH AND R. V. JONES, J. Appl. Phys. 37,1001 (1966). S. MIYAMOTO, N. TANAKA, AND S. IIDA, J. Phys. Sot. Japan 20, 753 (1965). S. DIXON, JR., AND D. C. LEO, J. Appl. Phys. 40,1414 (1969). J. NICOLAS, A. LAGRANGE, R. SROKJSSI, AND R. INGLEBERT, IEEE Tram Mognetics MAG-9, 546 (1973).