Magnetic behavior of aggregates of small γ-Fe2O3 particles

Journal of Magnetism and Magnetic Materials 123 (1993) 175-183 North-Holland

Magnetic behavior of aggregates of small

~/-Fe203 particles

S. Koutani, G. Gavoille Laboratoire de Min&alogie-Cristallographie et Physique lnfrarouge, URA CNRS no. 809, Universit~ de Nancy I, Facultd des Sciences, BP 239, 54506 Vandoeuvre les Nancy Cedex, France

and R. G6rardin Laboratoire de Chimie du Solide Min&al, URA CNRS no. 158, Universit~ de Nancy I, Facultd des Sciences, BP 239, 54506 Vandoeuvre les Nancy Cedex, France Received 7 July 1992; in revised form 16 September 1992

Aggregates of small (10 nm) -/-Fe20 3 crystallites dispersed in A1203 powder have been studied by magnetization measurements and M/Sssbauer spectroscopy. The magnetic behavior, ZFC magnetization, coercive field, remanent magnetization and magnetization in intermediate magnetic fields, has been shown to be sensitive to the packing fraction of the aggregates as the result of the dipolar interactions between the aggregates. Both the coercive field and the remanent magnetization decrease very quickly as the temperature increases owing to relaxation phenomena with relaxation time shorter than 1 min. On the other hand, M6ssbauer spectra at room temperature does not show any quadrupolar doublet implying relaxation time longer than 10 -8 s. Such long relaxation times are interpreted as resulting from the relaxation of correlated volumes containing a large number of crystallites. Assuming that the coupling between the crystallites only results from dipolar interactions we show that the magnetic properties and the relaxation process are very sensitive to the size of the crystallites and to the shape of the aggregates.

I. Introduction

Small single domain particles of ~-Fe203 are of great interest in magnetic recording. Numerous experimental and theoretical works concerning the magnetic behavior of such particles have been published so far. The magnetic structure as well as the reversal mode of the magnetization in an isolated equiaxed crystallite are now well known [1,2]. The reversal modes of the magnetization in acicular single domain particles have Correspondence to: Dr. S. Koutani, Laboratoire de Min&alogie-Cristallographie et Physique Infrarouge, URA CNRS no. 809, Universit6 de Nancy I, Facult6 des Sciences, BP 239, 54506 Vandoeuvre les Nancy Cedex, France. Tel.: +33-83-9127-50; telefax: + 33-83-40-64-92.

been the subject of many works and now there are reliable models [3,4]. The superparamagnetic behavior and the blocking process of the relaxation is also well understood for isolated single domain particles. The magnetic behavior of concentrated small particles and that of aggregates of small crystallites is however far from being well understood. Blocking temperatures of aggregates of nanometric crystallites (< 10 nm) ranging from 130 K up to more than 300 K have been reported [5-7] and the effect of the shape of the aggregates has been recognized [7]. If acicular particles of 1 ixm in length are single domain, equiaxed aggregates of the same size show a multidomain behavior [5]. The effect of the interactions between particles has been recognized long ago [8-10] but the data

0304-8853/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

t76

S. Koutani et al. /Aggregates o f small y-Fe 2 0 ~ particles

are usually interpreted in the framework of an isolated particles model with an effective uniaxial anisotropy [5,11]. Inter-particles interactions have been considered by Morup [11] in the molecular field approximation but that approximation may be inadequate for dipolar interactions since the average dipolar interaction of randomly packed particles vanishes. We report here on magnetization measurements and M6ssbauer spectroscopy experiments carried out on aggregates of small crystallites. The magnetic behavior is shown to be sensitive to the size of the aggregates as well as to their concentration. The relaxation phenomena are characterized by rather long relaxation times that bears evidence of the collective character of the relaxation phenomena. By only considering the dipolar interactions between the particles, the strong dependence of the magnetic behavior on the size of the crystallites and on the shape of the aggregates can be understood.

2. Sample preparation Small Fe304 particles are obtained by coprecipitation of iron chlorides by amonium hydroxyde as described in ref. [12]. The precipitate is filtered and washed in water and then dried at 80°C for 30 min. The X-ray diffraction pattern shows only the spinel structure with a cubic lattice parameter of 8.39 ,~. The size of the crystallites as deduced from the Scherrer formula is 10 nm. As the kinetics of oxidation of Fe304 into 3,-Fe20 3 depends on both the size of the crystallites and the procedure of preparation [13,14] the powder has been heated in air for 30 rain at different temperatures ranging from 150 to 300°C. X-ray diffraction experiments show that the reflexions of c~-Fe20 3 begin to appear above 250°C. The samples have been prepared by heating the magnetite in air at 200°C for 30 min. The resulting brown powder has a spinel structure with a lattice parameter of 8.34 A and the size of the crystallites is still 10 nm. Optical microscopy observations show aggregates of sizes up to a few fxm. The aggregates have been dispersed by a 50 W ultrasonic probe for 30 min. Such a dispersion observed by TEM consists of nearly spherical

Fig. 1. TEM image of the aggregates. The dark line corresponds to 200 nm.

crystallites with a mean diameter of 8 nm (or --- 2 nm) which form fractal aggregates with sizes ranging from a few crystallites up to 0.5 ~m (fig. 1). The sample L28, consisting of large aggregates, is obtained by mixing the as prepared -/F e 2 0 3 powder with A120 3 powder, with a concentration in -y-Fe203 of 28% in mass. Other samples, labelled Sc and consisting of small aggregates are obtained from the dispersed -/-Fez0 3 powder. A mixture of ~-Fe20 3 and AI20 3 with a concentration c in mass of ~-Fe203 is dispersed by ultrasonic probe for 30 min. Samples with c = 100, 30, 9 and 1.3% have been prepared. The samples are packed in cylindrical sample holders for magnetic measurements.

3. Magnetic measurements

3.1. Experimental procedure The magnetic measurements have been carried out with a vibrating sample magnetometer operating between 4.2 and 300 K in magnetic fields up to 20 kOe. Zero field cooled (ZFC) magnetization measurements have been obtained by the following procedure. The samples are cooled from room temperature to 4.2 K in a magnetic field smaller than 2 0 e . A given magnetic field is then applied and the magnetization

S. Koutani et al. /Aggregates of small y-Fe203 particles

0*-

E

o~ v

0.1

0.0

,

0

100

T

200

300

T (K) Fig. 2. ZFC magnetization curves in a 50 Oe magnetic field. From top to bottom $1.3, $9, S100 and L28 samples.

is recorded on heating at a rate of 2 K / m i n . Isothermal magnetization curves have been recorded in the following way. The samples are ZFC from room temperature to the temperature of measurement. The virgin magnetization curve and the hysteresis loop are recorded in magnetic fields up to 20 kOe. As relaxation phenomena appear in low magnetic fields, the rate of the magnetic field variations is properly controlled. The recording of a hysteresis loop takes 30 min.

177

blocking temperature T B of superparamagnetic clusters and a Curie-Weiss behavior is expected above T B. It must be noted that the S1.3 sample does not show any Curie-Weiss behavior below 300 K, i.e. well above the temperature of the maximum of the M / H curve. As we shall see below the coercive field of this sample does not vanish at 300 K, and the shape of the ZFC magnetization curve may arise from a progressive freezing resulting from a wide distribution of relaxation times. Another striking feature is the behavior of the L28 sample whose curve lies below that of the $100 sample i.e. well below the curve that we may expect for a $28 sample. The ZFC magnetization is controlled not only by the dilution of the specimens but also by the size of the aggregates. ZFC magnetization curves of the L28 sample in magnetic fields up to 600 Oe are reported in fig. 3. The maximum TM(H) of the M / H curve shifts to lower temperatures as H increases. We have plotted in fig. 4 H c versus T M which may be compared to the temperature dependence of the coercive field. This suggests that the ZFC magnetization is strongly related to the coercive field.

0.12

0,10

._a X

0,08

,/

3.2. ZFC magnetization measurements Z F C m a g n e t i z a t i o n m e a s u r e m e n t s carried out in a 50 O e m a g n e t i c field are r e p o r t e d in fig. 2. T h e M / H versus t e m p e r a t u r e curves of the S1.3 a n d $9 samples show a b r o a d m a x i m u m which shifts to higher tenaperatures as the ~ - F e 2 0 3 c o n c e n t r a t i o n increases. This is consistent with the data of EI-Hilo et al. [15] o b t a i n e d on m u c h more d i l u t e d F e 3 0 4 samples. T h e m a x i m u m of the M / H curve is usually i n t e r p r e t e d as the

0.06

0.04

I 100

I 200

300

T (K) Fig. 3. ZFC magnetization curves of the L28 sample in different magnetic fields: 100 Oe X, 300 Oe o, 400 Oe o and 600 Oe B.

178

S. Koutani et al. /Aggregates of small y-Fe20 3 particles 0.3

20o

0.2.

100 x

0

,

,-'-'w---°-, 100

0A

200

300

T (K) Fig. 4. Coercive field of the L28 sample (x) versus temperature. The dots correspond to the points of the (H/13, Tm) plane where Tm is temperature of the maximum of the ZFC magnetization in the magnetic field H.

0.0

i

T

I00

3.3. Coerciue field and isothermal remanent magnetization T h e coercive field Hc, the r e m a n e n t m a g n e t i zation M r a n d the differential susceptibility X at the coercive field have b e e n m e a s u r e d for the samples S1.3, S100 a n d L28 b e t w e e n 4.2 a n d 300 K. T h e data are r e p o r t e d in figs. 5 - 7 . T h e y are similar to those previously r e p o r t e d by Coey a n d Khalafalla [5]. A t 4.2 K the coercive fields of the

i

200

300

T (K) Fig. 6. Ratio of the remanent magnetization to the saturation magnetization versus temperature for the S1.3 *, L28 × and S100 o samples.

S100, S1.3 a n d L28 samples are 185, 222 a n d 207 Oe, respectively. T h e coercive field is n o t very sensitive n e i t h e r to the packing fraction n o r to the size of the aggregates a l t h o u g h it slightly increases with the packing fraction. I n any case it is m u c h larger t h a n expected for c o h e r e n t m a g n e -

i

0.20

2OO

o.xs E

o 100

0.10

0

I 100

~

1 200

0.05

~00

T (K) Fig. 5. Coercive fields versus temperature for the S1.3 *, L28 x and $100 o samples.

,

0

I

100

,

1

200

300 T (K) Fig. 7. Differential susceptibilities at the coercive field for the S1.3 *, L28 x and $100 o samples.

S. Koutani et al. /Aggregates of small "y-ge20 3 particles

tization reversal against single ion anisotropy for randomly orientated particles H c = 0.641 g 1 I / M s

(1)

which yields 75 Oe with the data for bulk ~/-Fe20 3 [13]. The coercive fields of the three samples show a similar temperature dependence. The sharp decrease of the coercive fields at low temperatures may be related to the relaxation phenomena which are clearly observed above 50 K. The ratio M r / M s of the remanent magnetization to the saturation magnetization is rather small for all the samples since it does not exceed 0.3 for the S1.3 sample at 4.2 K, that may be compared to 0.5 and 0.866 [16], the expected values for single domain particles with uniaxial or cubic anisotropy and this means that a large fraction of the particles have reversed their magnetization in zero magnetic field. Such low values are characteristic of multidomain or collective behavior. Like the coercive field, M r / M s decreases as the packing fraction increases and shows a strong temperature dependence. The differential susceptibilities at the coercive field have the same order of magnitude for the three samples but their temperature dependence strongly contrasts with that of the coercive field. Only a small increase is observed for the S100 and L28 samples as the temperature increases while a broad maximum is observed for the S1.3 sample. This suggests that the reversal mode of the magnetization depends slightly on the temperature in contrast to the coercive field and the remanent magnetization. 3.4. Magnetization in intermediate magnetic fields

The magnetization shows a reversible behavior in magnetic fields higher than 2 kOe at any temperature. The magnetization has been recorded between 2 and 20 kOe for all the samples at 300 K and for S1.3, S100 and L28 samples at different temperatures. In any case the data are well fitted by: M / M ~ = 1 - B/g'-H.

(2)

179

1.0

O.9

0.8

0,7 0.005

0.015

0.025

H-112 1m-1/21

Fig. 8. Plots of the ratio of the magnetization to the saturation magnetization versus to the reciprocal of the square root of the magnetic field at room temperature for the S1.3 e, $9 II, $30 E3, L28 x and S100 o samples.

Plots of M / M s v e r s u s 9 -1/2 are given in fig. 8 and the parameter B at 300 K is given in fig. 9. It increases as the packing fraction increases, the interaction between the aggregates makes the saturation more difficult. Moreover B increases with the size of the aggregates since the value of the large aggregate sample is larger than the expected value for a small aggregate sample with the same packing fraction. B is nearly temperature independent for the $1.3, $100 and L28 samples as reported in fig. 10. The temperature

13

g~

0

I

I

I

I

20

40

60

80

100

C% Fig. 9. Coefficient B of magnetization law in intermediate magnetic fields versus the concentration in mass in ~/-Fe20 3. T h e light dots correspond to the S samples while the cross corresponds to the L28 sample.

S. Koutani et al. / Aggregates of small y-Fe 20~ particles

18(1

1,00

15

B

0

0

~ IK

x

,0

o

0,99

~

10 C

.2 •-~

E

_f I

i

100

[

i

200

0,98

300

T (K) Fig. 1(1. T e m p e r a t u r e dependence of the coefficient B of the magnetization law in intermediate magnetic fields for the S1.3 e, L28 × and S100 © samples. 0198

I

i

I

,

I

i

I

,

I

,

I

-11 -9 - 7 -5 -3 -1

dependence of the saturation magnetization reported in fig. 11 follows the T 3/2 Bloch law for the samples S1.3, S100 and L28 below 200 K. At room t e m p e r a t u r e Ms(300 K)/M~(0 K) = 0.88 and the room t e m p e r a t u r e magnetization is within a few percent the usually reported value 350 e m u / c m 3 [13]. The exchange constant calculated 1,1

,

I

1

,

I

3

,

I

5

,

I

7

,

I

9

,

1

V e l o c i t y (turn/s)

Fig. 12. M6ssbauer spectra at 295 K for the S'50 (top) and S'90 (Bottom) samples. The lines correspond to the best fits to the data.

from the Bloch law is A = 10 -6 e r g / c m , a widely accepted value for ~/-Fe20 3 [2].

4. M6ssbauer spectroscopy

oo 0,9

0,8

0,7

,

0

I

1000

i

I

2000

,

I

3000

,

I

I

4000

I

5000

T3/2 (K3/2) Fig. 11. T e m p e r a t u r e dependence of the saturation magnetization for the S1.3 e, L28 × and $100 © samples. The straight line represents the best fit with the Bloch law.

57Fe M6ssbauer spectra recorded at room t e m p e r a t u r e on two samples are reported in fig. 12. Powder of small aggregates has been diluted with boron nitride and the samples S'50 and S'90 containing 50 and 90% of ~ - F % O 3 in mass respectively have been investigated. Although the S'90 spectrum is poorly resolved it shows the same features that the S'50 spectrum. None of the spectra shows a quadrupolar doublet and then relaxation p h e n o m e n a have relaxation times longer than 1 0 - 8 - 1 0 -9 s. Both spectra exhibit asymmetric line broadening and are fitted with an independent distribution of magnetic hyperfine fields model with Lorentzian-shaped sextets whose intensities are constrained to be in the ratio 3, 2, 1, 1, 2, 3 [17]. Only one distribution has been considered for the tetrahedral and octahe-

S. Koutani et al. /Aggregates of small y-Fe203 particles

0,010

181

minor H F distribution represents 9% of the full distribution and this is not inconsistent with reduced H F at the surface of small crystallites. One expects about 10% of the spins to be at the surface of crystallites with a diameter of 10 nm.

0,008 0,006 0,004

5. Discussion

0,002

0,008 0,006 0,004 0,002 0,000

0

100

200

300

400

500

H (kOe)

Fig. 13. Probability distribution profiles of the hyperfine field for the S'50 (top) and S'90 (bottom) samples.

dral sites of the lattice. The best fit to the experimental data is achieved with the same hyperfine parameters for both samples: 6 = 0.29 m m / s , 2E =-0.005 m m / s and F = 0.30 m m / s . The linewidths at half maximum F is slightly larger than expected (0.25 m m / s ) but this may arise from fluctuations of the quadrupolar interaction resulting from the disorder of the vacancies distribution on the octahedral sites. The derivated probability distribution profiles P ( H ) of the hyperfine fields are reported in fig. 13. All our data are similar to those recently obtained by De Bakker et al. [6] on their L121-303 -y-Fe20 3 sample at 160 K. The P ( H ) curves show two distributions, the most important one is peaked at H m = 473 kOe while the other one is centered around 200 kOe, the m e a n hyperfine field is H = 413 kOe. The ratio H(300 K ) / H ( 0 K) is 0.75 while Ms(300 K)/Ms(0 K) is 0.88. It must however be noticed that the magnetization is obtained in the limit of an infinite magnetic field while Mbssbauer spectra are recorded without any magnetic field. The

Our data are very similar to those previously obtained by Coey and Khalafalla [5]. The difference between the room temperature Mbssbauer spectra may result from slightly different crystalIRes and agglomerates sizes, but low temperature coercive fields and remanent magnetization are similar as well as their temperature dependence. In addition we have shown that the low temperature coercive field and the remanent magnetization increases as the packing fraction decreases while the saturation becomes easier. The average blocking temperature increases with the packing fraction. All these observations show the effect of the interactions between the aggregates. As many authors, Coey and Khalafalla have interpreted their data in terms of isolated single domain particles with and effective uniaxial anisotropy. Using their Kef f value and H c = 0.64Keff/M ~

(3)

for randomly orientated particles [13], one finds H c ---4000 Oe to be compared to 300 Oe measured at 4 K. Values of M r / M s as low as 0.2 are also inconsistent which such a model. An alternative way of interpreting their room temperature Mbssbauer spectra is to consider ferromagnetic correlated domain relaxing over the average barrier, A = Veffmsmc,

(4)

where H c is the 0 K coercive field and Veff the volume of the domains. Using the data of Coey and Khalafalla one finds V~rf = 1.5 × 10 -16 cm 3 i.e. nearly 10 3 times larger than the actual volume of the crystallites. As unambiguously shown by several experimental works [10,18,19] the inter-particles interaction is a strongly relevant parameter which must be then taken into account.

182

S. Koutani et al. /Aggregates of small y-Fe eO 3 particles

It is interesting to notice that the coercive field of acicular -,/-Fe20 3 particles used in magnetic recording media is rather well described by the so called "chain of spheres model" [20]. This model considers a linear chain of isotropic and single domain spherical particles interacting via dipolar interactions. The ground state corresponds to the alignment of the magnetic moments of the spheres along the chain axis. A low energy barrier for the reversal of the magnetization of the chain corresponds to a "fanning mode" which is an antiferromagnetic configuration in a direction perpendicular to chain axis. The barrier for a chain of n spheres of magnetic moments /, and diameter d is given by /.~2 n - 1

A,,

=

E

i

1

21]

E

~ - i=1 j=l

(5)

or =

d3Sn,

(6)

where for n > 10, S, = 1.5n - 2.37. The critical diameter for single domain behavior is about 50 nm [7] and the barrier for a chain of 10 spheres with the critical diameter is 5 × 10 -l~ erg. If the relaxation time follows the Arrhenius law r = r0e a / k r ,

(7)

with r 0 = 1 0 - m - 1 0 -12 s, the relaxation time of the chain at room temperature is larger than 105°° s. Such a chain behaves at room temperature as blocked single domain particles. The relaxation time drops t o 1 0 - 6 - 1 0 -s s for d = 10 nm in agreement with the data of ref. [7]. The dipolar interactions give a satisfactory description of the behavior of the chain of spheres, but for randomly oriented chains one expects M J M s = 0.5 in contrast with our data. One may notice that the dipolar interaction of a pair of spheres 1

r ~ r t3

D'~t~ = 7-5 ( 6,~ - 3-7T-- ) ,

(8)

where r is the vector between the centers of the spheres, vanishes when averaged over all orienta-

tions of r. Then the dipolar interactions are strongly frustrated in aggregates of arbitrary shape. The configuration of the magnetic moments of the crystallites must satisfy the fluxclosure condition and the aggregates have a multidomain character that may explain the low M r / M s ratio. The temperature dependence of H c and M J M s may be explained by relaxation phenomena with relaxation times shorter than 1 min while M6ssbauer experiments show that the relaxation times are longer than 1 0 - s - 1 0 -~ s. Such a relaxation time is much larger than that of an isolated crystallite with a barrier arising from the single ion anisotropy. The relaxation certainly concerns domains containing a large number of crystallites. We have shown that the magnetization becomes reversible in magnetic fields higher than 2 kOe and follows a 1 / ~ law for H ranging from 2 to 20 kOe. Such behavior is observed in random anisotropy ferromagnets and has been explained by Chudnovsky et al. [21]. The consideration of random anisotropy leads to an anisotropy of 106107 e r g / c m 3 and such figures are too large to be significant. We have however shown that the magnetization in the intermediate fields regime depends on the dipolar interactions between the aggregates and we consequently infer that the dipolar interactions are strongly relevant. If we consider a cylinder of radius r, assumed to be uniformly magnetized along its axis, the radial stray field at the edge of the cylinder given by [22]

fo s(( t )d t,

H = 2"rrM~

(9)

where J1 is the Bessel function, shows a logarithmic divergency. The magnetization is certainly not collinear to the axis near the edge of the cylinder. As the crystallites undoubtly have sharp edges and corners, strong spin canting at the surface is expected to arise as the result of the stray field singularities. This is consistent with micromagnetic calculations [2] and M6ssbauer spectroscopy experiments which show a strong canting at the surface of very small particles even in large magnetic fields [23-25].

S. Koutani et al. /Aggregates of small ~,-Fe203 particles

6. Conclusion

We have shown how the packing fraction and then the dipolar interactions between the aggregate modifies the magnetic behavior. We expect the intra-aggregate dipolar interactions to be strongly relevant. The size of the crystallites and the shape of the aggregates are then pertinent parameters. Aggregates of arbitrary shapes show a multidomain behavior owing to the frustration of the dipolar interactions. As the dipolar interactions between to nearest-neighbors crystallites increases as the crystallite volume, only small changes in the crystallite size may induce significant modifications in the blocking temperature. The relaxation phenomena are not related to single crystallite relaxation but rather to correlated domains containing many crystallites.

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183

[5] J.M.D. Coey and D. KhalafaUa, Phys. Stat. Sol. (a) 11 (1972) 229. [6] P.M.A. de Bakker, E. Degrave, R.E. Vandenberghe, L.H. Bowen, R.J. Pollard and R.M. Persoons, Phys. Chem. Minerals 18 (1991) 131. [7] E. Tronc and J.P. Jolivet, J. de Phys. 49 (1988) C8-1823. [8] E. Kneller, Proc. Intern. Conf. Magn. Nottingham (1964) 174. [9] H. Holmes, K. O'Grady, R.W. Chantrell and A. Bradbury, IEEE Trans. Magn. MAG-24 (1988) 1659. [10] G. Bottoni, J. Appl. Phys. 69 (1991) 4499. [11] S. M0rup, Hyper. Inter. 60 (1990) 959. [12] S.E. Khalafalla and G.W. Reimers, IEEE Trans. Magn. MAG-16 (1980) 178. [13] G. Bate, Magnetic oxydes, vol. II, ed. D.J. Graik (John Wiley, London, 1975) p. 689. [14] K. Haneda and A.H. Morrish, J. de Phys. 38 (1977) C1-321. [15] M. E1 Hilo, K. O'Grady, J. Popplewell, R.W. Chantrell and N. Ayoub, J. de Phys. 42 (1988) C8-1835. [16] E.D. Wolhfarth, J. Phys. 20 (1959) 295. [17] G. le Caer, J. Phys. E 12 (1979) 1083. [18] H.F. Huisman, IEEE Trans. Mag. MAG-18 (1982) 1095. [19] E. Tronc and D. Bonnin, J. Phys. Lett. 46 (1985) L437. [20] I.S. Jacobs and C.P. Bean, Phys. Rev. 100 (1955) 1060. [21] E.M. Chudnovsky and R.A. Serota, J. Phys. C 16 (1983) 4181. E.M. Chudnovsky, W.M. Saslow and R.A. Serota, Phys. Rev. B 33 (1986) 251. [22] D.J. Craik, J. Phys. D 7 (1974) 1566. [23] A.H. Morrish, K. Haneda and P.J. Schurer, J. de Phys. 37 (1976) C6-301. [24] A.H. Morrish and K. Haneda, J. Magn. Magn. Mater. 35 (1983) 105. [25] A. Ochi, K. Watanabe, M. Kiyana, T. Shinjo, Y. Bando and T. Takada, J. Phys. Soc. Jpn. 50 (1981).