The effect of multiple anisotropies in fine particles

Journal of Magnetism and Magnetic Materials 45 (1984) 91-99 North-Holland. Amsterdam

91

THE EFFECT OF MULTIPLE ANISOTROPIES

IN F I N E P A R T I C L E S

G. B O T T O N I , D. C A N D O L F O , A. C E C C H E T T I , F. M A S O L I 1st. Fisica, Universit~ di Ferrara, Via Paradiso 12, 44100 Ferrara, ltalv

and A.R. C O R R A D I Hercules Chem. Corp. (USA), 20 Red Lion Street, London WCIR 4PB, UK

To investigate the effects of multiple anisotropies, morphology and size on magnetic properties of fine particles, cobalt-modified materials with different shapes were tested at temperatures from liquid nitrogen to 400 K. Some interesting and original conclusions were drawn: (a) When multiple easy axes are available, thermal fluctuations can induce the magnetization to switch from one axis to the other; the overall effect will be an increase of the fraction of particles with superparamagnetic behaviour. (b) The phenomenon will be greater for materials where the conflicting anisotropy constants are similar (isotropic particles); thus, for a given composition, the lower the shape anisotropy and the larger the superparamagnetic fraction. (c) Porosity and particle defects will contribute to increase the super-paramagnetic fraction. (d) In practical media (tapes) the effect of the superparamagnetic fraction is much lower than expected: a "constricted magnetization" phenomenon could account for such behaviour. (e) The lack of interactions predicted for truly isotropic media is experimentally verified only at extremely low temperatures. (f) Partial orientation in the plane of the strongest anisotropy axis must be taken into account for explaining the behaviour of SFD; under such assumption, "quasi-spherical" particles will behave quite differently from elongated ones. (g) Rotational hysteresis, CF and (1 - S*) for isotropic particles seems to indicate that the rotational mechanism might not be accounted for by known models.

1. Introduction In 1 9 5 8 / 5 9 W o h l f a r t h and T o n g e [1,2] predicted the theoretical feasibility of isotropic particulate m e d i a with high squareness ( j r = M r / M . ~ ) . In o r d e r to achieve values of jr >/0.75 in r a n d o m assemblies, the particles should be " q u a s i - s p h e r i cal" with at least 6 equivalent m a g n e t o c r y s t a l l i n e easy directions [1] or should exploit the conflict between shape a n d m a g n e t o c r y s t a l l i n e a n i s t r o p y [2,3]. Particles of this k i n d were used for a new high density r e c o r d i n g system in 1 9 7 8 / 7 9 [4]: the m a t e r i a l was a ferritic solid s o l u t i o n [(uF e 2 0 3 ) l _ x _ , , ( F e 3 0 4 ) x ( C o F e 2 0 4 ) , . ] with particle size of 0.4 p~m a n d aspect ratio a p p r o x i m a t e l y 2-2.5. T h e d a t a of ref. [2] show that p r o v i d e d the shape a n i s o t r o p y axes forms a large angle 0 with the m a g n e t o c r y s t a l l i n e easy axes a n d the ratio between the two c o n s t a n t s (/~ = s / K ) is a p p r o x i -

m a t e l y 0.15-0.25, a high value of Jr should be achieved for r a n d o m assemblies. U n d e r these conditions, isotropic m e d i a could be p r o d u c e d having a variety of shapes a n d c o m p o s i t i o n . The only m a t e r i a l which satisfies the requirements is a c o b a l t - f e r r i t e phase. C o b a l t - d o p e d a n d cobalts u r f a c e - m o d i f i e d m a t e r i a l s are well k n o w n as magnetic recording m e d i a b u t up to 1978 [4] all develo p m e n t h a d the c o m m o n goal of increasing the coercivity a n d yet keeping the uniaxial c h a r a c t e r of elongated particles. W h e n m o d i f y i n g an originally p u r e uniaxial u-Fe203 particle with cobalt, a small increase of jr is f o u n d [5]; yet, because in such c o n d i t i o n s / ~ >> 0.25, the values of Jr at r o o m t e m p e r a t u r e did not exceed 0,7. It was f o u n d thatj~ is close to the value for uniaxial assemblies (Jr = 0.5) for C o - a d s o r b e d m a t e r i a l s a n d becomes increasingly higher the deeper the p e n e t r a t i o n of C o 2+ in the core of the particles. K h a l a f a l l a a n d M o r r i s h [6] investigated

0 3 0 4 - 8 8 5 3 / 8 4 / $ 0 3 . 0 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)

G. Bottoni et al. / Multiple anisotropies in fine partwles

92

the behaviour of cubic cobalt-doped iron oxide and found that for a cobalt content of 4.0 4.5% j, approaches unity at liquid helium temperature and becomes lower than 0.5 at room temperature. K6ster extended the investigation to highly elongated particles [7] and found the same behaviour as a function of temperature and cobalt concentration; in this work the particles size and shape was kept constant by preparing the sample from a single batch of ~,-Fe203 starter. Both refs. [6,7] report that the extent of the temperature dependence of coercivity is proportional to the amount of cobalt in the material. More recently, the temperature dependance of jr and H~ was investigated for both "quasi-spherical" and elongated cobalt modified materials [8]: it was found that the shape anisotropy plays a relevant role on such properties since the smaller the axial ratio (for constant cobalt content) the larger the temperature dependence of Jr and H~. In any case, a satisfactory explanation of the temperature dependence of Jr has not been given. Lemke predicts that no interactions should be present when the particles are fully isotropic [9]; Wohlfarth pointed out that for such a phenomenon to occur, the following relationship should be verified [10]:

M~)(H) = M~(~o) - 2 M ~ ( H ) ,

(1)

where M D ( H ) is the remanent magnetization attained after previous acquisition of a remanence in a saturation field H0, say, followed by the application of a direct reverse field H; Mr(oo) is the

5 CURLING

rr

# ~

-

l r d}

CO,EREN,

-

I

2

I

4

l

i

6

i i i i

8 10

,

....

20

S=dldo

Fig. 1. Rotational hysteresis integral ( R ) as a function of the reduced particle diameter S for the 3 most common magnetization reversal models (from Luborsky [11]).

remanent magnetization attained after application of an infinite field and Mr(H ) is the remanent magnetization after application of a field H. Finally, it is known that the value of the rotational hysteresis integral ( R ) for uniaxial particles may vary as reported in fig. 1 as a function of the reduced diameter d / d o [11]. R was reported to increase slightly for uniaxial particles when Co 2t is introduced because of the conflict of anisotropies [5] and decrease when the particles are extremely uniform prolate ellipsoids [12].

2. Materials

The materials under investigation were two assemblies of particles which give very high in-plane squareness on non-oriented tapes at room temperature (Jr >/0.75). The assemblies are fully isotropic in plane as jr is constant for all angles between the machine direction and the applied field. As the demagnetizing factor along the direction perpendicular to the plane is not known, we cannot ascertain whether the assemblies are also isotropic in space; yet, Jr (non-corrected for demagnetizing effects) in the perpendicular direction is at least 2 to 3 times greater than for oriented uniaxial particles; this is a preliminary requirement for the use of these sort of materials. The first sample (INP) is composed of particles which are "quasi-spherical" (aspect ratio approximately 1.2-1.8) and the size is 0.13 0.23 ~tm: no evident porosity is observed. Due to the very small size, high magnetic moment and coercivity, the particles appear as agglomerates (fig. 2B). The second sample (IG) is a powder from the trade showing a much greater aspect ratio (2.5-3.3) and a fairly large amount of porosity; the length is approximately 0.2-0.25 p,m and diameter approximately 0.04 ism (fig. 2A). For sake of comparison, the investigation includes a highly elongated cobalt-doped oxide (BDG) with aspect ratio 6-7, and dimensions (0.4-0.5)×(0.06-0.08) p~m2, a surface modified uniaxial oxide (NPC) and a pure ~,-Fe20 ) (NPX). Both NPC and NPX are fully uniaxial and the dimensions are (0.4) × (0.06) ~m 2.

93

G. Bottoni et aL / Multiple anisotropies in fine particles

0.9 .

~

(15 0.4

.

0.3

~

NPX

0.2 0.1

0

s.

~do

200

300

t,

,/00 T[K]

Fig. 3. Jr vs. T(K) for samples with p = 0.2-0.4.

Fig. 2. TEM micrographs of the IG (A) and 1NP (B) particles.

3. Experimental results and discussion

3.1. Remanence In fig. 3 the values of jr vs. T(K) are reported for powders with p ~ 0.2-0.4; the behaviour is the same as in refs. [6,7] (for IG and BDG) and [8]. NPX shows very little dependence on T; a similar behaviour was also found for hard barium ferrites [13]. The theoretical value of 0.5 for NPX [2] is not reached in this case, because of imperfections in the crystallites and contrasting interaction effects [14]. The data in table 1 show an increase ofj~ with dilution; this was also found in earlier works [5,15]

in apparent disagreement with other authors [16,17]. To make sure that the introduction of large amounts of cobalt does not lower the Curie temperature to the vicinity of the explored region of T, we have investigated the behaviour of M~ vs. T and r e p o r t e d the n o r m a l i z e d values of M ~ ( T ) / M J T = 77 K) in fig. 4: the results clearly rule out this possibility. In some cases, actually, the decrease of M~ for pure materials is greater than that of Co-modified ones. One possibility to explain the large lowering of jr with increasing T is if we assume that an increasingly large amount of particle become superparamagnetic as the temperature increases. If we assume that doping with cobalt introduces more easy axes at an angle with the shape anisotropy axis, then we can explain both the high values of jr at low T and the lowering of this parameter with increasing temperature. Large values of jr at low T are accounted for by refs. [1,2] and confirm the assumptions of ref. [3]. Actually, the value ofj~ for INP at 77 K is 0.86: exactly as predicted theoretically by Wohlfarth for 8 equivalent easy axes [1]. In the same references, a value of 0.76 is predicted for a planar distribu-

94

G. Bottoni et aL / Multiple anisotropies in fine particles

Table 1 Relevant magnetostatic parameters for materials IG compared with INP p (appar.)

T (°C)

H,. (Oe)

j

CF (%)

l-S*

R

(W,)m (erg g)

IG tape 1.2 × 10- 3 28 x 10- 3 28 × 10 3

20 20 20 - 190

650 685 613 5300

0.76 0.72 0.53 0.82

6.9 13.4 27.4 2.0

0.35 0.59 0.62 0.35

2.42 2.47 2.41

15 × 10 -s 16 × 105 16 x 105

INP tape lxl0 3 40 × 10 -3 40 x 10 .3

20 20 20 - 190

660 770 720 4400

0.82 0.77 0.58 0.87

10.0 20.0 7.0

0.55 0.42 0.67 0.69

2.64 2.56

17×105 16 x 105

in ref. [1]. If we a s s u m e t h a t i n c r e a s i n g n u m b e r s of s u p e r p a r a m a g n e t i c p a r t i c l e s are f o r m e d as t e m p e r a t u r e increases, we c o u l d give a r o u g h e s t i m a t i o n o f the n u m b e r of such p a r t i c l e s by a s s u m i n g t h a t - at e a c h v a l u e of T - the a m o u n t is p r o p o r t i o n a l to the r a t i o j r ( T ) / j r ( T = 77 K). Such ratio l e a d s to a n e s t i m a t e d 3 0 - 3 5 % of s u p e r p a r a m a g n e t i c p a r t i c l e s at r o o m t e m p e r a t u r e for I N P , IG and BDG materials. I n fig. 5 the e x p e r i m e n t a l hysteresis c u r v e for I G is r e p o r t e d (solid line) t o g e t h e r w i t h that of the

t i o n o f the s a m e i s o t r o p i c particles; we m a t c h this v a l u e for I G t a p e a n d for d i l u t e d s a m p l e s (see t a b l e 1) at l o w t e m p e r a t u r e . T h e i n c r e a s e o f the n u m b e r of easy axes m a k e s it easy for the m a g n e t i z a t i o n to switch f r o m o n e to the o t h e r axis as a result o f t h e r m a l f l u c t u a t i o n s , t h u s l o w e r i n g M r. T h e e x t r e m e c o n s e q u e n c e o f this p h e n o m e n o n is f o u n d for t w o easy axes f o r m i n g a 0 / 2 a n g l e a n d h a v i n g e q u a l v a l u e s for the a n i s o t r o p y c o n s t a n t : s u c h a p a r t i c l e w o u l d be s u p e r p a r a m a g n e t i c . T h i s p o s s i b i l i t y was also m e n t i o n e d

I

i

1.0

I

..

~

I

I

I

I

1

.---~.~

•

"

0.9-

"~

,,

" *~"~

"

• BDG

0.8-

~> INP -

-

......

~

~,,,~ "~.

NPC

NPX T(K)

0.7

I 100

I 150

I 200

I 250

I 300

I 350

I 400

I 450

Fig. 4. Ratio of saturation magnetization at generic temperature T and at T = 77 K. M~ is the extrapolated value at infinite field

G. Bottoni et aL / Multiple anisotropies in fine particles

95

,0 (emu/g) f+s

60. f

/

i

L j/if

/ "~ /

......... 4

6

HIKOe)

Fig. 5. Experimental hysteresis loop at 20 o C (f+s) compared with the loop which should be traced (f) if no superparamagnetic particles would be present; s = cycle for the superparamagnetic fraction.

superparamagnetic fraction (curve s) and the curve resulting from the subtraction of s from the experimental hysteresis loop (curve f). This figure was built from the experimental curve by subtracting the calculated amount of superparamagnetic particles (30%). Two other phenomena remain to be explained: (a) why do we reach such large jr values on tape at room temperature in spite of the superparamagnetic fraction, particularly when compared with the data on powders (fig. 3)? (b) why do IG and INP show a similar content of superpara (see fig. 3) in spite of the fact that INP has a much lower shape anisotropy (see fig. 2)? The first phenomenon could be explained in terms of "constricted magnetization" [12]: in a tape sample (or in high loaded assemblies), the particles which are superparamagnetic in dilutedrandom assemblies find themselves trapped among highly ferromagnetic particles; the effect of interactions is such t h a t - in order to minimize the magnetostatic e n e r g y - the scattered spins are forced to align themselves. This phenomenon occurs also in polycrystalline specimens where, by virtue of the high interactions, the superparamagnetic behaviour is largely decreased [18]. Furthermore, in a tape specimen, the distribution is

not random in space but only in plane as it will be shown later. The difference between "quasi-spherical" INP and "stubby" IG can be accounted for by the scattering influence that defects and porosity plays on IG materials: pores are sources of self-demagnetizing fields which tend to produce spontaneous shift of magnetization from one axis to another, thus increasing the probability of transaction from ferro to superparamagnetic compared with INP. The nature of INP might also have an effect on the molecular field energy of each spinel sublattice, thus producing a slight difference in the Curie-Weiss/N6el curves of M S vs. T when compared with those for IG or BDG (see fig. 4).

3.2. Coercivity Coercivity at room temperature is not drastically influenced by the presence of superparamagnetic particles: from fig. 6 it can be seen that an assembly with no superpara (f) would show approximately 100-150 Oe higher H c than the actual experimental assembly ( f + s). The influence of T on Hc (fig. 6) is therefore mainly accounted for by the temperature dependence of the magnetocrystalline anisotropy and by the ratio

96

G. Bottoni et al. / Multiple anisotropies in fine particles

aspect ratio from 1.2 1.6 to 2.5 makes these materials of great interest in industrial application. The IG tape sample was tested for H~ vs. 0 (angle between machine direction and applied field) in the planes xy, x z and y z . The results are reported in fig. 7. In the xy plane H c is practically constant, thus confirming the isotropic behaviour in-plane. In the x z and y z planes H~ goes through a maxim u m at approximately 50 60 ° . This maximum can be accounted for by the fact that as # increases, all particles will be brought at the same time to a critical angle 0~ between the particles' long axis (or the strongest of the axes) and the field for which coherent rotation may occur. The same plot of fig. 7 in the x z and y z planes if found for uniaxial particles. These measurements are not influenced by the geometrical demagnetizing factor as for H = H~ the magnetization is zero ( H u =

, Hc.IO3 (Oe)

IG E

4-

3-

2-

1-

NDM). NPX

1tO0

200

i 300

~0

T(K)

These data clearly show that, when the shape anisotropy s is large, the long axes will tend to be spontaneously oriented in plane.

Fig. 6. Coercivity vs. T(K).

3. 3. C F a n d l - S *

When a large shape anisotropy is acting (and s >> K ) the magnetization will tend to remain aligned with s and //~ be less influenced by T because s depends less sensitively on T (as can also be seen by the behaviour of H~ vs. T for N P X whose coercivity is mostly due to shape anisotropy). If we assume that for spherical particles He = H~ (magnetocrystalline anisotropy field), from the data of table 1 we can calculate that K~ for I N P varies between 8 and 1.3 × 105 e r g / c m 3 for T = 77 and 293 K, respectively. If we assume the thermal stability of these particles to be directly proportional to the variation of //~ between - 2 0 and + 60 o C, we could predict a loss of output between these temperatures of - 4 . 6 , - 5.1 and - 4 . 0 dB for IG, I N P and BDG, respectively. This conclusion becomes extremely important in the light of the application as high density recording media: the possibility of large improvements of stability offered by the particles with very low (if any) porosity when increasing the

H.)/H~]

~t = s / K .

C F and 1 - S* defined, respectively, as [(H~ x 100 [15], where H r = remanent coercivity, and as the slope of the hysteresis curve for

/

\ \

~

600

~" ~ ' ~

XY

~

XZ

lz tape

t

0°

I

_ _ ~

30°

~

J

I

6 0°

~ ,-ot,~+~

I

l

] - -

90°

Fig. 7. Coercivity vs. angle between the machine direction and the applied field for the tape sample IG at 2 0 o ( ` measured along the three planes xv+ xz and yz.

G. Bononi et al. / Multiple anisotropies in fine particles

H = / / ~ [19] were evaluated for samples with varying packing fraction p at room temperature and - 1 9 0 ° C . C F is found to increase with p as reported in ref. [17] and - for the same sample to decrease with decreasing T (table 1). This p h e n o m e n o n was previously observed by Khalafalla and Morrish [6] who also found that C F decreases with increasing cobalt content for cubic iron oxides. 1 - S* also increases with p but the effect of T is rather different than on CF: we observe in fact that while 1 - S* varies from 0.62 to 0.35 between 20 and - 190°C for IG, it remains practically constant for INP. The two parameters must therefore be influenced to a different degree by "intrinsic" and "extrinsic" effects (see also refs. [20,21]). We believe that the relationship between C F and 1 - S* built by Wohlfarth [21] only holds for materials with a similar magnetization reversal mechanism; Wohlfarth has shown that a different material such a s C r O 2 falls out of the linear relationship between C F and 1 - S*. Here we have another important exception: the data on the I N P sample (table 1) at - 1 9 0 ° C do not lie on the straight line of fig. 2 in ref. [20]. To account for this behaviour we must consider that the IG sample acquires a high orientation in plane and also partial orientation with the machine direction. The lowering of T decreases the extrinsic effects and what is left at - 1 9 0 ° C is the " t r u e " intrinsic S F D of the particles which, because of the higher degree of isotropy, is larger for I N P ; 1 - S* does therefore account for these "intrinsic" effects to a greater extent than CF. As a conclusion, we agree on a "technical" definition of S F D given by 1 - S * as in ref. [21] and also agree that 1 - S* gives a better representation of the "intrinsic" S F D than CF. As a help to standardize data from various sources we go along with K6ster [21] in recommending the use of 1 - S* as an indication for SFD. Yet, we also warn that only by assessing both C F and 1 - S* a clear picture of all magnetostatic behaviour can be drawn.

3. 4. Interactions As pointed out in the introduction, if no interactions are effective, eq. (1) should be verified. We

97

have evaluated h = H/H~ and m = M/Mr(oo ) for I G and I N P and reported the values of mD(h ) vs. h and 1 - 2 m r ( h ) vs. h. If eq. (1) is satisfied, the two curves must coincide. Figs. 8 and 9 clearly show that eq. (1) only holds for T = - 190°C. The conclusion is that for fully isotropic assemblies, interactions are practically ineffective at low temperatures. The reasons are twofold: a) Superparamagnetism is eliminated; at room temperature the assembly was a cluster of single domain particles in a superparamagnetic matrix which, in turn, is a favourable situation for interaction fields to be effective. b) //~(T = 77 K) is approximately 10 times greater than He(T= 293 K); thus, although internal interaction fields arising from particles magnetization ( H• = N~ M ) might still be active within the agglomerates, such fields are not high enough, compared with He, to produce any significant modification of the magnetization (as for very hard magnetic materials). The overall result is as if I F F = 0, i.e. H r = H" where I F F = [ ( H ' r - H r ) / H c ] and H~ is the " h a l f height remanent coercivity" [15]. To our knowledge, this is the first experimental verification of eq. (1).

3.5. Rotational hysteresis As the data are reported for room temperature only, the mass of particles contributing to the hysteresis losses had to be corrected by the super-

1.0

,

,

i

i

l

~

,

i

I ,

i

~

~ I-

'~ m,~ ,,

~ ~.~ "~ ~

20°C

,

-190°C

sample I

0.6

i

i

,

Mr(°°)

0,5-

-1.0

i

2Mr(H/H~)

N ~

I 0.8

-

~ ~%

~

~..~

IG i

k 10

Mo(H/Hc) Mr(°°)

m,i - ~ } ,

"~.. ~.

\ I

L 12

I

h. I 14

J

I 16

L

I 18

. I

" l 2.0

Fig. 8. R e d u c e d m a g n e t i z a t i o n m vs. r e d u c e d field h: a p p l i c a tion of eq. (1) to the s a m p l e I G at 20 a n d - 1 9 0 ° C .

G. Bottoni et a L / Multiple anisotropies in fine particles

98

1.(]

,

0.5

,

,

,

",~ " - .

•

,

i

i

i

i

i

i

20"C

' "~,,,,ii~.~.a;

"~"~'r: "I

190~C

"~'m~

~,~

-0.5

~'-..

sample INP -1 0

I 0.6

~

f 0.8

i

I 10

"-m

h I

+ 12

i

I 1.4

'

I 16

~

I 1.8

i 20

Fig. 9. As fig. 8 for sample 1NP. The significance of the data are the same as reported in fig. 8.

paramagnetic fraction. Both with and without such correction the rotational hysteresis integral ( R ) appears very large and reaches 2.4-2.6 when corrected. By assuming values of the exchange length 2At/2/Ms --- 150 A from Eagle and Mallinson [22], and Luborsky [11] and particles diameters from fig. 2, we can calculate the reduced diameter S to be approximately 3.3 for I N P and2.0 for IG. Even if these data assume an incorrect value for the exchange length (we have Co-p-Fe203 and not plain u-Fe203), we still would achieve S values greater than 2 even for exchange length varying from 120 (iron) to 200 A. Fig. 1 [11] shows that a curling mechanism could account for R = 2.5 when S = 2. Yet, the shape of I N P and I G particles would certainly not account for curling, nor would the values of H c vs. # in the XY plane (fig. 7). On the other hand, the R values are much greater than those theoretically predicted by fanning or coherent rotation. Could some sort of new "incoherent isotropic rotation" be foreseen for these particles?

tion. The effect of the superparamagnetic fraction is minimized on highly loaded tapes due to the beneficial effect of the constricted magnetization. This detrimental effect can be partially recovered by producing materials free from defects; the comparison between "fairly elongated" IG and "quasi-spherical" I N P seems to confirm this assumption. The coercivity is only marginally effected by the superparamagnetic fraction: this parameter depends instead on the magnetocrystalline anisotropy; its temperature dependence determines the behaviour of H c vs. T - s u c h behaviour can be ruled by the ratio bt = s/K which, in turn, can be easily modified, within certain limits, by modifications of the shape and composition of the particles. Stubby particles of the INP and IG type form random assemblies in-plane where the strongest of the axes lies. The increase of jr in the perpendicular direction is brought about by the other conflicting anisotropy axes. Data on CF and 1 - S* as a function of T show a peculiar behaviour for quasi-spherical I N P which seems to be fairly isotropic even in space and show a random distribution of axes responsible for large values of 1 - S * for any temperature. It was experimentally verified that isotropic assemblies show no effective interaction fields at low ( - 1 9 0 ° C ) temperatures. The values of the rotational hysteresis integral raises some question on the rotational mechanism of these particles.

Acknowledgement We wish to thank Dr. E. KOster of BASF (Ludwigshafen, F R G ) for his valuable suggestions and discussion even over those arguments in this text where our points of view might not be in full agreement.

4. Conclusions Data on Jr VS. T shows that by introducing new easy axes in particles originally uniaxial, a large fraction of particles which are superparamagnetic at room temperature is induced. The strong shape anisotropy of B D G and, particularly, NPC, reduces the extent of the superparamagnetic frac-

References [1] [2] [3] [4] [5]

E.P. Wohlfarth and D.G. Tonge, Phil. Mag. 2 (1957) 1333. E.P. Wohlfarth and D.G. Tonge, Phil. Mag. 3 (1958) 536. A.R. Corradi, MMISi Intern. Newsletter V-5 (1982) 86. J.U. Lemke, IEEE Trans. Magn. MAG-15 (1979) 1561. A.R. Corradi, P.G. Visigalli, G. Bottoni, D. Candolfo, A.

G. Bottoni et al. / Multiple anisotropies in fine particles

[6] [7] [8]

[9] [10] [11] [12]

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