IEEE TRANSACTIONS ON MAGNETICS, VOL. 26, NO. 1 , JANUARY 1990 219
MAGNETIC CORRELATIONS IN ALUMITE STUDIED BY " R O N DEPOLARISATION
W.H. Kraan and M.Th. Rekveldt,
Interfacultair Reactor Instituut, Delft University of Technology Mekelweg 15. 2629 JB Delft, The Netherlands
Abstract
-
A polarised neutron beam(A=0.36
nm) is transmitted both perpendicularly and at skew angles through Alumite films of various geometries. Three- dimensional depolarisation analysis is performed.A model containing the geometry of the needles in the alumite -nd a parameter K for the excess correla- tion between their magnetic moments over the reduced magnetisation is applied to describe the data. It appears that K becomes more negative as the magnetic interaction between the needles increases.
Introduction
The last few years many perpendicular recording experiments are presented in literature, most of which are carried out on CoCr. Alumite was proposed as a possible medium for perpendicular recording [1,2]. At present alumite is mainly used as a model material for verifying magnetic measurements and studying hys- teresis properties of "films" with perpendicular anisotropy.
Such films effectively consist of a 2-dimensional hexagonal lattice of ferromagnetic iron needles of a few pm length and 0.01-0.1 pm in diameter with their axes perpendicular to the film plane. This geometry makes alumite film an almost ideal two-dimensional system to study magnetic correlations between fer- romagnetic particles. Such studies may contribute to understanding the recording properties of such media. The neutron depolarisation technique used in this and our earlier papers has proved to be a very valuable technique for such studies
[3,4].
In analogy with the correlation theory for domains in a continuous medium, advanced earlier by Rekveldt
[5],
we introduced[3]
the parameter K:K = <ni.nitl>-m2
which describes the excess correlation between the magnetisation directions n. and ni+l in neighbouring needles over the square of the reduced magnetisation
m.
Our subsequent paper[4]
dealt with one alumite (YS-623) in the remanent states after in-plane and after perpendicular saturation.In the present paper a number of alumites of various filling fractions and needle diameters was studied by transmission experiments with polarised neutrons, followed by 3-dimensional polarisation analysis. The magnetic correlations between neighbouring needles will be determined as a function of the interaction strength of a specific needle with the magnetic field due to its neighbours.
Samples
We deal here with the so called "rigid alumites" prepared at Yamaha R&D Laboratory on 1.9 mm thick A1 substrates. Details on their preparation are found elsewhere [2]. The relevant properties are given in Table I.
Table
I:
properties of alumites[6]
Sample thick- pore cell filling Hc
U*)
K*)
eq
.
No.
ness t diam 6 size c fr. fYS [pm] [nml [ nm] eq.(7) [ Oe] (12) -617 -618 -619 -620 -621 -622
-623
-624
-625 -6264.5
30
62 1.530
624.5
43
91 1.743
914.0
58
113 1.158
1134.3
43
62 1.043
62 4.743
113 1.643
113 0.21 0.21 0.20 0.20 0.24 0.240.43
0.43
0.13 0.13 1488 1269950
875
531494
956
838
1050 1094 17 -0.25.7
0.05
11 0.1 4.1 0.29.3
0.05
2.6 0.333
- 0 . j7.7
0.05.9
0.1 2.0 0.2 * ) This paperThe meaning of 6 is obvious: t is identified with the length of the needles. The pores are filled with Fe and appear to be arranged in a hexagonal pattern [2] of
a
cell size denoted c. The values for the coercive force H are from magnetisation measurements in perpendiculag fields by Tokushima e.a.[6]
and checked by Huysmans e.a.[7]. The saturation magnetisa- tion is in accordance (except for YS-623) with the "filling fraction" f calculated for an hexagonal pattern with cell and pore sizes listed in Table I. assuming that the pores are completely filled with Fe.Experimental
When a polarised neutron beam passes through an alumite film, the polarisation vector P performs a Larmor precession about the magnetic induction inside the ferromagnetic needles. The vector
P
can be adjusted in a polarisation turner along any one of the (x.y.2) axes of the laboratory system. By means of a second polarisation turner after transmission the component ofP
-
as it emerges out of the sample-
along any one of these axes can be analysed. Thus, a(3x3) depolarisation matrix D . . (i,j=x,y,z; Fig.1) can
be measured. 1 J
Fig.1 Schematic view of the angle dependent neutron Manuscript received September
5,
1989. depolarisation experiment.220
The a n g l e 0 between t h e normal t o t h e f i l m and t h e t r a n s m i s s i o n d i r e c t i o n i s an a d d i t i o n a l v a r i a b l e .
For a l l alunites i n Table I t h e complete d e p o l a r i s a - t i o n m a t r i x was measured i n t h e magnetic s t a t e s :
( i ) " a s received" ,
I n a d d i t i o n , f o r YS-619, -623 and -624 d a t a were taken i n t h e remanent s t a t e s :
(ii) a f t e r magnetisation t o 10 kOe i n - p l a n e / / z and (iii) idem p e r p e n d i c u l a r t o t h e plane.
To enhance t h e s i g n a l t o b e measured, d a t a were taken from s t a c k s of
4
s u b s t r a t e s , each c a r r y i n g an a l u m i t e f i l m on both f a c e s , i n s t e a d of a s i n g l e f i l m . A s a consequence, t h e outcome o f t h e s i m u l a t i o n s o u t l i n e d below must be r a i s e d t o t h e power8
b e f o r e comparing w i t h t h e experimental d a t a .I n states (ii) and (iii) t h e samples were s t a c k e d w i t h t h e i r remanence a l t e r n a t e l y p a r a l l e l w i t h + / - z and +/-x. r e s p e c t i v e l y t o c a n c e l s t r a y f i e l d s due t o t h e remanence o f t h e i n d i v i d u a l f i l m s . I f n o t , t h e v e c t o r P w i l l p r e c e s s i n t h i s f i e l d b e f o r e and a f t e r t r a n s m i s s i o n through t h e f i l m s . T h i s l e a d s t o a r o t a - t i o n of t h e (x.y.2) c o o r d i n a t e system, which becomes apparent as a non-zero v a l u e f o r t h e non-diagonal elements. From t h e outcome of t h e s e elements i t was checked t h a t t h e s e f i e l d s a c t u a l l y canceled.
Model d e s c r i p t i o n
The model t o i n t e r p r e t t h e d a t a c o n s i s t s of Fe c y l i n d e r s ( n e e d l e s ) w i t h l e n g t h t and diameter 6 w i t h t h e i r axes p e r p e n d i c u l a r t o t h e p l a n e o f t h e f i l m , arranged i n a hexagonal l a t t i c e with c e l l s i z e c . The e f f e c t o f t h e s t r a y f i e l d o u t s i d e t h e n e e d l e s i s ne- g l e c t e d as appears from
a
schematic f i e l d c a l c u l a t i o n . S i n c e t h e t r a n s m i s s i o n d i r e c t i o ni s
v a r i e d by r o t a t - i n g t h e f i l m about t h e z - a x i s , DZz f o r each 0 e q u a l s t h e average c o s i n e ( t a k e n o v e r a l l t r a j e c t o r i e s ) of t h e t o t a l p r e c e s s i o n a n g l e@(e):
D~~ = < c o s @ ( e ) > . (2)
Formulas f o r t h e o t h e r d i a g o n a l elements follow from DZz by geometry.
@(e)
is t h e sum o f t h e p r e c e s s i o n a n g l e s @i through t h e i n d i v i d u a l n e e d l e s along a t r a j e c t o r y :8
@,(e)
=*
5.72 xi o Mse(e)
A =*
Ye(e).
( 3 )
e(0) [m] is t h e l e n g t h of t h e t r a j e c t o r y through t h e n e e d l e , Ms[A/m] is t h e s a t u r a t i o n magnetisation of Fe and A[nm] i s t h e neutron wavelength.I n t h e absence of magnetic c o r r e l a t i o n s w e may write
<02(e)> = < N ( e ) >
<+:(e)>.
(4)
where < N ( B ) > is t h e average number of n e e d l e s a l o n g t h e t r a j e c t o r y . To account f o r c o r r e l a t i o n s between t h e m a g n e t i s a t i o n d i r e c t i o n s o f t h e n e e d l e s a l o n g t h e t r a j e c t o r y , w e m u l t i p l y
<@:>
i n e q . ( 4 ) by (l+K)/(l-K), w i t h K d e f i n e d by e q . ( l ) . I n g e n e r a l@.(e)
and hence@(e)
are s m a l l , so t h e small a n g l e approximation f o r t h e c o s i n e is v a l i d . Now, e q . ( 2 ) . t a k e s t h e form:D z z ( e ) = 1
-
< N ( B ) >(z]
.
(5)
The number < N ( B ) > e q u a l s t h e product of t h e a r e a of t h e p r o j e c t i o n of a needle on t h e p l a n e of t h e alumite f i l m ( t a k e n a l o n g t h e neutron t r a j e c t o r y ) and t h e 2- dimensional d e n s i t y l / A c of t h e needles:
< N ( 8 ) > = ( t 6 s i n 8 + A ) . ( l / A c ) . P
where A
=L2J3
i s t h e c e l l area and a r e a . From t h i s follows t h e f i l l i n g c 4 f = A / A P c '<@:(e)>
i n e q . ( 5 ) is t h e average c e s s i o n a n g l e i n one n e e d l e . We A=%'
i s t h e f r a c t i o n f : P 4 s q u a r e of t h e t a k eei
e q u a l(6)
pore( 7 )
pre- t o Y ( e q . ( 3 ) ) times t h e volume of a needle d i v i d e d by i t s p r o j e c t i o n upon t h e p l a n e p e r p e n d i c u l a r t o t h e t r a n s m i s s i o n d i r e c t i o n . Hence:To account f o r t h e non p e r f e c t alignment of t h e n e e d l e s , w e introduced i n
[3]
a normalised g a u s s i a n d i s t r i b u t i o n W(al,a2) of h a l f width A , aland a 2 ( i n s e r t o f F i g . 2 ) b e i n g t h e d e v i a t i o n s o f t h e o r i e n t a t i o n o f a n e e d l e from t h e normal i n two orthogonal d i r e c t i o n s .A n average of e q . ( 5 ) weighed by W(al.a2) was taken o v e r al and a2. For t h i s average t h e q u a n t i t y
<N(e)><@:(e)>
i n e q . ( 5 ) i s transformed i n t o an expres- s i o n i n c l u d i n g aland a2. The r e s u l t i s w r i t t e n :D z z ( e ) =
ss
dalda2 W(al,a2) D:z(e.al,a2).(9)
*
Here t h e q u a n t i t y DZz(e.al.a2) r e s u l t s a f t e r sub- s t i t u t i o n o f e q s . ( 6 ) and
(8)
i n t o( 5 ) :
[--I
(10) b2e
Dz:(B,al,a2) = 1-
Af
l+K 2 cos29 l + Q 1-K with (11)4 t
2 2 112.
Q = - t a n[(+al)
+a2] n 6 and f given by e q . ( 7 ) . T h i s averaging is performed n u m e r i c a l l y , u s i n g t h e g e o m e t r i c a l q u a n t i t i e s t , 6 , c and A , t o g e t h e r w i t h t h e magnetic c o r r e l a t i o n K as parameters. For t h e given v a l u e s o f t. 6 and c (see Table I ) t h e outcome h a r d l y depends on A f o rl e
1>1so.
So i n t h i se
r e g i o n t h e c o r r e l a t i o n K remains t h e only parameter t o be f i t t e d t o t h e experimental d a t a .Around
O=O
on t h e o t h e r hand, t h e outcome appears t o be extremely s e n s i t i v e t o t h e choice o f both K and d .R e s u l t s and I n t e r p r e t a t i o n comparison between states (ii) and (iii)
Fig.2 c o n t a i n s t h e d a t a f o r YS-619 i n s t a t e s (ii) and (iii). Around
Q = O
t h e element DZz i n state (iii) appears t o be d r a m a t i c a l l y lower than i n s t a t e ( i i ) . This i s presumably due t o t h e f a c t t h a t i n s t a t e (ii) h a l f o f t h e n e e d l e s is "magnetically broken" a s w e suggested i n [4]. Beyond181=5°
t h e d i f f e r e n c e i n DZz between both states r e v e r s e s .The same is found i n YS-623 and 624. T h i s e f f e c t may a l s o be expressed i n terms of t h e parameter K. For
22 1 f u n c t i o n o f t h e dimensionless q u a n t i t y
U
= tS2/c3, ( 1 2 ) b e i n g p r o p o r t i o n a l t o t h e energy of t h e d i p o l e moment ( a $5't) o f a n e e d l e i n t h e r e s u l t a n t f i e l d ( a c - ~ ) due t o i t s neighbours.l
I
622 I I I I I I I I I ~ I I ' t h i s purpose, DZz o b t a i n e d f o l l o w i n g t h e procedure i n t h e p r e v i o u s s e c t i o n i s p l o t t e d i n F i g . 2 f o r t h e sets o f v a l u e s {K=O,A=O}. {K=0.2.A=0} and {K=O,A=O.O25}. For t h e f i r s t and l a s t s e t , t h e r e s u l t s c o i n c i d e f o r181>3°,
i l l u s t r a t i n g t h a t A has no i n f l u e n c e f o r 8 f a r away from 0. The i n f l u e n c e o f A around 8=0. on t h e o t h e r hand, i s e v i d e n t from t h e r e s u l t s around 8=0.1.0 I I I I I 0 . 9
DzZ
0 . 8-
0 . 7-
-
0 . 6 - -. .
. .
: .
0 . 5 1 I I. .
I I-zoo
02
oo
Pig.2 Measured (symbols) and s i m u l a t e d ( f u l l and i n t e r r u p t e d l i n e s ) r e s u l t f o r YS-619:
o : remanent s t a t e a f t e r 10 kOe in-plane ( i i ) ; A : idem a f t e r 10 kOe p e r p e n d i c u l a r l y ( i i i ) .
From i n t e r p o l a t i o n between t h e f i r s t two simula- t i 0 n s . a b e s t f i t w i t h t h e experimental d a t a c o r r e s - ponding t o states ( i i ) and (iii) f o r 181>15O i s ob- t a i n e d f o r K=0.10(5) and K=0.05(5), r e s p e c t i v e l y . T h i s could i n d i c a t e a weak p a r a l l e l c o r r e l a t i o n between n e e d l e s , e s t a b l i s h e d a f t e r i n - p l a n e magnetisa- t i o n , as a r e s u l t of t h e i r non p e r f e c t alignment. I n o r d e r f o r t h i s c o r r e l a t i o n t o o c c u r , t h e axes o f t h e n e e d l e s i n r e g i o n s of f i n i t e a r e a should have a s y s - t e m a t i c d e v i a t i o n from t h e normal. A f t e r removing t h e i n - p l a n e f i e l d , t h e n e e d l e s i n such a r e g i o n have p a r a l l e l m a g n e t i s a t i o n . The e x i s t e n c e of such r e g i o n s i m p l i e s K>O, by d e f i n i t i o n . I n t h e case o f perpen- d i c u l a r m a g n e t i s a t i o n such a mechanism is l a c k i n g .
The p r e s e n t r e s u l t s f o r D i n s t a t e (iii) are n o t c o n s i s t e n t w i t h o u r e a r l i e r r e s u l t s on YS-623 i n t h i s s t a t e , b u t more r e l i a b l e , because s t r a y f i e l d s due t o t h e remanence o f t h e i n d i v i d u a l f i l m s were e l i m i n a t e d by p r o p e r s t a c k i n g . I n t h e r e s u l t s given i n
[ 4 ]
s t r a y f i e l d s were n o t f u l l y e l i m i n a t e d , so t h e element DZz had t o be c o r r e c t e d . T h e r e f o r e , a s y s t e m a t i c e r r o r up t o 0.05 may be p r e s e n t i n t h o s e r e s u l t s . comparison between d i f f e r e n t a l u m i t e sAlthough a d i f f e r e n c e i n K between s t a t e s ( i i ) and (iii) can be d i s c e r n e d f o r a s i n g l e a l u m i t e , t h e f i t of K l a c k s t h e accuracy t o make a d i s t i n c t i o n between t h e magnetic states meaningful when comparing d i f - f e r e n t a l u m i t e s . So f o r t h i s comparison t h e outcome o f K i n s t a t e ( i ) i s considered a u s e f u l parameter. I n F i g . 3 t h e s e v a l u e s f o r K are p l o t t e d a s a z z I
I
t
1
0 10 2 0 30I
F i g . 3 C o r r e l a t i o n parameter K ( e q . ( l ) ) determined f o r t h e magnetic s t a t e "as received" ( i ) as a f u n c t i o n o f t h e q u a n t i t y U ( e q . ( 1 2 ) ) r e p r e - s e n t i n g t h e energy of a n e e d l e i n t h e r e s u l t a n t f i e l d due t o i t s neighbours.K a p p e a r s t o d e c r e a s e g r a d u a l l y from p o s i t i v e t o n e g a t i v e as U i n c r e a s e s . This means t h a t t h e alignment o f neighbouring n e e d l e s tends t o be more a n t i - p a r a l l e l as t h e i r d i p o l a r i n t e r a c t i o n i n c r e a s e s , which can be q u a l i t a t i v e l y understood.
Conclusion
Using t h e
3-D
Neutron D e p o l a r i s a t i o n Analysis i t a p p e a r s p o s s i b l e t o q u a n t i f y t h e magnetic c o r r e l a t i o n s between t h e i r o n n e e d l e s i n Alumites i n terms of a c o r r e l a t i o n parameter K . The v a l u e o f K depends upon t h e magnetic h i s t o r y of t h e a l u m i t e .It i s demonstrated t h a t K becomes less p o s i t i v e ( i . e . t h e c o r r e l a t i o n s tend t o be more a n t i - p a r a l l e l ) w i t h i n c r e a s i n g i n t e r a c t i o n between t h e n e e d l e s due t o t h e i r s i z e and d i s t a n c e . The same tendency i s shown a f t e r p e r p e n d i c u l a r m a g n e t i s a t i o n , with r e s p e c t t o i n - p l a n e m a g n e t i s a t i o n .
The a u t h o r s wish t o thank D r . T.Tokushima from Yamaha R&D L a b o r a t o r i e s f o r p r o v i d i n g t h e samples and t h e d a t a i n Table I. Prof.Dr.
J.J.Van
Loef i s acknow- ledged f o r c r i t i c a l l y r e a d i n g t h e manuscript.References
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