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The influence of the packing density on the magnetic behaviour of alumite media
Journal of Magnetismand Magnetic Materials 88 (1990) 236-246 North-Holland
236
THE I N F L U E N C E O F T H E P A C K I N G D E N S I T Y O N T H E M A G N E T I C OF A L U M I T E MEDIA
BEHAVIOUR
LI C H E N G - Z H A N G and J.C. L O D D E R UnioersiO, of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Received 19 January 1990
The influenceof the pore size, the ratio of length to diameter, the microstructureof the initial growth part of the Fe cylinder and the packing density of the Fe needles on the magnetic behaviour of alumite media are reviewed. It is found that the magnetization reversal is controlled by curling rotation,, if the applied field lies along the film normal. The Hc ± is mainly determined by the diameter of the needles, but it slightly decreases with increasing packing density. If the applied field deviates from the film normal, the magnetic behaviour of alumite media is strongly affected by the packing density. For alumite with a low packing density, the magnetization reve..,'sal is ~.~0ntrolledby a cos-type of incoherent rotation and a demagnetizingfield. For high packing densities, the reversal cat, '-. ~sidered as the superposition of a cos-type of incoherent rotation with perpendicular anisotropy and in-plane domain-wallm. tion. The alumite media can exhibit both perpendicular as well as longitudinal anisotropy by an appropriately controlled aspect ratio and the morphology of initial growth part of the iron needles.
1. Introduction Up to now the prospects of the latent potentialities of high density recording for C o - C r films having perpendicular anisotropy have strongly appealed tc many researchers for several years. It is known that alumite media consist of well-defined Fe-needles positioned perpendicular to the film plane in a regular array with their ferromagnetic pores separated by a nonmagnetic A120 3 matrix. A schematic drawing (fig. la) and a SEM photograph (fig. l b ) are given for a typical alumite sample. In the latter the initial growth part of the Fe needles can be clearly seen. It can already been said that these initial parts are playing an important role in the magnetic behaviour of such samples. In the case of most of the alumite media used, the pore size, in other words the diameter of the Fe needle, is less than 83.5 nm which is the calculated thickness of the Bloch wall. The basic unit is a single-domain cylinder. The distance between the iron cylinders and their diameter can be independently varied by using anodization to-
gether with an additional new process called " p o r e widening" [8]. Therefore, alumite is regarded as an ideal material for understanding the influence of the magnetostatic interactions on the magnetization reversal for media with perpendicular anisotropy. To some extent, a fully segregated C o - C r film with columnar microstructure can be thought to be a special case of alumite with a close packing density from the point of view of the magnetic behaviour. Obviously, the higher the packing density, the stronger the magnetostatic interaction between the iron needles will be. It was found that for alumite media the measured reduced coercivity versus the reduced diameter curve fits the theoretical curling model, if the applied field is applied along the film normal and strong enough to saturate it [1,2]. However, the magnetic beha~4our w~ill no longer obey curling if the applied field deviates from the film normal. In principle, no free magnetic charge is formed during curling, hence there is no magnetostatic interaction between the iron cylinders when the ap-
0304-8853/90/$03.50 © 1990 - ElsevierScience Publishers B.V. (North-Holland)
C.-Z. Li, J. C Lodder / Magnetic behaviour of alumite media Dc:
cettDiameter~ ~ ~ . ~ . ~ ; . . z ~ . ! . i ~ . .
Magneti c -- ~ Substance At20a. ~
stant k depends on the length-to-diameter ratio. According to the curling model, the coercivity along the film normal will be independent of the packing for the Alumite media. It was reported [1,6] and also confirmed by our own measurements, that H¢.L depends only on the pore diameter Dp and is independent of the cell diameter De, if the ratio of length to diameter of the iron needles is more than 15. These experimental data could prove that the magnetization reversal is controlled by curling rotation in alumita media. However, other experimental data have shown [2,7] that Hci slightly decreases with increasing packing density. For alumite media, assuming perfect ferromagnetic cylinders in a strict hexagonal array, the packing density of the ferromagnetic cylinders can be calculated from the formula [1]:
1
Barrier At
P = (¢r/2q~) ( Dp/Dc)2.
Fig. 1. (a) A schematic drawing of magnetic alumite media with a regular array of electrodeposited Fe needles in an A1203 matrix; (b) a SEM micrograph of a fractured alumite sample with a needle diameter of 60 nm, a cell size of 125 nm, and a thickness of 900 rim. The initial growth parts of the needles can be clearly seen.
plied field is parallel to the longer axis of the cylinder. The Hn for a curling model is given by [3-51: H . = N.M
-
237
-
(1) where Nz is the demagnetizing factor in the direction of the easy axis and R the radius. The con-
(2)
On the other hand, it was experimentally discovered [8] that the magnetization for alumite media is also directly proportional to the ratio of (Dp/Dc)2. In order to get to the heart of problem of why the above mentioned discrepancy happens we gathered and rearranged related data published in refs. [1,3,4,6,7]. Our discussion will centre on the influence of the packing density on the magnetic behaviour of alumite, because it is the preferred method for determining the effects of magnetostatic interactions on magnetic behaviour. It is known [1,2] that the coercivity along the film normal is mainly determined by the pore size of the iron cylinder. At the same time, it was also reported [1,7] that the magnetic behaviour of alumite media is still related to the ratio of length to diameter (aspect ratio) and microstructure of the initial growth of •h,, • -^^-~' ^ "~"----~--- in this paper an c~o~t is made to examine the effect of the packing density and the aspect ratio of the cylinders, the morphology of the initial part of the needle growth (the "roots": please refer to fig. lb) on the magnetic behaviour of alumite. It is the main purpose of this review to try to probe some of the internal relations of angular dependence of the coerciviy between the fully
238
c.-z. Li, J. C. Lodder / Magnetic behaviour of alumite media
segregated C o - C r film and the alumite media, because such C o - C r films can be microstructurally considered, to be an alumite medium with a high packing density.
2. Sample properties Four kinds of alumite medium specimens were chosen, namely: 1) In order to investigate the influence of the pore size (needle diameter) and packing density on the coercivity, a series of chosen alumite media were varied in pore and cell size. The properties are taken from the literature [6,8]. 2) To examine the influence of the aspect ratio of the needles on the magnetic behaviour, a series of alumite media having the same pore size of 440 A, and a packing density of 0.19 are taken from ref. [7]. These samples have different aspect ratios. 3) In order to investigate the influence of the morphology the initial growth part of the iron needle on the coercivity, a series of alumite media used have the same pore size of 440 A, the same packing density of 0.13 and an aspect ratio of more than 15, but have a different roots [1], all of which are shown in the schematic drawing of fig. 8. 4) The investigation of the influence of the packing density on the engular dependence of the magnetic behaviour, required four alumite media with different packing densities. These samples had the same pore size of 440 A, the same morphology of the initial growth part of the iron needle and their aspect ratio was more than 14 [6].
The thickness and cell size of the alumite media were measured by SEM [7]. In order to observe the cross-section and morphology of the iron cylinder, an ultra-microtorae was used to make a 500 A, thick slice of the films [6]. These slices were first placed in a saturated solution of HgCI 2 to dissolve the A1 substrate. The etched samples were then put into a mixture of phospofic- and chromic-acid solutions to separate the iron cylinders from the outer covering of A120 3. The samples having varying aspect ratios were obtained by mechanical polishing with a buff and alumina fine particles or silica sol. The Debye X-ray and electron diffraction patterns indicated that the iron cylinder was in a single crystalline state with growth along the [110] direction. The magnetic properties were measured using a VSM and torque magnetometer [1,6-8]. The packing density is equal to the porosity of the alumite medium, which can be calculated by formula (2). Generally, the actual packing density will be lower than the calculated one, because some voids are present.
o
o
The most relevar~: properties obtained are summarized in table 1.
3. Results and discussion A lot of experimental data show that in the alumite media the magnetization preferably lies along the film normal. It was pointed out [2] that the basic magnetic unit of the Fe alumite consists of a single-domain cylinder because the pore size for most of the alumite samples used is less than the calculated Bloch wall of about 835 ~,. At the same time, the Debye X-ray diffraction pattern and electron microscopy show [8] that the iron cylinder is a single crystal and its growth lies along the [110] direction, which is perpendicular to the medium normal.
Table 1 The influence of the packing density on the magnetic behaviour No. A B C D
Cell size (A) 1170 960 745 640
Pore size (A) 440 440 440 440
Packing density 0.13 0.19 0.32 0.43
He± (kA/m) 68 65.2 63.7 63.7
Aspect ratio 14 14 14 13
OR ~.
Rs j.
5.3 4.1 1.93 1.7
0.32 0.19 0.14 0.11
C.-Z. Li, J.C Lodder / Magnetic behaviour of alumite media
The dependellcc of the pore size on the cell size of the iron cylinders with He± as parameter is shown in fig. 2, which was directly quoted from the same graph reported by refs. [1,6] and confirmed by our own measurements. It can be seen from this figure that the coercivity along the film normal H¢± is strongly controlled by the diameter of the iron cylinder (Do) and decreases with increasing Dp. However, careful consideration is required to draw the following conclusion: For alumite meoia, He ± only depends on the pore diameter Dp and is independent of the cell diameter D¢; hence it is independent of the packing density. Based on the straight lines in fig. 2 the dependence of H c ± on the packing density with respect to the pore size of the iron cylinder is shown by the solid lines in fig. 3. It is dearly seen from this figure that as the packing density increases, if the coercivity along the film normal is kept constant, the pore size of the iron cylinder should be slightly reduced instead of remaining constant. This means that H c . is a function of the packing density, even though the degree of dependence of H¢.L on the packing density is quite small in comparison with the degree of dependence of He± on the pore size. It
°(
/
1200
800
-
56 400
_-
'
80 •
~
I
I
400
I
I
800
•
I
•
=
__t
1200
Fig. 2. The relation between the pore size (Dp) and cell size diameter (D c) for alumite having different coercivities (see also refs. [1,6]).
239
:,64 ~, :,so ,~ 120
~
6
4
.
.
11U HCJL
1¢0 90 80
kA/m t /
measured .
calculated
_~ ~._~. ~" ~>"J '~" ~
368 A :
--'"
,,
70
~,~.
60
!"'4t.,~.--.--~440 526.1 508 ,~ 504 A
....
355 A o~
...A,397A 0
A 49_7~
498 ,~
,t,-r
50
526 A
68a i
40
""~'~- - " -
660 ~
6sa ~,
"~-'---...~-o 668 A
3(' 20
~> P
781 A
I
I
I
I
I
I
l
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Fig. 3. The dependence of He± on the packing density ( P ) with respect to the pore size.
is known that as the pore size decreases Hc~ increases. Using the data from fig. 2 the coercivity along the film normal vs. pore size is plotted in fig. 4. In order to reduce the influence of packing density on the results for H ci as far as possible, only the sample with the largest Dp was chosen to draw He± vs. Dp in fig. 4. This means that the chosen samples are those with the lowest packing densities. Based on the measured graph of fig. 4, the unknown He± for the other sample, with unmeasured Dp, can be easily calculated and found by interpolation. With the aid of the interpolation method, a series of calculated He ± vs. packing density curves are plotted by dashed lines in fig. 3 where the pore size of the iron cylindersoare kept constant (264, 397, 526, 668 and 781 A, respectively). On the other hand, for a sample having a pore size of 440 the Hc ± vs. packing density curve is a measured one instead of a calculated one. All the calculated and measured curves reveal that the coercivity along the film normal is related to the packing density. The He± decreases with increasing packing density if the samples have the
C-Z. Li, J. C I_odder / Magnetic behaviour of alumite media
240
120 110 100 90
Hc~ - kAlm
T
397 ~,
80
70 60
k~sa6
50
40 30
~ =" Op (A)
20
" 1 ~ 1A
I
I
I
I
I
I
I
I
100
200
300
400
500
600
700
800
Fig. 4. The measured dependence of H e . on the pore size
(D~).
same pore size. However, the degree of dependence of He j. on the packing density for alumite media with large pore size of the iron cylinder is less than that with small pore size. Contparing the influence of the packing density on h~± with that of the pore size on He±, the degree of the influence for the packing density is much less than that for the pore size. For example, for alurnite media with a pore size of 526 A, the He. only reduces by 10.77o even though the packing density increases from 0.14 to 0.69. This action is equivalent to the reduction of the coerci,Aty for the alumite media, in which the packing density is kept constant at 0.14, but the pore size only needs to be increased from 490 to 526 A,; an increment of only 36 A. Whatever the consequences, this phenomenon can be considered as an indication of the existence of magnetostatic interactions between the iron cylinders in the alunfi*e media. We have discovered [2,9] that the measured reduced eoercivity vs. the reduced diama~er curve fits the theoretical curling model very well, if the applied field is along the film normal and is large enough to saturate it. This result is shown in fig. 5.
It can be seen from this figure that the measured reduced coercivity vs. the reduced diameter curve is almost identical with the theoretical predictions expected from the curling model, even though these specimens are made under quite different preparation conditions from those in ref. [2]. Based on the above experimental curves, it can be concluded that the magnetization reversal mechanism for alumite media must bz dominated by curling. Since this is so, according to the physical concept and the formula (1) for curling, the coercivity should be independent of the packing density. One of the reasons why such seemingly contradictory phenomena exist simultaneously in alumite media, i.e. although He± is mainly determined by the pore size but is still slightly influenced by the packing density, is probably that the magnetization slightly deviates from the film normal in the actual specimens used. As pointed out [2], once the magnetization deviates from the film normal, the magnetic behaviour will no longer obey curling and the influence of the magnetostatic interactions will gradually manifest tbem~e!ves. The experimental results from M~ssbauer spectra reveal [8] that the magnetization deviates about 15 ° from the film normal or at least 6% of the total magnetization lies in the opposite direction in alumite media. It is generally agreed that the magnetostatic interac-
Hc/Ha
l
g rotation 250Ah"
0.1
°°°
O
T
0
I
1
~0
Fig. 5, The relation between the measured and calculated reduced coercix4ty vs. the reduced diameter of the Fe needle.
C-Z. Li, J. C Lodder / Magnetic behaviour of alumite media
tions between the iron needles is closely related to the local demagnetizing field, but the latter is affected by both the aspect ratio and shape of the needles. Therefore we will concentrate our attention on hwestigating how the coercivity is affected by the above mentioned factors. In order to remove the influence of the pore size and packing density on the coercivity, a series of specimens with the same pore.size of 440/~ and packing density of 0.19, but had-hag a different ratio of length to diameter, are chosen from ref. [7]. The dependence of both He± and Hcu on the ratio of length to diameter is plotted in fig. 6. It is clearly seen from this figure that He± increases with the aspect ratio of the iron cylinders until the ratio reaches a certain value, beyond which He± remains constant. The Hcj. and HotI have almost constant values of 66.5 and 17.5 k A / m , respectively, when the aspect ratio is more than 20. In this case, the influence of the demagnetizing field on the coercivity can be neglected. However, as the aspect ratio decreases, He± and HclI will drastically decrease and increase, respectively. If this ratio is continuously reduced to less than about 2, the anisotropy of the alurnite media
80 -
Hc
(kA/m)
70
-I
°
o
HcJ. o
60
50
©o
© p
= 0.19o
Dp = 440 A
40 30
'° t 5
10
_t
!
£
°,,°2.......
15
20
25
30
Fig. 6. The dependence of the perpendicular and in-plane coercivity on the aspect ratio.
241
i[
100
Hc J.I Hc JL30
90 80 70 60 50 40 30 20
f
I I ! I !
t,
10 '~ ,~,spect ratio I I
Iv
i ,, 5
I
I,
I
10
15
20
25
30
Fig. 7. The relation between the measured and calculated relative perpendicular coercivity vs. aspect ratio.
will even char, ge from perpendicular to longitudinal. Thus, it can be said that the characteristic of the coerc',vity will be strongly affected by the ratio of length to diameter of the iron cylinders if the ratio is less than 15. Obviously, the smaller the ratio, the stronger the local demagnetizing field encountered by the iron needles iD alumite will be. Therefore, o.,,e~ential condition to make alumJte media exhibit excellent perpendicular an~sotropy is that the ratio of length to diameter should be large enough (for example > 20). The measured and calculated dependence of the relative perpendicular coe
C-Z. Li, J. C. Lodder / Magnetic behaviour of alumite media
242
H c ±/Hc z 30 changes as this ratio varies. The value of H¢x/H¢x3o will be drastically affected by the aspect ratio when this is lower than 15, especial in the range of Hc±/Hc±3o < 5. However, the He±~ H~ ± 30 only changes a little, when this ratio is more than 20. Combining this argument with the measured reduced coercivity vs. reduced diameter curve, it is again confirmed that for alumite media having perpendicular anisotropy no matter how the pore size and the aspect ratio change, the coercivity is dominated by the curling model. However, one point should be noted that, as is shown in table 2 for the alumite media used, the calculated values of H~j. still fall far short of the measured ones when this ratio varies from 4 to 30. This rather large discrepancy between the measured and calculated values of H c ± has yet to be explained. The coercivity for alumite media is also affected by the shape of the iron cylinder. Electronmiciescope observations have shown [1] that generally t~.e initial growth part of the iron cylinder consists of a various shapes like a circular cone, as is shown in the schematic drawing of fig. 8, but the rest of the cylinders are perpendicular to the film normal. Naturally, the existence of the circular cone shape of the initial growth part is Rkely to cause the formation of free poles on the sides of the iron cylinders. Of course, the presence of free poles will result in magnetostatic interactions between the iron cylinders. In order to investigate the influence of the shape of the initial growth part (cone size)
Table 2 The calculated and measure,'t Hc± for different aspect ratios of the iron cylinder Aspect
Calculated
Measured
4 5 8 10 15 20 25 30
18.6 44.3 63.2 87.2 99.2 103.8 106.4 107.7
40.5 44 53.5 58 64 66 66.5 67
10
HcJL I H c ,
3~ @
'
1
+oo A
I 0
5
A
A
I
I
I
I
10
15
20
25
"~,-A s p e c t ,i,
ratio ,
30
Fig. 8. The dependence of Hc. t / H c l I on the aspect ratio for various dimensions of the initial growth part of the Fe needles.
on the magnetic behaviour, three kinds of alumite media, taken from ref. [1] and having the same pore size of 440 ,~, and a packing density of 0.13 were examined" Samp,le ¢t I has a cone with a lower diameter of 800 A and a height of 1100 ]k. Sample # 2, 800 and 400 ,~,, respectively. Finally, for sample # 3 the initial part of the cylinder was grown with Cu consequently in this sample there will be no influence from the initial growth part of the Fe needle. It was reported [1] that no matter how the aspect ratio changes, H c.L will have almost equal values for the 3 kinds of spechnens, provided they have the same aspect ratios. However, the H~,, values of the above-mentioned samples are closely related to the shape of the initial growth of the iron cylinder. Experimental data reveal that no matter how the aspect ratio changes, for sample # 1 having the largest roots of 1100 A, He:i is the largest; for sample # 2 having a root-length of 400 A, H~H is intermediate and for specimen :~3 without any initial growth, He.I is the smallest.
C.-Z. Li, J. C. Lodder / Magnetic behaviour of alumite media
As long as the samples compared have the same aspect ratio, then the longer the root, the larger the HclI value will be. This fact suggests that the value of He ± for alumite media is not influenced by the initial growth, but that the in-plane coercivity will be strongly affected by it if the applied field makes an angle with the film normal. This is due to the appearance of the initial growth part and it strengthens the magnetostatic interactions between the iron cylinders. The magnetostatic interactions originate from the presence of the free poles on the side of the cylinder if the applied field is not parallel to the sample normal. It may be reasonable to assume that the presence of initial growth of the cylinder is likely to induce the magnetization to deviate from the normal direction, which must lead to an increase of the in-plane component of the magnetization. Therefore, the values of H~± and H¢II vs. the shape of the initial growth curves again confirm that the magnetization reversal mechanism is dominated by curling if the applied field ties in the direction of the film normal. However, the magnetic behaviour will gradually diverge from nucleation by curling, and the influence of the magnetostatic interactions on the coercivity will also strengthen, as the deviation of the applied field from the film normal i~,~creases. In fig. 8 Hcl/H~t i vs. the aspect ratio of the initial growth part for the above mentioned 3 samples are plotted. It can be seen from this figure that no matter how this ratio changes, the shorter the initial growth of the cylinder, the higher the values of H~./H¢It. Generally speaking, when the aspect ratio is more than 15, the values of H~./HcI I for 3 kinds of alumite media gradually tend towards their respective saturation values. It can also be seen that the effect of the aspect ratio on H~±/H~I I is quite remarkable, if this ratio is less than 15. For samples witheut any initial growth (~: 3), H~ ~_/H~II always remains larger than 1, although for all 3 samples H~j_/H~I I decreases monotonically with decreasing aspect ratio. However, for specimens ~ ! and # 2 with initial growth, there are some critical ratios, above which the value of H¢./H¢I ! remains > 1, but below this cfitica! ratio, the value of H, ./H~I I will be changed from > 1 to < 1. It was discovered that the larger
243
the initial growth of cylinder the higher the critical transition point of this ratio was. This fact suggests that at this time the orientation of the magnetization will be changed from perpendicular anisotropy ( H c . / H ¢ I t > 1) to longitudinal ( < 1). This means that the presence of the initial growth of the cylinder will result in the deterioration of perpendicular anisotropy for alumite media, because the ratio Hc±/H¢I I can be considered as a figure of merit for the use of the media for perpendicular recording. In general the larger the value of H¢./H¢I t the stronger the perpendicular anisotropy. One of the consequences of the influence of the shape of initial growth part of the cylinder on the magnetic behaviour for alumite is that the media can exhibit both perpendicular and longitudinal anisotropy provided the shape of the root and the aspect ratio of the needle can be appropriately controlled. Based on the above discussion, it is known that for alurnite media the coercivity is affected by 4 factors; the pore size, the aspect ratio, the morphology of she initial growth and ~he packing density. The determinative factor with respect to their influence on Hc ± is the pore size. In order to investigate the correlation between the angular dependence of the magnetic behaviour and packing density for alumite media, four samples were chosen, all havhag the same pore size of 440 A, the same morphology of initial growth and almost the same apect ratio. As shown in table 1, with increasing packing density, the coercivity H e . , squareness ratio Rs ± along the film normal and relative orientation ratio OR ± decreases. The squareness ratio R s . reflects the ratio of the remanence to the saturation magnetization in the direction of the sample normal. The OR± is the relative ratio of the squareness ratio value in the in-plane and normal direction of the sample. Th~ nnoldar clopondonee e,f the ncwmaliTed Rs with packing density P for 4 alumite media are shown in fig. 9 (note: all the squareness ratios are normalized by the value of Rs i along the film normal for the specimen with a packing density of 0.13). It can be clearly seen from this figure that no matter how the angle changes, the normalized Rs drastically decreases with increasing packing den-
244
C-Z. Li, J.C. Lodder / Magnetic behaviour of alumite mcdia
100 90 80
70 60 50 40 30 20 10
10
20
30
40
50
60
70
80
90
Fig. 9. The dependence of relative squareness ratio on the angle of the applied field with respect to the packing density.
constant if the angle is less than 40 o, but rapidly decreases with an increasing angle of more than 40 o. On the contrary, as the packing density increases, the relative coercivity decreases rather steeply with inceasing angle when it is less than 60 o but slightly decreases with increasing angle if
sity, except for an angle > 80 °. Similarly, the angular dependences of Hc(O)/Hc± with respect to the packing density for 4 samples are plotted in fig. 10. The relative coercivity Hc(O)/H,: ± sample # A, which has the lowest packing density, is almost
100 90
eo
,oi._ I
IHc-
-,\
50
~ p = 0.13
40
v p = 0.19 i . . . .~ . . A p = u.~z
30 20
~,.,.~_~~
"'~
rn=_.=sured ....
v p = 0.43
calculated t . . . . . .....
0.75 COS 0 + 0.25 Sin = 0 COS 0 P(O) + 0.39 (1-0.8 COS 2 e) "1/= . (1 -
P (8))
lO --
- ~
~
I
I
I
i
10
20
30
40
50
60
.....1 ........ 70
="0
I 80
L ~ 90
Fig. 10. The measured and calculated angular dependence of the coercivity with respect to the packin/5 density for alurmte.
C.-Z Li, J.C. Lodder / Magnetic behaviour of alumite media
0
is larger than 60 ° , i.e. the variation of H,:(O)/Hc± for alumite media with low and high packing density is just the opposite. In summary, the magnetic behaviour (relative coercivity, squareness ratio and orientation ratio) for alumite media will be greatly changed with varying packing density when the applied field is deviated from the film normal. It was pointed out [2,11] that the presence of magnetic poles on the side of the iron cylinders in alumite media (if the applied field deviates from the film normal) must result in mutually magnetic attraction between the cylinders along the film plane. With increasing packing density, this attraction will strengthen. Of course, it will strongly change the characteristic of the demagnetizing field. Therefore, the magnetization reversal must be closely related to the demagnetizing field. If the angular dependence of the magnetizing field is assumed to obey the sin20 law, the relative coercivity for alumite media can be calculated by [2,91:
Hc(O)/Hc±=acosO+(1-a)sinZO.
(3)
The calculated curve for a = 0.75 is shown by the dashed line in fig. 10. It can be clearly seen that the measured Hc(O)/tf,: ~ vs. angle curve for sample A with a pa,:!,ing density of 0.13 is in fairly good agreement ,.vith the calculated one. This means that the magnetization reversal is controlled by both a cos type of incoherent rotation and the demagnetizing field for alumite media with low packing density. However, the calculation procedure reveals that for other alumite media with high pacldng density (form example, p > 0.4) the calculated curve does not fit as well. Based on the morphology of alumite media with high packing density, it is perhaps reasonable to imagine that with increasing packing density, the distance IOCtW~Cll
trig
i r o n
),31_g~Ul~} __al . . . . ~ ; I t:l.lt l LugCo.~llg . . . .
S. O
g l1U. b.C . . t l!l .i .l_t ,
in some areas the initial growth parts of the cylinders contact each other. If this is true, alumite media with high packin~ density must exhibit a similar behaviour to a fully segregated CoCr film. It was found [11] that for a fully segregated CoCr film the magnetization reversaI can be considered as the superposition of a
245
cos-type of incoherent rotation with perpendicular anisotropy and in-plane domain-wall motion, which mainly results from the initial layer. The angular dependence of the coercivity can be calculated by [111:
Hc(O)/Hc±=COS(O)P(O ) + (Hcll/Hcx) x (a
- e(o)), (4)
where a is an adjustable parameter, in which P(O) represents the measured angular proportional function of incoherent rotation with perpendicular orientation of the magnetization to the in-plane domain-wall motion, which can be obtained from the measured dependence of the distribution of the hysteresis loss AWh on the applied field as a parameter of the angle [11]. As is shown in fig. 10, it is very interesting to find that the calculated H¢(O)/Hc. vs. angle curve ( a = 0 . 8 and Hc,/Hc±=0.39) is almost identical to the measured one for alumite media with a packing density of 0.43. The above-mentioned assumption can also be supported as following experimental data and theoretical calculations [1,12] for an alumite medium with a thickness of 1 p.m and pore size of 440 A,. The magnetic anisotropy constant is positive when the packing de,~ity is below 0.33, but negative if it i~ more than 0.33. When the packing density is equal to about 0.32, the magnetic anisotropy will become zero.
4. Conclusions
With a view to obtaining a better understanding of the correlation between the magnetization reversal and the morphology of alumite media, the m ...... of .1L.~ " .~.:.. "I I- - II: ~1 :L. I Kll, ~1lt .: _. i,' u cm.= ut~ pore ~i,_~, a~pect ,a.,.,. growth part of the Fe needles and packing density on the magnetic behaviour have been reviewed. Based on these discussions, the results can be summarized as follows: 1) If the applied field lies along the film normal and is large enough to saturate the sample, the measured reduced coercivity vs. reduced diam-
246
C.-Z. Li, J.C Lodder / Magnetic behaoiour of alumite media
eter curve fits the theoretical curling model very well. No matter how the aspect ratio changes, the variation of the measured He. with aspect ratio basically follows the calculated one predicted by the curling model. It seems that He± is not affected by the initial growth part of the iron cylinder. 2) The characteristic of H c j. for alumite media is mainly determined by the diameter .ff the iron cylinders, but He± still decreases slig:ltly with increasing packing density for the actual alumite media. 3) The alumite media can exhibit both perpendicular and longitudinal anisotropy by appropriate control of the aspect ratio and the morphology of the initial growth part of the iron cylinders. One of the essential conditions to achieve an excellent perpendicular anisotropy for alumite media is that the ratio of length to diameter should be about 20. Experimental data show that the coercivity along the film plane is closely related to the shape of the initial growth part of the Fe needle. 4) If the applied field deviates from the film normal, the magnetic behaviour (the coercivity, squareness ratio, orientation ratio and hysteresis loss, etc.) are greatly affected by the packing density. For alumite media with a low packing density, the magnetization rew.~rsal is controlled by a cos-type of incoherent rotation and demagnetization field. However, for the alumite media with a high packing density, the magnetization reversal can be considered as the superposition of a costype of incoherent rotation with perpendicular anisotropy and in-plane domain-wall motion.
This means that the angular dependence of the relative coercivity ( H c ( O ) / H c j_) for alumite media starts exhibiting a more or less typical behaviour for a fully segregated CoCr film at high packing densities.
Acknowledgements The authors would like to thank Mr. Eelco Sterringa, who is researching this subject in more detail for his MSc thesis, for his contributions to this paper. We also like to thank Professor Dr. Th.J.A. Popma for his continued support.
References [1] K.I. Arai, Text of 56th Annual Meeting o! Magn. Soc. Japan (1988) p. 25 (in Japanese). [2] J.C. Lodder and Li Cheng-Zhang, IEEE Trans. Magn. MAG-25 (1989) 4171. [3] A. Aharony, Phys. Stat. Sol. 16 (1966) 3. [4] A. Aharony, IEEE Trans. Magn. MAG-22 (1986) 147. [5] G.T.A. Huysmans, J.C. Lodder and J. Wakui, J. Appl. Phys. 64 (1988) 2016. [6] N. Tsuya, T. Tokushima, M. Shiraki, Y. Wakui, S. Iwasaki and Y. Nakamura, IEEE Trans. Magn. MAG-23 (1987) 2242. [7] K.I. Arai, Y. Wakui, K. Ohmou and T. Tokushima, IEEE Trans. Magn. MAG-23 (1987) 2245. [8] T. Tsuya, T. Tokushima, M. ShirarJ, Y. Wakui, Y. Umehara, H. Nakamura, Y. Katsumata and Y. Saitom, J. Magn. Soc. Japan 11 (1987) 55 (in Japanese). [9] J.C. Lodder and Li Cheng-Zhang, J. Magn. Soc. of Japan 13 Suppl. $1. (1989) 659. [10] J.A. Osborn, Phys. Rev. 67 (1945) 351. [11] J.C. Lodder and Li Cheng-ZbaDg, J. Magn. Magn. Mat. 74 (1988) 74. [12] M. Masuda, S. Shiomi and M. Shiraki, Japan. J. Appl. Phys. 26 (1987) 1680.
236
THE I N F L U E N C E O F T H E P A C K I N G D E N S I T Y O N T H E M A G N E T I C OF A L U M I T E MEDIA
BEHAVIOUR
LI C H E N G - Z H A N G and J.C. L O D D E R UnioersiO, of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Received 19 January 1990
The influenceof the pore size, the ratio of length to diameter, the microstructureof the initial growth part of the Fe cylinder and the packing density of the Fe needles on the magnetic behaviour of alumite media are reviewed. It is found that the magnetization reversal is controlled by curling rotation,, if the applied field lies along the film normal. The Hc ± is mainly determined by the diameter of the needles, but it slightly decreases with increasing packing density. If the applied field deviates from the film normal, the magnetic behaviour of alumite media is strongly affected by the packing density. For alumite with a low packing density, the magnetization reve..,'sal is ~.~0ntrolledby a cos-type of incoherent rotation and a demagnetizingfield. For high packing densities, the reversal cat, '-. ~sidered as the superposition of a cos-type of incoherent rotation with perpendicular anisotropy and in-plane domain-wallm. tion. The alumite media can exhibit both perpendicular as well as longitudinal anisotropy by an appropriately controlled aspect ratio and the morphology of initial growth part of the iron needles.
1. Introduction Up to now the prospects of the latent potentialities of high density recording for C o - C r films having perpendicular anisotropy have strongly appealed tc many researchers for several years. It is known that alumite media consist of well-defined Fe-needles positioned perpendicular to the film plane in a regular array with their ferromagnetic pores separated by a nonmagnetic A120 3 matrix. A schematic drawing (fig. la) and a SEM photograph (fig. l b ) are given for a typical alumite sample. In the latter the initial growth part of the Fe needles can be clearly seen. It can already been said that these initial parts are playing an important role in the magnetic behaviour of such samples. In the case of most of the alumite media used, the pore size, in other words the diameter of the Fe needle, is less than 83.5 nm which is the calculated thickness of the Bloch wall. The basic unit is a single-domain cylinder. The distance between the iron cylinders and their diameter can be independently varied by using anodization to-
gether with an additional new process called " p o r e widening" [8]. Therefore, alumite is regarded as an ideal material for understanding the influence of the magnetostatic interactions on the magnetization reversal for media with perpendicular anisotropy. To some extent, a fully segregated C o - C r film with columnar microstructure can be thought to be a special case of alumite with a close packing density from the point of view of the magnetic behaviour. Obviously, the higher the packing density, the stronger the magnetostatic interaction between the iron needles will be. It was found that for alumite media the measured reduced coercivity versus the reduced diameter curve fits the theoretical curling model, if the applied field is applied along the film normal and strong enough to saturate it [1,2]. However, the magnetic beha~4our w~ill no longer obey curling if the applied field deviates from the film normal. In principle, no free magnetic charge is formed during curling, hence there is no magnetostatic interaction between the iron cylinders when the ap-
0304-8853/90/$03.50 © 1990 - ElsevierScience Publishers B.V. (North-Holland)
C.-Z. Li, J. C Lodder / Magnetic behaviour of alumite media Dc:
cettDiameter~ ~ ~ . ~ . ~ ; . . z ~ . ! . i ~ . .
Magneti c -- ~ Substance At20a. ~
stant k depends on the length-to-diameter ratio. According to the curling model, the coercivity along the film normal will be independent of the packing for the Alumite media. It was reported [1,6] and also confirmed by our own measurements, that H¢.L depends only on the pore diameter Dp and is independent of the cell diameter De, if the ratio of length to diameter of the iron needles is more than 15. These experimental data could prove that the magnetization reversal is controlled by curling rotation in alumita media. However, other experimental data have shown [2,7] that Hci slightly decreases with increasing packing density. For alumite media, assuming perfect ferromagnetic cylinders in a strict hexagonal array, the packing density of the ferromagnetic cylinders can be calculated from the formula [1]:
1
Barrier At
P = (¢r/2q~) ( Dp/Dc)2.
Fig. 1. (a) A schematic drawing of magnetic alumite media with a regular array of electrodeposited Fe needles in an A1203 matrix; (b) a SEM micrograph of a fractured alumite sample with a needle diameter of 60 nm, a cell size of 125 nm, and a thickness of 900 rim. The initial growth parts of the needles can be clearly seen.
plied field is parallel to the longer axis of the cylinder. The Hn for a curling model is given by [3-51: H . = N.M
-
237
-
(1) where Nz is the demagnetizing factor in the direction of the easy axis and R the radius. The con-
(2)
On the other hand, it was experimentally discovered [8] that the magnetization for alumite media is also directly proportional to the ratio of (Dp/Dc)2. In order to get to the heart of problem of why the above mentioned discrepancy happens we gathered and rearranged related data published in refs. [1,3,4,6,7]. Our discussion will centre on the influence of the packing density on the magnetic behaviour of alumite, because it is the preferred method for determining the effects of magnetostatic interactions on magnetic behaviour. It is known [1,2] that the coercivity along the film normal is mainly determined by the pore size of the iron cylinder. At the same time, it was also reported [1,7] that the magnetic behaviour of alumite media is still related to the ratio of length to diameter (aspect ratio) and microstructure of the initial growth of •h,, • -^^-~' ^ "~"----~--- in this paper an c~o~t is made to examine the effect of the packing density and the aspect ratio of the cylinders, the morphology of the initial part of the needle growth (the "roots": please refer to fig. lb) on the magnetic behaviour of alumite. It is the main purpose of this review to try to probe some of the internal relations of angular dependence of the coerciviy between the fully
238
c.-z. Li, J. C. Lodder / Magnetic behaviour of alumite media
segregated C o - C r film and the alumite media, because such C o - C r films can be microstructurally considered, to be an alumite medium with a high packing density.
2. Sample properties Four kinds of alumite medium specimens were chosen, namely: 1) In order to investigate the influence of the pore size (needle diameter) and packing density on the coercivity, a series of chosen alumite media were varied in pore and cell size. The properties are taken from the literature [6,8]. 2) To examine the influence of the aspect ratio of the needles on the magnetic behaviour, a series of alumite media having the same pore size of 440 A, and a packing density of 0.19 are taken from ref. [7]. These samples have different aspect ratios. 3) In order to investigate the influence of the morphology the initial growth part of the iron needle on the coercivity, a series of alumite media used have the same pore size of 440 A, the same packing density of 0.13 and an aspect ratio of more than 15, but have a different roots [1], all of which are shown in the schematic drawing of fig. 8. 4) The investigation of the influence of the packing density on the engular dependence of the magnetic behaviour, required four alumite media with different packing densities. These samples had the same pore size of 440 A, the same morphology of the initial growth part of the iron needle and their aspect ratio was more than 14 [6].
The thickness and cell size of the alumite media were measured by SEM [7]. In order to observe the cross-section and morphology of the iron cylinder, an ultra-microtorae was used to make a 500 A, thick slice of the films [6]. These slices were first placed in a saturated solution of HgCI 2 to dissolve the A1 substrate. The etched samples were then put into a mixture of phospofic- and chromic-acid solutions to separate the iron cylinders from the outer covering of A120 3. The samples having varying aspect ratios were obtained by mechanical polishing with a buff and alumina fine particles or silica sol. The Debye X-ray and electron diffraction patterns indicated that the iron cylinder was in a single crystalline state with growth along the [110] direction. The magnetic properties were measured using a VSM and torque magnetometer [1,6-8]. The packing density is equal to the porosity of the alumite medium, which can be calculated by formula (2). Generally, the actual packing density will be lower than the calculated one, because some voids are present.
o
o
The most relevar~: properties obtained are summarized in table 1.
3. Results and discussion A lot of experimental data show that in the alumite media the magnetization preferably lies along the film normal. It was pointed out [2] that the basic magnetic unit of the Fe alumite consists of a single-domain cylinder because the pore size for most of the alumite samples used is less than the calculated Bloch wall of about 835 ~,. At the same time, the Debye X-ray diffraction pattern and electron microscopy show [8] that the iron cylinder is a single crystal and its growth lies along the [110] direction, which is perpendicular to the medium normal.
Table 1 The influence of the packing density on the magnetic behaviour No. A B C D
Cell size (A) 1170 960 745 640
Pore size (A) 440 440 440 440
Packing density 0.13 0.19 0.32 0.43
He± (kA/m) 68 65.2 63.7 63.7
Aspect ratio 14 14 14 13
OR ~.
Rs j.
5.3 4.1 1.93 1.7
0.32 0.19 0.14 0.11
C.-Z. Li, J.C Lodder / Magnetic behaviour of alumite media
The dependellcc of the pore size on the cell size of the iron cylinders with He± as parameter is shown in fig. 2, which was directly quoted from the same graph reported by refs. [1,6] and confirmed by our own measurements. It can be seen from this figure that the coercivity along the film normal H¢± is strongly controlled by the diameter of the iron cylinder (Do) and decreases with increasing Dp. However, careful consideration is required to draw the following conclusion: For alumite meoia, He ± only depends on the pore diameter Dp and is independent of the cell diameter D¢; hence it is independent of the packing density. Based on the straight lines in fig. 2 the dependence of H c ± on the packing density with respect to the pore size of the iron cylinder is shown by the solid lines in fig. 3. It is dearly seen from this figure that as the packing density increases, if the coercivity along the film normal is kept constant, the pore size of the iron cylinder should be slightly reduced instead of remaining constant. This means that H c . is a function of the packing density, even though the degree of dependence of H¢.L on the packing density is quite small in comparison with the degree of dependence of He± on the pore size. It
°(
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800
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56 400
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I
I
800
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I
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Fig. 2. The relation between the pore size (Dp) and cell size diameter (D c) for alumite having different coercivities (see also refs. [1,6]).
239
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6
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.
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I
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l
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0.2
0.3
0.4
0.5
0.6
0.7
Fig. 3. The dependence of He± on the packing density ( P ) with respect to the pore size.
is known that as the pore size decreases Hc~ increases. Using the data from fig. 2 the coercivity along the film normal vs. pore size is plotted in fig. 4. In order to reduce the influence of packing density on the results for H ci as far as possible, only the sample with the largest Dp was chosen to draw He± vs. Dp in fig. 4. This means that the chosen samples are those with the lowest packing densities. Based on the measured graph of fig. 4, the unknown He± for the other sample, with unmeasured Dp, can be easily calculated and found by interpolation. With the aid of the interpolation method, a series of calculated He ± vs. packing density curves are plotted by dashed lines in fig. 3 where the pore size of the iron cylindersoare kept constant (264, 397, 526, 668 and 781 A, respectively). On the other hand, for a sample having a pore size of 440 the Hc ± vs. packing density curve is a measured one instead of a calculated one. All the calculated and measured curves reveal that the coercivity along the film normal is related to the packing density. The He± decreases with increasing packing density if the samples have the
C-Z. Li, J. C I_odder / Magnetic behaviour of alumite media
240
120 110 100 90
Hc~ - kAlm
T
397 ~,
80
70 60
k~sa6
50
40 30
~ =" Op (A)
20
" 1 ~ 1A
I
I
I
I
I
I
I
I
100
200
300
400
500
600
700
800
Fig. 4. The measured dependence of H e . on the pore size
(D~).
same pore size. However, the degree of dependence of He j. on the packing density for alumite media with large pore size of the iron cylinder is less than that with small pore size. Contparing the influence of the packing density on h~± with that of the pore size on He±, the degree of the influence for the packing density is much less than that for the pore size. For example, for alurnite media with a pore size of 526 A, the He. only reduces by 10.77o even though the packing density increases from 0.14 to 0.69. This action is equivalent to the reduction of the coerci,Aty for the alumite media, in which the packing density is kept constant at 0.14, but the pore size only needs to be increased from 490 to 526 A,; an increment of only 36 A. Whatever the consequences, this phenomenon can be considered as an indication of the existence of magnetostatic interactions between the iron cylinders in the alunfi*e media. We have discovered [2,9] that the measured reduced eoercivity vs. the reduced diama~er curve fits the theoretical curling model very well, if the applied field is along the film normal and is large enough to saturate it. This result is shown in fig. 5.
It can be seen from this figure that the measured reduced coercivity vs. the reduced diameter curve is almost identical with the theoretical predictions expected from the curling model, even though these specimens are made under quite different preparation conditions from those in ref. [2]. Based on the above experimental curves, it can be concluded that the magnetization reversal mechanism for alumite media must bz dominated by curling. Since this is so, according to the physical concept and the formula (1) for curling, the coercivity should be independent of the packing density. One of the reasons why such seemingly contradictory phenomena exist simultaneously in alumite media, i.e. although He± is mainly determined by the pore size but is still slightly influenced by the packing density, is probably that the magnetization slightly deviates from the film normal in the actual specimens used. As pointed out [2], once the magnetization deviates from the film normal, the magnetic behaviour will no longer obey curling and the influence of the magnetostatic interactions will gradually manifest tbem~e!ves. The experimental results from M~ssbauer spectra reveal [8] that the magnetization deviates about 15 ° from the film normal or at least 6% of the total magnetization lies in the opposite direction in alumite media. It is generally agreed that the magnetostatic interac-
Hc/Ha
l
g rotation 250Ah"
0.1
°°°
O
T
0
I
1
~0
Fig. 5, The relation between the measured and calculated reduced coercix4ty vs. the reduced diameter of the Fe needle.
C-Z. Li, J. C Lodder / Magnetic behaviour of alumite media
tions between the iron needles is closely related to the local demagnetizing field, but the latter is affected by both the aspect ratio and shape of the needles. Therefore we will concentrate our attention on hwestigating how the coercivity is affected by the above mentioned factors. In order to remove the influence of the pore size and packing density on the coercivity, a series of specimens with the same pore.size of 440/~ and packing density of 0.19, but had-hag a different ratio of length to diameter, are chosen from ref. [7]. The dependence of both He± and Hcu on the ratio of length to diameter is plotted in fig. 6. It is clearly seen from this figure that He± increases with the aspect ratio of the iron cylinders until the ratio reaches a certain value, beyond which He± remains constant. The Hcj. and HotI have almost constant values of 66.5 and 17.5 k A / m , respectively, when the aspect ratio is more than 20. In this case, the influence of the demagnetizing field on the coercivity can be neglected. However, as the aspect ratio decreases, He± and HclI will drastically decrease and increase, respectively. If this ratio is continuously reduced to less than about 2, the anisotropy of the alurnite media
80 -
Hc
(kA/m)
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-I
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o
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= 0.19o
Dp = 440 A
40 30
'° t 5
10
_t
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20
25
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Fig. 6. The dependence of the perpendicular and in-plane coercivity on the aspect ratio.
241
i[
100
Hc J.I Hc JL30
90 80 70 60 50 40 30 20
f
I I ! I !
t,
10 '~ ,~,spect ratio I I
Iv
i ,, 5
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I,
I
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20
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30
Fig. 7. The relation between the measured and calculated relative perpendicular coercivity vs. aspect ratio.
will even char, ge from perpendicular to longitudinal. Thus, it can be said that the characteristic of the coerc',vity will be strongly affected by the ratio of length to diameter of the iron cylinders if the ratio is less than 15. Obviously, the smaller the ratio, the stronger the local demagnetizing field encountered by the iron needles iD alumite will be. Therefore, o.,,e~ential condition to make alumJte media exhibit excellent perpendicular an~sotropy is that the ratio of length to diameter should be large enough (for example > 20). The measured and calculated dependence of the relative perpendicular coe
C-Z. Li, J. C. Lodder / Magnetic behaviour of alumite media
242
H c ±/Hc z 30 changes as this ratio varies. The value of H¢x/H¢x3o will be drastically affected by the aspect ratio when this is lower than 15, especial in the range of Hc±/Hc±3o < 5. However, the He±~ H~ ± 30 only changes a little, when this ratio is more than 20. Combining this argument with the measured reduced coercivity vs. reduced diameter curve, it is again confirmed that for alumite media having perpendicular anisotropy no matter how the pore size and the aspect ratio change, the coercivity is dominated by the curling model. However, one point should be noted that, as is shown in table 2 for the alumite media used, the calculated values of H~j. still fall far short of the measured ones when this ratio varies from 4 to 30. This rather large discrepancy between the measured and calculated values of H c ± has yet to be explained. The coercivity for alumite media is also affected by the shape of the iron cylinder. Electronmiciescope observations have shown [1] that generally t~.e initial growth part of the iron cylinder consists of a various shapes like a circular cone, as is shown in the schematic drawing of fig. 8, but the rest of the cylinders are perpendicular to the film normal. Naturally, the existence of the circular cone shape of the initial growth part is Rkely to cause the formation of free poles on the sides of the iron cylinders. Of course, the presence of free poles will result in magnetostatic interactions between the iron cylinders. In order to investigate the influence of the shape of the initial growth part (cone size)
Table 2 The calculated and measure,'t Hc± for different aspect ratios of the iron cylinder Aspect
Calculated
Measured
4 5 8 10 15 20 25 30
18.6 44.3 63.2 87.2 99.2 103.8 106.4 107.7
40.5 44 53.5 58 64 66 66.5 67
10
HcJL I H c ,
3~ @
'
1
+oo A
I 0
5
A
A
I
I
I
I
10
15
20
25
"~,-A s p e c t ,i,
ratio ,
30
Fig. 8. The dependence of Hc. t / H c l I on the aspect ratio for various dimensions of the initial growth part of the Fe needles.
on the magnetic behaviour, three kinds of alumite media, taken from ref. [1] and having the same pore size of 440 ,~, and a packing density of 0.13 were examined" Samp,le ¢t I has a cone with a lower diameter of 800 A and a height of 1100 ]k. Sample # 2, 800 and 400 ,~,, respectively. Finally, for sample # 3 the initial part of the cylinder was grown with Cu consequently in this sample there will be no influence from the initial growth part of the Fe needle. It was reported [1] that no matter how the aspect ratio changes, H c.L will have almost equal values for the 3 kinds of spechnens, provided they have the same aspect ratios. However, the H~,, values of the above-mentioned samples are closely related to the shape of the initial growth of the iron cylinder. Experimental data reveal that no matter how the aspect ratio changes, for sample # 1 having the largest roots of 1100 A, He:i is the largest; for sample # 2 having a root-length of 400 A, H~H is intermediate and for specimen :~3 without any initial growth, He.I is the smallest.
C.-Z. Li, J. C. Lodder / Magnetic behaviour of alumite media
As long as the samples compared have the same aspect ratio, then the longer the root, the larger the HclI value will be. This fact suggests that the value of He ± for alumite media is not influenced by the initial growth, but that the in-plane coercivity will be strongly affected by it if the applied field makes an angle with the film normal. This is due to the appearance of the initial growth part and it strengthens the magnetostatic interactions between the iron cylinders. The magnetostatic interactions originate from the presence of the free poles on the side of the cylinder if the applied field is not parallel to the sample normal. It may be reasonable to assume that the presence of initial growth of the cylinder is likely to induce the magnetization to deviate from the normal direction, which must lead to an increase of the in-plane component of the magnetization. Therefore, the values of H~± and H¢II vs. the shape of the initial growth curves again confirm that the magnetization reversal mechanism is dominated by curling if the applied field ties in the direction of the film normal. However, the magnetic behaviour will gradually diverge from nucleation by curling, and the influence of the magnetostatic interactions on the coercivity will also strengthen, as the deviation of the applied field from the film normal i~,~creases. In fig. 8 Hcl/H~t i vs. the aspect ratio of the initial growth part for the above mentioned 3 samples are plotted. It can be seen from this figure that no matter how this ratio changes, the shorter the initial growth of the cylinder, the higher the values of H~./H¢It. Generally speaking, when the aspect ratio is more than 15, the values of H~./HcI I for 3 kinds of alumite media gradually tend towards their respective saturation values. It can also be seen that the effect of the aspect ratio on H~±/H~I I is quite remarkable, if this ratio is less than 15. For samples witheut any initial growth (~: 3), H~ ~_/H~II always remains larger than 1, although for all 3 samples H~j_/H~I I decreases monotonically with decreasing aspect ratio. However, for specimens ~ ! and # 2 with initial growth, there are some critical ratios, above which the value of H¢./H¢I ! remains > 1, but below this cfitica! ratio, the value of H, ./H~I I will be changed from > 1 to < 1. It was discovered that the larger
243
the initial growth of cylinder the higher the critical transition point of this ratio was. This fact suggests that at this time the orientation of the magnetization will be changed from perpendicular anisotropy ( H c . / H ¢ I t > 1) to longitudinal ( < 1). This means that the presence of the initial growth of the cylinder will result in the deterioration of perpendicular anisotropy for alumite media, because the ratio Hc±/H¢I I can be considered as a figure of merit for the use of the media for perpendicular recording. In general the larger the value of H¢./H¢I t the stronger the perpendicular anisotropy. One of the consequences of the influence of the shape of initial growth part of the cylinder on the magnetic behaviour for alumite is that the media can exhibit both perpendicular and longitudinal anisotropy provided the shape of the root and the aspect ratio of the needle can be appropriately controlled. Based on the above discussion, it is known that for alurnite media the coercivity is affected by 4 factors; the pore size, the aspect ratio, the morphology of she initial growth and ~he packing density. The determinative factor with respect to their influence on Hc ± is the pore size. In order to investigate the correlation between the angular dependence of the magnetic behaviour and packing density for alumite media, four samples were chosen, all havhag the same pore size of 440 A, the same morphology of initial growth and almost the same apect ratio. As shown in table 1, with increasing packing density, the coercivity H e . , squareness ratio Rs ± along the film normal and relative orientation ratio OR ± decreases. The squareness ratio R s . reflects the ratio of the remanence to the saturation magnetization in the direction of the sample normal. The OR± is the relative ratio of the squareness ratio value in the in-plane and normal direction of the sample. Th~ nnoldar clopondonee e,f the ncwmaliTed Rs with packing density P for 4 alumite media are shown in fig. 9 (note: all the squareness ratios are normalized by the value of Rs i along the film normal for the specimen with a packing density of 0.13). It can be clearly seen from this figure that no matter how the angle changes, the normalized Rs drastically decreases with increasing packing den-
244
C-Z. Li, J.C. Lodder / Magnetic behaviour of alumite mcdia
100 90 80
70 60 50 40 30 20 10
10
20
30
40
50
60
70
80
90
Fig. 9. The dependence of relative squareness ratio on the angle of the applied field with respect to the packing density.
constant if the angle is less than 40 o, but rapidly decreases with an increasing angle of more than 40 o. On the contrary, as the packing density increases, the relative coercivity decreases rather steeply with inceasing angle when it is less than 60 o but slightly decreases with increasing angle if
sity, except for an angle > 80 °. Similarly, the angular dependences of Hc(O)/Hc± with respect to the packing density for 4 samples are plotted in fig. 10. The relative coercivity Hc(O)/H,: ± sample # A, which has the lowest packing density, is almost
100 90
eo
,oi._ I
IHc-
-,\
50
~ p = 0.13
40
v p = 0.19 i . . . .~ . . A p = u.~z
30 20
~,.,.~_~~
"'~
rn=_.=sured ....
v p = 0.43
calculated t . . . . . .....
0.75 COS 0 + 0.25 Sin = 0 COS 0 P(O) + 0.39 (1-0.8 COS 2 e) "1/= . (1 -
P (8))
lO --
- ~
~
I
I
I
i
10
20
30
40
50
60
.....1 ........ 70
="0
I 80
L ~ 90
Fig. 10. The measured and calculated angular dependence of the coercivity with respect to the packin/5 density for alurmte.
C.-Z Li, J.C. Lodder / Magnetic behaviour of alumite media
0
is larger than 60 ° , i.e. the variation of H,:(O)/Hc± for alumite media with low and high packing density is just the opposite. In summary, the magnetic behaviour (relative coercivity, squareness ratio and orientation ratio) for alumite media will be greatly changed with varying packing density when the applied field is deviated from the film normal. It was pointed out [2,11] that the presence of magnetic poles on the side of the iron cylinders in alumite media (if the applied field deviates from the film normal) must result in mutually magnetic attraction between the cylinders along the film plane. With increasing packing density, this attraction will strengthen. Of course, it will strongly change the characteristic of the demagnetizing field. Therefore, the magnetization reversal must be closely related to the demagnetizing field. If the angular dependence of the magnetizing field is assumed to obey the sin20 law, the relative coercivity for alumite media can be calculated by [2,91:
Hc(O)/Hc±=acosO+(1-a)sinZO.
(3)
The calculated curve for a = 0.75 is shown by the dashed line in fig. 10. It can be clearly seen that the measured Hc(O)/tf,: ~ vs. angle curve for sample A with a pa,:!,ing density of 0.13 is in fairly good agreement ,.vith the calculated one. This means that the magnetization reversal is controlled by both a cos type of incoherent rotation and the demagnetizing field for alumite media with low packing density. However, the calculation procedure reveals that for other alumite media with high pacldng density (form example, p > 0.4) the calculated curve does not fit as well. Based on the morphology of alumite media with high packing density, it is perhaps reasonable to imagine that with increasing packing density, the distance IOCtW~Cll
trig
i r o n
),31_g~Ul~} __al . . . . ~ ; I t:l.lt l LugCo.~llg . . . .
S. O
g l1U. b.C . . t l!l .i .l_t ,
in some areas the initial growth parts of the cylinders contact each other. If this is true, alumite media with high packin~ density must exhibit a similar behaviour to a fully segregated CoCr film. It was found [11] that for a fully segregated CoCr film the magnetization reversaI can be considered as the superposition of a
245
cos-type of incoherent rotation with perpendicular anisotropy and in-plane domain-wall motion, which mainly results from the initial layer. The angular dependence of the coercivity can be calculated by [111:
Hc(O)/Hc±=COS(O)P(O ) + (Hcll/Hcx) x (a
- e(o)), (4)
where a is an adjustable parameter, in which P(O) represents the measured angular proportional function of incoherent rotation with perpendicular orientation of the magnetization to the in-plane domain-wall motion, which can be obtained from the measured dependence of the distribution of the hysteresis loss AWh on the applied field as a parameter of the angle [11]. As is shown in fig. 10, it is very interesting to find that the calculated H¢(O)/Hc. vs. angle curve ( a = 0 . 8 and Hc,/Hc±=0.39) is almost identical to the measured one for alumite media with a packing density of 0.43. The above-mentioned assumption can also be supported as following experimental data and theoretical calculations [1,12] for an alumite medium with a thickness of 1 p.m and pore size of 440 A,. The magnetic anisotropy constant is positive when the packing de,~ity is below 0.33, but negative if it i~ more than 0.33. When the packing density is equal to about 0.32, the magnetic anisotropy will become zero.
4. Conclusions
With a view to obtaining a better understanding of the correlation between the magnetization reversal and the morphology of alumite media, the m ...... of .1L.~ " .~.:.. "I I- - II: ~1 :L. I Kll, ~1lt .: _. i,' u cm.= ut~ pore ~i,_~, a~pect ,a.,.,. growth part of the Fe needles and packing density on the magnetic behaviour have been reviewed. Based on these discussions, the results can be summarized as follows: 1) If the applied field lies along the film normal and is large enough to saturate the sample, the measured reduced coercivity vs. reduced diam-
246
C.-Z. Li, J.C Lodder / Magnetic behaoiour of alumite media
eter curve fits the theoretical curling model very well. No matter how the aspect ratio changes, the variation of the measured He. with aspect ratio basically follows the calculated one predicted by the curling model. It seems that He± is not affected by the initial growth part of the iron cylinder. 2) The characteristic of H c j. for alumite media is mainly determined by the diameter .ff the iron cylinders, but He± still decreases slig:ltly with increasing packing density for the actual alumite media. 3) The alumite media can exhibit both perpendicular and longitudinal anisotropy by appropriate control of the aspect ratio and the morphology of the initial growth part of the iron cylinders. One of the essential conditions to achieve an excellent perpendicular anisotropy for alumite media is that the ratio of length to diameter should be about 20. Experimental data show that the coercivity along the film plane is closely related to the shape of the initial growth part of the Fe needle. 4) If the applied field deviates from the film normal, the magnetic behaviour (the coercivity, squareness ratio, orientation ratio and hysteresis loss, etc.) are greatly affected by the packing density. For alumite media with a low packing density, the magnetization rew.~rsal is controlled by a cos-type of incoherent rotation and demagnetization field. However, for the alumite media with a high packing density, the magnetization reversal can be considered as the superposition of a costype of incoherent rotation with perpendicular anisotropy and in-plane domain-wall motion.
This means that the angular dependence of the relative coercivity ( H c ( O ) / H c j_) for alumite media starts exhibiting a more or less typical behaviour for a fully segregated CoCr film at high packing densities.
Acknowledgements The authors would like to thank Mr. Eelco Sterringa, who is researching this subject in more detail for his MSc thesis, for his contributions to this paper. We also like to thank Professor Dr. Th.J.A. Popma for his continued support.
References [1] K.I. Arai, Text of 56th Annual Meeting o! Magn. Soc. Japan (1988) p. 25 (in Japanese). [2] J.C. Lodder and Li Cheng-Zhang, IEEE Trans. Magn. MAG-25 (1989) 4171. [3] A. Aharony, Phys. Stat. Sol. 16 (1966) 3. [4] A. Aharony, IEEE Trans. Magn. MAG-22 (1986) 147. [5] G.T.A. Huysmans, J.C. Lodder and J. Wakui, J. Appl. Phys. 64 (1988) 2016. [6] N. Tsuya, T. Tokushima, M. Shiraki, Y. Wakui, S. Iwasaki and Y. Nakamura, IEEE Trans. Magn. MAG-23 (1987) 2242. [7] K.I. Arai, Y. Wakui, K. Ohmou and T. Tokushima, IEEE Trans. Magn. MAG-23 (1987) 2245. [8] T. Tsuya, T. Tokushima, M. ShirarJ, Y. Wakui, Y. Umehara, H. Nakamura, Y. Katsumata and Y. Saitom, J. Magn. Soc. Japan 11 (1987) 55 (in Japanese). [9] J.C. Lodder and Li Cheng-Zhang, J. Magn. Soc. of Japan 13 Suppl. $1. (1989) 659. [10] J.A. Osborn, Phys. Rev. 67 (1945) 351. [11] J.C. Lodder and Li Cheng-ZbaDg, J. Magn. Magn. Mat. 74 (1988) 74. [12] M. Masuda, S. Shiomi and M. Shiraki, Japan. J. Appl. Phys. 26 (1987) 1680.