- Email: [email protected]
Charged walls in implanted garnets
328
Journal of Magnetism and Magnetic Materials 24 (1981) 328-338 North-Holland Publishing Company
CHARGED WALLS IN IMPLANTED GARNETS I.B. PUCHALSKA and J.P. JAKUBOVICS * Laboratoire de Magn~tisme et d'Optique des Solides, CNRS, 1, place Aristide Briand, 92190 Meudon Bellevue, France Received in original form 22 June 1981; in revised form 10 July 1981 The domain structure around non-implanted discs in implanted garnets has been investigated as a function of the strength of in-plane fields, H//, applied in various directions. When H//is in a hard direction, the observed domain structures can be explained by the theory of Shir and Lin [ 14]. When H//is in an easy direction or at 30° to it, charged walls are still present for values of HI/for which the theory predicts saturation of the implanted layer. This result is attributed to demagnetizing effects. The dependence of the length of charged walls on the diameter of non-implanted discs and on H//has been studied.
1. Introduction Implanted garnets have been at the centre of interest in many laboratories because of their promising future in a new technology of bubble devices. This technology was proposed by Wolfe, North and Lai in 1973 [1.]. Implantation was initially introduced to suppress hard bubbles in garnets, but it was later discovered that the implanted layer may be used to control bubble displacement around non-implanted elements [2]. The mechanism of bubble movement around nonimplanted contiguous discs was first explained by Almasi et al. [3] who proposed that charged walls were responsible for the motion of bubbles in a rotating field. Since then, many authors have investigated charged walls in implanted layers, their origin and mechanism of movement in in-plane fields [ 4 - 1 0 ] . Kleman and Puchalska [ 11 ] have proposed models of spin distribution in positively and negatively charged 120 ° walls as well as in saw-tooth (zig-zag) walls. It has been shown that in negative walls the spin configuration is similar to the classical crossBloch line; in positive walls, the spin configuration is radial. * On leave of absence from Department of Metallurgy and Science of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, England. 0304-8853/81/0000-0000/$02.75 © 1981 North-Holland
The purpose of this paper is to present a detailed study of the shape, position and length of charged walls in in-plane fields, H//, of different values applied in various directions.
2. Experimental procedure The sample investigated was a SmYLuCaGe garnet fabricated by LETI-Grenoble. The characteristics of this sample were as follows: thickness = 1.83/am, thickness of implanted layer = 0.5 gm, saturation magnetic induction 47rMs = 383 G, collapse field = 181 Oe. In a specimen with its surface exactly parallel to (111), the preferred directions of magnetization in the implanted layer are [113c], [121], [211], [1 lx], [ i x ] ] and [ x ] ] ] , where 1 < x < 2. The value o f x depends on the uniaxial, induced and cubic anisotropy energies and the demagnetizing energy [5]. When a bias field H i is applied, the in-plane component of the magnetization has the preferred directions [112], [121] and [?.11] if H± is upwards (i.e. pointing from the substrate towards the implanted layer) and [ 112], [ ] 2 i ] and [211] if H± is downwards. The orientation of the specimen was determined by X-ray diffraction. The [111] axis was found to be tilted at 0.57 ° with its projection lying between [ ] 2 ] ] and [ 2 ] ] ] , as shown in fig. 1. In a slightly misoriented specimen, the preferred
LB. Puchalska,J.P. Jakubovics/ Chargedwalls in implantedgarnets
[~2[]
30~0' ,,~41 °
0°
240* ~
[i12]
[211]
1 2 0 " 180°
Fig. 1. Schematic representation of bubble equilibrium positions for the specimen used. Bubbles move from positions marked by open circles to those marked by full circles when the in-plane field is reduced to zero. The specimen orientation is also indicated. The bold arrow marks the projection of [111].
directions of the in-plane component may deviate from the above crystallographic directions. The preferred directions may, however, be determined by the bubble-disc method [12], based on the principle that the equilibrium positions of the bubble are towards the in-plane hard directions if H± is upwards and towards the easy directions if H± is downwards, so that the equilibrium positions relative to the specimen are unchanged if the sense of H± is reversed [I 3]. The results of the easy axis determination are shown in fig. 1. In this work the Faraday effect was used to observe bubbles and the Bitter technique to investigate charged walls. To study charged walls in HI~ >i O, H//was applied in eight directions: in three easy directions (near [121], [211] and [112]), in three hard directions (near [121], [211] and [112,])and in two directions at 30 ° to easy directions (near [10]] and []01]). In each direction, H//was increased to 60 Oe and reduced to 0 before starting the observations. The field was then gradually increased and the domain structure was recorded in fields of 0, 5.5, 11, 14.5, 16, 22 and 40 Oe. The maximum value H//= 40 Oe was chosen as a conventional value of in-plane field for bubble movement. In all experiments, a bias field H i ~ 200 Oe was applied downwards.
329
3. Results and discussion Figs. 2, 3 and 4 show Bitter patterns of charged walls inH/~ > 0 applied at 180 ° ([121] - hard doirection), at 0 ([12]] - easy direction) and at 120 ([211] - easy direction), respectively. The arrangement of charged walls around a disc labelled y in fig. 2a in all cases studied is depicted in fig. 5. (Note: black charged walls are henceforth referred to as BW and white charged walls as WW.)
3.1. Shape and position of the walls In several previous publications showing domain configurations around non-implanted discs, each charged wall is seen to be the boundary of a small domain (called a propeller domain e.g. in ref. [5]) on one side; the other side of the domain is delimited by an uncharged wall (see e.g. fig. 4 of ref. [9]). In the present study, the uncharged walls are not shown up by the Bitter technique. The reason for this may be that in other cases, the uncharged walls were N6el walls whereas in this case they may be Bloch walls which are known to have weaker stray fields and therefore attract fewer colloid particles. The presence of uncharged walls must however be assumed. The proximity of discs to each other results in the domains around neighbouring discs interacting in some cases, especially in small 1-1//.Fig. 2 shows that when H//is applied at 180 °, the charged walls change their position several times as H// increases. Major rearrangements of the domain structure must therefore have taken place when H//was originally reduced from 60 Oe to 0. The charged walls around both discs x and y undergo "whip" motion [5] from 0 to 11 Oe and from 5.5 to 14 Oe, respectively. Disc z has a more complicated structure around it which only disappears in H//= 22 Oe. In H//>t 22 Oe, the arrangement of charged walls around all discs is similar, the charged walls having undergone "flip" motion [5] in some cases (e.g. discs x and y from 16.5 to 22 Oe). "Whip" and "flip" of charged walls in rotating in-plane fields of constant amplitude have been interpreted before [9]. The present observations show that both "whip" and "flip" can also occur when H//of increasing magnitude is applied in a fixed direction (fig. 6). "Whip" is a domain wall motion process enabling the size of domains with favourably oriented magnetiza-
330
LB. Puchalska, J.P. Jakubovics / Charged walls in implanted garnets
Fig. 2. Bitter patterns inH//applied at 180 °. Values of H~~ are (a) 0, (b) 5 . 5 0 e , (c) 11 Oe, (d) 14.0, (e) 1 6 . 5 0 e , (f) 22 Oe. The diameter of disc x is 20 t~m.
LB. Puchalska, J.P. Jakubovics / Charged walls in implanted garnets
f
Fig. 3. Bitter patterns inH//applied at 0 °. Values of H~~ are (a) 0, (b) 5 . 5 0 e , (c) 11 Oe, (d) 1 6 . 5 0 e , (e) 22 Oe, (f) 40 Oe.
331
332
LB. Puchalska, J.P. Jakubovics / Charged walls in implanted garnets
Fig. 4. Bitter patterns in H//applied at 120 °. Values of H//are (a) 0, (b) 5 . 5 0 e , (c) 11 Oe, (d) 14 Oe, (e) 22 Oe, (f) 40 Oe
LB. Puehalska, J.P. Jakubovics / Charged walls in implanted garnets
T
0* ....
~
9o~
333
300*
_ __
I Hu
.
I ill
a
i r
14 or 165 22
)
40
)
b
Fig. 7. Interpretation of the behaviour of charged walls around an isolated disc in H//applied at 0 ° . (a) H//= 0, (b) H ~ 40 Oe. \
4
Fig. 5. Schematic diagrams of the arrangement of charged wails in various values of H//applied in various directions. BWs are shown as solid lines and WWs as dashed lines.
tions to expand and others to contract. It therefore occurs in low fields (fig. 6a to c). "Flip" is mostly a magnetization rotation process in which the magnetization direction inside the propeller domains rotates, causing previously uncharged walls to become charged and vice versa. This process therefore takes place in higher fields (fig. 6c to d). During "whip" motion, the charged portion of walls becomes extended. In order to reduce the magnetostatic energy, the walls take up a zig-zag shape just before and just after the "whip" (e.g. disc x in fig. 2b). In HI/>~ 22 Oe, the black walls around the discs are in the opposite direction to the applied field. (Note that as H i is downward, BWs, which act as bubble carriers, are negatively charged.) Fig. 3 shows the arrangement of charged walls in HI~ applied at 0 °. In this case, no major rearrange-
I
ment of walls occurs as H// increases. In H//--- 0, BWs are in the [211] positions, - 6 0 ° from being opposite the H// direction. As H// increases, this angle changes to ~ - 4 5 ° in H//= 40 Oe, as explained in fig. 7. The arrangement of the walls in H//applied at 120 ° is shown in fig. 4. In H//= 0, BWs are in the [112] direction. Some of the walls whip in H//= 11 Oe (see disc x), others change to zig-zag shape (see e.g. disc y) and whip in 14 Oe. In H//= 40 Oe the walls behave differently at different discs. The BW is in a position either ~+45 ° (disc x) or ~ - 4 5 ° (disc w in fig. 2a) from being opposite the H// direction, as explained in fig. 8. The observed phenomena may be interpreted using the critical curve for three fold symmetry proposed by Shir and Lin [14]. The critical curve, an asteroid with three vertices along the hard magnetization directions, represents the neutral stability of magnetization. For a given field represented by a vector drawn from the centre of the asteroid, magnetization directions corresponding to stationary energy states are parallel to lines that pass through the tip of the field
H ii
15' o
b
c
5
15"
d
Fig. 6. Interpretation of the behaviour of charged walls around an isolated disc in H/I applied at 180 ° . H // increases from a to d.
o
b
Fig. 8. Interpretation of the domain structure around (a) disc x, (b) disc w, in fig. 4f.
LB. Puchalska,J.P.JakubovicsI Chargedwallsin implantedgarnets
334 0°
[211]
/
\
300~/
[1117]
{
260'
270*(
,,
/
\\ \
~
i/I \~4~,,
"\
"\
90"
lirFM~
/I
i"
180'
E11] Fig. 9. Graphical determination of magnetization directions for H//= 11 Oe, 22 Oe and 40 Oe (thick arrows) applied in an easy direction (0°) and a hard direction (180°). M 3 is always drawn from the vertex of the asteroid at 180° to the tip of the field vector. (For clarity, M 3 is only shown for the case H//= 40 Oe in the hard direction).
vector and are tangents to the asteroid. The magnetization direction is unstable if it is pointing away from the tip of the field vector. If the magnetization direc-
0°
,/
\
2211]~300011Z
\
/~112]
", 60 °
180"
[11] Fig. 10. Graphical determination of magnetization directions for 1t//= 11, 22 and 40 Oe applied at 90° and 270° (thick arrows).
tion is pointing towards the tip of the field vector, it is stable if it makes an acute angle with it and metastable otherwise [5]. Fig. 9 shows the asteroid and magnetization distributions for HI/= 11,22 and 40 Oe applied in easy and hard directions. The corresponding diagram for HI~ applied at 90 ° and 270 ° is shown in fig. 10. The in-plane anisotropy field, HK1 (radius of the circumscribed circle of the asteroid) is given by HK1 ~ 5H~/, where H~/is the smallest value of in-plane field necessary to move a bubble around a disc [ 13 ]. This enables HI/and HK1 to be determined. It was found that HK1 ~ 110 Oe for the specimen described here. The magnetization directions appear to be given correctly up to H//= HK1 when H//is in a hard direction (compare figs. 6 and 9). Wheh 11//is applied at 180 °, M1 M2 are the stable magnetizations. M3 becomes metastable with energy increasing as H// increases. The area magnetized parallel to M3 decreases by whip motion of walls (fig. 6c) and then M3 rotates to M2 accompanied by wall flip (fig. 6d). However, when H//is in an easy direction, fig. 9 predicts that only M3 is stable;Ml and M2 are metastable up to H//= ½HK1. For H//> -~HKI, M3 is the only stable magnetization direction so that the specimen should be saturated and no charged walls should be present. Similarly, fig. 10 shows that there is only one stable magnetization direction for H//> 0.393HK1 (see eq. (13) of ref. [ 14]). Nevertheless, charged walls are still present when H//exceeds these values. Hence the theory of Shir and Lin [14] does not explain the observed domain structures when 11//has a large value in an easy direction or at 30 ° to it. The discrepancy between the predicted and observed domain structure may be due to the presence of demagnetizing fields at the edge of the nonimplanted disc. If the implanted layer were saturated, the edge of the disc would carry a high density of charge, leading to a large magnetostatic energy. The propeller domains form in order to decrease this energy. Even when H//is large enough to saturate a homogeneous implanted layer according to the theory, it may not be large enough to saturate the regions close to the edges of non-implanted discs. Fig. 11 shows a diagram of the positions of the BWs (denoted by crosses) and bubble positions (spots) versus the direction of H~/. The positions of the BWs were measured in the static way described
LB. Puchalska, J.P. Jakubovics / Charged wallsin implanted garnets
335
above. The positions o f bubbles were observed in
O (degrees)
H//= 40 Oe.
18C
Charged walls and bubbles are found to be at the same positions, even though their methods o f observation are different (Bitter pattern and Faraday effect, respectively). In nine cases, including the hard directions, 60 °, 180 ° and 300°), the bubbles are in the antiparallel position to H//. In other cases the bubbles and charged walls are at some angle to the antiparallel position. The dispersion o f bubble positions with respect to H//is not very regular, especially in the 90 ° , 105 ° , 120 ° and 135 ° directions, which may be due to the tilting o f the [111] axis (see fig. 1). Some l o c a l a n i s o t r o p y due to the non-implanted disc [6] may be also a reason for this asymmetry.
120
60 J~ o
0
300
240
180
3.2. Length of charged walls in the remanent state
o
,
'
40
'
1½0 '
1~0 ' 2~0 '
3b0 ' 3~0~
(~ H ( d e g r e e s )
Fig. 10. Variation of 0, the equilibrium position of bubbles (circles) and BWs (crosses) with CH, the angle between H// and [i2]1.
Fig. 12 shows a Bitter pattern of the charged walls attached to discs o f different diameters in H//= O. The length, L, of walls attached to three discs with different diameters, D (disc x, D = 20/~m, disc v, D = 15/am and disc u , D = 9/zm, see fig. 2a) was measured. The measurements are set out in table 1. In each case
Fig. 12. Bitter pattern of charged walls in H//= 0 after application of H~~= 60 Oe at 270 °.
LB. Puchalska,J.P. Jakubovics/ Chargedwallsin implantedgarnets
336
Table 1 Length of the BWs and WWs,L, and L/D, as a function of D, with H//applied in different directions D = 20 ttm
D = 15 t~m
D = 9 ttm
L Ozm)
LID
L (um)
LID
L O~m)
LID
0°
BW WW
18.5 20.0
0.93 1.00
15.4 20.0
1.03 1.33
7.7 9.2
0.86 1.02
60°
BW WW
18.6 10.8
0.93 0.54
9.2 7.7
0.61 0.51
9.2 9.2
1.02 1.02
90°
BW WW
20.0 16.9
1.00 0.84
10.8 10,0
0.72 0.67
7.7 7.7
0.86 0.86
120°
BW WW
18.5 20.0
0.93 1.00
10.0 10.8
0.67 0.72
6.2 6.2
0.69 0.69
180°
BW WW
20.0 21.5
1.00 1.08
15.4 17.0
1.03 1.13
9.2 9.2
1.03 1.03
240°
BW WW
14.6 20.0
0.73 1.00
10.0 27.7
0.67 1.85
6.2 6.2
0.69 0.69
270°
BW WW
20.0 20.0
1.00 1.00
16.9 12.3
1.13 0.82
13.8 10.8
1.53, 1.20
300°
BW WW
15.4 15.4
0.77 0.77
10.0 12.3
0.67 0.82
6.2 7.7
0.69 ,0.86
Mean
BW WW BW+WW
18.2 +-0.7 18.1 +- 1.3 18.1+-0.7
0.92 -+0.04 0.90 +-0.06 0.91+-0.04
12.2 +- 1.1 0.82 +-0.07 14.7 +-2.3 0.98 +-0.15 13.5_+1.3 0.90+-0.09
8.3 -+0.9 8.3 +-0.6 8.3_+0.5
0.92 +-0.10 0.92 +-0.06 0.92_+0.06
H//= 60 Oe was applied in the direction shown in the first column and then reduced to zero. The length of the BWs and WWs depends strongly on D. The correlation between L and D probably arises from the need to minimise the magnetostatic energy at the edge of the disc. When two propeller domains are present adjacent to the disc, the magnetic pole density is minimised if the charge and uncharged walls subtend an angle of 90 ° along the edge of the disc. If the shape of the propeller domains around discs of different diameter D is the same, then the size of the propeller domains should be proportional to D, so that LID should be independent of D. The average values of LID for different D are seen to be in good agreement. The large deviation occurring in a few individual cases is probably due to metastable domain configurations. The overall average value is LID = 0.91 -+ 0.04.
3.3. Length of charged walls in HI~ --/=0 The lengths of BWs attached to disc x (D = 20/am) in different values of H~~ applied in eight different
directions are shown in fig. 13. In most cases the initial length, Lo, is equal to or slightly smaller than D. In two cases, when Itl/was reduced to 0 from the [ ] ] 2 ] direction (240 °) and the [).11] direction (300°), Lo is significantly smaller than D. In all cases L decreases with increasing H/l, but not always uniformly. In some directions L becomes greater than Lo in intermediate values of HI~, see table 2. This increase is due to "whip" motion of the wall. But finally in HI~ = 40 Oe, which is a normal working field for bubble movement around circuits, the walls become small and 0.19
< L4o/Lo < 0.43.
The behaviour in values of It// approaching 40 Oe may be understood qualitatively with reference to figs. 6 and 7. When H//is applied in a hard direction, the propeller domains and surrounding domain are magnetized in equally favourable directions (fig. 6d). As HI~ increases, the magnetization of the domains rotates towards H//. The charge density on the charged wall decreases and the wall therefore attracts
LB. Puchalska, J.P. Jakubovics / Charged walls in implanted garnets
and their magnetization rotates towards H//, decreasing the charge density of the charged wall. Again the length of wall visible by ferrofluid decreases. The differences in behaviour can be seen by comparing the charged walls near disc z in figs. 2f and 3f. In the latter, the charged walls appear to be pressed against the edge of the disc.
L(~m) ./\
3O ./
:\
/'
".
\
/" ..
20
~_~
--
HII a t
•
'\
%
0 °
x
,,
60'
o
,,
90 °
.
337
o
\ . +"~.. Z > . . 10
4. Conclusions 0 30 ~
,, . ,
x
0 +
20
"-~©/" +
The position, shape and length of charged walls in a garnet specimen with an implanted layer have been investigated. The investigations were made in a bias field, H i , and in different values of in-plane field, H//>1 0 applied in eight different directions. The following conclusions may be drawn.
H, G~ 180"
•
240 * 270" 300*
~. "\
x+"..-
-x.
~'\
""...~"'. ,, .. \ b •, . . . . ~ , . . - -~,, ~. ~......
10
6
'
1'0
2'o
3'0
'
~o:
Hil
(Oe)
Fig. 13. Length of BWs, L, as a function of H~~applied in different directions. fewer colloid #articles, especially further away from the non-implanted disc. When H//is applied in an easy direction, the propeller domains are magnetized in a less favourable direction than the surrounding domain (fig. 7b). The size of the propeller domains decreases
1. "Whip" and "flip" motion, similar to that observed in rotating in-plane fields, have been observed in some cases when HI~ of increasing magnitude was applied in a fixed direction. Generally, "whip" occurs before "flip" as H// increases. 2. In the present specimen, only charged walls were made visible by the Bitter technique. Uncharged walls must also be present to complete the boundaries of propeller domains. The invisibility of uncharged wails has been attributed to the assumption that they are of the Bloch type in the present specimen. The dependence o f the configuration of charged walls on H//has been interpreted in terms of the behaviour of the propeller domains.
Table 2 Length of BWs, L, as a function of H~~applied in different directions
H// (Oe)
~at/ / 0o
tt// at 60 o
~,// at 90o
n// at 120o
~/// at 180o
n//
L (#m)
L (#m)
L O~m) L O~m)
L (#m)
L ~m)
at 240
o
H// at 270°
H// at 3000
L O~m)
L (um)
0
18.5
20.0
20.0
18.5
20.0
14.6
20.0
15.4
5.5
20.0
20.0
18.5
20.0
30.8
13.8
ll.5
II.0
14.0
18.5
18.5
30.8
29.0
11.5
20.0 17.7
16.5
12.0
18.5
18.5
20.8
20.0
10.8
22.0
II.0
14.6
I0.0
13.6
6.2
40.0
8.0
8.0
7.0
7.0
L4o/Lo
0.43
0.40
0.35
0.37
10.8
5.4
20.0 12.3
5.4
3.8
4.6
7.7
4.6
0.19
0.31
0.38
0.29
8.5
338
LB. Puchalska, J.P. Jakubovics / Charged walls in implanted garnets
3. The domain structures observed in small H//in all directions, and in all 11//in hard directions can be interpreted by the graphical method using the critical curve (three-vertex asteroid). However, this m e t h o d is inadequate for interpreting the results when a large H//is applied in easy directions or at 30 ° to them ( H / / > ~ H K for easy directions, H,, > 0.393HK1 at 30 ). The presence o f charged walls in these cases may be due to demagnetizing effects. These effects are being studied theoretically. 4. The length of charged walls in H//= 0 is determined by the diameter of the non-implanted disc, because o f the c o m m o n shape of propeller domains. The dependence o f the length o f charged walls on 11// can also be interpreted in terms of the behaviour of propeller domains. 5. As charged walls were present even in the highest H//applied in the present experiments, it is o f interest to investigate domain structures in higher
values of rill.
Acknowledgements We are grateful to Dr. H. Niedoba for carrying out the X-ray determination o f the crystal orientation,
J.P.J. acknowledges C.N.R.S. for a Research Fellowship.
References [1] R. Wolfe, J.C. North and Y.P. Lai, Appl. Phys. Lett. 18 (1973) 581. [2] R. Wolfe, J.C. North, W.A. Johnson, R.R. Spiwak, L.J. Varnerin and R.F. Fisher, AIP Conf. Proc. 10 (1973) 339. [3] G.S. Almasi, E.A. Giess, R.J. Hendel, G.E. Keefe, Y.S. Lin and M. Slusarczuk, AlP Conf. Proc. 24 (1975) 630. [4] I.B. Puchalska, H. Jouve and R.H. Wade, J. Appl. Phys. 48 (1977) 2069. [5] Y.S. Lin, D.B. Dove, S. Schwarzl and C.C. Shir, IEEE Trans. Magn. MAG-14 (1978) 494. [6] H. Jouve and I.B. Puchalska, IEEE Trans. Magn. MAG15 (1979) 1016. [7] H. Callen, J. Appl. Phys. 50 (1979) 1457. [8] C.C. Shir and Y.S. Lin, J. Appl. Phys. 50 (1979) 2270. [9] D.B. Dove and S. Schwarzl, J. Appl. Phys. 50 (1979) 5906. [10] A. Hubert, IEEE Trans. Magn. MAG-15 (1979) 1251. [11] M. Kleman and I.B. Puchalska, J. Magn. Magn. Mat. 15-18 (1980) 1473. [12] H. Niedoba and I.B. Puchalska, J. Appl. Phys. 52 (1981) 4726. [13] Y.S. Lin, G.S. Almasi, D.B. Dove, G.E. Keefe and C.C. Shir, J. Appl. Phys. 50 (1979) 2258. [14] C.C. Shir and Y.S. Lin, J. Appl. Phys. 50 (1979) 4246.
Journal of Magnetism and Magnetic Materials 24 (1981) 328-338 North-Holland Publishing Company
CHARGED WALLS IN IMPLANTED GARNETS I.B. PUCHALSKA and J.P. JAKUBOVICS * Laboratoire de Magn~tisme et d'Optique des Solides, CNRS, 1, place Aristide Briand, 92190 Meudon Bellevue, France Received in original form 22 June 1981; in revised form 10 July 1981 The domain structure around non-implanted discs in implanted garnets has been investigated as a function of the strength of in-plane fields, H//, applied in various directions. When H//is in a hard direction, the observed domain structures can be explained by the theory of Shir and Lin [ 14]. When H//is in an easy direction or at 30° to it, charged walls are still present for values of HI/for which the theory predicts saturation of the implanted layer. This result is attributed to demagnetizing effects. The dependence of the length of charged walls on the diameter of non-implanted discs and on H//has been studied.
1. Introduction Implanted garnets have been at the centre of interest in many laboratories because of their promising future in a new technology of bubble devices. This technology was proposed by Wolfe, North and Lai in 1973 [1.]. Implantation was initially introduced to suppress hard bubbles in garnets, but it was later discovered that the implanted layer may be used to control bubble displacement around non-implanted elements [2]. The mechanism of bubble movement around nonimplanted contiguous discs was first explained by Almasi et al. [3] who proposed that charged walls were responsible for the motion of bubbles in a rotating field. Since then, many authors have investigated charged walls in implanted layers, their origin and mechanism of movement in in-plane fields [ 4 - 1 0 ] . Kleman and Puchalska [ 11 ] have proposed models of spin distribution in positively and negatively charged 120 ° walls as well as in saw-tooth (zig-zag) walls. It has been shown that in negative walls the spin configuration is similar to the classical crossBloch line; in positive walls, the spin configuration is radial. * On leave of absence from Department of Metallurgy and Science of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, England. 0304-8853/81/0000-0000/$02.75 © 1981 North-Holland
The purpose of this paper is to present a detailed study of the shape, position and length of charged walls in in-plane fields, H//, of different values applied in various directions.
2. Experimental procedure The sample investigated was a SmYLuCaGe garnet fabricated by LETI-Grenoble. The characteristics of this sample were as follows: thickness = 1.83/am, thickness of implanted layer = 0.5 gm, saturation magnetic induction 47rMs = 383 G, collapse field = 181 Oe. In a specimen with its surface exactly parallel to (111), the preferred directions of magnetization in the implanted layer are [113c], [121], [211], [1 lx], [ i x ] ] and [ x ] ] ] , where 1 < x < 2. The value o f x depends on the uniaxial, induced and cubic anisotropy energies and the demagnetizing energy [5]. When a bias field H i is applied, the in-plane component of the magnetization has the preferred directions [112], [121] and [?.11] if H± is upwards (i.e. pointing from the substrate towards the implanted layer) and [ 112], [ ] 2 i ] and [211] if H± is downwards. The orientation of the specimen was determined by X-ray diffraction. The [111] axis was found to be tilted at 0.57 ° with its projection lying between [ ] 2 ] ] and [ 2 ] ] ] , as shown in fig. 1. In a slightly misoriented specimen, the preferred
LB. Puchalska,J.P. Jakubovics/ Chargedwalls in implantedgarnets
[~2[]
30~0' ,,~41 °
0°
240* ~
[i12]
[211]
1 2 0 " 180°
Fig. 1. Schematic representation of bubble equilibrium positions for the specimen used. Bubbles move from positions marked by open circles to those marked by full circles when the in-plane field is reduced to zero. The specimen orientation is also indicated. The bold arrow marks the projection of [111].
directions of the in-plane component may deviate from the above crystallographic directions. The preferred directions may, however, be determined by the bubble-disc method [12], based on the principle that the equilibrium positions of the bubble are towards the in-plane hard directions if H± is upwards and towards the easy directions if H± is downwards, so that the equilibrium positions relative to the specimen are unchanged if the sense of H± is reversed [I 3]. The results of the easy axis determination are shown in fig. 1. In this work the Faraday effect was used to observe bubbles and the Bitter technique to investigate charged walls. To study charged walls in HI~ >i O, H//was applied in eight directions: in three easy directions (near [121], [211] and [112]), in three hard directions (near [121], [211] and [112,])and in two directions at 30 ° to easy directions (near [10]] and []01]). In each direction, H//was increased to 60 Oe and reduced to 0 before starting the observations. The field was then gradually increased and the domain structure was recorded in fields of 0, 5.5, 11, 14.5, 16, 22 and 40 Oe. The maximum value H//= 40 Oe was chosen as a conventional value of in-plane field for bubble movement. In all experiments, a bias field H i ~ 200 Oe was applied downwards.
329
3. Results and discussion Figs. 2, 3 and 4 show Bitter patterns of charged walls inH/~ > 0 applied at 180 ° ([121] - hard doirection), at 0 ([12]] - easy direction) and at 120 ([211] - easy direction), respectively. The arrangement of charged walls around a disc labelled y in fig. 2a in all cases studied is depicted in fig. 5. (Note: black charged walls are henceforth referred to as BW and white charged walls as WW.)
3.1. Shape and position of the walls In several previous publications showing domain configurations around non-implanted discs, each charged wall is seen to be the boundary of a small domain (called a propeller domain e.g. in ref. [5]) on one side; the other side of the domain is delimited by an uncharged wall (see e.g. fig. 4 of ref. [9]). In the present study, the uncharged walls are not shown up by the Bitter technique. The reason for this may be that in other cases, the uncharged walls were N6el walls whereas in this case they may be Bloch walls which are known to have weaker stray fields and therefore attract fewer colloid particles. The presence of uncharged walls must however be assumed. The proximity of discs to each other results in the domains around neighbouring discs interacting in some cases, especially in small 1-1//.Fig. 2 shows that when H//is applied at 180 °, the charged walls change their position several times as H// increases. Major rearrangements of the domain structure must therefore have taken place when H//was originally reduced from 60 Oe to 0. The charged walls around both discs x and y undergo "whip" motion [5] from 0 to 11 Oe and from 5.5 to 14 Oe, respectively. Disc z has a more complicated structure around it which only disappears in H//= 22 Oe. In H//>t 22 Oe, the arrangement of charged walls around all discs is similar, the charged walls having undergone "flip" motion [5] in some cases (e.g. discs x and y from 16.5 to 22 Oe). "Whip" and "flip" of charged walls in rotating in-plane fields of constant amplitude have been interpreted before [9]. The present observations show that both "whip" and "flip" can also occur when H//of increasing magnitude is applied in a fixed direction (fig. 6). "Whip" is a domain wall motion process enabling the size of domains with favourably oriented magnetiza-
330
LB. Puchalska, J.P. Jakubovics / Charged walls in implanted garnets
Fig. 2. Bitter patterns inH//applied at 180 °. Values of H~~ are (a) 0, (b) 5 . 5 0 e , (c) 11 Oe, (d) 14.0, (e) 1 6 . 5 0 e , (f) 22 Oe. The diameter of disc x is 20 t~m.
LB. Puchalska, J.P. Jakubovics / Charged walls in implanted garnets
f
Fig. 3. Bitter patterns inH//applied at 0 °. Values of H~~ are (a) 0, (b) 5 . 5 0 e , (c) 11 Oe, (d) 1 6 . 5 0 e , (e) 22 Oe, (f) 40 Oe.
331
332
LB. Puchalska, J.P. Jakubovics / Charged walls in implanted garnets
Fig. 4. Bitter patterns in H//applied at 120 °. Values of H//are (a) 0, (b) 5 . 5 0 e , (c) 11 Oe, (d) 14 Oe, (e) 22 Oe, (f) 40 Oe
LB. Puehalska, J.P. Jakubovics / Charged walls in implanted garnets
T
0* ....
~
9o~
333
300*
_ __
I Hu
.
I ill
a
i r
14 or 165 22
)
40
)
b
Fig. 7. Interpretation of the behaviour of charged walls around an isolated disc in H//applied at 0 ° . (a) H//= 0, (b) H ~ 40 Oe. \
4
Fig. 5. Schematic diagrams of the arrangement of charged wails in various values of H//applied in various directions. BWs are shown as solid lines and WWs as dashed lines.
tions to expand and others to contract. It therefore occurs in low fields (fig. 6a to c). "Flip" is mostly a magnetization rotation process in which the magnetization direction inside the propeller domains rotates, causing previously uncharged walls to become charged and vice versa. This process therefore takes place in higher fields (fig. 6c to d). During "whip" motion, the charged portion of walls becomes extended. In order to reduce the magnetostatic energy, the walls take up a zig-zag shape just before and just after the "whip" (e.g. disc x in fig. 2b). In HI/>~ 22 Oe, the black walls around the discs are in the opposite direction to the applied field. (Note that as H i is downward, BWs, which act as bubble carriers, are negatively charged.) Fig. 3 shows the arrangement of charged walls in HI~ applied at 0 °. In this case, no major rearrange-
I
ment of walls occurs as H// increases. In H//--- 0, BWs are in the [211] positions, - 6 0 ° from being opposite the H// direction. As H// increases, this angle changes to ~ - 4 5 ° in H//= 40 Oe, as explained in fig. 7. The arrangement of the walls in H//applied at 120 ° is shown in fig. 4. In H//= 0, BWs are in the [112] direction. Some of the walls whip in H//= 11 Oe (see disc x), others change to zig-zag shape (see e.g. disc y) and whip in 14 Oe. In H//= 40 Oe the walls behave differently at different discs. The BW is in a position either ~+45 ° (disc x) or ~ - 4 5 ° (disc w in fig. 2a) from being opposite the H// direction, as explained in fig. 8. The observed phenomena may be interpreted using the critical curve for three fold symmetry proposed by Shir and Lin [14]. The critical curve, an asteroid with three vertices along the hard magnetization directions, represents the neutral stability of magnetization. For a given field represented by a vector drawn from the centre of the asteroid, magnetization directions corresponding to stationary energy states are parallel to lines that pass through the tip of the field
H ii
15' o
b
c
5
15"
d
Fig. 6. Interpretation of the behaviour of charged walls around an isolated disc in H/I applied at 180 ° . H // increases from a to d.
o
b
Fig. 8. Interpretation of the domain structure around (a) disc x, (b) disc w, in fig. 4f.
LB. Puchalska,J.P.JakubovicsI Chargedwallsin implantedgarnets
334 0°
[211]
/
\
300~/
[1117]
{
260'
270*(
,,
/
\\ \
~
i/I \~4~,,
"\
"\
90"
lirFM~
/I
i"
180'
E11] Fig. 9. Graphical determination of magnetization directions for H//= 11 Oe, 22 Oe and 40 Oe (thick arrows) applied in an easy direction (0°) and a hard direction (180°). M 3 is always drawn from the vertex of the asteroid at 180° to the tip of the field vector. (For clarity, M 3 is only shown for the case H//= 40 Oe in the hard direction).
vector and are tangents to the asteroid. The magnetization direction is unstable if it is pointing away from the tip of the field vector. If the magnetization direc-
0°
,/
\
2211]~300011Z
\
/~112]
", 60 °
180"
[11] Fig. 10. Graphical determination of magnetization directions for 1t//= 11, 22 and 40 Oe applied at 90° and 270° (thick arrows).
tion is pointing towards the tip of the field vector, it is stable if it makes an acute angle with it and metastable otherwise [5]. Fig. 9 shows the asteroid and magnetization distributions for HI/= 11,22 and 40 Oe applied in easy and hard directions. The corresponding diagram for HI~ applied at 90 ° and 270 ° is shown in fig. 10. The in-plane anisotropy field, HK1 (radius of the circumscribed circle of the asteroid) is given by HK1 ~ 5H~/, where H~/is the smallest value of in-plane field necessary to move a bubble around a disc [ 13 ]. This enables HI/and HK1 to be determined. It was found that HK1 ~ 110 Oe for the specimen described here. The magnetization directions appear to be given correctly up to H//= HK1 when H//is in a hard direction (compare figs. 6 and 9). Wheh 11//is applied at 180 °, M1 M2 are the stable magnetizations. M3 becomes metastable with energy increasing as H// increases. The area magnetized parallel to M3 decreases by whip motion of walls (fig. 6c) and then M3 rotates to M2 accompanied by wall flip (fig. 6d). However, when H//is in an easy direction, fig. 9 predicts that only M3 is stable;Ml and M2 are metastable up to H//= ½HK1. For H//> -~HKI, M3 is the only stable magnetization direction so that the specimen should be saturated and no charged walls should be present. Similarly, fig. 10 shows that there is only one stable magnetization direction for H//> 0.393HK1 (see eq. (13) of ref. [ 14]). Nevertheless, charged walls are still present when H//exceeds these values. Hence the theory of Shir and Lin [14] does not explain the observed domain structures when 11//has a large value in an easy direction or at 30 ° to it. The discrepancy between the predicted and observed domain structure may be due to the presence of demagnetizing fields at the edge of the nonimplanted disc. If the implanted layer were saturated, the edge of the disc would carry a high density of charge, leading to a large magnetostatic energy. The propeller domains form in order to decrease this energy. Even when H//is large enough to saturate a homogeneous implanted layer according to the theory, it may not be large enough to saturate the regions close to the edges of non-implanted discs. Fig. 11 shows a diagram of the positions of the BWs (denoted by crosses) and bubble positions (spots) versus the direction of H~/. The positions of the BWs were measured in the static way described
LB. Puchalska, J.P. Jakubovics / Charged wallsin implanted garnets
335
above. The positions o f bubbles were observed in
O (degrees)
H//= 40 Oe.
18C
Charged walls and bubbles are found to be at the same positions, even though their methods o f observation are different (Bitter pattern and Faraday effect, respectively). In nine cases, including the hard directions, 60 °, 180 ° and 300°), the bubbles are in the antiparallel position to H//. In other cases the bubbles and charged walls are at some angle to the antiparallel position. The dispersion o f bubble positions with respect to H//is not very regular, especially in the 90 ° , 105 ° , 120 ° and 135 ° directions, which may be due to the tilting o f the [111] axis (see fig. 1). Some l o c a l a n i s o t r o p y due to the non-implanted disc [6] may be also a reason for this asymmetry.
120
60 J~ o
0
300
240
180
3.2. Length of charged walls in the remanent state
o
,
'
40
'
1½0 '
1~0 ' 2~0 '
3b0 ' 3~0~
(~ H ( d e g r e e s )
Fig. 10. Variation of 0, the equilibrium position of bubbles (circles) and BWs (crosses) with CH, the angle between H// and [i2]1.
Fig. 12 shows a Bitter pattern of the charged walls attached to discs o f different diameters in H//= O. The length, L, of walls attached to three discs with different diameters, D (disc x, D = 20/~m, disc v, D = 15/am and disc u , D = 9/zm, see fig. 2a) was measured. The measurements are set out in table 1. In each case
Fig. 12. Bitter pattern of charged walls in H//= 0 after application of H~~= 60 Oe at 270 °.
LB. Puchalska,J.P. Jakubovics/ Chargedwallsin implantedgarnets
336
Table 1 Length of the BWs and WWs,L, and L/D, as a function of D, with H//applied in different directions D = 20 ttm
D = 15 t~m
D = 9 ttm
L Ozm)
LID
L (um)
LID
L O~m)
LID
0°
BW WW
18.5 20.0
0.93 1.00
15.4 20.0
1.03 1.33
7.7 9.2
0.86 1.02
60°
BW WW
18.6 10.8
0.93 0.54
9.2 7.7
0.61 0.51
9.2 9.2
1.02 1.02
90°
BW WW
20.0 16.9
1.00 0.84
10.8 10,0
0.72 0.67
7.7 7.7
0.86 0.86
120°
BW WW
18.5 20.0
0.93 1.00
10.0 10.8
0.67 0.72
6.2 6.2
0.69 0.69
180°
BW WW
20.0 21.5
1.00 1.08
15.4 17.0
1.03 1.13
9.2 9.2
1.03 1.03
240°
BW WW
14.6 20.0
0.73 1.00
10.0 27.7
0.67 1.85
6.2 6.2
0.69 0.69
270°
BW WW
20.0 20.0
1.00 1.00
16.9 12.3
1.13 0.82
13.8 10.8
1.53, 1.20
300°
BW WW
15.4 15.4
0.77 0.77
10.0 12.3
0.67 0.82
6.2 7.7
0.69 ,0.86
Mean
BW WW BW+WW
18.2 +-0.7 18.1 +- 1.3 18.1+-0.7
0.92 -+0.04 0.90 +-0.06 0.91+-0.04
12.2 +- 1.1 0.82 +-0.07 14.7 +-2.3 0.98 +-0.15 13.5_+1.3 0.90+-0.09
8.3 -+0.9 8.3 +-0.6 8.3_+0.5
0.92 +-0.10 0.92 +-0.06 0.92_+0.06
H//= 60 Oe was applied in the direction shown in the first column and then reduced to zero. The length of the BWs and WWs depends strongly on D. The correlation between L and D probably arises from the need to minimise the magnetostatic energy at the edge of the disc. When two propeller domains are present adjacent to the disc, the magnetic pole density is minimised if the charge and uncharged walls subtend an angle of 90 ° along the edge of the disc. If the shape of the propeller domains around discs of different diameter D is the same, then the size of the propeller domains should be proportional to D, so that LID should be independent of D. The average values of LID for different D are seen to be in good agreement. The large deviation occurring in a few individual cases is probably due to metastable domain configurations. The overall average value is LID = 0.91 -+ 0.04.
3.3. Length of charged walls in HI~ --/=0 The lengths of BWs attached to disc x (D = 20/am) in different values of H~~ applied in eight different
directions are shown in fig. 13. In most cases the initial length, Lo, is equal to or slightly smaller than D. In two cases, when Itl/was reduced to 0 from the [ ] ] 2 ] direction (240 °) and the [).11] direction (300°), Lo is significantly smaller than D. In all cases L decreases with increasing H/l, but not always uniformly. In some directions L becomes greater than Lo in intermediate values of HI~, see table 2. This increase is due to "whip" motion of the wall. But finally in HI~ = 40 Oe, which is a normal working field for bubble movement around circuits, the walls become small and 0.19
< L4o/Lo < 0.43.
The behaviour in values of It// approaching 40 Oe may be understood qualitatively with reference to figs. 6 and 7. When H//is applied in a hard direction, the propeller domains and surrounding domain are magnetized in equally favourable directions (fig. 6d). As HI~ increases, the magnetization of the domains rotates towards H//. The charge density on the charged wall decreases and the wall therefore attracts
LB. Puchalska, J.P. Jakubovics / Charged walls in implanted garnets
and their magnetization rotates towards H//, decreasing the charge density of the charged wall. Again the length of wall visible by ferrofluid decreases. The differences in behaviour can be seen by comparing the charged walls near disc z in figs. 2f and 3f. In the latter, the charged walls appear to be pressed against the edge of the disc.
L(~m) ./\
3O ./
:\
/'
".
\
/" ..
20
~_~
--
HII a t
•
'\
%
0 °
x
,,
60'
o
,,
90 °
.
337
o
\ . +"~.. Z > . . 10
4. Conclusions 0 30 ~
,, . ,
x
0 +
20
"-~©/" +
The position, shape and length of charged walls in a garnet specimen with an implanted layer have been investigated. The investigations were made in a bias field, H i , and in different values of in-plane field, H//>1 0 applied in eight different directions. The following conclusions may be drawn.
H, G~ 180"
•
240 * 270" 300*
~. "\
x+"..-
-x.
~'\
""...~"'. ,, .. \ b •, . . . . ~ , . . - -~,, ~. ~......
10
6
'
1'0
2'o
3'0
'
~o:
Hil
(Oe)
Fig. 13. Length of BWs, L, as a function of H~~applied in different directions. fewer colloid #articles, especially further away from the non-implanted disc. When H//is applied in an easy direction, the propeller domains are magnetized in a less favourable direction than the surrounding domain (fig. 7b). The size of the propeller domains decreases
1. "Whip" and "flip" motion, similar to that observed in rotating in-plane fields, have been observed in some cases when HI~ of increasing magnitude was applied in a fixed direction. Generally, "whip" occurs before "flip" as H// increases. 2. In the present specimen, only charged walls were made visible by the Bitter technique. Uncharged walls must also be present to complete the boundaries of propeller domains. The invisibility of uncharged wails has been attributed to the assumption that they are of the Bloch type in the present specimen. The dependence o f the configuration of charged walls on H//has been interpreted in terms of the behaviour of the propeller domains.
Table 2 Length of BWs, L, as a function of H~~applied in different directions
H// (Oe)
~at/ / 0o
tt// at 60 o
~,// at 90o
n// at 120o
~/// at 180o
n//
L (#m)
L (#m)
L O~m) L O~m)
L (#m)
L ~m)
at 240
o
H// at 270°
H// at 3000
L O~m)
L (um)
0
18.5
20.0
20.0
18.5
20.0
14.6
20.0
15.4
5.5
20.0
20.0
18.5
20.0
30.8
13.8
ll.5
II.0
14.0
18.5
18.5
30.8
29.0
11.5
20.0 17.7
16.5
12.0
18.5
18.5
20.8
20.0
10.8
22.0
II.0
14.6
I0.0
13.6
6.2
40.0
8.0
8.0
7.0
7.0
L4o/Lo
0.43
0.40
0.35
0.37
10.8
5.4
20.0 12.3
5.4
3.8
4.6
7.7
4.6
0.19
0.31
0.38
0.29
8.5
338
LB. Puchalska, J.P. Jakubovics / Charged walls in implanted garnets
3. The domain structures observed in small H//in all directions, and in all 11//in hard directions can be interpreted by the graphical method using the critical curve (three-vertex asteroid). However, this m e t h o d is inadequate for interpreting the results when a large H//is applied in easy directions or at 30 ° to them ( H / / > ~ H K for easy directions, H,, > 0.393HK1 at 30 ). The presence o f charged walls in these cases may be due to demagnetizing effects. These effects are being studied theoretically. 4. The length of charged walls in H//= 0 is determined by the diameter of the non-implanted disc, because o f the c o m m o n shape of propeller domains. The dependence o f the length o f charged walls on 11// can also be interpreted in terms of the behaviour of propeller domains. 5. As charged walls were present even in the highest H//applied in the present experiments, it is o f interest to investigate domain structures in higher
values of rill.
Acknowledgements We are grateful to Dr. H. Niedoba for carrying out the X-ray determination o f the crystal orientation,
J.P.J. acknowledges C.N.R.S. for a Research Fellowship.
References [1] R. Wolfe, J.C. North and Y.P. Lai, Appl. Phys. Lett. 18 (1973) 581. [2] R. Wolfe, J.C. North, W.A. Johnson, R.R. Spiwak, L.J. Varnerin and R.F. Fisher, AIP Conf. Proc. 10 (1973) 339. [3] G.S. Almasi, E.A. Giess, R.J. Hendel, G.E. Keefe, Y.S. Lin and M. Slusarczuk, AlP Conf. Proc. 24 (1975) 630. [4] I.B. Puchalska, H. Jouve and R.H. Wade, J. Appl. Phys. 48 (1977) 2069. [5] Y.S. Lin, D.B. Dove, S. Schwarzl and C.C. Shir, IEEE Trans. Magn. MAG-14 (1978) 494. [6] H. Jouve and I.B. Puchalska, IEEE Trans. Magn. MAG15 (1979) 1016. [7] H. Callen, J. Appl. Phys. 50 (1979) 1457. [8] C.C. Shir and Y.S. Lin, J. Appl. Phys. 50 (1979) 2270. [9] D.B. Dove and S. Schwarzl, J. Appl. Phys. 50 (1979) 5906. [10] A. Hubert, IEEE Trans. Magn. MAG-15 (1979) 1251. [11] M. Kleman and I.B. Puchalska, J. Magn. Magn. Mat. 15-18 (1980) 1473. [12] H. Niedoba and I.B. Puchalska, J. Appl. Phys. 52 (1981) 4726. [13] Y.S. Lin, G.S. Almasi, D.B. Dove, G.E. Keefe and C.C. Shir, J. Appl. Phys. 50 (1979) 2258. [14] C.C. Shir and Y.S. Lin, J. Appl. Phys. 50 (1979) 4246.