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Magnetisation reversal mechanism in CoCr media for perpendicular magnetic recording
~
ELSEVIER
Journal of Magnetism and Magnetic Materials 168 (1997) 321-335
Iournalof
magnetism and magnetic materials
Magnetisation reversal mechanism in Co-Cr media for perpendicular magnetic recording S. de Haan, J.C. Lodder* MESA Research Institute, University of Twente, Information Storage Techn. Group, P.O. Box 217, 7500 AE Ensehede, NetJ~erlands
Received 12 July 1996; revised 12 November 1996
Abstract In this study C o - C r thin films with perpendicular anisotropy are investigated. Three films with values for/-/'~ of 11, 90 and 170 kA/m have been selected for this paper. Besides the coercivity several other parameters such as the Ho/l--lk, Cr-segregation, domain structure, column sizes, etc. were studied by VSM, SEM, NMR, M F M , A F M and selective etching. The anomalous Hall effect (AHE) has been used to record the hysteresis curves of submicron Hall crosses. This very sensitive technique in combination with e-beam lithography and ion-beam etching resulted in the recording of AHE hysteresis loops with dimensions of the Hall crosses as small as 0.3 x 0.3 ~tm2. The AHE loops of three samples, with less than 60 columns, show different micromagnetic properties. Only the sample with H~± = 90 kA/m shows clear steps in the curves above the noise level. The largest steps correspond with the reversal of one column and the total number of steps was five times the number of columns for this sample. The different reversal mechanisms observed by the AHE are related to the differences in structure, coercivity and domain size. PACS: 75.70 Keywords: Co-Cr; Reversal mechanism; Thin film; Hall effect; Micromagnetism
1. Introduction T h e interest in u l t r a - h i g h d e n s i t y m a g n e t i c rec o r d i n g is still growing. T w o i m p o r t a n t r e a s o n s are its e n o r m o u s p o t e n t i a l for d a t a s t o r a g e a n d the fact t h a t the p r i n c i p a l limits for r e c o r d i n g will n o t be r e a c h e d w i t h i n the next 20 years. T h e u l t i m a t e state
* Corresponding author. Tel.: + 31-53-4892750; fax: + 3153-4893343; e-mail: [email protected].
for a Co--Cr m e d i u m for e x a m p l e is p r e d i c t e d to be 400 M b y t e / m m 2 a n d will be r e a c h e d a r o u n d the y e a r 2020 [ t ] . This c o r r e s p o n d s to bit sizes of 50 x 50 n m z. T o achieve this density the k n o w l e d g e of the m i c r o m a g n e t i c b e h a v i o u r in r e l a t i o n to its m a c r o s c o p i c a l a n d i t s s t r u c t u r a l p a r a m e t e r s becomes more and more important. T h e m i c r o m a g n e t i c a p p r o a c h to this p r o b l e m is severely l i m i t e d b y the n u m b e r of Co--Cr c o l u m n s which can be simulated. D u e to the c o m p l e x i t y of the p r o b l e m only a few h u n d r e d c o l u m n s can
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de Haa,. J.C Lodder ./.hmrmd q/Magnetism and Magnetic Materials 168 (1997) 321-335
be simulated even with the most advanced supercomputers. In 1987 Lodder et al. [2] studied the reversal mechanism by calculating the H~±/Hk and observing the domain pattern of the samples with Kerr microscopy. From this study it has been shown that Co Cr samples with H c ± / H k - 0.02 have long stripe domains. Short stripes occur for values around 0.05 and short stripes or a dot-like domain pattern are present in samples with H ~ f f H k >~ 0.1. In the present study three samples with different values for H ~ / H k were studied with a number of techniques such as VSM, torque, NMR, A F M and SEM. The ~meso'-magnetic behaviour of the samples is studied by using a very sensitive technique: the anomalous Hall effect (AHE) applied on submicron Hall crosses. This technique offers us the possibility to bridge the gap between the macromagnetic and the micromagnetic behaviours responsible for the reversal mechanism. Finally, the results are compared with simulated hysteresis curves obtained with an array of 5 x 5 columns.
3. M a c r o s c o p i c m a g n e t i c p a r a m e t e r s
We consider the macroscopical parameters of the samples first. Fig. 1 shows the VSM hysteresis curves for the three films, both perpendicular and
10
Sample S 1
-5
-10 -2000
a)
• -lOOO
Perpendicular o H-field [kA/m]
lOOO
20oo
8 6 4
Sample $2 ~~Perpendicular
0 2. Experimental procedure To study the relation between the reversal[ mechanism, the film structure and the micromagnetic and macromagnetic behaviours, three C o - C r samples with different deposition parameters were prepared. The major difference was the substrate temperature (TO during deposition, as it is known that this parameter influences the film growth in such a way that large differences :in structure and magnetic properties occur. Tlhis resulted in three samples with a low, a medium and a high coercivity, hereafter expressed as S1, $2 and $3, respectively. The low arid high coercive films were prepared by R F magnetron sputtering at a substrate temperature of 40 and 150°C, respectively. The medium H~ film was RF-sputtered at RT. All samples were deposited on Si substrates which had been covered first with an oxide layer of about 70 nm (SiO2). After deposition (and etching for the submicron samples) the wafers were cut into 1 x 1 cm 2 samples for measurement.
N-2
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Fig. 1. The perpendicular and in-plane hysteresis curves of the three samples measured with a VSM.
323
S. de Haan, J.C. Lodder / Journal of Magnetism and Magnetie Materials" 168 (1997) 321 335
in-plane. An Oxford VSM with a maximum field of 3 T was used for the measurements. The differences in coercivity (He±) can immediately be observed in the 'perpendicular' curves. The in-plane curves also show differences, especially near the crossing of the x-axis (at H = He) where, for the $2 sample, a large contribution from an initial layer (IL) can be observed (in-plane component of the magnetisation). The volume of the I L can be estimated by comparing the height of the jump with the height of the total loop. The IL of S1 and $3 is about 10% and for sample $2 about 16% of the total loop. The H~± can be determined both from the perpendicular VSM and the A H E loops and, as expected, the results show similar values. The calculated I-Io±/Hk predicts according to the theory 1-2] for the lowcoercivity sample S1 a stripe domain pattern and for the other two samples a dot-like domain pattern. T h e macroscopicM parameters obtained by several techniques are listed in Table 1.
and the film thickness t is estimated from the sputtering time. The results are shown in Table 2. Differences in the surface roughness were found by the use of an AFM. SI has a smooth surface, but sample $3, prepared at the high substrate temperature, a rather rough surface. The chemical inhomogeneities were studied by the SVCo spin-echo N M R technique [3] and by selective chemical etching of the Cr and successive SEM observations [4]. The N M R measures the hyperfine field interactions or the resonance frequencies of the material and is used here to study the compositional inhomogeneities. A spin-echo spectrum of C o - C r consists of a main line frequency (M) and of satellites. The main line frequency arises from Co nuclei which have only Co atoms as nearest neighbours (NN), for example, the hyperfine field of a Co nucleus in pure FCC Co has a main line frequency of 217 M H z and for pure H C P Co of 225.5 MHz. The exact frequency depends on the crystal structure, morphology and chemical inhomogeneities. If the Co is diluted by Cr ( < 1-2 a t % Cr), beside the main line frequency the first satellite peak (Satl) appears in the spectrum at 177 M H z and is caused by Co nuclei which have one Cr atom at the N N site. A second salMlite line
4. Microscopic parameters (microstructure) The column diameter (D) of the C o - C r samples was measured by SEM observations of the surface
Table 1 Macroscopical parameters measured by VSM, AHE and torque, the thickness t and the %Cr are determined from sputter time and target composition Sample
t (nm)
%Cr (target)
Ms (kA/m)
H~l (VSM) (kA/m)
H~._(AHE) (kA/m)
/ark (kA/m)
ilL (vol%)
HeL/H k
$1 $2 $3
320 200 320
22 23 22
236 329 428
13 89 173
11 9:1 169
244 306 501
11 16 10
I).04 0.29 0.34
Table 2 Summary of the microscopicalparameters with t the film thickness, D the column size ~md M the main line frequency Sample
S1 S2 $3
t (nm) 320 200 320
D (SEM) (nm)
M (NMR) (MHz)
%Co enriched (NMR)
60 75 70
< 150 207 3i2
Bulk 90 97
Stripes visible after etching?
Domain size
(MFM) (nm)
NO
~---
Faint Faint
t47 25:8
324
S. de lIaan, ,1.C. Lodder / Journal of Magnetism and Magnetic Materials 168 (1997) 321-335
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Fig. 2. NMR spectra of the three samples S1 (a), $2 (b) and
s3 (c). (Sat2) appears at about 130 M H z for Co nuclei with two Cr atoms at the N N sites (at about 5 at% Cr), etc. To apply this technique the frequencies of the peaks in the measured spectrum are compared with those of powdered samples with a known composition. F r o m Fig. 2b and Fig. 2c it can be seen that both samples $2 and $3 show a main line frequency (M) of, respectively, 207 and 213 MHz, characteristic of the presence of highly enriched Co
areas. S2 has components with 90% Co and S3 with 97% Co. On the other hand, sample S1 has no M peak above the 150 M H z which indicates that there are no Co-enriched areas and that there is a homogeneous distribution of the Cr through the sample. Another technique to study the segregation is the selective chemical etching of the Cr from the surface of the samples and by the observation of the surface afterwards in a SEM. The results are shown in Fig. 3a-Fig. 3f with the samples before etching at the left-hand side and those after etching at the right-hand side. In Fig. 3d and Fig. 3f there are faint stripes visible in $2 and $3 after 7 h of chemical etching of the samples. This is also an indication for compositional separation and the presence of a chrysanthemum p a t t e r n (CP) structure [4]. On the other hand, sample S1 shows no chemical inhomogeneities inside the columns, even after 14 h of etching. This confirms the N M R results for this sample with a homogeneous Cr distribution. A magnetic force microscope was used, in the dynamic mode, for observing the 'magnetic surface' of the samples. A commercially available tungsten tip covered with a Co/Ni layer was applied for scanning a 2 x 2 gm 2 area of each sample. The images were recorded in the remanent state after a field of 64 kA/m was applied perpendicular to the sample. The domain size determined by the M F M of $2 and $3 are, respectively, 1 4 7 ~ n d 258 nm. Together with the column size it can be estimated that the number of columns for one domain in the remanent state is about 5 and 14 for these two samples. Unfortunately, it was not possible to measure the domain size of the low coercive sample S1. The magnetic tip influenced the magnetisation beneath the tip too much, even when the tip was replaced by a magnetic tip with a soft magnetic layer of Ni/Fe. F r o m this sample a Kerr image was recorded which showed long stripe domains.
5. Anomalous Hall measurements on submicron samples
With conventional techniques, such as VSM or Kerr it is not possible to observe the micromagnetic
ii i ii!! i, if::
S. de Haan, J.C. Lodder / Journal of Magnetism and Magnetic Materials 168 (1997) 321 335
325
Fig. 3. SEM images of sample S1 (a, b), $2 (c, d) and $3 (e, t): as-deposited (left) and after chemical etching (right).
switching of individual columns in a hysteresis lo0p. The m a x i m u m sensitivity of a commercial V S M is typically in the order of 10-7 kA/m, whereas the magnetic m o m e n t involved in the switching
of one C o Cr c o l u m n is of the order of 10-12 kA/m. With the A H E technique a sensitivity of 10 -14 k A / m can be reached. The principle of A H E measurements on submicron Hall samples in
S. de Haan, .I.C Lodder / Journal ojMagnetism and Magnetic Materials 168 (1997) 321-335
326
Co-Cr -->, width: 100 Nm
iSi/Si02
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co-Or Fig. 5. SEM photograph of the 0.3 x 0.3 g m 2 Hall cross after the e-beam lithography and etching processes.
5.1. Demagnetisation
/
w
I
d~
Co-Crcolumns
Fig. 4. The Hall pattern used for the submicron Hail structures: (a) a 1.0 x 1.0 cm 2 Hall sample with the contact points and the cot~tact paths; (b) a detail of the Hall cross; (c) the centre of the Hall cross with C o - C r columns and the active area (w is the size e f the Hall cross).
C:o--Cr was first used in 1987 by Webb and Schultz [5]. Their samples had thickness of 1-1.4 gm and a smallest Hall cross size of 0.7 gm. Our samples were prepared by e-beam lithography and ionbeam etching. Using this process samples with a smallest Hall cross dimensions of 0.3 x 0.3 gm 2 could be prepared. A description of the anomalous Hall measurement set-up is given in Ref. /6]. Fig. 4 shows a drawing of the Hall cross with a limited number of columns inside the Hall cross. The SEM photograph (Fig. 5) shows the smallest Hall cross which could be made and from which a hysteresis curve was recorded.
We will discuss first some aspects of the recorded hysteresis loops which are the results of the smaller dimensions of the Hall cross. As can be seen from the SEM image (Fig. 5) large areas of the C o - C r near the cross have been removed by etching. This reduces the perpendicular component of the demagnetising factor (Nz) inside the Hall cross and therefore the recorded hysteresis loops will become less sheared. In Fig. 6 two AHE curves are drawn for an unetched 10 x 10 mm 2 sample (dashed line) and for an etched sample with a Hall cross of 0.3 x 0.3 gm 2 (solid line). The curves are normalised to the maximum and minimum value of the Hall voltage in the loop in order to compare the shape and especially the slopes of the two curves. Fig. 7 shows the upper part of several Hall hysteresis curves of Hall crosses of different size (active area: w = 10.0mm, 0.8 gm, 0.7 ~tm, 0.5 gm and 0.3 gm). In a uniformly magnetised sheet, cylinder or sphere there will be 'charges' at the surface. These 'magnetic charges' produce an internal demagnetising field Ha ( = - NaM) which is proportional and opposite to the magnetisation (M) and which is responsible for the shearing of the hysteresis loop. The internal magnetic field Hi is therefore equal to the sum of the applied magnetic field (Ha) and the demagnetising field (Ha). The sample
S. de Haan, J.C. Lodder / Journal of Magnetism and Magnetic Materials 16~¢ (1997) 321 335
327
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H-field[kA/m] Fig. 7. The upper part of normalised AHE hysteresis curves of $2 samples with different sizes of the Hall cross (w = 0.3, 0.5, 0.7, 0.8 pm and with w = 10 mm). g e o m e t r y of a s u b m i c r o n s a m p l e is different f r o m a u n i f o r m l y m a g n e t i s e d thin film, w h i c h results in a l o w e r d e m a g n e t i s i n g field in the z - d i r e c t i o n a n d therefore N~ < 1, Nx > 0 a n d Ny > 0. F r o m Fig. 7 it is clear t h a t the d r o p in N~ with w is c o n s i d e r a b l e for w < 1 gm. T o calculate the c h a n g e in N~ the t a n g e n t of the curve at Vnau = 0 V was d e t e r m i n e d . T h e N~ for the 1 0 x 1 0 m m 2 s a m p l e is a s s u m e d to be e q u a l to 1, the N~ for the 0.3 x 0.3 g m 2 t h e n b e c o m e s N~ = 0.65.
I n Fig. 8 the N~ is p t o t t e d as a function of the w i d t h (w) of the H a l l cross for s a m p l e $2, represent° ed b y the squares. It shows that the d r o p in N~ is less t h a n 10% for structures larger than 1 g m but decreases r a p i d l y for the s u b m i c r o n structures with d e c r e a s i n g w. T h e "central' v o l u m e in the H a l l cross a p p r o a c h e s a cube with decreasing w for which Nz equals 0.33. T h e higher value of w = 0.3 g m can therefore m a i n l y be a t t r i b u t e d to the influence of the c o n t a c t paths.
S. de ttaaH, J.C. Lodder / Journal (~[Magnetism and Magnetic Materials 168 (1997) 321-335
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H-?ield [kA/m] Fig. 8. Values for Nz as a function of Hall cross width (w) of the samples in Fig. 7 and for a sample with w = 2.0 ~m (squares): The dashed line represents the theoretical values for a block with dimension (w x w x 200 nm 3) and the solid line for a strip with width w (all with the same film thickness).
The theoretical values of a block and a long strip with the same thickness have been obtained by computer calculations [7]. F r o m the difference in Nz between the theoretical curves of the blocks and the strips it can be concluded that the contact paths have a significant influence on the demagnetisation in the cross. The measured values of the real Hall crosses are in agreement with these curves as the same trend with w can be seen and all values of Nz are higher than those of the strips.
Fig. 9. Details of the AHE hysteresis curves of $2 near the coercivity (H = Ho) of an unetched 10 x 10 m m 2 sample (~O-) and for a sample with a Hall cross of 0.3 x 0.3 pm 2 (- x ~ (lines are added as a guide to the eye).
with reduced dimensions of the cross. The precise shape of the cross and the etch angle can also have an effect on the pinning. This increase in coercivity is, however, not observed in the other two samples where the coercivity is independent of the Hall cross size. A possible explanation is that for sample (S1) the coercivity is so low that the reversal is not hindered by the edges and for the high coercive sample that there is a more particulate-like reversal mechanism without d.w.m.
5.2. Coercivity 5.3. A H E curves and measurement noise
Another significant difference in the curves is a change in coercivity for the $2 sample due to a change in Hall cross dimensions. Fig. 9 is an enlargement of Fig. 6 near the coercive field and demonstrates the increase in coercivity for the small Hall cross (- x -), compared to the unetched sample ( - O - ) . The increase is from 90 to 104 kA/m, an increase of 16%. This cannot be explained by a change in internal field due to demagnetisation as the magnetisation in the sample is zero at the coercive field and therefore zero at the demagnetising field also. The larger coercivity can be caused by the edges of the Hall cross which can act as pinning point if the reversal takes place by domain wall motion (d.w.m.). This explanation is confirmed by the fact that the coercivity for these C o - C r films increases
To reveal more of the details of the reversal mechanism hidden in the hysteresis curves, the A H E curves were recorded with very small field steps. The samples which will be discussed here are two submicron $2 samples with dimensions of the Hall cross of, respectively, 0.3 and 0.6 gm, two $3 samples (w = 0.4 and 0.5 gm) and one S1 sample (w = 0.4 txm). To achieve a good signal-to-noise ratio for the A H E measurements the time constant was set to z = 300 ms and the measured Hall voltage was averaged over three readings of the lock-in amplifier at each field. The size of the field steps was chosen to be small enough to minimise the chance that two successive independent steps (above noise level) in the Hall voltage would be detected as one
S. de Haan, J.C. Lodder / Journal o f Magnetism and Magnetic Materials 168 (1997) 321-335
single step (a step in the Hall signal is defined as the change in Hall signal for two successive field values). After each field step the p r o g r a m waited until the field was stable ( ~ 5 s). The size of the field steps was also adjusted to the shape of the hysteresis curve (small field steps if the Hall signal changes fast). The total number of measuring points was 4000 for each A H E loop, resulting in a 9 h recording time for each loop. In all samples the thermal noise was much smaller than the noise from other sources. A lot of noise is probably caused by the contacts in the sample holder which can rotate through two axes. These contacts and the unshielded wires near the sample will give the m a j o r contribution to the noise. In Fig. 10 the A H E loops are shown for the three samples with an enlargement of a typical area in the steep part of the loop. These graphs show that there are only steps in the A H E hysteresis curve for the $2 sample. The largest j u m p s correspond to the switching of one average-sized column. Between the jumps there is an area in which the Hall voltage is almost constant ('plateau'). A closer look at this area (Fig. 11) reveals that there is also an increase in the signal in this part of the curve. F r o m an enlargement of this 'plateau' it can be calculated that the slope is 30 times the slope of the Hall curve in saturation. This means that this effect is not caused by the normal Hall effect but by a very small increase in the A H E voltage for these very small field steps. The noise in the curves was measured by determining 4 x the rms noise at saturation which contains about 95% of all data points and is about 0.033% of the total signal (100% = 2 x Ms). As the n u m b e r of columns in the centre of the Hall cross in this sample is about 25, and most of the A H E signal is derived from the Hall cross we expect that the n u m b e r of j u m p s would be about 25 if the reversal would take place by the switching of the individual columns independently of each other. To study the behaviour of the switching units in more detail several statistical analyses were carried out. The hysteresis curves were recorded m a n y times and the field values of the large steps were studied as a function of the applied field. This distribution of the step sizes as a function of the applied field shows that there are significant
329
differences in successive measurements with the same sample. For these results Fig. 12 is; a typical example (the small steps below the noise level have not been plotted). It shows that even for the two branches in the same loop, the distribution is different for the ascending and the descending branch and that most of the large steps occur around the coercive field (He ~ 90 kA/m). The largest steps around 2 - 3 % correspond to one column. In another sample of $2, with a Hall cross size of 0.6 x 0.6 gm 2, steps in the curve can be also seen. Again the largest steps correspond to the switching of one column. As the number of columns is much larger than for the first sample, the individual jumps are more difficult to measure. This is also due to the fact that for A H E measurements the absolute value of the Hall voltage, corresponding to one column, is inversely proportional with the Hall cross dimensions. As can be seen from the A H E curves in Fig. 10a, Fig. 10b, Fig. 10e and Fig. 10f there are no steps observed in the low and the high coercive samples. We think that the reason is that sample $1 has such a low coercivity that the domain wall motion takes place very gradually with a change in the field that no step occurs above the noise level. For the highcoercivity film $3 we propose that the reversal takes place by the rotation of very small units inside the C o - C r columns and that those units are exchange decoupled and switch independently from each other. Table 3 gives a s u m m a r y of the relevant parameters. The number of columns in the central area of the Hall cross (fourth column) has been estimated as the number of columns that fits in the active area. The numbers in column 2 correspond to different cross sizes and 'bulk' with a sample of size 10 x 10 m m 2.
5.4. Analysis of AHE loops To study the AHE-hysteresis curves in more detail, each A H E curve was divided into five separate curves. Each curve contains only the steps with a certain step siz e and each of these step sizedistinguished partial hysteresis loops (SPH-loops) can be considered as the hysteresis loop of all the magnetic 'volumes' within a certain range. Each
S. de Haan, ,/.C. Lodder ,' .Jozo'nal o/Magnetism and Magnetic Materials 168 (1997) 321-335
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f)
Fig. 10. Anomalous Hail effect hysteresis loops (Jeff) and details of these loops (right) of the samples S1 (a, b), S2 (c, d) and $3 (e, f), respectively.
S. de Haan, J. C. Ladder~Journal of Magnetism and Magnetic Materials 168 (1997) 321 335
range of jump sizes is denoted by a class, and those classes are defined in Table 4, where AM is the change in magnetic moment of each step. In F'ig. 13 the division of an AHE curve of sample $2 in five SPH loops is shown for the loop in Fig. 10c, with the division in classes as given in Table 4. According to this table the loops of Class 1 contain the large steps, Class 2 the small steps, Classes 3 and 4 the small positive and negative steps and also noise, and Class 5 the small negative steps.
331
Class 1 contains the 'large' (irreversible',) steps of volumes > 30 nm 3. Table 5 gives the results of one classification of a typical hysteresis loop. F r o m this table it can be seen that Class 5 has about 5%, which corresponds to steps in the 'reverse' direction, but Class 1 has the largest component with almost 60% (59.6% and 58%). As Class 4 has only 24%, we can assume that the noise is a minor component in the hysteresis curve as Class 4 contains both the noise and a reversible c o m p o n e n t of the magnefisation.
-307.0 m
m
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0
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-309.0 e~ o
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t
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O~ C~
-~
.......... ~P l ~ t e ~
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x
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.....
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....,---.-o'-
•
...........
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! i
...........
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i
l
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/
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. 4 [ . . . . . . . . . ~.................. ~-........................C. . . . . . . .
-315.0
..1000
400
0
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500
lL000
H-field [kA/m] -317.0
175.0
,I 177.0
1 179.0
I 1B1.0
I 183.0
I 185.0
187.0
Fig. 12. D i s t r i b u t i o n ,of t h e s t e p s in t h e h y s t e r e s i s c u r v e o f s a m p l e $ 2 a s a f u n c t i o n o f t h e a p p l i e d fie~d, d e r i v e d f r o m t h e l o o p in Fig. 10c, w i t h [ ] for t h e a s c e n d i n g b r a n c h a n d x for t h e d e s c e n d i n g branclh (tlhe v e r y s m a l l s t e p s b e l o w t h e n o i s e level have been omitted).
H[kR/m] Fig. 11. E n l a r g e m e n t o f Fig. 10d, s h o w i n g t h e i n c r e a s e in H a l l voltage on the 'plateau'.
Table 3 S u r v e y o f t h e s u b m i c r o n a n d t h e 10 x 10 m m z ( ' b u l k ' ) H a l l s a m p l e s m e a s u r e d w i t h t h e A H E Sample
S1 S1 S1 S1 ( b u l k ) $2 $2 $2 (bulk) $3 $3 $3 ( b u l k )
Hall-cross size (w) (gm) ~ 0.4 ~ 0.5 ~ 1.1 ~ 0.3 ~ 0.6 ~ 0.4 ~ 0.6 -
Column diameter (SEM) (nm) ~ ~ ~ ~ ~ ~ ~ N ~ ~
60 60 60 60 75 75 75 70 70 70
Number of c o l u m n s in Hall cross ~ 60 ~ 100 ~ 400 ~ 25 ~ 100 ~ 40 ~ 100 -
Domain (MFM) (rim) -. -. . . -. -. N 147 -. ~ 258
size
~r c
(AHE) (kA/m) 13 14 .
.
.
. 13 108 103 88 168 163 173
S t e p s in curve?
No No No Yes Yes No No -
S. de Haan, J.C Lodder "Jouraal of Magnetism and Magnetic Materials 168 (1997) 321-335
332
35
; :
25t
o
15 ¢,q
5
•~ -5
Table 4 Step sizes for the classes used to classify the five SPH loops Class
Step size (% of 2 M s )
Specification
1 2 3 4 5
AM > 0.3 011 < AM < 0.3 0.0 < AM < 0.1 --0.1 < AM < 0.0 AM < - 0.1
Large pos. step Small pos. step Very small pos. step Very small neg. step Small neg. step
-15 Table 5 The % of 2M~ for a typical AHE loop of sample $2 for the ascending branch and descending branch and the Hc of the individual SPH loops
-25 -35 -1000 (a)
-500
0 500 H-field [kA/m]
1000
Sample S2
5
3 ~
Ascending branch (%) Descending branch (%) Hc (kA/m)
Class 1
2
3
4
59.6 58.0 145
28.1 4 0 . 6 23.8 31.4 4 0 . 0 23.9 117 33 43
5
4.8 5.7 70
2
esl 1
~o £-1
-5 -200-150-100 -50 0 50 100 150 200 (b) H-field [kA/ml Fig. 13. (a) SPH loop of sample $2 (with w = 0.3 gm) with the classification according to Table 4 and (b) a detail of (a). T h e l o o p of Class 1 has the largest coercivity a n d the He decreases for the l o o p s w h i c h c o n t a i n the smaller v o l u m e s b u t does n o t b e c o m e zero, n o t even for Classes 4 a n d 5 (see last r o w of T a b l e 5). This indicates t h a t these l o o p s h a v e also a signific a n t m a g n e t i c origin, as m e r e noise w o u l d n o t result in a coercivity for these loops. 5.5. C o m p u t e r s i m u l a t i o n s
T h e reversal of a small n u m b e r of c o l u m n s which c a n be m e a s u r e d b y the a n o m a l o u s H a l l effect gives
us the o p p o r t u n i t y to c o m p a r e a n d e v a l u a t e these results with c o m p u t e r simulations. T h e c o m p u t e r m o d e l has been d e s c r i b e d in Ref. I-8]. This m o d e l t a k e s i n t o a c c o u n t the e x t e r n a l field, the a n i s o t r o p y energy, the d e m a g n e t i s i n g energy a n d the e x c h a n g e coupling. T h e L a n d a u Lifschitz e q u a t i o n is solved to o b t a i n the d y n a m i c m a g n e t i s a t i o n process. T h e H a l l cross was s i m u l a t e d b y a n a r r a y of 5 x 5 e x c h a n g e d e c o u p l e d particles (columns). E a c h c o l u m n was d i v i d e d i n t o 6 x 6 x 18 cubic cells with cell d i m e n s i o n s of 8.5 n m 3. T h e particles are m a g n e t o s t a t i c a l l y c o u p l e d a n d in this case n o exchange c o u p l i n g b e t w e e n the c o l u m n s was considered. T h e field step b e t w e e n two successive p o i n t s is 1.6 k A / m . I n these c o m p u t e r s i m u l a t i o n s we s t u d i e d the influence of an I L o f 0, 2 a n d 8 % of the t o t a l s a m p l e v o l u m e on the hysteresis l o o p . I n the r e m a i n i n g of this p a p e r we will call these s a m p l e s A, B a n d C, respectively. T h e initial layer was s i m u l a t e d b y assigning a r a n d o m i n - p l a n e m a g n e t i s a t i o n to a certain n u m b e r of cubic cells in the l o w e r two rows of the particles n e a r the substrate. I n real s a m p l e s this c o m p o n e n t can be p a r t of an initial l a y e r a n d / o r d i s t r i b u t e d t h r o u g h o u t the sample.
333
S. de Haan, J.C. Lodder / Journal of Magnetism and Magnetic Materials 168 (1997) 321 335
As macroscopical input parameters for our simulation model we used realistic parameters obtained by VSM and torque (M~ = 400 kA/m and Ka = 1.6 x 105 J/m3). Except for the IL the sample has a perpendicular anisotropy with a spread in easy axis of 1.8 ° from the film normal. In Fig. 14 the three simulated hysteresis curves are presentedl Several changes can be observed with the increase in IL volume. Starting from the saturated state, the drop in magnetisation with decreasing field takes place much earlier with the
presence of the IL. T h e value of the reverse field at which the first large step occurs ( c o r r e s p o n d i n g to the switching of one or m o r e columns) is also m u c h l o w e r for the s a m p l e s with an IL. The t o t a l contrib u t i o n of the small (reversible) p a r t s of the m a g n e t isation, before the first large step t a k e s place is 2.5, 3.9 a n d 10.6%, respectively, for s a m p l e s A, B a n d C. Also can be seen from the size of the large steps that the n u m b e r of c o l u m n s which switch i n d e p e n d e n t l y is 14 a n d l 0 for s a m p l e s g a n d C a n d o n l y 3 for s a m p l e A. T h e largest n u m b e r of c o l u m n s switching t o g e t h e r in one field step is 5 for s a m p l e A a n d b o t h 3 for s a m p l e s B a n d C. R e m a r k a b l e changes for the coercivity (410, 403 a n d 310 k A / m ) a n d the s a t u r a t i o n field (760, 750 a n d 620 k A / m ) only occur for s a m p l e C with the large I L c o m p o n e n t of 8%. F r o m these: d a t a we c o n c l u d e t h a t the presence of a large I L o r i n - p l a n e c o m p o n e n t of the m a g n e t i s a t i o n facilitates the reversal, lowers the coercivity a n d results in the switching of smaller units (less switching of m o r e t h a n one c o l u m n at a time). T h e results of all the s i m u l a t i o n s are s u m m a r i s e d in T a b l e 6. T h e ' p l a t e a u x ' in Fig. 15 which is a n e n l a r g e m e n t o f a p a r t of the curve of Fig. 14c shows significant similarities with the ' p l a t e a u ' in Fig. 11 of s a m p l e S2. T h e g r a d u a l decrease (or increase) of the m a g n e t i s a t i o n can be seen, o n l y there are n o 'reverse' steps a n d there is of course no m e a s u r e m e n t noise. F o r a l a r g e r I L c o m p o n e n t the increase of the m a g n e t i s a t i o n p e r unit of the a p p t i e d field of the ' p l a t e a u ' is larger.
1.25
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0.50
t
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7
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~ -0.50 r
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]
I
,
I
,
I
-800 -600 -400 -200
I
i
0
I
,
I
,
I
i
200 400 600 800
H-field [kA/m] Fig. 14. Simulated hysteresis loops for an array of 5 x 5 Co-Cr columns with an IL volume of 0% (a), 2% (b) and 8% (c).
Table 6 Summary of the results obtained by computer simulation of an array of 5 x 5 Co-Cr columns with a different thickness of the initial layer (IL) Sample
A
IL volume put in model (%) Contribution of the IL (%) (AM/Ms < 0.3%) Number of columns switching individually Switching of first column at field (kA/m) Total reversed volume before first column (%) Largest number of columns switching together Saturation field (kA/m) Coercivity (kA/m) He of Class 1 Hc of Class 2 H; of Class 3
0 2.48 3 -
221
0.23 5 750 410 408 - 626 - 395
B
C
2 3.94 14 58 0.784 3 760 403 - 338 - 424 -- 253
1056 10 -16 6.87 3 620 310 - 309 -- 451 112
8
334
S. de Haan, J. C. Lodder / Journal qf Magnetism and Magnetic Materials 168 (1997) 321-335
-0.15
30
"--
(i)
20
-- '-I
'Plateau'
,
-0.25
~
10
f f j
~
@
~ , , , o ,* o ° ° " s ° l ' ' ' ° * * * * H ° ° '
..................................
-20
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-30
-0.30 -440
~
i -420
~ -400
-380
-360
-340
(a)
; l : l
I ~ l l l
Ii
I
r
-800-600-400-200 0 200 400 600 800 H-field [kA/m]
H-field [kA/m]
®
Fig. ,5. 'Plateau' in the simulated hysteresis curve of Fig. 14c.
r We also divided the curves into separate curves with different step sizes in the same way as has been done in Fig. 13 for a real C o - C r sample. A t y p i c a l example is shown in Fig. 16 for sample C. The loops of Class 1 correspond to the steps of multiple column switching (AM > 5:0%), Class 2 with the switching one column at a time (3.0% < AM < 5.0%), and Class 3 with very small changes (0.0% < AM < 3.0%). The curves with reverse step, s (Classes .4 and 5) as shown for the real A H E measurement are not present, resulting in only three S P H loops. F o r all the three samples the coercivity of the Class 3 loops is much lower than for the Class 1 and Class 2 loops. This is in agreement with measurement results and an indication that the small and in-plane components are responsible for the Class 3 contribution to the total hysteresis loop. Unfortunately, the model is not sophisticated enough to simulate the more complicated CP structure of sample $2 and $3.
6. Discussion and conclusions The reversal mechanism of C o - C r has been studied intensively during the last decades but a clear answer whether the reversal takes place by
~" 2
iI
t"'l
-~o i-2
@l
;t
I:
i
r~
.li® i i
I i I i -6 -800 -600 -400 -200 0 200 400 600 800 (b) H-field [kA/m]
Fig. 16. (a) SPH loop of the simulated hysteresis curve of sample C (1) = switching of more than 1 column, (2) = switching of one column, (3) = switching of units smaller than one column). (b) A detail of (a).
d.w.m, or by a rotation mechanism has not been obtained for all samples with different coercivities and composition. We started with three films of different coercivities and different microstructures. The measurements on 'bulk' samples and the A H E measurements on submicron samples of the three samples reveal that the reversal mechanism in the three samples with Ho values of 11, 90 and 170 k A / m is different both on a macroscopic and on a 'meso'-scopic scale.
S. de Haan, J.C. Lodder / Journal o f Magnetism and Magnetic Materials 168 (1997) 321 335
The low-coercivity sample $1 has a low H c ± / H k value corresponding to a stripe domain in the remanent state. The A H E measurements show no jumps as the reversal takes place by a continuous d.w.m, in very small steps. Sample S2 shows small jumps in the A H E curve, the largest comparable to the reversal of one column, and also a very gradual increase in Hall signal which can be attributed to a combination of domain wall motion and rotation of (parts of) a column. The high coercivity film $3 has probably a reversal mechanism by rotation of the magnetisation of very small volumes. This is in agreement with the microstructure as has been shown by N M R and SEM imaging after selective chemical etching (CP structure and high compositional separation (CS)). More evidence was found recently by Takei et al. [9]. They found by SANS (small-angle neutron scattering) that the magnetic unit for C o - C r films with a high CS was smaller than that of a grain. Furthermore, H o n o et al. [10] showed by A P F I M (atom probe field ion microscopy) studies that compositional fluctuations are present inside the grains of Co Cr sputtered films which correspond to the CP structure. The dependence of the Hc on the size of the Hall cross for the $2 sample is attributed to pinning of the domain walls at the edges of the Hall cross which becomes relatively more important for smaller Hall crosses. This dependence is not present in the other two samples as there is no d.w.m, in the $3 sample and in the Sl sample the pinning at the edges is no obstruction for striping out of the domains in the other directions. From the results of the computer simulations we have seen that an initial layer (or in-plane) component lowers the coercivity and the saturation field and facilitates the reversal of smaller units. If the real C o - C r sample has a CP structure the in-plane components (magnetic and non-magnetic) are also distributed inside the columns making the reversal of parts of the column more probable. This makes it more likely that in the case of a CP structure the reversal can take place by the switching of small units, smaller than one column as we have seen for the AHE measurements. A more sophisticated computer model is necessary to simulate the CP structure.
335
We have also seen that the 'plateau' in the real A H E measurement has much resemblance with the simulation and that the slope can be attributed to the reversal of very small magnetic volumes. G o o d agreement was also found for the hysteresis loops which were divided into loops with large medium and small steps (SPH loops). The most significant result here was that the coercivity of the Class 3 loops was much smaller than that for the Class 1 and Class 2 loops for both the measurement and the simulations.
Acknowledgements We would like to thank the D I M E S Institute in Delft for the support in the preparation of the submicron samples, especially for the e-beam lithography. Dr. Maeda of N T T is acknowledged for the preparation of the high- and low-coercivity samples and for the selective chemical etching of the samples and for taking the N M R spectra. Furthermore, we would like to thank Matthijs van Kooten for performing the computer simulations. This research has been financially supported by CAMST, a program of the EC.
References [1] Y. Nakamura, J. Magn. Soc. Japan 15 (Suppl. $2) (1991) 497. [2] J.C. Lodder, D. Wind, Th.J.A. Popma and A. Hubert, IEEE Trans. Magn. 23 (5) (1987) 2055. [3] K. Takei and Y. Maeda, Jpn. J. Appl. Phys. 30 (6B)(!991) Ll125. [4] Y. Maeda, S. Hirono and M. Asahi, Jpn. J. Appl. Phys. 24 (12) (1985) L951. [5] B.C. Webb and S. Schultz, IEEE Trans. Magn. 24 (1988) 3006. [6] S. de Haan, J.C. Lodder and Th.J.A.Popma, J. Magn. Soc. Japan Suppl. $2 15 (1991) 349. [7] J.G.Th. te Lintelo, J.C. Lodder, J. Engemann and ThJ.A. Popma, J. Magn. Magn. Mater. 115 (1992) 333. [8] M. van Kooten, S. de Haan, J.C. Lodder and Th.J.A. Popma, J. Appl. Phys. 75 (10) (1994) 5508. [9] K. Takei, J. Suzuki, Y. Maeda and Y. Morii, IEEE Trans. Magn. 30 (6) (1994) 4029. [10] K. Hono, S.S. Babu, Y. Maeda, N. Hasegawa and T. Sakurai, Appl. Phys. Lett. 62 (20) (1993) 2504.
ELSEVIER
Journal of Magnetism and Magnetic Materials 168 (1997) 321-335
Iournalof
magnetism and magnetic materials
Magnetisation reversal mechanism in Co-Cr media for perpendicular magnetic recording S. de Haan, J.C. Lodder* MESA Research Institute, University of Twente, Information Storage Techn. Group, P.O. Box 217, 7500 AE Ensehede, NetJ~erlands
Received 12 July 1996; revised 12 November 1996
Abstract In this study C o - C r thin films with perpendicular anisotropy are investigated. Three films with values for/-/'~ of 11, 90 and 170 kA/m have been selected for this paper. Besides the coercivity several other parameters such as the Ho/l--lk, Cr-segregation, domain structure, column sizes, etc. were studied by VSM, SEM, NMR, M F M , A F M and selective etching. The anomalous Hall effect (AHE) has been used to record the hysteresis curves of submicron Hall crosses. This very sensitive technique in combination with e-beam lithography and ion-beam etching resulted in the recording of AHE hysteresis loops with dimensions of the Hall crosses as small as 0.3 x 0.3 ~tm2. The AHE loops of three samples, with less than 60 columns, show different micromagnetic properties. Only the sample with H~± = 90 kA/m shows clear steps in the curves above the noise level. The largest steps correspond with the reversal of one column and the total number of steps was five times the number of columns for this sample. The different reversal mechanisms observed by the AHE are related to the differences in structure, coercivity and domain size. PACS: 75.70 Keywords: Co-Cr; Reversal mechanism; Thin film; Hall effect; Micromagnetism
1. Introduction T h e interest in u l t r a - h i g h d e n s i t y m a g n e t i c rec o r d i n g is still growing. T w o i m p o r t a n t r e a s o n s are its e n o r m o u s p o t e n t i a l for d a t a s t o r a g e a n d the fact t h a t the p r i n c i p a l limits for r e c o r d i n g will n o t be r e a c h e d w i t h i n the next 20 years. T h e u l t i m a t e state
* Corresponding author. Tel.: + 31-53-4892750; fax: + 3153-4893343; e-mail: [email protected].
for a Co--Cr m e d i u m for e x a m p l e is p r e d i c t e d to be 400 M b y t e / m m 2 a n d will be r e a c h e d a r o u n d the y e a r 2020 [ t ] . This c o r r e s p o n d s to bit sizes of 50 x 50 n m z. T o achieve this density the k n o w l e d g e of the m i c r o m a g n e t i c b e h a v i o u r in r e l a t i o n to its m a c r o s c o p i c a l a n d i t s s t r u c t u r a l p a r a m e t e r s becomes more and more important. T h e m i c r o m a g n e t i c a p p r o a c h to this p r o b l e m is severely l i m i t e d b y the n u m b e r of Co--Cr c o l u m n s which can be simulated. D u e to the c o m p l e x i t y of the p r o b l e m only a few h u n d r e d c o l u m n s can
0304-8853/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PH S 0 3 0 4 - 88 5 3 ( 9 6 ) 0 0 7 3 3-0
322
S.
de Haa,. J.C Lodder ./.hmrmd q/Magnetism and Magnetic Materials 168 (1997) 321-335
be simulated even with the most advanced supercomputers. In 1987 Lodder et al. [2] studied the reversal mechanism by calculating the H~±/Hk and observing the domain pattern of the samples with Kerr microscopy. From this study it has been shown that Co Cr samples with H c ± / H k - 0.02 have long stripe domains. Short stripes occur for values around 0.05 and short stripes or a dot-like domain pattern are present in samples with H ~ f f H k >~ 0.1. In the present study three samples with different values for H ~ / H k were studied with a number of techniques such as VSM, torque, NMR, A F M and SEM. The ~meso'-magnetic behaviour of the samples is studied by using a very sensitive technique: the anomalous Hall effect (AHE) applied on submicron Hall crosses. This technique offers us the possibility to bridge the gap between the macromagnetic and the micromagnetic behaviours responsible for the reversal mechanism. Finally, the results are compared with simulated hysteresis curves obtained with an array of 5 x 5 columns.
3. M a c r o s c o p i c m a g n e t i c p a r a m e t e r s
We consider the macroscopical parameters of the samples first. Fig. 1 shows the VSM hysteresis curves for the three films, both perpendicular and
10
Sample S 1
-5
-10 -2000
a)
• -lOOO
Perpendicular o H-field [kA/m]
lOOO
20oo
8 6 4
Sample $2 ~~Perpendicular
0 2. Experimental procedure To study the relation between the reversal[ mechanism, the film structure and the micromagnetic and macromagnetic behaviours, three C o - C r samples with different deposition parameters were prepared. The major difference was the substrate temperature (TO during deposition, as it is known that this parameter influences the film growth in such a way that large differences :in structure and magnetic properties occur. Tlhis resulted in three samples with a low, a medium and a high coercivity, hereafter expressed as S1, $2 and $3, respectively. The low arid high coercive films were prepared by R F magnetron sputtering at a substrate temperature of 40 and 150°C, respectively. The medium H~ film was RF-sputtered at RT. All samples were deposited on Si substrates which had been covered first with an oxide layer of about 70 nm (SiO2). After deposition (and etching for the submicron samples) the wafers were cut into 1 x 1 cm 2 samples for measurement.
N-2
-4 .15 -8 -2ooo
-~ ha-prone -1000
b)
0 H-f~Xl [ka/ml
1000
2000
15 10
Sample S3
5
-5
-10
e)
-15 -2000
S
-looO
Perpendicular 0
1000
2000
H-field [kA/m]
Fig. 1. The perpendicular and in-plane hysteresis curves of the three samples measured with a VSM.
323
S. de Haan, J.C. Lodder / Journal of Magnetism and Magnetie Materials" 168 (1997) 321 335
in-plane. An Oxford VSM with a maximum field of 3 T was used for the measurements. The differences in coercivity (He±) can immediately be observed in the 'perpendicular' curves. The in-plane curves also show differences, especially near the crossing of the x-axis (at H = He) where, for the $2 sample, a large contribution from an initial layer (IL) can be observed (in-plane component of the magnetisation). The volume of the I L can be estimated by comparing the height of the jump with the height of the total loop. The IL of S1 and $3 is about 10% and for sample $2 about 16% of the total loop. The H~± can be determined both from the perpendicular VSM and the A H E loops and, as expected, the results show similar values. The calculated I-Io±/Hk predicts according to the theory 1-2] for the lowcoercivity sample S1 a stripe domain pattern and for the other two samples a dot-like domain pattern. T h e macroscopicM parameters obtained by several techniques are listed in Table 1.
and the film thickness t is estimated from the sputtering time. The results are shown in Table 2. Differences in the surface roughness were found by the use of an AFM. SI has a smooth surface, but sample $3, prepared at the high substrate temperature, a rather rough surface. The chemical inhomogeneities were studied by the SVCo spin-echo N M R technique [3] and by selective chemical etching of the Cr and successive SEM observations [4]. The N M R measures the hyperfine field interactions or the resonance frequencies of the material and is used here to study the compositional inhomogeneities. A spin-echo spectrum of C o - C r consists of a main line frequency (M) and of satellites. The main line frequency arises from Co nuclei which have only Co atoms as nearest neighbours (NN), for example, the hyperfine field of a Co nucleus in pure FCC Co has a main line frequency of 217 M H z and for pure H C P Co of 225.5 MHz. The exact frequency depends on the crystal structure, morphology and chemical inhomogeneities. If the Co is diluted by Cr ( < 1-2 a t % Cr), beside the main line frequency the first satellite peak (Satl) appears in the spectrum at 177 M H z and is caused by Co nuclei which have one Cr atom at the N N site. A second salMlite line
4. Microscopic parameters (microstructure) The column diameter (D) of the C o - C r samples was measured by SEM observations of the surface
Table 1 Macroscopical parameters measured by VSM, AHE and torque, the thickness t and the %Cr are determined from sputter time and target composition Sample
t (nm)
%Cr (target)
Ms (kA/m)
H~l (VSM) (kA/m)
H~._(AHE) (kA/m)
/ark (kA/m)
ilL (vol%)
HeL/H k
$1 $2 $3
320 200 320
22 23 22
236 329 428
13 89 173
11 9:1 169
244 306 501
11 16 10
I).04 0.29 0.34
Table 2 Summary of the microscopicalparameters with t the film thickness, D the column size ~md M the main line frequency Sample
S1 S2 $3
t (nm) 320 200 320
D (SEM) (nm)
M (NMR) (MHz)
%Co enriched (NMR)
60 75 70
< 150 207 3i2
Bulk 90 97
Stripes visible after etching?
Domain size
(MFM) (nm)
NO
~---
Faint Faint
t47 25:8
324
S. de lIaan, ,1.C. Lodder / Journal of Magnetism and Magnetic Materials 168 (1997) 321-335
~o
oo 0
v
fcc Co (217 Mhz)
°°°°C O
I
o ct-b CbOo
hcp Co (225.5 MHz)
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Frequency (MHz)
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C)
O--O-aO-,
200 Frequency (Mtlz)
o e
a
M 207 MHz
200 Frequency (MIIz)
O
O
250
Fig. 2. NMR spectra of the three samples S1 (a), $2 (b) and
s3 (c). (Sat2) appears at about 130 M H z for Co nuclei with two Cr atoms at the N N sites (at about 5 at% Cr), etc. To apply this technique the frequencies of the peaks in the measured spectrum are compared with those of powdered samples with a known composition. F r o m Fig. 2b and Fig. 2c it can be seen that both samples $2 and $3 show a main line frequency (M) of, respectively, 207 and 213 MHz, characteristic of the presence of highly enriched Co
areas. S2 has components with 90% Co and S3 with 97% Co. On the other hand, sample S1 has no M peak above the 150 M H z which indicates that there are no Co-enriched areas and that there is a homogeneous distribution of the Cr through the sample. Another technique to study the segregation is the selective chemical etching of the Cr from the surface of the samples and by the observation of the surface afterwards in a SEM. The results are shown in Fig. 3a-Fig. 3f with the samples before etching at the left-hand side and those after etching at the right-hand side. In Fig. 3d and Fig. 3f there are faint stripes visible in $2 and $3 after 7 h of chemical etching of the samples. This is also an indication for compositional separation and the presence of a chrysanthemum p a t t e r n (CP) structure [4]. On the other hand, sample S1 shows no chemical inhomogeneities inside the columns, even after 14 h of etching. This confirms the N M R results for this sample with a homogeneous Cr distribution. A magnetic force microscope was used, in the dynamic mode, for observing the 'magnetic surface' of the samples. A commercially available tungsten tip covered with a Co/Ni layer was applied for scanning a 2 x 2 gm 2 area of each sample. The images were recorded in the remanent state after a field of 64 kA/m was applied perpendicular to the sample. The domain size determined by the M F M of $2 and $3 are, respectively, 1 4 7 ~ n d 258 nm. Together with the column size it can be estimated that the number of columns for one domain in the remanent state is about 5 and 14 for these two samples. Unfortunately, it was not possible to measure the domain size of the low coercive sample S1. The magnetic tip influenced the magnetisation beneath the tip too much, even when the tip was replaced by a magnetic tip with a soft magnetic layer of Ni/Fe. F r o m this sample a Kerr image was recorded which showed long stripe domains.
5. Anomalous Hall measurements on submicron samples
With conventional techniques, such as VSM or Kerr it is not possible to observe the micromagnetic
ii i ii!! i, if::
S. de Haan, J.C. Lodder / Journal of Magnetism and Magnetic Materials 168 (1997) 321 335
325
Fig. 3. SEM images of sample S1 (a, b), $2 (c, d) and $3 (e, t): as-deposited (left) and after chemical etching (right).
switching of individual columns in a hysteresis lo0p. The m a x i m u m sensitivity of a commercial V S M is typically in the order of 10-7 kA/m, whereas the magnetic m o m e n t involved in the switching
of one C o Cr c o l u m n is of the order of 10-12 kA/m. With the A H E technique a sensitivity of 10 -14 k A / m can be reached. The principle of A H E measurements on submicron Hall samples in
S. de Haan, .I.C Lodder / Journal ojMagnetism and Magnetic Materials 168 (1997) 321-335
326
Co-Cr -->, width: 100 Nm
iSi/Si02
"
~
J
1.0 x 1.0
(Co-Cr)
co-Or Fig. 5. SEM photograph of the 0.3 x 0.3 g m 2 Hall cross after the e-beam lithography and etching processes.
5.1. Demagnetisation
/
w
I
d~
Co-Crcolumns
Fig. 4. The Hall pattern used for the submicron Hail structures: (a) a 1.0 x 1.0 cm 2 Hall sample with the contact points and the cot~tact paths; (b) a detail of the Hall cross; (c) the centre of the Hall cross with C o - C r columns and the active area (w is the size e f the Hall cross).
C:o--Cr was first used in 1987 by Webb and Schultz [5]. Their samples had thickness of 1-1.4 gm and a smallest Hall cross size of 0.7 gm. Our samples were prepared by e-beam lithography and ionbeam etching. Using this process samples with a smallest Hall cross dimensions of 0.3 x 0.3 gm 2 could be prepared. A description of the anomalous Hall measurement set-up is given in Ref. /6]. Fig. 4 shows a drawing of the Hall cross with a limited number of columns inside the Hall cross. The SEM photograph (Fig. 5) shows the smallest Hall cross which could be made and from which a hysteresis curve was recorded.
We will discuss first some aspects of the recorded hysteresis loops which are the results of the smaller dimensions of the Hall cross. As can be seen from the SEM image (Fig. 5) large areas of the C o - C r near the cross have been removed by etching. This reduces the perpendicular component of the demagnetising factor (Nz) inside the Hall cross and therefore the recorded hysteresis loops will become less sheared. In Fig. 6 two AHE curves are drawn for an unetched 10 x 10 mm 2 sample (dashed line) and for an etched sample with a Hall cross of 0.3 x 0.3 gm 2 (solid line). The curves are normalised to the maximum and minimum value of the Hall voltage in the loop in order to compare the shape and especially the slopes of the two curves. Fig. 7 shows the upper part of several Hall hysteresis curves of Hall crosses of different size (active area: w = 10.0mm, 0.8 gm, 0.7 ~tm, 0.5 gm and 0.3 gm). In a uniformly magnetised sheet, cylinder or sphere there will be 'charges' at the surface. These 'magnetic charges' produce an internal demagnetising field Ha ( = - NaM) which is proportional and opposite to the magnetisation (M) and which is responsible for the shearing of the hysteresis loop. The internal magnetic field Hi is therefore equal to the sum of the applied magnetic field (Ha) and the demagnetising field (Ha). The sample
S. de Haan, J.C. Lodder / Journal of Magnetism and Magnetic Materials 16~¢ (1997) 321 335
327
1.20 o m
1.00
"~ E
0..~0
c
0.20
L
"
/
Il ~ r/~lg//tll
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[ kA/rn]
Fig. 6. The normalised AHE hysteresis curves of the unetched S2 sample 10 x 10 mm 2 (dashed curve) and of the etched sample with a Hall cross of 0.3 x 0.3 gm 2 (solid curve). 1.10 t.00 0.90 O . BO
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H-field[kA/m] Fig. 7. The upper part of normalised AHE hysteresis curves of $2 samples with different sizes of the Hall cross (w = 0.3, 0.5, 0.7, 0.8 pm and with w = 10 mm). g e o m e t r y of a s u b m i c r o n s a m p l e is different f r o m a u n i f o r m l y m a g n e t i s e d thin film, w h i c h results in a l o w e r d e m a g n e t i s i n g field in the z - d i r e c t i o n a n d therefore N~ < 1, Nx > 0 a n d Ny > 0. F r o m Fig. 7 it is clear t h a t the d r o p in N~ with w is c o n s i d e r a b l e for w < 1 gm. T o calculate the c h a n g e in N~ the t a n g e n t of the curve at Vnau = 0 V was d e t e r m i n e d . T h e N~ for the 1 0 x 1 0 m m 2 s a m p l e is a s s u m e d to be e q u a l to 1, the N~ for the 0.3 x 0.3 g m 2 t h e n b e c o m e s N~ = 0.65.
I n Fig. 8 the N~ is p t o t t e d as a function of the w i d t h (w) of the H a l l cross for s a m p l e $2, represent° ed b y the squares. It shows that the d r o p in N~ is less t h a n 10% for structures larger than 1 g m but decreases r a p i d l y for the s u b m i c r o n structures with d e c r e a s i n g w. T h e "central' v o l u m e in the H a l l cross a p p r o a c h e s a cube with decreasing w for which Nz equals 0.33. T h e higher value of w = 0.3 g m can therefore m a i n l y be a t t r i b u t e d to the influence of the c o n t a c t paths.
S. de ttaaH, J.C. Lodder / Journal (~[Magnetism and Magnetic Materials 168 (1997) 321-335
328
100
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150
H-?ield [kA/m] Fig. 8. Values for Nz as a function of Hall cross width (w) of the samples in Fig. 7 and for a sample with w = 2.0 ~m (squares): The dashed line represents the theoretical values for a block with dimension (w x w x 200 nm 3) and the solid line for a strip with width w (all with the same film thickness).
The theoretical values of a block and a long strip with the same thickness have been obtained by computer calculations [7]. F r o m the difference in Nz between the theoretical curves of the blocks and the strips it can be concluded that the contact paths have a significant influence on the demagnetisation in the cross. The measured values of the real Hall crosses are in agreement with these curves as the same trend with w can be seen and all values of Nz are higher than those of the strips.
Fig. 9. Details of the AHE hysteresis curves of $2 near the coercivity (H = Ho) of an unetched 10 x 10 m m 2 sample (~O-) and for a sample with a Hall cross of 0.3 x 0.3 pm 2 (- x ~ (lines are added as a guide to the eye).
with reduced dimensions of the cross. The precise shape of the cross and the etch angle can also have an effect on the pinning. This increase in coercivity is, however, not observed in the other two samples where the coercivity is independent of the Hall cross size. A possible explanation is that for sample (S1) the coercivity is so low that the reversal is not hindered by the edges and for the high coercive sample that there is a more particulate-like reversal mechanism without d.w.m.
5.2. Coercivity 5.3. A H E curves and measurement noise
Another significant difference in the curves is a change in coercivity for the $2 sample due to a change in Hall cross dimensions. Fig. 9 is an enlargement of Fig. 6 near the coercive field and demonstrates the increase in coercivity for the small Hall cross (- x -), compared to the unetched sample ( - O - ) . The increase is from 90 to 104 kA/m, an increase of 16%. This cannot be explained by a change in internal field due to demagnetisation as the magnetisation in the sample is zero at the coercive field and therefore zero at the demagnetising field also. The larger coercivity can be caused by the edges of the Hall cross which can act as pinning point if the reversal takes place by domain wall motion (d.w.m.). This explanation is confirmed by the fact that the coercivity for these C o - C r films increases
To reveal more of the details of the reversal mechanism hidden in the hysteresis curves, the A H E curves were recorded with very small field steps. The samples which will be discussed here are two submicron $2 samples with dimensions of the Hall cross of, respectively, 0.3 and 0.6 gm, two $3 samples (w = 0.4 and 0.5 gm) and one S1 sample (w = 0.4 txm). To achieve a good signal-to-noise ratio for the A H E measurements the time constant was set to z = 300 ms and the measured Hall voltage was averaged over three readings of the lock-in amplifier at each field. The size of the field steps was chosen to be small enough to minimise the chance that two successive independent steps (above noise level) in the Hall voltage would be detected as one
S. de Haan, J.C. Lodder / Journal o f Magnetism and Magnetic Materials 168 (1997) 321-335
single step (a step in the Hall signal is defined as the change in Hall signal for two successive field values). After each field step the p r o g r a m waited until the field was stable ( ~ 5 s). The size of the field steps was also adjusted to the shape of the hysteresis curve (small field steps if the Hall signal changes fast). The total number of measuring points was 4000 for each A H E loop, resulting in a 9 h recording time for each loop. In all samples the thermal noise was much smaller than the noise from other sources. A lot of noise is probably caused by the contacts in the sample holder which can rotate through two axes. These contacts and the unshielded wires near the sample will give the m a j o r contribution to the noise. In Fig. 10 the A H E loops are shown for the three samples with an enlargement of a typical area in the steep part of the loop. These graphs show that there are only steps in the A H E hysteresis curve for the $2 sample. The largest j u m p s correspond to the switching of one average-sized column. Between the jumps there is an area in which the Hall voltage is almost constant ('plateau'). A closer look at this area (Fig. 11) reveals that there is also an increase in the signal in this part of the curve. F r o m an enlargement of this 'plateau' it can be calculated that the slope is 30 times the slope of the Hall curve in saturation. This means that this effect is not caused by the normal Hall effect but by a very small increase in the A H E voltage for these very small field steps. The noise in the curves was measured by determining 4 x the rms noise at saturation which contains about 95% of all data points and is about 0.033% of the total signal (100% = 2 x Ms). As the n u m b e r of columns in the centre of the Hall cross in this sample is about 25, and most of the A H E signal is derived from the Hall cross we expect that the n u m b e r of j u m p s would be about 25 if the reversal would take place by the switching of the individual columns independently of each other. To study the behaviour of the switching units in more detail several statistical analyses were carried out. The hysteresis curves were recorded m a n y times and the field values of the large steps were studied as a function of the applied field. This distribution of the step sizes as a function of the applied field shows that there are significant
329
differences in successive measurements with the same sample. For these results Fig. 12 is; a typical example (the small steps below the noise level have not been plotted). It shows that even for the two branches in the same loop, the distribution is different for the ascending and the descending branch and that most of the large steps occur around the coercive field (He ~ 90 kA/m). The largest steps around 2 - 3 % correspond to one column. In another sample of $2, with a Hall cross size of 0.6 x 0.6 gm 2, steps in the curve can be also seen. Again the largest steps correspond to the switching of one column. As the number of columns is much larger than for the first sample, the individual jumps are more difficult to measure. This is also due to the fact that for A H E measurements the absolute value of the Hall voltage, corresponding to one column, is inversely proportional with the Hall cross dimensions. As can be seen from the A H E curves in Fig. 10a, Fig. 10b, Fig. 10e and Fig. 10f there are no steps observed in the low and the high coercive samples. We think that the reason is that sample $1 has such a low coercivity that the domain wall motion takes place very gradually with a change in the field that no step occurs above the noise level. For the highcoercivity film $3 we propose that the reversal takes place by the rotation of very small units inside the C o - C r columns and that those units are exchange decoupled and switch independently from each other. Table 3 gives a s u m m a r y of the relevant parameters. The number of columns in the central area of the Hall cross (fourth column) has been estimated as the number of columns that fits in the active area. The numbers in column 2 correspond to different cross sizes and 'bulk' with a sample of size 10 x 10 m m 2.
5.4. Analysis of AHE loops To study the AHE-hysteresis curves in more detail, each A H E curve was divided into five separate curves. Each curve contains only the steps with a certain step siz e and each of these step sizedistinguished partial hysteresis loops (SPH-loops) can be considered as the hysteresis loop of all the magnetic 'volumes' within a certain range. Each
S. de Haan, ,/.C. Lodder ,' .Jozo'nal o/Magnetism and Magnetic Materials 168 (1997) 321-335
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Fig. 10. Anomalous Hail effect hysteresis loops (Jeff) and details of these loops (right) of the samples S1 (a, b), S2 (c, d) and $3 (e, f), respectively.
S. de Haan, J. C. Ladder~Journal of Magnetism and Magnetic Materials 168 (1997) 321 335
range of jump sizes is denoted by a class, and those classes are defined in Table 4, where AM is the change in magnetic moment of each step. In F'ig. 13 the division of an AHE curve of sample $2 in five SPH loops is shown for the loop in Fig. 10c, with the division in classes as given in Table 4. According to this table the loops of Class 1 contain the large steps, Class 2 the small steps, Classes 3 and 4 the small positive and negative steps and also noise, and Class 5 the small negative steps.
331
Class 1 contains the 'large' (irreversible',) steps of volumes > 30 nm 3. Table 5 gives the results of one classification of a typical hysteresis loop. F r o m this table it can be seen that Class 5 has about 5%, which corresponds to steps in the 'reverse' direction, but Class 1 has the largest component with almost 60% (59.6% and 58%). As Class 4 has only 24%, we can assume that the noise is a minor component in the hysteresis curve as Class 4 contains both the noise and a reversible c o m p o n e n t of the magnefisation.
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Fig. 12. D i s t r i b u t i o n ,of t h e s t e p s in t h e h y s t e r e s i s c u r v e o f s a m p l e $ 2 a s a f u n c t i o n o f t h e a p p l i e d fie~d, d e r i v e d f r o m t h e l o o p in Fig. 10c, w i t h [ ] for t h e a s c e n d i n g b r a n c h a n d x for t h e d e s c e n d i n g branclh (tlhe v e r y s m a l l s t e p s b e l o w t h e n o i s e level have been omitted).
H[kR/m] Fig. 11. E n l a r g e m e n t o f Fig. 10d, s h o w i n g t h e i n c r e a s e in H a l l voltage on the 'plateau'.
Table 3 S u r v e y o f t h e s u b m i c r o n a n d t h e 10 x 10 m m z ( ' b u l k ' ) H a l l s a m p l e s m e a s u r e d w i t h t h e A H E Sample
S1 S1 S1 S1 ( b u l k ) $2 $2 $2 (bulk) $3 $3 $3 ( b u l k )
Hall-cross size (w) (gm) ~ 0.4 ~ 0.5 ~ 1.1 ~ 0.3 ~ 0.6 ~ 0.4 ~ 0.6 -
Column diameter (SEM) (nm) ~ ~ ~ ~ ~ ~ ~ N ~ ~
60 60 60 60 75 75 75 70 70 70
Number of c o l u m n s in Hall cross ~ 60 ~ 100 ~ 400 ~ 25 ~ 100 ~ 40 ~ 100 -
Domain (MFM) (rim) -. -. . . -. -. N 147 -. ~ 258
size
~r c
(AHE) (kA/m) 13 14 .
.
.
. 13 108 103 88 168 163 173
S t e p s in curve?
No No No Yes Yes No No -
S. de Haan, J.C Lodder "Jouraal of Magnetism and Magnetic Materials 168 (1997) 321-335
332
35
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Table 4 Step sizes for the classes used to classify the five SPH loops Class
Step size (% of 2 M s )
Specification
1 2 3 4 5
AM > 0.3 011 < AM < 0.3 0.0 < AM < 0.1 --0.1 < AM < 0.0 AM < - 0.1
Large pos. step Small pos. step Very small pos. step Very small neg. step Small neg. step
-15 Table 5 The % of 2M~ for a typical AHE loop of sample $2 for the ascending branch and descending branch and the Hc of the individual SPH loops
-25 -35 -1000 (a)
-500
0 500 H-field [kA/m]
1000
Sample S2
5
3 ~
Ascending branch (%) Descending branch (%) Hc (kA/m)
Class 1
2
3
4
59.6 58.0 145
28.1 4 0 . 6 23.8 31.4 4 0 . 0 23.9 117 33 43
5
4.8 5.7 70
2
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-5 -200-150-100 -50 0 50 100 150 200 (b) H-field [kA/ml Fig. 13. (a) SPH loop of sample $2 (with w = 0.3 gm) with the classification according to Table 4 and (b) a detail of (a). T h e l o o p of Class 1 has the largest coercivity a n d the He decreases for the l o o p s w h i c h c o n t a i n the smaller v o l u m e s b u t does n o t b e c o m e zero, n o t even for Classes 4 a n d 5 (see last r o w of T a b l e 5). This indicates t h a t these l o o p s h a v e also a signific a n t m a g n e t i c origin, as m e r e noise w o u l d n o t result in a coercivity for these loops. 5.5. C o m p u t e r s i m u l a t i o n s
T h e reversal of a small n u m b e r of c o l u m n s which c a n be m e a s u r e d b y the a n o m a l o u s H a l l effect gives
us the o p p o r t u n i t y to c o m p a r e a n d e v a l u a t e these results with c o m p u t e r simulations. T h e c o m p u t e r m o d e l has been d e s c r i b e d in Ref. I-8]. This m o d e l t a k e s i n t o a c c o u n t the e x t e r n a l field, the a n i s o t r o p y energy, the d e m a g n e t i s i n g energy a n d the e x c h a n g e coupling. T h e L a n d a u Lifschitz e q u a t i o n is solved to o b t a i n the d y n a m i c m a g n e t i s a t i o n process. T h e H a l l cross was s i m u l a t e d b y a n a r r a y of 5 x 5 e x c h a n g e d e c o u p l e d particles (columns). E a c h c o l u m n was d i v i d e d i n t o 6 x 6 x 18 cubic cells with cell d i m e n s i o n s of 8.5 n m 3. T h e particles are m a g n e t o s t a t i c a l l y c o u p l e d a n d in this case n o exchange c o u p l i n g b e t w e e n the c o l u m n s was considered. T h e field step b e t w e e n two successive p o i n t s is 1.6 k A / m . I n these c o m p u t e r s i m u l a t i o n s we s t u d i e d the influence of an I L o f 0, 2 a n d 8 % of the t o t a l s a m p l e v o l u m e on the hysteresis l o o p . I n the r e m a i n i n g of this p a p e r we will call these s a m p l e s A, B a n d C, respectively. T h e initial layer was s i m u l a t e d b y assigning a r a n d o m i n - p l a n e m a g n e t i s a t i o n to a certain n u m b e r of cubic cells in the l o w e r two rows of the particles n e a r the substrate. I n real s a m p l e s this c o m p o n e n t can be p a r t of an initial l a y e r a n d / o r d i s t r i b u t e d t h r o u g h o u t the sample.
333
S. de Haan, J.C. Lodder / Journal of Magnetism and Magnetic Materials 168 (1997) 321 335
As macroscopical input parameters for our simulation model we used realistic parameters obtained by VSM and torque (M~ = 400 kA/m and Ka = 1.6 x 105 J/m3). Except for the IL the sample has a perpendicular anisotropy with a spread in easy axis of 1.8 ° from the film normal. In Fig. 14 the three simulated hysteresis curves are presentedl Several changes can be observed with the increase in IL volume. Starting from the saturated state, the drop in magnetisation with decreasing field takes place much earlier with the
presence of the IL. T h e value of the reverse field at which the first large step occurs ( c o r r e s p o n d i n g to the switching of one or m o r e columns) is also m u c h l o w e r for the s a m p l e s with an IL. The t o t a l contrib u t i o n of the small (reversible) p a r t s of the m a g n e t isation, before the first large step t a k e s place is 2.5, 3.9 a n d 10.6%, respectively, for s a m p l e s A, B a n d C. Also can be seen from the size of the large steps that the n u m b e r of c o l u m n s which switch i n d e p e n d e n t l y is 14 a n d l 0 for s a m p l e s g a n d C a n d o n l y 3 for s a m p l e A. T h e largest n u m b e r of c o l u m n s switching t o g e t h e r in one field step is 5 for s a m p l e A a n d b o t h 3 for s a m p l e s B a n d C. R e m a r k a b l e changes for the coercivity (410, 403 a n d 310 k A / m ) a n d the s a t u r a t i o n field (760, 750 a n d 620 k A / m ) only occur for s a m p l e C with the large I L c o m p o n e n t of 8%. F r o m these: d a t a we c o n c l u d e t h a t the presence of a large I L o r i n - p l a n e c o m p o n e n t of the m a g n e t i s a t i o n facilitates the reversal, lowers the coercivity a n d results in the switching of smaller units (less switching of m o r e t h a n one c o l u m n at a time). T h e results of all the s i m u l a t i o n s are s u m m a r i s e d in T a b l e 6. T h e ' p l a t e a u x ' in Fig. 15 which is a n e n l a r g e m e n t o f a p a r t of the curve of Fig. 14c shows significant similarities with the ' p l a t e a u ' in Fig. 11 of s a m p l e S2. T h e g r a d u a l decrease (or increase) of the m a g n e t i s a t i o n can be seen, o n l y there are n o 'reverse' steps a n d there is of course no m e a s u r e m e n t noise. F o r a l a r g e r I L c o m p o n e n t the increase of the m a g n e t i s a t i o n p e r unit of the a p p t i e d field of the ' p l a t e a u ' is larger.
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Table 6 Summary of the results obtained by computer simulation of an array of 5 x 5 Co-Cr columns with a different thickness of the initial layer (IL) Sample
A
IL volume put in model (%) Contribution of the IL (%) (AM/Ms < 0.3%) Number of columns switching individually Switching of first column at field (kA/m) Total reversed volume before first column (%) Largest number of columns switching together Saturation field (kA/m) Coercivity (kA/m) He of Class 1 Hc of Class 2 H; of Class 3
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2 3.94 14 58 0.784 3 760 403 - 338 - 424 -- 253
1056 10 -16 6.87 3 620 310 - 309 -- 451 112
8
334
S. de Haan, J. C. Lodder / Journal qf Magnetism and Magnetic Materials 168 (1997) 321-335
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r We also divided the curves into separate curves with different step sizes in the same way as has been done in Fig. 13 for a real C o - C r sample. A t y p i c a l example is shown in Fig. 16 for sample C. The loops of Class 1 correspond to the steps of multiple column switching (AM > 5:0%), Class 2 with the switching one column at a time (3.0% < AM < 5.0%), and Class 3 with very small changes (0.0% < AM < 3.0%). The curves with reverse step, s (Classes .4 and 5) as shown for the real A H E measurement are not present, resulting in only three S P H loops. F o r all the three samples the coercivity of the Class 3 loops is much lower than for the Class 1 and Class 2 loops. This is in agreement with measurement results and an indication that the small and in-plane components are responsible for the Class 3 contribution to the total hysteresis loop. Unfortunately, the model is not sophisticated enough to simulate the more complicated CP structure of sample $2 and $3.
6. Discussion and conclusions The reversal mechanism of C o - C r has been studied intensively during the last decades but a clear answer whether the reversal takes place by
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d.w.m, or by a rotation mechanism has not been obtained for all samples with different coercivities and composition. We started with three films of different coercivities and different microstructures. The measurements on 'bulk' samples and the A H E measurements on submicron samples of the three samples reveal that the reversal mechanism in the three samples with Ho values of 11, 90 and 170 k A / m is different both on a macroscopic and on a 'meso'-scopic scale.
S. de Haan, J.C. Lodder / Journal o f Magnetism and Magnetic Materials 168 (1997) 321 335
The low-coercivity sample $1 has a low H c ± / H k value corresponding to a stripe domain in the remanent state. The A H E measurements show no jumps as the reversal takes place by a continuous d.w.m, in very small steps. Sample S2 shows small jumps in the A H E curve, the largest comparable to the reversal of one column, and also a very gradual increase in Hall signal which can be attributed to a combination of domain wall motion and rotation of (parts of) a column. The high coercivity film $3 has probably a reversal mechanism by rotation of the magnetisation of very small volumes. This is in agreement with the microstructure as has been shown by N M R and SEM imaging after selective chemical etching (CP structure and high compositional separation (CS)). More evidence was found recently by Takei et al. [9]. They found by SANS (small-angle neutron scattering) that the magnetic unit for C o - C r films with a high CS was smaller than that of a grain. Furthermore, H o n o et al. [10] showed by A P F I M (atom probe field ion microscopy) studies that compositional fluctuations are present inside the grains of Co Cr sputtered films which correspond to the CP structure. The dependence of the Hc on the size of the Hall cross for the $2 sample is attributed to pinning of the domain walls at the edges of the Hall cross which becomes relatively more important for smaller Hall crosses. This dependence is not present in the other two samples as there is no d.w.m, in the $3 sample and in the Sl sample the pinning at the edges is no obstruction for striping out of the domains in the other directions. From the results of the computer simulations we have seen that an initial layer (or in-plane) component lowers the coercivity and the saturation field and facilitates the reversal of smaller units. If the real C o - C r sample has a CP structure the in-plane components (magnetic and non-magnetic) are also distributed inside the columns making the reversal of parts of the column more probable. This makes it more likely that in the case of a CP structure the reversal can take place by the switching of small units, smaller than one column as we have seen for the AHE measurements. A more sophisticated computer model is necessary to simulate the CP structure.
335
We have also seen that the 'plateau' in the real A H E measurement has much resemblance with the simulation and that the slope can be attributed to the reversal of very small magnetic volumes. G o o d agreement was also found for the hysteresis loops which were divided into loops with large medium and small steps (SPH loops). The most significant result here was that the coercivity of the Class 3 loops was much smaller than that for the Class 1 and Class 2 loops for both the measurement and the simulations.
Acknowledgements We would like to thank the D I M E S Institute in Delft for the support in the preparation of the submicron samples, especially for the e-beam lithography. Dr. Maeda of N T T is acknowledged for the preparation of the high- and low-coercivity samples and for the selective chemical etching of the samples and for taking the N M R spectra. Furthermore, we would like to thank Matthijs van Kooten for performing the computer simulations. This research has been financially supported by CAMST, a program of the EC.
References [1] Y. Nakamura, J. Magn. Soc. Japan 15 (Suppl. $2) (1991) 497. [2] J.C. Lodder, D. Wind, Th.J.A. Popma and A. Hubert, IEEE Trans. Magn. 23 (5) (1987) 2055. [3] K. Takei and Y. Maeda, Jpn. J. Appl. Phys. 30 (6B)(!991) Ll125. [4] Y. Maeda, S. Hirono and M. Asahi, Jpn. J. Appl. Phys. 24 (12) (1985) L951. [5] B.C. Webb and S. Schultz, IEEE Trans. Magn. 24 (1988) 3006. [6] S. de Haan, J.C. Lodder and Th.J.A.Popma, J. Magn. Soc. Japan Suppl. $2 15 (1991) 349. [7] J.G.Th. te Lintelo, J.C. Lodder, J. Engemann and ThJ.A. Popma, J. Magn. Magn. Mater. 115 (1992) 333. [8] M. van Kooten, S. de Haan, J.C. Lodder and Th.J.A. Popma, J. Appl. Phys. 75 (10) (1994) 5508. [9] K. Takei, J. Suzuki, Y. Maeda and Y. Morii, IEEE Trans. Magn. 30 (6) (1994) 4029. [10] K. Hono, S.S. Babu, Y. Maeda, N. Hasegawa and T. Sakurai, Appl. Phys. Lett. 62 (20) (1993) 2504.