- Email: [email protected]
Cu multilayers
Journal of Magnetism and Magnetic Materials 125 (1993) 209-220 North-Holland
Magnetic coupling and magnetic anisotropy in Fe/Co and Fe/Cu multilayers 6.F. Bakkaloglu a, M.F. Thomas a, R.J. Pollard b, P.J. Grundy b, V. Lewis ’ and K. O’Grady ’ ’ Department of Physics, University of Liverpool, Liverpool L69 3BX, UK b Department of Pure and Applied Physics, University of Salford, Salford M5 4W, UK ’ Magnetic Materials Research Group, School of Electronic Engineering Science, UCNW, Bangor LL57 IOT, UK
Received 28 October 1992
Magnetisation measurements of magnetic multilayer samples of Fe/Co and Fe/Cu having equal layer thickness of Fe and Co and Fe and Cu, respectively, were carried out at room temperature using an alternating gradient force magnetometer (AGFM). Comparison of the saturation magnetisation measurements with calculated values of magnetisation indicated that the magnetic moments of the Fe layer and the Co layer are ferromagnetically coupled. Mijssbauer spectroscopy studies at room temperature and at 4.2 K show that in the Fe/Cu multilayers and some of the Fe/Co multilayers the magnetic easy axis lies in the plane of sample. In several other Fe/Co multilayers a normal component of magnetisation is observed and it is necessary to introduce a magnetic anisotropy term favouring a magnetic easy axis normal to the sample plane. Measurements of hysteresis cycles and applied field Mossbauer studies enable the magnetic anisotropy of the samples to be evaluated.
1. Introduction
The study of coupling between magnetic moments of magnetic layers through a nonmagnetic material has attracted much attention in recent years. Among the various combinations of elements used in multilayers the coupling between the magnetic moments of adjacent magnetic layers is of interest. The magnitude of exchange coupling in ferromagnetic/ ferromagnetic/ ferromagnetic systems can be very large [l]. Magnetic multilayers can be made to have a number of properties favourable for applications in high density magnetic recording media. They can be prepared with soft magnetic properties and a high magnetisation 121. An additional favourable property is for the magnetisation to be Correspondence to: Dr M.F. Thomas, Department of Physics, University of Liverpool, Liverpool L69 3BX, UK.
aligned normal to the plane of the layers. Normally this is not an energetically favourable domain configuration but magnetic anisotropies may be introduced via the interfaces between layers and it is of interest to understand whether these can cause anisotropy that produces a magnetic easy axis normal to the layers. In this study we present the magnetic properties of Fe/Co multilayer systems by comparing with those of Fe/Cu multilayers. The measurements on the coupling between the magnetic moments of Fe and Co layers and information on the magnetic anisotropy of Fe/Co and Fe/Cu multilayer samples were obtained using an alternating gradient force magnetometer (AGFM). The direction of the magnetic easy axis in each multilayer sample was established using Mossbauer spectroscopy. The magnetic anisotropy constants were measured by using Mossbauer spectra to monitor the rotation of the magnetisa-
0304-8853/93/%06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved
Information Storage: Basic and Applied
210
ii. F. Bakkaloglu
tion under fields.
the
influence
2. Experimental A computer system (Atom
of applied
rt ul. / Mugnetism
of Fe / Co and Fe / Cu multiluyen
magnetic
fabricate Fe/Co multilayers with0 layer thicknesses of 150, 75, 50, 30, 20 and 10 A, and Fe/Q multilayers with layer thickness of 30 and 20 A. The thicknesses of Fe and Co layers in the Fe/Co samples and of Fe and Cu layers in the Fe/Cu samples are equal. All samples have been deposited onto commercially available iron free polyimide with a thickness of 0.05 mm. The sub-
technique controlled magnetron sputtering Tech 2000 series) was used to
(a)
W Fig.
1. Characterisation
of samples: (a) TEM diffraction pattern
micrograph from0 the (Col:O A/Fe150 &X20 multilayer from the (Co150 A/Fe150 A)x 20 multilayer sample.
sample;
(b) Electron
Information Storage: Basic and Applied
6.F. Bakkaloglu et al. / Magnetism of Fe / Co and Fe / Cu multilayers
strate temperature was near to room temperature during deposition and a constant pressure of 3 mTorr of Ar was maintained in the sputtering system. The system was calibrated by determining the calibration film thickness by X-ray fluorescence for each material. The multilayer films were characterised by cross sectional electron microscopy and electron diffraction. Films were prepared for microscopy by a microtome technique. The cross sections were then observed in a JEOL 200CX TEM. Layering )r the Fe/C: films was seen in the 150/150 A and 75/75 A films. An illustoration of a, TEM micrograph of the 20 X (Fe150 A/Co150 A) film is shown in fig. l(a). The micrographs
Y-ray --
k
211
reveal polycrystalline Dfilms with a grain size of between 100 and 150 A. Diffraction patterns from the Fe/Co films show the iron to be in the bee phase. Fyr the samples with thick layers (150, 75 and 50 A) the Co is in the hcp phase but for those with layer thicknesses 30, 20 and 10 A the rings can be indexed assuming either hcp or bee structure. It is reported [31 that in Fe/Co multilayers formed by dc triode sputtering the Co layers have hcp structure above 40 A thickness but that for thinner layers the hcp rings disappear and only the rings of the bee iron are seen. Diffraction patterns from the 20 and 30 A Fe/Cu films reveal the iron to be bee and the copper to be in the fee phase. Figure l(b) shows a diffrac-
0
4
P
(a)
(b)
Y-ray i
1 B
T
-
Y-ray
4
8
(c)
P
(d)
Fig. 2. Schematic diagrams for (a) Mossbauer measurements on Fe/Co and Fe/Cu multilayers room-temperature hysteresis measurements; (c) Mossbauer measurements with applied field on Fe/Co initial magnetisation lies in the sample plane; and (d) Mdssbauer measurements on Fe/Co samples initial magnetisation lies out of the sample plane.
at room temperature; (b) and Fe/Cu samples whose where a component of the
Information Storage: Basic and Applied
212
6.F. Bakkaloglu et al. / Magnetism of Fe /Co and Fe / CM multilayers
tion pattern from the 20 X (Fe150 A/Co150 A> film. The diffraction micrographs show no sign of preferred orientation in the multilayers. The Miissbauer spectra themselves show characteristic absorption lines tf bee iron for all samples except the Fe/Cu 10 A. This latter sample is the only one to show Mossbauer evidence of iron in a non-crystalline environment. The hysteresis measurements were carried out at room temperature using a Princeton Micromag Model 2000 alternating gradient force magnetometer (AGFM). In this technique a chosen dc magnetic field was applied parallel to the plane of the sample and an ac magnetic field was superimposed along the direction of the dc field. The frequency of the ac field was matched to the vibrational frequency of the sample suspension. The voltage signal was generated from the sample displacement via a piezoelectric mounting crystal. By automatic stepping of the dc field, hysteresis cycles of the samples were obtained for the geometry in which the magnetising field is parallel to the plane of the layers. The system was calibrated on a standard nickel foil and achieves a sensitivity of 10 nemu. In the Mossbauer experiments a conventional double ramp constant acceleration spectrometer was used in the transmission mode. The samples were not enriched with “Fe and consequently were not strongly absorbing with maximum absorption intensities in the range of 1%. Applied fields of up to 10 T could be obtained using superconducting Helmholtz coils. The magnetic configuration allowed different experimental geometries to be used. For multilayers where the easy axis of magnetisation lies in the plane of the layers, the field and y-ray beam were directed along the normal to the layers while for the multilayers in which the magnetisation has a component normal to the plane of the sample, the field was applied in the plane of the layers, perpendicular to the y-ray beam.
normal to the layers is determined by Mossbauer spectra. The spectra of the Fe/Co multilayers taken at room temperature with the experimental geometry shown in fig. 2(a) are illustrated in fig. 3. It is seen that they consist of magnetic sextets. The relative intensities of the outer : middle: inner doublet components of the sextet pattern are theoretically predicted to be 3: (4 sin*8/1 + COSTS): 1, where the angle 0 shown in fig. 2(a) is that between the y-ray beam directed along the normal to the plane of the layers and the mean direction of the Fe spins (the direction of the mean Fe magnetisation). It should be stressed that this method measures the mean value of 4 sin28/1 + cos28 but does not give information on any possible distribution in the values of 0. Values of 0 reported in tables 1 and 2 are deduced assuming a sharp value of 0. The spectra of fig. 3 show that different values are measured for the mean direction of the iron magnetic moment in different multilayer samples. In these spectra the intensities of the inner lines
1
I1 -10.0
3. Results and analysis The average direction that the Fe magnetisation of a given multilayer sample makes with the
-8.0
I -8.0
-4.0
‘d -2.0
” I
I 0.0
I
I
2.0
4.0
I1 8.0
1
8.0
100
Velocity (mm/se& Fig. 3. Spectra taken at 290 K of Fe/Co samples with layer thickness ranging from 150 to 10 A and fitted with two sextet components.
Information Storage: Basic and Applied
8.F. Bakkaloglu et al. / Magnetism of Fe/Co
3 and 4 are not well fitted due to a small distribution of hyperfine fields within each major component. Estimates of the error in the value of the angle 0 deduced from these spectra were obtained by evaluating the goodness of fit parameter x2 as the value of the angle 0 is stepped through the region of best fit. From the resulting x2 versus 19variation the errors shown in tables 1 and 2 are obtained.
213
with the easy axes in the sample plane. The second comprises the samples with the easy axes at some angle to the sample plane. The results of the hysteresis measurements on these samples are presented in these groups. All hysteresis measurements were carried out at room temperature applying dc and ac fields parallel to the sample plane in the geometry illustrated in fig. 2(b). The r:sults on thf samples of 10 A Fe/Co and 30 A and 20 A Fe/Cu multilayers which have their magnetic easy direction in the sample plane, i.e. 8 = 90”, are shown in fig. 4. Since these samples have relatively low coercive fields and high loop slope with narrow loop width, they have fairly soft magnetif properties. For the samples of 75, 50 and 20 A Fe/Co multilayers where 8 # 90”, the hysteresis results
3.1. Hysteresis measurements The Mossbauer measurements described above on the Fe/Co and the Fe/Cu multilayers show that these samples may be classified into two distinct groups in terms of the alignment of their easy axes. The first group comprises the samples
b -1E-2 I -5Et2
0
-SE+3
and Fe / Cu multilayers
I
I
I
I
I
I
I
a 0
I
I
I
n
lo4
I
I +5E+2
+lE-2
H ILkI
-1E-2 _:IE+i I
Fig. 4. M-H
hysteresis
I
I
I
I
I_
-i
+*+3
cycles of the Fe/Co sample (a) with layer thickness of 10 ,& and the Fe/Cu samples of 30 and 20 A (b, c) whose initial magnetisations lie in the sample plane.
with layer thicknesses
Information Storage: Basic and Applied
214
6. F. Bakkaloglu et al. / Magnetism
qf Fe / Co and Fe / Cu multilayers
are shown in fig. 5. The hysteresis cycles of these samples are seen to consist of two parts, the central cycle caused by irreversible motion of domain boundaries and reversible shoulders leading from the central cycle to the saturation state. This shape of hysteresis cycle confirms that these samples possess a component of magnetic moment normal to the sample plane. The reversible shoulders of these cycles represent a rotation of the ferromagnetic moment of the sample from its initial direction into the plane of the sample as the applied field in the plane of the sample is increased. As the layer thickness of these samples decreases and the importance of the interface layers increases it is seen that irreversible part of the cycle becomes wider and the slope of the shoulders decreases. The saturation values of the magnetisation M of the Fe/Co and Fe/Cu multilayers obtained
-Et3
Fig. 5. H-M
hysteresis
from figs. 4 and 5 are listed in table 1, where they are compared with the values MJcalc) calculated assuming ferromagnetic (parallel) coupling of the magnetic moments of Fe and Co layers and M,,(calc) assuming antiferromagnetic (antiparallel) coupling between Fe and Co layers. These calculations were carried out assuming the standard crystalline bee structure for Fe with the bulk value for the lattice constant a = 2.87 A and an hcp structure fof Co with bulk yalue lattice constants a = 2.51 A and c = 4.07 A. The Fe primitive cell has two atoms with intrinsic magnetic moments of 2.2~~ and the Co primitive cell two atoms with intrinsic magnetic moments of 1.72~~. It is clear from the values in table 1 that the antiferromagnetic predictions are an order of magnitude smaller than the observed values, while ferromagnetic predictions are consistent with the observed values to within - 10%. For Fe/Cu
0
cycles of the (a) 75, (b) SO and Cc) 20 A Fe/Co samples the sample plane.
_1 +x+3
whose initial magnetisations
lie at finite angles to
Information Storage: Basic and Applied
6.F. Bakkaloglu et al. / Magnetism of Fe/Co
and Fe / Cu multilayers
215
Table 1 Measurements of the mean direction of magnetisation and measured and calculated values of the magnitude of this magnetisation. B(Moss) represents the magnetisation direction obtained from Miissbauer measurements at 290 K. MtAGFM) represents the magnetisation measured by AGFM. M,(calc) and MA,(calc) represent the calculated magnetisation values for ferromagnetic and antiferromagnetic couplings, respectively, M,(imp) represents the improved calculations of magnetisation incorporating the effects of interface layers. All values of magnetisation are in (emu cmm3) Thickness
(A)
B(Miiss)
M(AGMF) (emu cm-“)
M,(calc) (emu cm-‘)
M&alc) (emu cm-“)
M,(imp) (emu cm-3)
1680 1720 1730 1710 1950
1600 + 1590+_ 1590+ 1600 + 1590*
153*1 148* 1 148kl 147+1 148+1
1720+ 1650 f 169Ok 1740 * 1890 k
Fe/Co
15 50 30 20 10
51*1 42&l 55+2 40+2 9Ok2
Fe/Cu
30 20
90*4 9Ok2
k 10 +_10 * 10 f 10 * 10
820 f 10 740+ 10
samples the observed and calculated values are consistent with complete alignment of the magnetic moments of the Fe layers either through ferromagnetic coupling or by alignment of the magnetic moment of each Fe layer. Improved calculations on the magnetisation of the Fe/Co multilayers M,(imp) assume ferromagnetic coupling but also consider the effect of the interface layers between Fe and Co layers of mean thickness 9 A which have been inferred from the accompanying hyperfine field studies [4]. The mean magnetic moment in these interface layers which have an average composition of 50% Fe and 50% Co is given as 2.38~~ from the Slater-Pauling graph [5]. The calculations for the pure Fe and Co layers in this improved approach were carried out in the same way as in the approach described above. An expression for the magnetisation M in the improved calculation may be written as M=
c
N.p.n,
(1)
Fe,FeCo,Co
where the sum is taken over the pure Fe layer, the pure Co layer and the FeCo interface layer. For the relevant layer N is the number of atoms per unit area, jZ is the mean magnetic moment, and n is the number of the layers per unit thickness. The results of the calculations given in table 1 as M,(imp) show higher values of magnetisation
10 10 10 10 10
870 f 10 870 f 10
10 10 10 10 10
0 0
than those assuming only pure metallic layers due to the enhancement of the magnetic moments of Fe and Co atoms in FeCo alloy interface layer. The results of the calculations incorporating the interface layers are in better agreement with the experimental values. The lack of information on the magnetic moments of iron atoms in mixed Fe/Cu interface layers prevents a similar calculation being made for the Fe/Cu multilayer samples. However, the results of studies of the hyperfine fields in Fe/Cu multilayers [4,6] show that the iron moment in these interface layers is reduced below that in pure iron. Thus any calculation incorporating the effect of interface layers would result in a value of M, which is less than that predicted by the pure layer cal$ulations shown in table 1. Further, since the 20 fi sample has more interface layers than the 30 A sample the reduction in M, predicted for this 20 A layer sample yould be greater than that predicted for the 30 A sample. These expectations are seen to be consistent with the values shown in table 1 for the Fe/Cu samples. It is illuminating to plot the measured magnetic moment per period per unit area (M X t) against periodic thickness t. This is shown in fig. 6, where it is seen that (M x t ) increases linearly with periodic thickness for Fe/Co and Fe/Cu samples. Extrapolating back towards zero thickness, however, contrasting behaviour is observed. For the Fe/Cu samples zero magnetic moment
Information Storage: Basic and Applied
0.F.
216
Bakkaloglu et al. / Magnetism of Fe /Co and Fe / Cu multilayws
occurs at finite thickness (5 f 1 A> indicating a magnetic dead layer. For the Fe/Co samples the finite intercept on the magnetic axis as the periodic thickness tends to zero indicates the enhancement of magnetic moment at Fe/Co interfaces.
000 0.25 000 1 0.40
s .z
4
3.2. Applied field Miissbaue,* measurements
/
o.oo0.50 0.10
The Mossbauer measurements were used to monitor the alignment of the magnetisation vector of the iron atoms when external magnetic fields were applied to the samples at 4.2 K. For the samples whose initial magnetisation vectors lay in the sample plane the geometry of the experiment is illustrated in fig. 2(c). For the samples where a component of the initial magnetisation vector lay out of the sample plane the external field is applied parallel to the sample plane as shown in fig. 2(d). The evolution of the Miissbauer spectra of the 20 A Fe/Co multilayer with increasing field applied as in fig. 2(d) is shown in fig. 7. Values for the mean angles 8 between the iron magnetisation and the sample normal, as the applied field B is increased, are listed in table 2. The intensities of the second and fifth lines are seen to
k
2.6
-
i 2.0 0) r 2 1.6
-
0
2.4
E
0.50 0.00 0.00 : 0.75
0.00 -0.50
/i
I
1
-10.0
-6.0
1
-8.0 -4.0 -2.0 0.0 2.0 4.0 8.0 8.0 Velocity
10.0
(mmlsec)
Fig. 7. Miissbauer spectra of the 20 ,& Fe/Co sample increasing applied field taken at 4.2 K.
with
increase with increasing external field strength and the intensity ratio eventually becomes 3 : 4 : 1 at an applied field of 0.18 T indicating that the angle ~9 between the iron magnetisation vector and y-ray beam has become 90”. At larger values of applied field the angles obtained via the intensities of lines 2 and 5 in the spectra can be
Thickness -
Fe/Co
/
Btext) (T)
sin’fI
H
0.000 0.0 17
0.73 f 0.01 0.94 * 0.02 I .OO+ 0.004
sY+ I 76+2 YOf 4
50
0.000 0.025 0.050 0.075
0.45 0.60 0.64 I .oo
42* I s1+2 s3*1 90+x
20
0.000
0.45 + 0.01
0.050 0.080
0.60+ 0.03
I 5152
0.91 + 0.03 0.96 + 0.02 0.98 + 0.01 I .oo* 0.004
73+3 7x+3 x3+4 90 f 4
75
(A)
0.010
t
,,
:,
Table 2 Values of (sin’@) and hence 0 obtained from Miissbauer spectra in applied fields on 75, 50 and 20 A Fe/Co multilayers. The angle 8 is that between the iron magnetic moment and the y-ray beam
x
YE
$8 IL
T
20
40
60
80
100
120
140
160
(xl@)
t(cm)
Fig. 6. Graph of magnetic moment per period per unit area (M x ) versus periodic thickness I. Measurements on Fe/Cu samples are shown as filled circles and measurements on Fe/Co samples as open circles. Extrapolating to low values of periodic thickness shows a magnetic dead layer in Fe/Cu while in Fe/Co the intercept confirms the enhanced magnetism of the interfaces.
0.100 0.120 0.180
f + + *
0.02 0.03 0.01 0.02
42+
Information Storage: Basic and Applied
6.F. Bakkaloglu et al. / Magnetismof Fe/Co and Fe / Cu multilayers No held
samples with the magnetic easy axis in the sample plane can be written as E = K,
-10.0
-8.0 -&o -4.0
-2.0
0.0
2.0
4.0
6.0
8.0 10.0
Velocity (mmlsec) Fig. 8. The spectra of the 10 A Fe/Co sample taken with increasing applied field at 4.2 K.
checked by measurement of the total field B, at the nucleus. The total field is related to the hyperfine field B,, and applied field by B, = [B& +B2+2BBhf sin 61‘I2 . The agreement between the two methods was satisfactory. The zvolution of the Miissbauer spectra from the 10 A Fe/Co sample where the experimental geometry is that of fig. 2(c) is shown in fig. 8. It can be seen from this figure that the intensities of the second and fifth lines decrease with increasing external field strength. At the external field of 2.5 T the intensity ratio becomes 3 : 0 : 1 indicating that the magnetisation vector is aligned along the y-ray beam. The variation of the direction of magnetisation with applied field, monitored in this way by the Mossbauer spectra is analysed in terms of magnetic anisotropy in section 4.
sin24 - PB cos 8,
Types of anisotropy
B(loc) = B(ext) - ~~$4,
(3)
where M is the component of magnetisation parallel to the applied field. For the geometry in which the applied field is applied parallel to the sample plane B(loc) = B(ext).
(4)
These expressions assume that the demagnetisation factor for these multilayer samples can be treated as if they were uniform homogeneous magnetic materials. Minimising the energy E in eq. (2) by applying the condition dE/d6’ = 0 gives the expression (5)
and anisotropy
constants
Graphs of cos 0 versus local fi$ld B for samples B = 90” and for the 30 A Fe/Co sample which shows a similar hysteresis cycle are shown in fig. 9. The gradients of the graphs in fig. 9 yield values of p/2K, from which the mean atomic anisotropy constant K, for each sample was evalwith
4.1. Samples with 13= 90” An e;pression the 10 A Fe/Co
(2)
where K, is the anisotropy constant, 4 and 8 are the angles between magnetisation vector and sample plane and between magnetisation vector and applied field respectively. In this expression it is assumed that the iron and cobalt components of the combined magnetisation remain parallel and p represents the mean atomic magnetic moment. For Fe/Co samples with equal layer thicknesses of Fe and Co the value of p is taken as 1.81 X 1O-23 J/T. For Fe/Cu samples, where only the iron atoms possess magnetic moments and magnetic anisotropy, F = 2.04 X 1O-23 J/T. The geometry for these measurements is shown in fig. 2(c). In this geometry the local magnetic field is not simply the applied field but is modified by the demagnetisation factor. For this geometry where the applied field is normal to the sample plane the relationship for the local field B(loc) is given by [7]:
cos 0 = (p/2Kp)B. 4. Discussion:
217
for the apisotropy eaergy for and 30 A and 20 A Fe/Cu
Information Storage: Basic and Applied
d;.F. Bakkaloglu et al. / Magnetism of Fe/Co
218
(b)
1Oi Fe/Co
1 .o
(a) 3OA Fe/Co
and Fe / Cu mu1tilayer.s
uated. These table 3.
values
of
K,
are
presented
in
4.2. Samples with 0 # 90” 0.6
t - _.~.~ B(ioc)
(c)
30 i Fe/Cu
(d)
. ,I’ /.
1
4 0.4
CT)
2Oi Fe/Cu
1 .o
0.0
_
0.4
0.0
, 0.4
0.0
B(loc) (T)
BUoc) (T)
Fig. 9. Graphs of cos fJ versus local field B(loc) for (a) 30 A Fe/Co; (b) 10 ,& Fe/Co; (c) 30 A Fe/Cu; and (d) 20 A Fe/Cu samples.
The observation in the 75, 50 and 20 A Fe/Co samples that the easy axis is at a finite angle to the normal to the sample plane, requires a term to represent an anisotropy component K, normal to the sample plane. Possible expressions representing this new situation with anisotropy constant K, in plane and K, normal to plane may be written as E = K, sin20 + K, sin’4,
(6)
E = K, sin40 + K, sin’4.
(7)
Equation (6) is rejected as this expression does not give a minimum in energy E in the range of 0” 5 8 2 90” and thus would not explain the direction of magnetisation at zero field. However, the expression of eq. (7) does give such a minimum and is the simplest hypothesis that can represent the observed behaviour. For samples Fe/Co with thickness0 10 A and0 Fe/Cu samples with thickness 20 A and 30 A the same expression holds but with K, = 0. The anisotropy energy of eq. (7) for the geometry shown in fig. 2(d) can be written as E = K, sin”0 + K, sin”+ - FB sin 0. Applying the condition expression is obtained 4K,
Table 3 Values of anisotropy constants K, and K, in J/atom evaluated from the applied field Miissbauer measurements at 4.2 K Thickness Fe/Co
Fe/Cu
(A)
K,(x
1O-‘4)
75 50 30 20 10
0.38 f 0.03 0.92kO.19 - 3.5 1.07+0.16 - 5.4
30 20
- 4.9 - 5.0
K,(x
lo-*“)
0.26 + 0.02 1.02*0.21 1.21*0.18
When be sin’s
d E/d0
B = 0, the equilibrium = K,/2
= 0, the following
sin O-pB=O.
sin%-2K,
K,.
(8)
(9) angle
(Y is seen to
( 10)
Using the values of 0 for these samples measured in this geometry as the applied field is varied, the values of K, and K, for these samples were calculated from eqs. (9) and (10). Mean values of K, and K, are given in table 3 for each sample. The values in table 3, given in Joules per atom, apparently show that the anisotropy constant K, is much greater,for the samples with the magneti-
Information Storage: Basic and Applied
6. F. Bakkaloglu et al. / Magnetism
sation lying in the plane of the samples (0 = 900) than for samples where the magnetisation is not confined to the plane (0 # 900). However, these relatively large values of K, for 8 = 90” samples are extremely sensitive to small changes in the demagnetisation term which is employeOd in the evaluation of B. For example in the 30 A Fe/Co sample a 10% increase in the demagnetisation term changes the value of K, per atom from 3.5 X 1O-24 J to 0.9 x 1O-24 J. The values of the demagnetisation terms were evaluated assuming that the samples were homogeneous magnetic materials rather than layers of different magnetic materials. The layer structure of the samples could well lead to effective demagnetisation effects from interface layers resulting in changes in the demagnetisation term that would cause large variations in the values of K, derived in this geometry. Thus while relative comparisons between K, values for samples with 8 = 90” are likely to be valid, comparisons of values of K, derived from the different experimental geometries shown in figs. 2(c) and (d) are not considered to be reliable. Within this set of 8 = 90 samples it can be seen that the anisotropy constant K, increases as the layer thickness decreases and the interfaces play a more important role in the samples. In the case of the 0 # 90” samples, demagnetisation plays no part in the evaluation of the anisotropy constants and the values are more reliable. Comparison of the 4.2 K values of K, and K, shows that, like the 8 = 90” samples, the values of the anisotropy constants increase as the layer thickness decreases. There seems to be no straightforward relation between layer thickness and the angle 0 made by the magnetisation to the normal to the sample plane. Whether this is a result of random influences during the sputtering deposition of the layers or complex magnetic interactions between the magnetic Fe and Co layers will be studied in further investigations on magnetic samples. 4.3. Search for in-plane anisotropy A set of measurements was carried out to test for a component of anisotropy in the sample
of Fe/Co
and Fe / Cu multilayers
219
77K (35.270)
-10.0 -8.0-8.0 -4.0 -?.O 0.0 2.0 4.0 6.0 8.0 10.0
Velocity (mm/set) Fig. 10. Spectra of the 20 A Fe/Co sample taken at 77 K with the variation of the sample position. The first spectrum is taken with the sample in a position in which the normal to the sample is parallel to the y-ray beam (0, 0). The second spectrum is taken in a position in which the normal to the sample is rotated to the right to make an angle of - 35” to the y-ray beam c-35”, 0). The third spectrum is taken in a position in which the normal to the sample is rotated to the left to make an angle of 35” to the y-ray beam (35”, 0). The fourth, fifth and sixth spectra are taken by keeping in the position in which the third spectrum is turning the sample through angles of 90”, 180” and 90”), (35”, 1803 and (35”, 270”), respectively, around axis.
the sample taken, but 270”, (35”, its normal
plane. Figure 10 shows the spectra of 20 A thick Fe/Co sample taken at 77 K. The first spectrum is taken in the usual geometry of fig. 2(a). The second spectrum is taken by turning the sample so that the normal to the sample plane is rotated to the right to make an angle of 0 = - 35” to the y-ray beam and third spectrum is taken by turning the sample so that the normal to the sample plane is rotated to the left to make an angle of f3= 35” to the y-ray beam. This position of the sample is also specified by azimuthal angle 4 = 0. In the next three spectra 0 is kept at 35” but the sample is rotated about its normal axis by succes-
Information Storage: Basic and Applied
220
ii.F.
Bakkaloglu et al. / Magnetism of Fe /Co and Fe / Cu mu1tilayer.s
sive stages to give azimuthal angles 4 = 90“, 180 and 270”, respectively. It can be seen from these spectra that there is no significant change in the intensities of the second and fifth lines of the spectra as the angle 4 is varied. If there was a preferred direction of magnetisation in the plane of the sample it would cause a change in the intensity ratio of these lines of the spectra shown in fig. 10. The absence of any change within the accuracy of the measuremeat means that the magnetisation vector of the 20 A thick Fe/Co sample can be visualised as a cone whose axis is the normal to the sample plane. It should, however, be borne in mind that the statistics of these spectra are not good and thus a weak preferred direction may not be detected.
of planar and normal anisotropy constants and values of these constants were evaluated from a set of measurements in which an applied field was used to collapse the cone and rotate the resulting moment into the sample plane. Other samples showed the more expected planar anisotropy. No evidence was found for any inplane anisotropy.
Acknowledgements
6FB acknowledges the support of a grant from Atatiirk University, Turkey, throughout this work, and the financial support of the SERC is acknowledged.
References 5. Conclusions
The iron and cobalt layers of a set of sputtered multilayer samples have been shown to be ferromagnetically coupled. Improved agreement between calculated and experimental values of magnetisation was obtained when explicit account was taken of interface layers whose presence is inferred from accompanying studies on hyperfine fields in these samples. The unexpected result was the cone anisotropy observed in some Fe/Co layers. This anisotropy was parameterised in terms
[I] L.M. Falicov et al., J. Mater. Res. 5 (1900) 12YY. [2] Y. Hoshi, M. Seki and M. Naoe, J. Physique Coil. (1988) u-1793. [31 R. Krishnan, H.O. Gupta, H. Lassri. C. Sella and M. Kaabouchi, J. Appl. Phys. 70 (1991) 6421. [4] 6.F. Bakkaloglu, M.F. Thomas, R.J. Pollard and P.J. Grundy, J. Magn. Magn. Mater. I25 (1993) 221. [5] A.H. Morrish, The Physical Principles of Magnetism (Willey, New York, 1965). [6] H.M. van Noort, F.J.A. den Broeder and H.J.G. Draaisma. J. Magn. Magn. Mater. 51 (1985) 273. [7] E.C. Stoner and E.P. Wohlfarth. Proc. Trans. R. Sot. 240 (1948) 599.
Magnetic coupling and magnetic anisotropy in Fe/Co and Fe/Cu multilayers 6.F. Bakkaloglu a, M.F. Thomas a, R.J. Pollard b, P.J. Grundy b, V. Lewis ’ and K. O’Grady ’ ’ Department of Physics, University of Liverpool, Liverpool L69 3BX, UK b Department of Pure and Applied Physics, University of Salford, Salford M5 4W, UK ’ Magnetic Materials Research Group, School of Electronic Engineering Science, UCNW, Bangor LL57 IOT, UK
Received 28 October 1992
Magnetisation measurements of magnetic multilayer samples of Fe/Co and Fe/Cu having equal layer thickness of Fe and Co and Fe and Cu, respectively, were carried out at room temperature using an alternating gradient force magnetometer (AGFM). Comparison of the saturation magnetisation measurements with calculated values of magnetisation indicated that the magnetic moments of the Fe layer and the Co layer are ferromagnetically coupled. Mijssbauer spectroscopy studies at room temperature and at 4.2 K show that in the Fe/Cu multilayers and some of the Fe/Co multilayers the magnetic easy axis lies in the plane of sample. In several other Fe/Co multilayers a normal component of magnetisation is observed and it is necessary to introduce a magnetic anisotropy term favouring a magnetic easy axis normal to the sample plane. Measurements of hysteresis cycles and applied field Mossbauer studies enable the magnetic anisotropy of the samples to be evaluated.
1. Introduction
The study of coupling between magnetic moments of magnetic layers through a nonmagnetic material has attracted much attention in recent years. Among the various combinations of elements used in multilayers the coupling between the magnetic moments of adjacent magnetic layers is of interest. The magnitude of exchange coupling in ferromagnetic/ ferromagnetic/ ferromagnetic systems can be very large [l]. Magnetic multilayers can be made to have a number of properties favourable for applications in high density magnetic recording media. They can be prepared with soft magnetic properties and a high magnetisation 121. An additional favourable property is for the magnetisation to be Correspondence to: Dr M.F. Thomas, Department of Physics, University of Liverpool, Liverpool L69 3BX, UK.
aligned normal to the plane of the layers. Normally this is not an energetically favourable domain configuration but magnetic anisotropies may be introduced via the interfaces between layers and it is of interest to understand whether these can cause anisotropy that produces a magnetic easy axis normal to the layers. In this study we present the magnetic properties of Fe/Co multilayer systems by comparing with those of Fe/Cu multilayers. The measurements on the coupling between the magnetic moments of Fe and Co layers and information on the magnetic anisotropy of Fe/Co and Fe/Cu multilayer samples were obtained using an alternating gradient force magnetometer (AGFM). The direction of the magnetic easy axis in each multilayer sample was established using Mossbauer spectroscopy. The magnetic anisotropy constants were measured by using Mossbauer spectra to monitor the rotation of the magnetisa-
0304-8853/93/%06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved
Information Storage: Basic and Applied
210
ii. F. Bakkaloglu
tion under fields.
the
influence
2. Experimental A computer system (Atom
of applied
rt ul. / Mugnetism
of Fe / Co and Fe / Cu multiluyen
magnetic
fabricate Fe/Co multilayers with0 layer thicknesses of 150, 75, 50, 30, 20 and 10 A, and Fe/Q multilayers with layer thickness of 30 and 20 A. The thicknesses of Fe and Co layers in the Fe/Co samples and of Fe and Cu layers in the Fe/Cu samples are equal. All samples have been deposited onto commercially available iron free polyimide with a thickness of 0.05 mm. The sub-
technique controlled magnetron sputtering Tech 2000 series) was used to
(a)
W Fig.
1. Characterisation
of samples: (a) TEM diffraction pattern
micrograph from0 the (Col:O A/Fe150 &X20 multilayer from the (Co150 A/Fe150 A)x 20 multilayer sample.
sample;
(b) Electron
Information Storage: Basic and Applied
6.F. Bakkaloglu et al. / Magnetism of Fe / Co and Fe / Cu multilayers
strate temperature was near to room temperature during deposition and a constant pressure of 3 mTorr of Ar was maintained in the sputtering system. The system was calibrated by determining the calibration film thickness by X-ray fluorescence for each material. The multilayer films were characterised by cross sectional electron microscopy and electron diffraction. Films were prepared for microscopy by a microtome technique. The cross sections were then observed in a JEOL 200CX TEM. Layering )r the Fe/C: films was seen in the 150/150 A and 75/75 A films. An illustoration of a, TEM micrograph of the 20 X (Fe150 A/Co150 A) film is shown in fig. l(a). The micrographs
Y-ray --
k
211
reveal polycrystalline Dfilms with a grain size of between 100 and 150 A. Diffraction patterns from the Fe/Co films show the iron to be in the bee phase. Fyr the samples with thick layers (150, 75 and 50 A) the Co is in the hcp phase but for those with layer thicknesses 30, 20 and 10 A the rings can be indexed assuming either hcp or bee structure. It is reported [31 that in Fe/Co multilayers formed by dc triode sputtering the Co layers have hcp structure above 40 A thickness but that for thinner layers the hcp rings disappear and only the rings of the bee iron are seen. Diffraction patterns from the 20 and 30 A Fe/Cu films reveal the iron to be bee and the copper to be in the fee phase. Figure l(b) shows a diffrac-
0
4
P
(a)
(b)
Y-ray i
1 B
T
-
Y-ray
4
8
(c)
P
(d)
Fig. 2. Schematic diagrams for (a) Mossbauer measurements on Fe/Co and Fe/Cu multilayers room-temperature hysteresis measurements; (c) Mossbauer measurements with applied field on Fe/Co initial magnetisation lies in the sample plane; and (d) Mdssbauer measurements on Fe/Co samples initial magnetisation lies out of the sample plane.
at room temperature; (b) and Fe/Cu samples whose where a component of the
Information Storage: Basic and Applied
212
6.F. Bakkaloglu et al. / Magnetism of Fe /Co and Fe / CM multilayers
tion pattern from the 20 X (Fe150 A/Co150 A> film. The diffraction micrographs show no sign of preferred orientation in the multilayers. The Miissbauer spectra themselves show characteristic absorption lines tf bee iron for all samples except the Fe/Cu 10 A. This latter sample is the only one to show Mossbauer evidence of iron in a non-crystalline environment. The hysteresis measurements were carried out at room temperature using a Princeton Micromag Model 2000 alternating gradient force magnetometer (AGFM). In this technique a chosen dc magnetic field was applied parallel to the plane of the sample and an ac magnetic field was superimposed along the direction of the dc field. The frequency of the ac field was matched to the vibrational frequency of the sample suspension. The voltage signal was generated from the sample displacement via a piezoelectric mounting crystal. By automatic stepping of the dc field, hysteresis cycles of the samples were obtained for the geometry in which the magnetising field is parallel to the plane of the layers. The system was calibrated on a standard nickel foil and achieves a sensitivity of 10 nemu. In the Mossbauer experiments a conventional double ramp constant acceleration spectrometer was used in the transmission mode. The samples were not enriched with “Fe and consequently were not strongly absorbing with maximum absorption intensities in the range of 1%. Applied fields of up to 10 T could be obtained using superconducting Helmholtz coils. The magnetic configuration allowed different experimental geometries to be used. For multilayers where the easy axis of magnetisation lies in the plane of the layers, the field and y-ray beam were directed along the normal to the layers while for the multilayers in which the magnetisation has a component normal to the plane of the sample, the field was applied in the plane of the layers, perpendicular to the y-ray beam.
normal to the layers is determined by Mossbauer spectra. The spectra of the Fe/Co multilayers taken at room temperature with the experimental geometry shown in fig. 2(a) are illustrated in fig. 3. It is seen that they consist of magnetic sextets. The relative intensities of the outer : middle: inner doublet components of the sextet pattern are theoretically predicted to be 3: (4 sin*8/1 + COSTS): 1, where the angle 0 shown in fig. 2(a) is that between the y-ray beam directed along the normal to the plane of the layers and the mean direction of the Fe spins (the direction of the mean Fe magnetisation). It should be stressed that this method measures the mean value of 4 sin28/1 + cos28 but does not give information on any possible distribution in the values of 0. Values of 0 reported in tables 1 and 2 are deduced assuming a sharp value of 0. The spectra of fig. 3 show that different values are measured for the mean direction of the iron magnetic moment in different multilayer samples. In these spectra the intensities of the inner lines
1
I1 -10.0
3. Results and analysis The average direction that the Fe magnetisation of a given multilayer sample makes with the
-8.0
I -8.0
-4.0
‘d -2.0
” I
I 0.0
I
I
2.0
4.0
I1 8.0
1
8.0
100
Velocity (mm/se& Fig. 3. Spectra taken at 290 K of Fe/Co samples with layer thickness ranging from 150 to 10 A and fitted with two sextet components.
Information Storage: Basic and Applied
8.F. Bakkaloglu et al. / Magnetism of Fe/Co
3 and 4 are not well fitted due to a small distribution of hyperfine fields within each major component. Estimates of the error in the value of the angle 0 deduced from these spectra were obtained by evaluating the goodness of fit parameter x2 as the value of the angle 0 is stepped through the region of best fit. From the resulting x2 versus 19variation the errors shown in tables 1 and 2 are obtained.
213
with the easy axes in the sample plane. The second comprises the samples with the easy axes at some angle to the sample plane. The results of the hysteresis measurements on these samples are presented in these groups. All hysteresis measurements were carried out at room temperature applying dc and ac fields parallel to the sample plane in the geometry illustrated in fig. 2(b). The r:sults on thf samples of 10 A Fe/Co and 30 A and 20 A Fe/Cu multilayers which have their magnetic easy direction in the sample plane, i.e. 8 = 90”, are shown in fig. 4. Since these samples have relatively low coercive fields and high loop slope with narrow loop width, they have fairly soft magnetif properties. For the samples of 75, 50 and 20 A Fe/Co multilayers where 8 # 90”, the hysteresis results
3.1. Hysteresis measurements The Mossbauer measurements described above on the Fe/Co and the Fe/Cu multilayers show that these samples may be classified into two distinct groups in terms of the alignment of their easy axes. The first group comprises the samples
b -1E-2 I -5Et2
0
-SE+3
and Fe / Cu multilayers
I
I
I
I
I
I
I
a 0
I
I
I
n
lo4
I
I +5E+2
+lE-2
H ILkI
-1E-2 _:IE+i I
Fig. 4. M-H
hysteresis
I
I
I
I
I_
-i
+*+3
cycles of the Fe/Co sample (a) with layer thickness of 10 ,& and the Fe/Cu samples of 30 and 20 A (b, c) whose initial magnetisations lie in the sample plane.
with layer thicknesses
Information Storage: Basic and Applied
214
6. F. Bakkaloglu et al. / Magnetism
qf Fe / Co and Fe / Cu multilayers
are shown in fig. 5. The hysteresis cycles of these samples are seen to consist of two parts, the central cycle caused by irreversible motion of domain boundaries and reversible shoulders leading from the central cycle to the saturation state. This shape of hysteresis cycle confirms that these samples possess a component of magnetic moment normal to the sample plane. The reversible shoulders of these cycles represent a rotation of the ferromagnetic moment of the sample from its initial direction into the plane of the sample as the applied field in the plane of the sample is increased. As the layer thickness of these samples decreases and the importance of the interface layers increases it is seen that irreversible part of the cycle becomes wider and the slope of the shoulders decreases. The saturation values of the magnetisation M of the Fe/Co and Fe/Cu multilayers obtained
-Et3
Fig. 5. H-M
hysteresis
from figs. 4 and 5 are listed in table 1, where they are compared with the values MJcalc) calculated assuming ferromagnetic (parallel) coupling of the magnetic moments of Fe and Co layers and M,,(calc) assuming antiferromagnetic (antiparallel) coupling between Fe and Co layers. These calculations were carried out assuming the standard crystalline bee structure for Fe with the bulk value for the lattice constant a = 2.87 A and an hcp structure fof Co with bulk yalue lattice constants a = 2.51 A and c = 4.07 A. The Fe primitive cell has two atoms with intrinsic magnetic moments of 2.2~~ and the Co primitive cell two atoms with intrinsic magnetic moments of 1.72~~. It is clear from the values in table 1 that the antiferromagnetic predictions are an order of magnitude smaller than the observed values, while ferromagnetic predictions are consistent with the observed values to within - 10%. For Fe/Cu
0
cycles of the (a) 75, (b) SO and Cc) 20 A Fe/Co samples the sample plane.
_1 +x+3
whose initial magnetisations
lie at finite angles to
Information Storage: Basic and Applied
6.F. Bakkaloglu et al. / Magnetism of Fe/Co
and Fe / Cu multilayers
215
Table 1 Measurements of the mean direction of magnetisation and measured and calculated values of the magnitude of this magnetisation. B(Moss) represents the magnetisation direction obtained from Miissbauer measurements at 290 K. MtAGFM) represents the magnetisation measured by AGFM. M,(calc) and MA,(calc) represent the calculated magnetisation values for ferromagnetic and antiferromagnetic couplings, respectively, M,(imp) represents the improved calculations of magnetisation incorporating the effects of interface layers. All values of magnetisation are in (emu cmm3) Thickness
(A)
B(Miiss)
M(AGMF) (emu cm-“)
M,(calc) (emu cm-‘)
M&alc) (emu cm-“)
M,(imp) (emu cm-3)
1680 1720 1730 1710 1950
1600 + 1590+_ 1590+ 1600 + 1590*
153*1 148* 1 148kl 147+1 148+1
1720+ 1650 f 169Ok 1740 * 1890 k
Fe/Co
15 50 30 20 10
51*1 42&l 55+2 40+2 9Ok2
Fe/Cu
30 20
90*4 9Ok2
k 10 +_10 * 10 f 10 * 10
820 f 10 740+ 10
samples the observed and calculated values are consistent with complete alignment of the magnetic moments of the Fe layers either through ferromagnetic coupling or by alignment of the magnetic moment of each Fe layer. Improved calculations on the magnetisation of the Fe/Co multilayers M,(imp) assume ferromagnetic coupling but also consider the effect of the interface layers between Fe and Co layers of mean thickness 9 A which have been inferred from the accompanying hyperfine field studies [4]. The mean magnetic moment in these interface layers which have an average composition of 50% Fe and 50% Co is given as 2.38~~ from the Slater-Pauling graph [5]. The calculations for the pure Fe and Co layers in this improved approach were carried out in the same way as in the approach described above. An expression for the magnetisation M in the improved calculation may be written as M=
c
N.p.n,
(1)
Fe,FeCo,Co
where the sum is taken over the pure Fe layer, the pure Co layer and the FeCo interface layer. For the relevant layer N is the number of atoms per unit area, jZ is the mean magnetic moment, and n is the number of the layers per unit thickness. The results of the calculations given in table 1 as M,(imp) show higher values of magnetisation
10 10 10 10 10
870 f 10 870 f 10
10 10 10 10 10
0 0
than those assuming only pure metallic layers due to the enhancement of the magnetic moments of Fe and Co atoms in FeCo alloy interface layer. The results of the calculations incorporating the interface layers are in better agreement with the experimental values. The lack of information on the magnetic moments of iron atoms in mixed Fe/Cu interface layers prevents a similar calculation being made for the Fe/Cu multilayer samples. However, the results of studies of the hyperfine fields in Fe/Cu multilayers [4,6] show that the iron moment in these interface layers is reduced below that in pure iron. Thus any calculation incorporating the effect of interface layers would result in a value of M, which is less than that predicted by the pure layer cal$ulations shown in table 1. Further, since the 20 fi sample has more interface layers than the 30 A sample the reduction in M, predicted for this 20 A layer sample yould be greater than that predicted for the 30 A sample. These expectations are seen to be consistent with the values shown in table 1 for the Fe/Cu samples. It is illuminating to plot the measured magnetic moment per period per unit area (M X t) against periodic thickness t. This is shown in fig. 6, where it is seen that (M x t ) increases linearly with periodic thickness for Fe/Co and Fe/Cu samples. Extrapolating back towards zero thickness, however, contrasting behaviour is observed. For the Fe/Cu samples zero magnetic moment
Information Storage: Basic and Applied
0.F.
216
Bakkaloglu et al. / Magnetism of Fe /Co and Fe / Cu multilayws
occurs at finite thickness (5 f 1 A> indicating a magnetic dead layer. For the Fe/Co samples the finite intercept on the magnetic axis as the periodic thickness tends to zero indicates the enhancement of magnetic moment at Fe/Co interfaces.
000 0.25 000 1 0.40
s .z
4
3.2. Applied field Miissbaue,* measurements
/
o.oo0.50 0.10
The Mossbauer measurements were used to monitor the alignment of the magnetisation vector of the iron atoms when external magnetic fields were applied to the samples at 4.2 K. For the samples whose initial magnetisation vectors lay in the sample plane the geometry of the experiment is illustrated in fig. 2(c). For the samples where a component of the initial magnetisation vector lay out of the sample plane the external field is applied parallel to the sample plane as shown in fig. 2(d). The evolution of the Miissbauer spectra of the 20 A Fe/Co multilayer with increasing field applied as in fig. 2(d) is shown in fig. 7. Values for the mean angles 8 between the iron magnetisation and the sample normal, as the applied field B is increased, are listed in table 2. The intensities of the second and fifth lines are seen to
k
2.6
-
i 2.0 0) r 2 1.6
-
0
2.4
E
0.50 0.00 0.00 : 0.75
0.00 -0.50
/i
I
1
-10.0
-6.0
1
-8.0 -4.0 -2.0 0.0 2.0 4.0 8.0 8.0 Velocity
10.0
(mmlsec)
Fig. 7. Miissbauer spectra of the 20 ,& Fe/Co sample increasing applied field taken at 4.2 K.
with
increase with increasing external field strength and the intensity ratio eventually becomes 3 : 4 : 1 at an applied field of 0.18 T indicating that the angle ~9 between the iron magnetisation vector and y-ray beam has become 90”. At larger values of applied field the angles obtained via the intensities of lines 2 and 5 in the spectra can be
Thickness -
Fe/Co
/
Btext) (T)
sin’fI
H
0.000 0.0 17
0.73 f 0.01 0.94 * 0.02 I .OO+ 0.004
sY+ I 76+2 YOf 4
50
0.000 0.025 0.050 0.075
0.45 0.60 0.64 I .oo
42* I s1+2 s3*1 90+x
20
0.000
0.45 + 0.01
0.050 0.080
0.60+ 0.03
I 5152
0.91 + 0.03 0.96 + 0.02 0.98 + 0.01 I .oo* 0.004
73+3 7x+3 x3+4 90 f 4
75
(A)
0.010
t
,,
:,
Table 2 Values of (sin’@) and hence 0 obtained from Miissbauer spectra in applied fields on 75, 50 and 20 A Fe/Co multilayers. The angle 8 is that between the iron magnetic moment and the y-ray beam
x
YE
$8 IL
T
20
40
60
80
100
120
140
160
(xl@)
t(cm)
Fig. 6. Graph of magnetic moment per period per unit area (M x ) versus periodic thickness I. Measurements on Fe/Cu samples are shown as filled circles and measurements on Fe/Co samples as open circles. Extrapolating to low values of periodic thickness shows a magnetic dead layer in Fe/Cu while in Fe/Co the intercept confirms the enhanced magnetism of the interfaces.
0.100 0.120 0.180
f + + *
0.02 0.03 0.01 0.02
42+
Information Storage: Basic and Applied
6.F. Bakkaloglu et al. / Magnetismof Fe/Co and Fe / Cu multilayers No held
samples with the magnetic easy axis in the sample plane can be written as E = K,
-10.0
-8.0 -&o -4.0
-2.0
0.0
2.0
4.0
6.0
8.0 10.0
Velocity (mmlsec) Fig. 8. The spectra of the 10 A Fe/Co sample taken with increasing applied field at 4.2 K.
checked by measurement of the total field B, at the nucleus. The total field is related to the hyperfine field B,, and applied field by B, = [B& +B2+2BBhf sin 61‘I2 . The agreement between the two methods was satisfactory. The zvolution of the Miissbauer spectra from the 10 A Fe/Co sample where the experimental geometry is that of fig. 2(c) is shown in fig. 8. It can be seen from this figure that the intensities of the second and fifth lines decrease with increasing external field strength. At the external field of 2.5 T the intensity ratio becomes 3 : 0 : 1 indicating that the magnetisation vector is aligned along the y-ray beam. The variation of the direction of magnetisation with applied field, monitored in this way by the Mossbauer spectra is analysed in terms of magnetic anisotropy in section 4.
sin24 - PB cos 8,
Types of anisotropy
B(loc) = B(ext) - ~~$4,
(3)
where M is the component of magnetisation parallel to the applied field. For the geometry in which the applied field is applied parallel to the sample plane B(loc) = B(ext).
(4)
These expressions assume that the demagnetisation factor for these multilayer samples can be treated as if they were uniform homogeneous magnetic materials. Minimising the energy E in eq. (2) by applying the condition dE/d6’ = 0 gives the expression (5)
and anisotropy
constants
Graphs of cos 0 versus local fi$ld B for samples B = 90” and for the 30 A Fe/Co sample which shows a similar hysteresis cycle are shown in fig. 9. The gradients of the graphs in fig. 9 yield values of p/2K, from which the mean atomic anisotropy constant K, for each sample was evalwith
4.1. Samples with 13= 90” An e;pression the 10 A Fe/Co
(2)
where K, is the anisotropy constant, 4 and 8 are the angles between magnetisation vector and sample plane and between magnetisation vector and applied field respectively. In this expression it is assumed that the iron and cobalt components of the combined magnetisation remain parallel and p represents the mean atomic magnetic moment. For Fe/Co samples with equal layer thicknesses of Fe and Co the value of p is taken as 1.81 X 1O-23 J/T. For Fe/Cu samples, where only the iron atoms possess magnetic moments and magnetic anisotropy, F = 2.04 X 1O-23 J/T. The geometry for these measurements is shown in fig. 2(c). In this geometry the local magnetic field is not simply the applied field but is modified by the demagnetisation factor. For this geometry where the applied field is normal to the sample plane the relationship for the local field B(loc) is given by [7]:
cos 0 = (p/2Kp)B. 4. Discussion:
217
for the apisotropy eaergy for and 30 A and 20 A Fe/Cu
Information Storage: Basic and Applied
d;.F. Bakkaloglu et al. / Magnetism of Fe/Co
218
(b)
1Oi Fe/Co
1 .o
(a) 3OA Fe/Co
and Fe / Cu mu1tilayer.s
uated. These table 3.
values
of
K,
are
presented
in
4.2. Samples with 0 # 90” 0.6
t - _.~.~ B(ioc)
(c)
30 i Fe/Cu
(d)
. ,I’ /.
1
4 0.4
CT)
2Oi Fe/Cu
1 .o
0.0
_
0.4
0.0
, 0.4
0.0
B(loc) (T)
BUoc) (T)
Fig. 9. Graphs of cos fJ versus local field B(loc) for (a) 30 A Fe/Co; (b) 10 ,& Fe/Co; (c) 30 A Fe/Cu; and (d) 20 A Fe/Cu samples.
The observation in the 75, 50 and 20 A Fe/Co samples that the easy axis is at a finite angle to the normal to the sample plane, requires a term to represent an anisotropy component K, normal to the sample plane. Possible expressions representing this new situation with anisotropy constant K, in plane and K, normal to plane may be written as E = K, sin20 + K, sin’4,
(6)
E = K, sin40 + K, sin’4.
(7)
Equation (6) is rejected as this expression does not give a minimum in energy E in the range of 0” 5 8 2 90” and thus would not explain the direction of magnetisation at zero field. However, the expression of eq. (7) does give such a minimum and is the simplest hypothesis that can represent the observed behaviour. For samples Fe/Co with thickness0 10 A and0 Fe/Cu samples with thickness 20 A and 30 A the same expression holds but with K, = 0. The anisotropy energy of eq. (7) for the geometry shown in fig. 2(d) can be written as E = K, sin”0 + K, sin”+ - FB sin 0. Applying the condition expression is obtained 4K,
Table 3 Values of anisotropy constants K, and K, in J/atom evaluated from the applied field Miissbauer measurements at 4.2 K Thickness Fe/Co
Fe/Cu
(A)
K,(x
1O-‘4)
75 50 30 20 10
0.38 f 0.03 0.92kO.19 - 3.5 1.07+0.16 - 5.4
30 20
- 4.9 - 5.0
K,(x
lo-*“)
0.26 + 0.02 1.02*0.21 1.21*0.18
When be sin’s
d E/d0
B = 0, the equilibrium = K,/2
= 0, the following
sin O-pB=O.
sin%-2K,
K,.
(8)
(9) angle
(Y is seen to
( 10)
Using the values of 0 for these samples measured in this geometry as the applied field is varied, the values of K, and K, for these samples were calculated from eqs. (9) and (10). Mean values of K, and K, are given in table 3 for each sample. The values in table 3, given in Joules per atom, apparently show that the anisotropy constant K, is much greater,for the samples with the magneti-
Information Storage: Basic and Applied
6. F. Bakkaloglu et al. / Magnetism
sation lying in the plane of the samples (0 = 900) than for samples where the magnetisation is not confined to the plane (0 # 900). However, these relatively large values of K, for 8 = 90” samples are extremely sensitive to small changes in the demagnetisation term which is employeOd in the evaluation of B. For example in the 30 A Fe/Co sample a 10% increase in the demagnetisation term changes the value of K, per atom from 3.5 X 1O-24 J to 0.9 x 1O-24 J. The values of the demagnetisation terms were evaluated assuming that the samples were homogeneous magnetic materials rather than layers of different magnetic materials. The layer structure of the samples could well lead to effective demagnetisation effects from interface layers resulting in changes in the demagnetisation term that would cause large variations in the values of K, derived in this geometry. Thus while relative comparisons between K, values for samples with 8 = 90” are likely to be valid, comparisons of values of K, derived from the different experimental geometries shown in figs. 2(c) and (d) are not considered to be reliable. Within this set of 8 = 90 samples it can be seen that the anisotropy constant K, increases as the layer thickness decreases and the interfaces play a more important role in the samples. In the case of the 0 # 90” samples, demagnetisation plays no part in the evaluation of the anisotropy constants and the values are more reliable. Comparison of the 4.2 K values of K, and K, shows that, like the 8 = 90” samples, the values of the anisotropy constants increase as the layer thickness decreases. There seems to be no straightforward relation between layer thickness and the angle 0 made by the magnetisation to the normal to the sample plane. Whether this is a result of random influences during the sputtering deposition of the layers or complex magnetic interactions between the magnetic Fe and Co layers will be studied in further investigations on magnetic samples. 4.3. Search for in-plane anisotropy A set of measurements was carried out to test for a component of anisotropy in the sample
of Fe/Co
and Fe / Cu multilayers
219
77K (35.270)
-10.0 -8.0-8.0 -4.0 -?.O 0.0 2.0 4.0 6.0 8.0 10.0
Velocity (mm/set) Fig. 10. Spectra of the 20 A Fe/Co sample taken at 77 K with the variation of the sample position. The first spectrum is taken with the sample in a position in which the normal to the sample is parallel to the y-ray beam (0, 0). The second spectrum is taken in a position in which the normal to the sample is rotated to the right to make an angle of - 35” to the y-ray beam c-35”, 0). The third spectrum is taken in a position in which the normal to the sample is rotated to the left to make an angle of 35” to the y-ray beam (35”, 0). The fourth, fifth and sixth spectra are taken by keeping in the position in which the third spectrum is turning the sample through angles of 90”, 180” and 90”), (35”, 1803 and (35”, 270”), respectively, around axis.
the sample taken, but 270”, (35”, its normal
plane. Figure 10 shows the spectra of 20 A thick Fe/Co sample taken at 77 K. The first spectrum is taken in the usual geometry of fig. 2(a). The second spectrum is taken by turning the sample so that the normal to the sample plane is rotated to the right to make an angle of 0 = - 35” to the y-ray beam and third spectrum is taken by turning the sample so that the normal to the sample plane is rotated to the left to make an angle of f3= 35” to the y-ray beam. This position of the sample is also specified by azimuthal angle 4 = 0. In the next three spectra 0 is kept at 35” but the sample is rotated about its normal axis by succes-
Information Storage: Basic and Applied
220
ii.F.
Bakkaloglu et al. / Magnetism of Fe /Co and Fe / Cu mu1tilayer.s
sive stages to give azimuthal angles 4 = 90“, 180 and 270”, respectively. It can be seen from these spectra that there is no significant change in the intensities of the second and fifth lines of the spectra as the angle 4 is varied. If there was a preferred direction of magnetisation in the plane of the sample it would cause a change in the intensity ratio of these lines of the spectra shown in fig. 10. The absence of any change within the accuracy of the measuremeat means that the magnetisation vector of the 20 A thick Fe/Co sample can be visualised as a cone whose axis is the normal to the sample plane. It should, however, be borne in mind that the statistics of these spectra are not good and thus a weak preferred direction may not be detected.
of planar and normal anisotropy constants and values of these constants were evaluated from a set of measurements in which an applied field was used to collapse the cone and rotate the resulting moment into the sample plane. Other samples showed the more expected planar anisotropy. No evidence was found for any inplane anisotropy.
Acknowledgements
6FB acknowledges the support of a grant from Atatiirk University, Turkey, throughout this work, and the financial support of the SERC is acknowledged.
References 5. Conclusions
The iron and cobalt layers of a set of sputtered multilayer samples have been shown to be ferromagnetically coupled. Improved agreement between calculated and experimental values of magnetisation was obtained when explicit account was taken of interface layers whose presence is inferred from accompanying studies on hyperfine fields in these samples. The unexpected result was the cone anisotropy observed in some Fe/Co layers. This anisotropy was parameterised in terms
[I] L.M. Falicov et al., J. Mater. Res. 5 (1900) 12YY. [2] Y. Hoshi, M. Seki and M. Naoe, J. Physique Coil. (1988) u-1793. [31 R. Krishnan, H.O. Gupta, H. Lassri. C. Sella and M. Kaabouchi, J. Appl. Phys. 70 (1991) 6421. [4] 6.F. Bakkaloglu, M.F. Thomas, R.J. Pollard and P.J. Grundy, J. Magn. Magn. Mater. I25 (1993) 221. [5] A.H. Morrish, The Physical Principles of Magnetism (Willey, New York, 1965). [6] H.M. van Noort, F.J.A. den Broeder and H.J.G. Draaisma. J. Magn. Magn. Mater. 51 (1985) 273. [7] E.C. Stoner and E.P. Wohlfarth. Proc. Trans. R. Sot. 240 (1948) 599.