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Fe(001) magnetic trilayers
Journal of Magnetism North-Holland
and Magnetic Materials
116 (1992) L3054310
Letter to the Editor
Strong temperature dependence of the 90” coupling in Fe/Al/Fe( 001) magnetic trilayers C.J. Gutierrez,
J.J. Krebs,
M.E. Filipkowski
and G.A. Prinz
Naval Research Laboratory, Washington, DC 20375-5000, USA Received
21 May 1992; in revised form 7 July 1992
The temperature dependence of the unusual magnetic 90” coupling in epitaxial Fe/AI/Fe(OOl) trilayers has been determined. Trilayers with Al thickness near 15 A exhibit a rapid decrease of coupling strength (Btr) with increasing temperature. This temperature dependence is well described by the relations B,, = I@,(1 - T/T,)* or B,, = BP2 exp(- T/7’,) which contrast with the approximately linear temperature dependence previously reported for 180” coupled systems.
The coupling of ferromagnetic films through a non-magnetic interlayer has become an important theme in solid state magnetism following the ground-breaking papers by Griinberg et al. [l] and Fert et al. [21. The early work revealed a bilinear exchange coupling energy per unit area of the form Ec = -2A,,(M,
*&),
(1)
where M, and i& are unit vectors along the magnetic moments of the two magnetic layers. These vectors lie 180” apart in zero field if A,, is negative. Recently, it was found that, in certain cases, one also requires a biquadratic coupling mechanism of the form [3] E;: = -2Bi,(M,
+Q2
(2)
to explain the behavior of the coupled magnetic layers. For negative Bi2, the moments in the two layers prefer to lie at 90” to one another, in plane, in zero applied field. This effect was originally observed [3,41 in the Fe/Cr/Fe(OOl) system at those Cr thicknesses where A,, = 0. More reCorrespondence to: Dr. J.J. Krebs, Naval Research Laboratory, Code 6340.1, Washington, DC 20375-5000, USA. Tel.: + I-202-767-3603; telefax: + l-202-767-1697. 0304-8853/92/$05&l
0 1992 - Elsevier
Science
Publishers
cently, 90” coupling has been observed in the Fe/Al/Fe(OOl) system 151,where it can be comparable in strength to the 180” coupling, and also in Co/Cu/Co@Ol) [61. The temperature dependence of the 180” coupling has been studied in several laboratories for the Fe/Cr/Fe system with generally consistent results [7-91. The coupling constant A,, falls slowly and nearly linearly with increasing temperature, extrapolating to zero near 1000 K. This result has been interpreted to be a consequence of the two-dimensional nature of the coupled system [lo]. Similar behavior has been observed in Co/Cu(OOl) superlattices [ll]. In contrast, for Fe/Cu/Fe(OOl), A,, falls by roughly a factor of two between 77 and 295 K [12]. In this paper, we report the’temperature dependence of the 90” coupling in the Fe/Al/Fe (001) system. The recent theoretical model by Slonczewski 1131, which was constructed to explain the 90” coupling seen in Fe/Cr/Fe, showed that the 90” term can result from static fluctuations in the 180” term caused by interface roughness. We show that this mechanism appears to be in general agreement with the form of the temperature dependence of the 90” coupling found here for Fe/Al/Fe(OOl). However, the magni-
B.V. All rights reserved
L306
C.J. Gutierrez et al. / 90” coupling in Fe /Al / Fe(OO1) trilayers
tude of the temperature dependence is larger than expected. A series of Fe/Al/Fe trilayers was fabricated by molecular beam epitaxy on ZnSe-epilayered GaAs(001) substrates [14]. The two Fe layers of a given trilayer have the same nominal thickness which were in the range 45 to 75 A, while the Al layer thicknesses described here ranged ofrom 13 to 16 A (1 monolayer of Al(OO1) = 2.0 A). Flux rates were monitored with a residual gas analyzer and calibrated by X-ray fluorescence for Fe, or via Auger analysis (AES) using the known mean free path for Al. Typical rates (in A/min) were 6 for Fe and 4 for Al. The MBE base vacuum was typically < 5 x lo-” Torr, while the growth vacuum was generally < 8 x 1O-10 Torr. Such vac-
uum conditions are important to avoid 0 and C contamination (< 1% by in-situ AES analysis) at these low growth rates for a strong oxygen-gettering material like Al. The first Fe(001) layer was epitaxially grown on ZnSe at 175°C using established procedures known to yield excellent magnetic properties [14]. Based on our own studies to optimize growth conditions of Al on Fe and Fe on Al, the Al growth was carried out at 125°C and and two sets of samples were produced with the second Fe layer grown at either - 10°C and or near 165°C. Although FMR characterization indicates only a small magnetic difference between the two Fe layers of a given sample produced in this way, the reflection high energy electron diffraction
(4 ZnSe
04 Fe
I
(d)
Fe II Fig. 1. Typical (110) and (100) RHEED patterns fyr a thin Al Fe/Al/Fe sample grown on ZnSe. (a) the Zn~e(OO1) epilayer grown on GaAs(OO1) at 350°C; (b) the 1st Fe(OO1)46 A thick layer grown on ZnSe at 175°C; (c) the intervening 16 A thick Al layer grown at 125°C; and (d) the second 46 .& thick Fe layer grown at 165°C.
C.J. Gutierrez et al. / 90” coupling in Fe /AI / Fe(OO1) trilayers
(RHEED) characterization clearly indicates that signifi’cant growth-induced structural differences are present. For example, the RHEED patterns of the first Fe layer (Fe-I) grown on ZnSe in fig. l(b) consist of sharp streak features indicative of flat monocrystalline growth. However, the RHEED patterns of the finished Al growth on this flat Fe-I surface (fig. l(c)) consists of broadened streaks and Laue-like spot features indicating a roughened Al/vacuum interface. Finally, as shown in fig. l(d), the Fe-II layer grown on this corrugated Al surface yields a fainter Laue-like RHEED pattern with virtually no streaks present, indicating that the surface of the Fe-II film is rougher. This roughness may play a role in the coupling behavior found for Fe/Al/Fe(OOl). The magnetic properties of the samples were measured by means of SQUID magnetometry between 10 and 390 K, and also by 35 GHz ferromagnetic resonance (FMR) at room and selected lower temperatures. Note that the magnetometer measures only the component of the magnetization M along the applied field H. The M vs. H loops (H ll[lOO]) of a Fe/Al/Fe sample which has a preferred 90” orientation state in zero field are shown in fig. 2 for three different temperatures. At high fields, the moments M, and M2 are both aligned along the field H. As H is reduced but still with the same sign, there is a well-defined transition region in which the moment drops to nearly half its high field value followed by a plateau for which M, is approximately perpendicular to M2 and both are nearly along magnetically easy (100) directions. This type of behavior in Fe/Al and also Fe/Cr sandwiches was first detected by Ruhrig et al. [3] and described in detail there. Co/Cu/Co sandwiches can also display this effect for suitable Cu thicknesses [6]. In the present work, we are primarily interested in the temperature dependence of the 90” coupling, described by Bi2, which causes the transition. In particular, one should note in fig. 2 the considerable increase in the field at which the transition region occurs as one moves from 300 to 10 K, signalling an increase in B,, as the temperature is lowered. We now discuss briefly how quantitative values of B,, can be determined from such M vs. H
I307
T 0.: y
E
E
O -0.5
E
-1
S? 2 E z
,.:
150K
-
O -0.5
-1
I...‘..,‘., -300 -500
@.‘.I”.1 100 300
-100 H
500
(W
Fig. 2. M vs. H hysteresis loops of an Fe/Al/Fe(OLll) sample for H along an in-plane (1tJO) direction. The Al and Fe layer thicknesses are 13 and 64 A, respectively. Data were taken at the labelled temperatures. Note that at 10 K the sample does not saturate until = 700 Oe.
loops at constant T [15]. The energy per unit area of an Fe/Al/Fe sandwich can be written as E TOT= W,D,+
W,D,+E,+E;:
(3)
in which w and Di, respectively, are the usual volume energy density and thickness of the ith Fe layer and the coupling energies are given by eqs. (1) and (2). We temporarily neglect the 180” coupling (i.e., take A,, = 0) in eq. (3). The expression for Wi with H 11[100]is w = +K, cos 4ei + K” cos2( ei - ?r/4) - M,H cm 6,,
(4)
C.J. Gutierrez et al. / 90” coupling in Fe /Al / Fe(OO1) triiayers
L308
where Bi is the in-plane angle between Mi and [ 1001. For fixed values of K,, K, and B,,, one can minimize ETOT with respect to both 8, and 8,. (For simplicity, we take K,, K,, Mi and Di to be the same for both layers, which we found to be a good approximation.) The corresponding total moment along the applied field can then be calculated and is shown in fig. 3 for several different values of the reduced 90” coupling constant Jo = B,,/2M,D, where it4, is the saturation magnetization of an Fe film. It is assumed in the calculation that at each field the sandwich is in its lowest energy configuration. Note that at low Jo values there is an abrupt first order jump in the moment at a field HJ, and this becomes a second order change for large Jo (specifically for Jo 2 OSK, when K, = 0). The relationship between the desired Jo values and the HJ values (which can be measured) is shown in the inset of fig. 3. Our data reflect this calculated behavior. The above results assume K, and K, to be constants, independent of temperature. Supplemental calculations show that the jump field HJ
values are only weakly dependent on the K, and K, values if one uses their temperature variation based on earlier Fe film FMR studies [Xl. FMR data at = 115 K on an Fe/Al/Fe sandwich confirmed that K, and K, have the anticipated weak temperature dependence and hence cannot be the source of the observed shifts in the transition region. One also can estimate the maximum observable value of A,, in the samples from the zero-field value of the fractional magnetization M/M,. If A,, < 0 (antiferromagnetic coupling), then the calculated M,,/M, falls between 0 and 0.5 for H = 0. We use this to estimate that I A,, I I I B,, I for all the Fe/Al/Fe samples studied here. The values of K,/M, Ku/M and the effective magnetization 47rM’ were determined for each of the two Fe films in a sandwich from the FMR data in the usual way [16]. In general, separate FMR lines could be seen for the two Fe layers with similar but not equal Ki and 47rM’ values due to the small structural difference evident in fig. 1. The FMR parameters of one of the samples studied are given in the caption of fig. 3.
1
0.8
0.6
400
600
800
H VW Fig. 3. Calculated equilibrium M,, /MS values versus applied magnetic field for the model described in the text. (Only the first quadrant values are shown.) The individual curves are labelled by their reduced 90” couping contant Jo = - B,, /2M, D. Inset shows the derived relation between Ja and the corresponding jump field H,. The anisotropy parameters used are K, /M = 220 Oe and K, /M = 40 Oe.
C.J. Gutierrez et al. / 90” coupling in Fe /AI / Fe(OO1) trilayers
100 .
J,(T)
.
I J,(O)
surfaces are rough and the mean Cr thickness is such that a terraced thickness variation causes a deviation of size AJ in the 180” coupling A,, over an exchange length within the Fe layers, then one will obtain a - 2B,,(MM, - M2j2 term with magnitude given by
(1 - T/To)’
-_)-
J,(O) I 66.4 09
Te = 566 K
-
J,(O) I 63.2 01
To I 417 K
---f-
J,(O)
To I 400 K
i 44.3 Oe
wo9
60 &
B,, = -2[(AJ)2L/a?4] 20
0
0
60
100
150
200
250
300
350
400
100
J,(T)
60
= Jo(O) exp (-T/T_)
J,(O) z SO Oe
Te = 199 K
-J,(O)
z 66 01
Ta = 151 K
----J,(O)
~4600
T-=134
-.-
K
60
-Jo
40
20
0
/
50
100
150
200 T
250
300
350
400
W)
Fig. 4. Measured and fitted temperature dependence of the 90” coupling constant Ja for three Fe/Al/Fe samples. Their Al and Fe thicknesses and the sfcond .Fe growth temperaturzs are, despectively: (squares) 16 Aa 46 A,0150”C; (circles) 13 A, 64 A, - 10°C; (triangles) 14 A, 73 A, 180°C. The fitting parameters used in (a) Jo = Jo(OX1- T/T,,)’ and (b) J, = J,(O) exp( - T/ T,-,) are also indicated.
By using M vs. H data of the type shown in fig. 2 at different temperatures (or the easier to acquire M vs. T data at fixed HI, one then can determine the reduced B,, values shown in fig. 4 for the Fe/Al/Fe samples described in the caption. We note that Jo changes by a factor of five or more between 10 and 300 K and can be well approximated by Jo =Jo(OXl - T/T,,j2 with To values in the range 400 to 600 K (see fig. 4(a)). As mentioned earlier, Slonczewski 1131 has carried out a model calculation to explain the existence and order of magnitude of the 90” coupling coefficient found in Fe/Cr/Fe sandwich structures. Briefly, he points out that if the layer
coth rrD/L,
(5)
with A being the exchange stiffness in the Fe layer, L the terrace width and D the Fe layer thickness. For reasonable values of A, D and L (2 X 10M6 erg/cm, 50 .& and 100 L& respectively [131), one expects B,, to be of order 0.03(AJj2 (B,, and AJ in units of erg/cm2), so that one should expect to see clear evidence for A,, values roughly an order of magnitude larger than B,, for some Al thicknesses in Fe/Al/Fe. We do not find large enough A,, values for any of our Fe/Al/Fe samples, nor are the Ai2 values found by Fuss et al. [5], who investigated a wide range of Al thicknesses using wedged-thickness Fe/Al/Fe sandwiches, large enough. Because of the possibility of rapid fluctuations in A,, which are unobservable due to averaging, the authors of ref. [5] did not find the inconsistencies between the observed magnitudes of A,, and B,, to be persuasive enough to question the static fluctuation model. Hence, the magnitude argument remains an open question. A more important consequence of eq. (5) is that it predicts the temperature dependence of B,, should be that of (AJ)2, which in turn is that of (A,2)2. At the present time, however, the temperature dependence of A,, in Fe/Al/Fe has not been isolated clearly. Nevertheless, it should be noted that Al2 is observed to decrease approximately linearly with T for other reported 180” coupled systems [7-9,111. If A12(T) is also linear for Fe/Al/Fe, our observed B12(T) a (1 - T/TJ2 is not inconsistent with Slonczewski’s model that static fluctuations in A,, due to interface roughness are the physical origin of the 90” coupling. To account for the strong temperature dependence of B,, which we observe, it is required that the linear temperature dependence of A,, in Fe/Al/Fe must be
L310
C.J. Gutierrez et al. / 90” coupling in Fe /Al / Fe(OO1) trilayers
significantly faster than those previously reported in refs. [7-9,111. It should be pointed out that the observed data for two of the samples of fig. 4 are slightly better fit by the exponential form
Jo = Jo(O)ew( - T/T,). At present, there is no published theory to account for this exponential behavior for the 90” coupling but recent results by Edwards [171 may provide one.
Acknowledgements
CJG acknowledges support as a National Research Council Postdoctoral Associate, and MEF acknowledges support as an Office of Naval Technology Postdoctoral Fellow. We especially thank D. Ring for invaluable technical support, and the Office of Naval Research for financial support.
References [l] P. Griinberg, R. Schreiber, Y. Pang, M.O. Brodsky and H. Sowers, Phys. Rev. Lett. 57 (1986) 2442. F. Saurenbach, U. Walz, L. Hinchey, P. Griinberg and W. Zinn, J. Appl. Phys. 63 (1988) 3473. [2] M.N. Baibich, J.M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich and J. Chazelas, Phys. Rev. Lett. 61 (1988) 2472.
[31 M. Ruhrig, R. Schafer, A. Hubert, R. Mosler, J.A. Wolf, S. Demokritov and P. Griinberg, Phys. Stat. Sol. (a) 125 (1991) 635. [41 J. Unguris, R.J. Celotta and D.T. Pierce, Phys. Rev. Lett. 67 (1991) 140. [51 A. Fuss, S. Demokritov, P. Griinberg and W. Zinn, J. Magn. Magn. Mater. 103 (1992) L221. [61 B. Heinrich, J.F. Cochran, M. Kowalewski, J. Kirschner, Z. Celinski, A.S Arrott and K. Myrtle, Phys. Rev. B 44 (1991) 9348. [71 A. Chaiken, T.M. Tritt, D.J. Gillespie, J.J. Krebs, P. Lubitz, M.Z. Harford and G.A. Prinz, J. Appl. Phys. 69 (1991) 4798. [81 A. Barthelemy, A. Fert, M.N. Baibich, S. Hadjoudj, F. Petroff, P. Etienne, R. Cabenel, S. Lequin, F. Nguyen Van Dau and G. Creuzet, J. Appl. Phys. 67 (1990) 5908. [91 S. Demokritov, J.A. Wolf, P. Griinherg and W. Zinn, Proc. MRS 231 (1992) 133. DO1 J.R. Cullen and K.B. Hathaway, Phys. Rev. B (submitted). [ill S.S.P. Parkin, R. Bhadra and K.P. Roche, Phys. Rev. Lett. 66 (1991) 2152. [121 Z. Celinski and B. Heinrich, J. Magn. Magn. Mater. 99 (1991) L25. [131 J.C. Slonczewski, Phys. Rev. Lett. 67 (1991) 3172. [141 G.A. Prinz, B.T. Jonker, J.J. Krebs, J.M. Ferrari and F. Kovanic, Appl. Phys. Lett. 48 (1986) 1756. J.J. Krebs, B.T. Jonker and G.A. Prinz, J. Appl. Phys. 61 (1987) 3744. [151 For a similar analysis of the effects of 90” coupling (for Fe/Cr/Fe in that case), see U. Kobler, R. Wiechers, A. Fuss and W. Zinn, J. Magn. Magn. Mater. 103 (1992) 236. Ml J.J. Krebs, F.J. Rachford, P. Lubitz and G.A. Prinz, J. Appl. Phys. 53 (1982) 8058. 1171 D.M. Edwards, NATO Advanced Workshop on Magnetism and Structure of Systems of Reduced Dimensions, Cargese, Corsica (June 1992) to be published. See also, D.M. Edwards, J. Mathon, R.B. Moniz and M.S. Phan, Phys. Rev. Lett. 67 (1991) 492.
and Magnetic Materials
116 (1992) L3054310
Letter to the Editor
Strong temperature dependence of the 90” coupling in Fe/Al/Fe( 001) magnetic trilayers C.J. Gutierrez,
J.J. Krebs,
M.E. Filipkowski
and G.A. Prinz
Naval Research Laboratory, Washington, DC 20375-5000, USA Received
21 May 1992; in revised form 7 July 1992
The temperature dependence of the unusual magnetic 90” coupling in epitaxial Fe/AI/Fe(OOl) trilayers has been determined. Trilayers with Al thickness near 15 A exhibit a rapid decrease of coupling strength (Btr) with increasing temperature. This temperature dependence is well described by the relations B,, = I@,(1 - T/T,)* or B,, = BP2 exp(- T/7’,) which contrast with the approximately linear temperature dependence previously reported for 180” coupled systems.
The coupling of ferromagnetic films through a non-magnetic interlayer has become an important theme in solid state magnetism following the ground-breaking papers by Griinberg et al. [l] and Fert et al. [21. The early work revealed a bilinear exchange coupling energy per unit area of the form Ec = -2A,,(M,
*&),
(1)
where M, and i& are unit vectors along the magnetic moments of the two magnetic layers. These vectors lie 180” apart in zero field if A,, is negative. Recently, it was found that, in certain cases, one also requires a biquadratic coupling mechanism of the form [3] E;: = -2Bi,(M,
+Q2
(2)
to explain the behavior of the coupled magnetic layers. For negative Bi2, the moments in the two layers prefer to lie at 90” to one another, in plane, in zero applied field. This effect was originally observed [3,41 in the Fe/Cr/Fe(OOl) system at those Cr thicknesses where A,, = 0. More reCorrespondence to: Dr. J.J. Krebs, Naval Research Laboratory, Code 6340.1, Washington, DC 20375-5000, USA. Tel.: + I-202-767-3603; telefax: + l-202-767-1697. 0304-8853/92/$05&l
0 1992 - Elsevier
Science
Publishers
cently, 90” coupling has been observed in the Fe/Al/Fe(OOl) system 151,where it can be comparable in strength to the 180” coupling, and also in Co/Cu/Co@Ol) [61. The temperature dependence of the 180” coupling has been studied in several laboratories for the Fe/Cr/Fe system with generally consistent results [7-91. The coupling constant A,, falls slowly and nearly linearly with increasing temperature, extrapolating to zero near 1000 K. This result has been interpreted to be a consequence of the two-dimensional nature of the coupled system [lo]. Similar behavior has been observed in Co/Cu(OOl) superlattices [ll]. In contrast, for Fe/Cu/Fe(OOl), A,, falls by roughly a factor of two between 77 and 295 K [12]. In this paper, we report the’temperature dependence of the 90” coupling in the Fe/Al/Fe (001) system. The recent theoretical model by Slonczewski 1131, which was constructed to explain the 90” coupling seen in Fe/Cr/Fe, showed that the 90” term can result from static fluctuations in the 180” term caused by interface roughness. We show that this mechanism appears to be in general agreement with the form of the temperature dependence of the 90” coupling found here for Fe/Al/Fe(OOl). However, the magni-
B.V. All rights reserved
L306
C.J. Gutierrez et al. / 90” coupling in Fe /Al / Fe(OO1) trilayers
tude of the temperature dependence is larger than expected. A series of Fe/Al/Fe trilayers was fabricated by molecular beam epitaxy on ZnSe-epilayered GaAs(001) substrates [14]. The two Fe layers of a given trilayer have the same nominal thickness which were in the range 45 to 75 A, while the Al layer thicknesses described here ranged ofrom 13 to 16 A (1 monolayer of Al(OO1) = 2.0 A). Flux rates were monitored with a residual gas analyzer and calibrated by X-ray fluorescence for Fe, or via Auger analysis (AES) using the known mean free path for Al. Typical rates (in A/min) were 6 for Fe and 4 for Al. The MBE base vacuum was typically < 5 x lo-” Torr, while the growth vacuum was generally < 8 x 1O-10 Torr. Such vac-
uum conditions are important to avoid 0 and C contamination (< 1% by in-situ AES analysis) at these low growth rates for a strong oxygen-gettering material like Al. The first Fe(001) layer was epitaxially grown on ZnSe at 175°C using established procedures known to yield excellent magnetic properties [14]. Based on our own studies to optimize growth conditions of Al on Fe and Fe on Al, the Al growth was carried out at 125°C and and two sets of samples were produced with the second Fe layer grown at either - 10°C and or near 165°C. Although FMR characterization indicates only a small magnetic difference between the two Fe layers of a given sample produced in this way, the reflection high energy electron diffraction
(4 ZnSe
04 Fe
I
(d)
Fe II Fig. 1. Typical (110) and (100) RHEED patterns fyr a thin Al Fe/Al/Fe sample grown on ZnSe. (a) the Zn~e(OO1) epilayer grown on GaAs(OO1) at 350°C; (b) the 1st Fe(OO1)46 A thick layer grown on ZnSe at 175°C; (c) the intervening 16 A thick Al layer grown at 125°C; and (d) the second 46 .& thick Fe layer grown at 165°C.
C.J. Gutierrez et al. / 90” coupling in Fe /AI / Fe(OO1) trilayers
(RHEED) characterization clearly indicates that signifi’cant growth-induced structural differences are present. For example, the RHEED patterns of the first Fe layer (Fe-I) grown on ZnSe in fig. l(b) consist of sharp streak features indicative of flat monocrystalline growth. However, the RHEED patterns of the finished Al growth on this flat Fe-I surface (fig. l(c)) consists of broadened streaks and Laue-like spot features indicating a roughened Al/vacuum interface. Finally, as shown in fig. l(d), the Fe-II layer grown on this corrugated Al surface yields a fainter Laue-like RHEED pattern with virtually no streaks present, indicating that the surface of the Fe-II film is rougher. This roughness may play a role in the coupling behavior found for Fe/Al/Fe(OOl). The magnetic properties of the samples were measured by means of SQUID magnetometry between 10 and 390 K, and also by 35 GHz ferromagnetic resonance (FMR) at room and selected lower temperatures. Note that the magnetometer measures only the component of the magnetization M along the applied field H. The M vs. H loops (H ll[lOO]) of a Fe/Al/Fe sample which has a preferred 90” orientation state in zero field are shown in fig. 2 for three different temperatures. At high fields, the moments M, and M2 are both aligned along the field H. As H is reduced but still with the same sign, there is a well-defined transition region in which the moment drops to nearly half its high field value followed by a plateau for which M, is approximately perpendicular to M2 and both are nearly along magnetically easy (100) directions. This type of behavior in Fe/Al and also Fe/Cr sandwiches was first detected by Ruhrig et al. [3] and described in detail there. Co/Cu/Co sandwiches can also display this effect for suitable Cu thicknesses [6]. In the present work, we are primarily interested in the temperature dependence of the 90” coupling, described by Bi2, which causes the transition. In particular, one should note in fig. 2 the considerable increase in the field at which the transition region occurs as one moves from 300 to 10 K, signalling an increase in B,, as the temperature is lowered. We now discuss briefly how quantitative values of B,, can be determined from such M vs. H
I307
T 0.: y
E
E
O -0.5
E
-1
S? 2 E z
,.:
150K
-
O -0.5
-1
I...‘..,‘., -300 -500
@.‘.I”.1 100 300
-100 H
500
(W
Fig. 2. M vs. H hysteresis loops of an Fe/Al/Fe(OLll) sample for H along an in-plane (1tJO) direction. The Al and Fe layer thicknesses are 13 and 64 A, respectively. Data were taken at the labelled temperatures. Note that at 10 K the sample does not saturate until = 700 Oe.
loops at constant T [15]. The energy per unit area of an Fe/Al/Fe sandwich can be written as E TOT= W,D,+
W,D,+E,+E;:
(3)
in which w and Di, respectively, are the usual volume energy density and thickness of the ith Fe layer and the coupling energies are given by eqs. (1) and (2). We temporarily neglect the 180” coupling (i.e., take A,, = 0) in eq. (3). The expression for Wi with H 11[100]is w = +K, cos 4ei + K” cos2( ei - ?r/4) - M,H cm 6,,
(4)
C.J. Gutierrez et al. / 90” coupling in Fe /Al / Fe(OO1) triiayers
L308
where Bi is the in-plane angle between Mi and [ 1001. For fixed values of K,, K, and B,,, one can minimize ETOT with respect to both 8, and 8,. (For simplicity, we take K,, K,, Mi and Di to be the same for both layers, which we found to be a good approximation.) The corresponding total moment along the applied field can then be calculated and is shown in fig. 3 for several different values of the reduced 90” coupling constant Jo = B,,/2M,D, where it4, is the saturation magnetization of an Fe film. It is assumed in the calculation that at each field the sandwich is in its lowest energy configuration. Note that at low Jo values there is an abrupt first order jump in the moment at a field HJ, and this becomes a second order change for large Jo (specifically for Jo 2 OSK, when K, = 0). The relationship between the desired Jo values and the HJ values (which can be measured) is shown in the inset of fig. 3. Our data reflect this calculated behavior. The above results assume K, and K, to be constants, independent of temperature. Supplemental calculations show that the jump field HJ
values are only weakly dependent on the K, and K, values if one uses their temperature variation based on earlier Fe film FMR studies [Xl. FMR data at = 115 K on an Fe/Al/Fe sandwich confirmed that K, and K, have the anticipated weak temperature dependence and hence cannot be the source of the observed shifts in the transition region. One also can estimate the maximum observable value of A,, in the samples from the zero-field value of the fractional magnetization M/M,. If A,, < 0 (antiferromagnetic coupling), then the calculated M,,/M, falls between 0 and 0.5 for H = 0. We use this to estimate that I A,, I I I B,, I for all the Fe/Al/Fe samples studied here. The values of K,/M, Ku/M and the effective magnetization 47rM’ were determined for each of the two Fe films in a sandwich from the FMR data in the usual way [16]. In general, separate FMR lines could be seen for the two Fe layers with similar but not equal Ki and 47rM’ values due to the small structural difference evident in fig. 1. The FMR parameters of one of the samples studied are given in the caption of fig. 3.
1
0.8
0.6
400
600
800
H VW Fig. 3. Calculated equilibrium M,, /MS values versus applied magnetic field for the model described in the text. (Only the first quadrant values are shown.) The individual curves are labelled by their reduced 90” couping contant Jo = - B,, /2M, D. Inset shows the derived relation between Ja and the corresponding jump field H,. The anisotropy parameters used are K, /M = 220 Oe and K, /M = 40 Oe.
C.J. Gutierrez et al. / 90” coupling in Fe /AI / Fe(OO1) trilayers
100 .
J,(T)
.
I J,(O)
surfaces are rough and the mean Cr thickness is such that a terraced thickness variation causes a deviation of size AJ in the 180” coupling A,, over an exchange length within the Fe layers, then one will obtain a - 2B,,(MM, - M2j2 term with magnitude given by
(1 - T/To)’
-_)-
J,(O) I 66.4 09
Te = 566 K
-
J,(O) I 63.2 01
To I 417 K
---f-
J,(O)
To I 400 K
i 44.3 Oe
wo9
60 &
B,, = -2[(AJ)2L/a?4] 20
0
0
60
100
150
200
250
300
350
400
100
J,(T)
60
= Jo(O) exp (-T/T_)
J,(O) z SO Oe
Te = 199 K
-J,(O)
z 66 01
Ta = 151 K
----J,(O)
~4600
T-=134
-.-
K
60
-Jo
40
20
0
/
50
100
150
200 T
250
300
350
400
W)
Fig. 4. Measured and fitted temperature dependence of the 90” coupling constant Ja for three Fe/Al/Fe samples. Their Al and Fe thicknesses and the sfcond .Fe growth temperaturzs are, despectively: (squares) 16 Aa 46 A,0150”C; (circles) 13 A, 64 A, - 10°C; (triangles) 14 A, 73 A, 180°C. The fitting parameters used in (a) Jo = Jo(OX1- T/T,,)’ and (b) J, = J,(O) exp( - T/ T,-,) are also indicated.
By using M vs. H data of the type shown in fig. 2 at different temperatures (or the easier to acquire M vs. T data at fixed HI, one then can determine the reduced B,, values shown in fig. 4 for the Fe/Al/Fe samples described in the caption. We note that Jo changes by a factor of five or more between 10 and 300 K and can be well approximated by Jo =Jo(OXl - T/T,,j2 with To values in the range 400 to 600 K (see fig. 4(a)). As mentioned earlier, Slonczewski 1131 has carried out a model calculation to explain the existence and order of magnitude of the 90” coupling coefficient found in Fe/Cr/Fe sandwich structures. Briefly, he points out that if the layer
coth rrD/L,
(5)
with A being the exchange stiffness in the Fe layer, L the terrace width and D the Fe layer thickness. For reasonable values of A, D and L (2 X 10M6 erg/cm, 50 .& and 100 L& respectively [131), one expects B,, to be of order 0.03(AJj2 (B,, and AJ in units of erg/cm2), so that one should expect to see clear evidence for A,, values roughly an order of magnitude larger than B,, for some Al thicknesses in Fe/Al/Fe. We do not find large enough A,, values for any of our Fe/Al/Fe samples, nor are the Ai2 values found by Fuss et al. [5], who investigated a wide range of Al thicknesses using wedged-thickness Fe/Al/Fe sandwiches, large enough. Because of the possibility of rapid fluctuations in A,, which are unobservable due to averaging, the authors of ref. [5] did not find the inconsistencies between the observed magnitudes of A,, and B,, to be persuasive enough to question the static fluctuation model. Hence, the magnitude argument remains an open question. A more important consequence of eq. (5) is that it predicts the temperature dependence of B,, should be that of (AJ)2, which in turn is that of (A,2)2. At the present time, however, the temperature dependence of A,, in Fe/Al/Fe has not been isolated clearly. Nevertheless, it should be noted that Al2 is observed to decrease approximately linearly with T for other reported 180” coupled systems [7-9,111. If A12(T) is also linear for Fe/Al/Fe, our observed B12(T) a (1 - T/TJ2 is not inconsistent with Slonczewski’s model that static fluctuations in A,, due to interface roughness are the physical origin of the 90” coupling. To account for the strong temperature dependence of B,, which we observe, it is required that the linear temperature dependence of A,, in Fe/Al/Fe must be
L310
C.J. Gutierrez et al. / 90” coupling in Fe /Al / Fe(OO1) trilayers
significantly faster than those previously reported in refs. [7-9,111. It should be pointed out that the observed data for two of the samples of fig. 4 are slightly better fit by the exponential form
Jo = Jo(O)ew( - T/T,). At present, there is no published theory to account for this exponential behavior for the 90” coupling but recent results by Edwards [171 may provide one.
Acknowledgements
CJG acknowledges support as a National Research Council Postdoctoral Associate, and MEF acknowledges support as an Office of Naval Technology Postdoctoral Fellow. We especially thank D. Ring for invaluable technical support, and the Office of Naval Research for financial support.
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[31 M. Ruhrig, R. Schafer, A. Hubert, R. Mosler, J.A. Wolf, S. Demokritov and P. Griinberg, Phys. Stat. Sol. (a) 125 (1991) 635. [41 J. Unguris, R.J. Celotta and D.T. Pierce, Phys. Rev. Lett. 67 (1991) 140. [51 A. Fuss, S. Demokritov, P. Griinberg and W. Zinn, J. Magn. Magn. Mater. 103 (1992) L221. [61 B. Heinrich, J.F. Cochran, M. Kowalewski, J. Kirschner, Z. Celinski, A.S Arrott and K. Myrtle, Phys. Rev. B 44 (1991) 9348. [71 A. Chaiken, T.M. Tritt, D.J. Gillespie, J.J. Krebs, P. Lubitz, M.Z. Harford and G.A. Prinz, J. Appl. Phys. 69 (1991) 4798. [81 A. Barthelemy, A. Fert, M.N. Baibich, S. Hadjoudj, F. Petroff, P. Etienne, R. Cabenel, S. Lequin, F. Nguyen Van Dau and G. Creuzet, J. Appl. Phys. 67 (1990) 5908. [91 S. Demokritov, J.A. Wolf, P. Griinherg and W. Zinn, Proc. MRS 231 (1992) 133. DO1 J.R. Cullen and K.B. Hathaway, Phys. Rev. B (submitted). [ill S.S.P. Parkin, R. Bhadra and K.P. Roche, Phys. Rev. Lett. 66 (1991) 2152. [121 Z. Celinski and B. Heinrich, J. Magn. Magn. Mater. 99 (1991) L25. [131 J.C. Slonczewski, Phys. Rev. Lett. 67 (1991) 3172. [141 G.A. Prinz, B.T. Jonker, J.J. Krebs, J.M. Ferrari and F. Kovanic, Appl. Phys. Lett. 48 (1986) 1756. J.J. Krebs, B.T. Jonker and G.A. Prinz, J. Appl. Phys. 61 (1987) 3744. [151 For a similar analysis of the effects of 90” coupling (for Fe/Cr/Fe in that case), see U. Kobler, R. Wiechers, A. Fuss and W. Zinn, J. Magn. Magn. Mater. 103 (1992) 236. Ml J.J. Krebs, F.J. Rachford, P. Lubitz and G.A. Prinz, J. Appl. Phys. 53 (1982) 8058. 1171 D.M. Edwards, NATO Advanced Workshop on Magnetism and Structure of Systems of Reduced Dimensions, Cargese, Corsica (June 1992) to be published. See also, D.M. Edwards, J. Mathon, R.B. Moniz and M.S. Phan, Phys. Rev. Lett. 67 (1991) 492.