ELSEVIER Journal of Magnetism and Magnetic Materials 153 (1996) 5-10
~ i ~ Journal of magnetism 4~H and
magnetic
~ H materials
Magnetisation studies in Tb-Fe/Pt single and multilayers
H. Lassri a,1, R. Krishnan a, *, M. Baran b
a Laboratoire de Magn3tisme et d'Optique de l'Universit3 de Versailles, CNRS, URA 1531, F-92195 Meudon, France b Institute of Physics, Polish Academy of Sciences, al Lomikow 32/46, PL-02 668 Warsaw, Poland
Received 5 January 1995; revised 25 July 1995
Abstract
We have studied the magnetisation in a single Tb-Fe layer and TbFe/Pt multilayers under fields up to 5 T and as a function of temperature. We have analysed the results in terms of the mean field model and extracted some fundamental parameters. For instance, the exchange integrals JFe-Fe = 40 X 10-~6 erg, JFe-Tb = 19 X 10-16 erg and local anisotropy K I at 50 K is 42 × 107 erg cm -3 and the wall energy at 50 K is 1.09 erg cm -2.
1. Introduction
Amorphous rare earth-transition metal alloy films, of which the combination Fe~_ xTbx is typical, have been intensely studied as they are important from both fundamental and applied points o f view. Indeed, there is a plethora of publications on this topic [1,2].
These films are now used commercially for mag- neto-optical information storage. These layers are chemically very reactive and hence have to be pro- tected either by a dielectric or a metallic layer. It is interesting to study the effect of T b - F e / P t inter- faces. In order to amplify interface effects it is preferable to study T b - F e / P t multilayers. In earlier work we concentrated on the surface anisotropy and the magneto-optical properties in magnetic fields H < 2 T, which was of an insufficient strength to saturate the samples at low temperatures [3]. In the present work we have carried out magnetisation stud- ies in fields of up to 5 T and over a wide range of
* Corresponding author. Fax: + 33-4507-5822.
Permanent address: Facult6 des Sciences, Ain chok, Univer- site Hassan II, Route d'el Jadida km-8, Casablanca, Morocco.
temperatures. We analyse our results in terms of mean field theory and extract the exchange integrals.
2. Experimental details
The T b - F e / P t multilayers were prepared by se- quential rf sputtering using a mosaic target. The system was pumped down using a turbomolecular pump to a pressure of 1 × l0 -7 Torr and was baked overnight at a temperature o f about 70°C. The thick- nesses of the layers were measured in situ using a pre-calibrated quartz oscillator. Water-cooled glass substrates were used. The Pt layer thickness t(Pt) was fixed at 20 A, and that of T b - F e , t(Th-Fe), was
o
varied from 50 to 204 A. The number of bilayers was in the range 4 - 1 0 . The top layer in all cases was 50 A of Pt, which also served to protect the magnetic layer from oxidation. A single layer of T b - F e 1500 A thick with a Pt protective layer was also prepared.
The magnetisation and the M - H loops were mea- sured in the range 4 - 3 0 0 K, using a SQUID magne- tometer with a maximum applied field of 5 T, The lowest measurement temperature at which measure-
0304-8853/96/$15.00 © 1996 Elsevier Science B.V. All fights reserved
SSDI 0 3 0 4 - 8 8 5 3 ( 9 5 ) 0 0 5 2 6 - 9
6 H. Lassri et al./Journal of Magnetism and Magnetic Materials 153 (1996) 5-10 ments could be made was restricted by the coercivity
of the sample.
3. Results and discussions 3.1. Single layer F e - T b
The composition of the T b - F e layer was found to be Fes4Tb16 as measured by electron probe micro- analysis. This composition differs slightly from the samples previously investigated [3].
Fig. 1 shows the temperature dependence of the magnetic moment (/Za). Below about 200 K the magnetic moment is seen to decrease, indicating antiferromagnetic coupling between the Fe and Tb moments. The Tb concentration is not sufficient to produce any compensation of moments. Large coer- civities prevented measurements below 50 K. The alloy magnetic moment can be written as
M ( T ) = I MFo(T) - MTb(T) I
= N/ZB I( 1 -- x) gFeSF¢(T) -- XgTbJTb ( T ) I ,
(1)
where N is the number of atoms per unit volume, gj.
is the LandO factor with j = Fe and Tb (gF~ = 2.0, gTb = 1.5), JTb is the total angular momentum of Tb, SEe is the Fe spin moment, and /z B is the Bohr magneton.
Magnetisation measurements of amorphous T b - F e made in high fields (up to 12 T) gave value for the Tb moment (/ZTb), assuming the Fe moment to be 1.7/x B [4]. Similar calculations yield /ZTb = 7.6/X B, which agrees well with our earlier measurements reported in Ref. [4]. This value is smaller than the
o, t
[ I I
0 100 200 30JO ~"
T ( K )
Fig. 1. Temperature dependence of the magentic moment of amorphous Tbl6Fe84 film. The continuous line is the calculated one.
theoretical value of g T b J T b / d , B = 9/x a, indicating a non-collinear Tb spin structure, due to the strong local random anisotropy of Tb. In fact, our conver- sion electron M~Sssbauer studies also revealed that even the spin structure of Fe is non-collinear [5].
The mean field theory has been successfully ap- plied in the past to several kinds of amorphous alloys, in order to explain the temperature depen- dence of the magnetisation [6]. The sub-network magnetisation can be written as:
SFe(T) : Sve(O)Bs( gee tXBHFeSFJkBT), (2a) J T b ( T ) = JTb(O)Bj( g T b I ~ B H T b J T b / k B T ) , (2b) where J T b ( 0 ) = ( J ) is the total angular momentum of Tb, SFe is the Fe spin moment, and the other terms have their usual meanings.
The molecular fields HFe,T b above are determined by the relations
HF~ = 2 JFeFe ZFeFeSve/ gve ~B
+ 2JFeVbZFeTb( gTb -- 1 ) J v b / g F e /ZB, (3a) HTb = 2 JYbFe ZYbFe( gTb -- 1) SF~/gTb tx B
+ 2JTbTbZTbvb(gTb -- 1)2JTb/gVbtXB, (3b) where JFeFe, JFeTb and JTbYb a r e the exchange inte- grals for the various interactions and zij (i -= Fe and j = Tb) are the nearest-neighbour coordination. Of course the atoms are distributed at random, and in amorphous alloys z is normally taken to be 12. In our case we have corrected this value by taking into account the actual concentration of Fe, namely, by including the factor 1 - x.
The best fit was obtained, as shown by the contin- uous line in Fig. 1, for the following set of values:
JVeFe = 40 X 10- 16 erg, JFeTb = 19 × 10- 16 erg, JTbTb = 2 × 10 - 1 6 e r g .
Fig. 2 shows the temperature dependence of the Fe and Tb sub-network magnetisation calculated on the basis of the model and the various parameters de- scribed above.
We measured the Curie temperature (T c) of the single-layer sample and found it to be 440 K. Hein- man et al. [7] proposed the following relation be- tween T c and the various parameters as follows:
3kT c = (aveF~ + arbrb) + {(av~Fe + aTbTt,) 2 . ~1/2
-- 4 ( aTbTbaFeFe -- aTbVeaTbFe) ~ , ( 4 a )
H. Lassri et aL /Journal of Magnetism and Magnetic Materials 153 (1996) 5-10 7
2 [ 10
1 5
I I I
0 I00 200 300
T (K)
Fig. 2. C~culated temperature dependence of the Fe and Tb sub-networkmagneticmoments.
where
aFeFe = ZFeFcJFeFeSFe(SFe + 1), (4b)
aTbTb = ZTbTbJTbTbJTb(JTb + 1)( gTb -- 1) 2, (4c)
aFeTb aTbFe = ZFeTb ZTbFe(JTbFe) 2( gTb -- 1 )2
XSFo(SFe + l) J¢ (JT + 1). (40)
Introducing the values of the various parameters obtained by the mean field analysis described above, in the above relations, we calculate T c = 435 K, in good agreement with the experimental value.
3.2. Study ofthe coercivefield
We have studied the temperature dependence of the coercive field of the single-layer T b - F e sample.
Fig. 3 shows the M-H loop at 50 K. Due to the limitation of the field (Hma x = 5 T), measurements were not be possible at lower temperatures. Alben et al. [8] proposed a relation between the coercive field H c and the local anisotropy K 1, the uniaxial anisotropy K u, and other physical parameters, as follows:
Hc = (1/4~r )( K?/KuM )( Ra/d) 3, (5) where R a is the structural correlation length, gener- ally taken to be 10 A, and d is the domain wall
o200-
0
-100
-200
-6 -4 -2
/
2 4
r i ( T )
Fig. 3. M - H loop of single layer amorphous 'l-b16Fe84 at 50 K.
width, which is related to the exchange constant A and K u as follows:
d= rr( a/Ku) 1/2. (6)
The exchange constant A can be calculated after Hasegawa [9] from the relation
a = Vyb_TbJTb_Tb ( gWb- 1)2j2~x2/rTb-Tb
+ ( VTb- Fe + VFe- T0) JTb- Fe( gTb -- 1) JTbSFe
× x ( 1 -- x)/rTb_Fe
+ VFe_FeJFe_FeSFe(1 -- X)2/rFe_Fe, (7) where ui_ j is the maximum permissible atom pairs per unit volume extended to first neighbours (in our case, we take it to be 2), rij are the interatomic distances, which are taken to be; rF~F¢ = 2.5 A,, rFeTb = 3.0 ,~ and rTbTb = 3.5 ,~, in accordance with the structural data of Harris et al. [10]. Using the values of J i - j obtained above, the exchange constant A was calculated from Eq. (7), and the uniaxial anisotropy Ku values from our earlier work, part of which is reported in Ref. [4]. With a knowledge of A and using Eq. (6), we calculated the domain wall width d. The wall energy cr can be calculated from
Table 1
Some magnetic parameters of single-layer amorphous Tbl6Fes4 at 50 and 290 K
T ( K ) M (emu cm -3 ) A ( 1 0 - 8 erg cm - I ) Ku (106 erg cm - 3 ) Hc (kOe) d(,~) Ki (107 erg cm - 3 ) tr (erg cm -2 )
50 131 30.3 3.9 41 87 42 1.1
290 194 17.5 2.0 1.0 93 6.2 0.60
8 H. Lassri et al./Journal of Magnetism and Magnetic Materials 153 (1996) 5-10
I I
100
2 0 0T ( K )
Fig. 4. Temperature dependence of H c.
3oo
o" = "rr 4 ( A / K ) 1/ 2. T h e results are presented in Table 1. It is seen that d decreases at low temperature, due to an increase in anisotropy. Our value of ~r agrees well with that published by Mimura et al. [11].
Fig. 4 shows the temperature dependence of H c of the single Tb16Fe84 layer. It can be seen that H c decreases rapidly with increasing temperature. K~
was calculated using the experimental values of H c and Eq. (5). The results at 290 and 50 K are given in Table 1. It is interesting to note that the random local anisotropy is two orders of magnitude higher at 50 K than the coherent uniaxial anisotropy, which in these films is known to arise from the sputtering process.
3.3. T b F e / P t multilayers
The magnetic and magneto-optical properties are sensitive to the TbFe layer thickness as reported in our previous studies [3]. Both the uniaxial anisotropy and the coercivity decreases with decreasing t ( T b - Fe). In this work we concentrate on the magnetic properties at low temperatures. First let us consider the temperature dependence of the magnetisation in these multilayers. Fi~. 5 shows the results for t ( T b - Fe) = 180 and 100 A, which are typical. The result for the single layer is also given for comparison. In all cases the general trend is the same. However, at all temperatures the magnetisation is seen to increase as the TbFe layer thickness decreases. The magneti- sation in multilayers can be expressed by the phe- nomenological model as follows:
MML = M b + 2 ~ M i n t / t , (8)
F e T b / Pt
30~-,o.o * *
• e • e •
200
e • •
1oo
. I
1oo
• tr,v, = 100J~
• tv-rb = 180A
• Fe~Tbx6
%, = 20 A
200 3 0 0
T(K)
Fig. 5. Temperature dependence of the magnetisation in TbFe/Pt multilayers for two different layer thicknesses 180 and 180 A.
Also shown for comparison is the result for the single layer.
where MML, M b and Min t are the magnetisations of the multilayer, the bulk material and interface mate- rial, respectively, t and 3 are the magnetic and interface layer thicknesses, respectively. Plotting MML × t as a function of t yields a straight line, whose slope gives M b and the intercept on the ordinate axis gives the product 2 3Min t. For instance, Fig. 6 shows such a plot at 50 K. By analysing the data at different temperatures, we calculated both M b and 2(~Min t as a function of temperature. The temperature dependences of MMO and 28Min t are shown in Fig. 7. M b is found to agree very well with the data obtained on the single-layer sample (Fig. 1).
O f course, Min t can be determined only if 6 is
J
4o
30
7~ 20
10
0 100 200
Fig. 6. The t(Tb-Fe) dependence of the product t(Tb-Fe) × MML
at 5 0 K.
H. Lassri et al. /Journal o f Magnetism and Magnetic Materials 153 (1996) 5 - 1 0 9
..~ 18
-- 12
e l
o r
20o
I
3 o'
T(K)
O
0 100 200 300 ~
T(K)
Fig. 7. Temperature dependence of M b and the product t × 2t~Mia t.
known. Nevertheless, it can seen from Fig, 7 that the temperature dependence of Min t is characteristic of a ferromagnet and not a ferrimagnet; If one assumes an interfacial alloy thickness to be 5 A, which is reason- able and normally found in sputtered materials, then the magnetisation of this alloy layer is found to be close to 1700 emu cm -3. This result shows that the layer formed at the interface due to mixing, is essen- tially a F e - P t alloy.
The magnetisation of this interracial alloy layer is expected to be in the film plane and was confirmed as such in our earlier studies of the torque curves and the shapes of the perpendicular M - H loops of T h F e / P t [3]. At room temperature, the M - H loop of the multilayers becomes more and more sheared with decreasing T b - F e layer thickness due to a strong exchange coupling between these two kinds of layers of relatively soft and hard materials, with in-plane and perpendicular anisotropy, respectively [3]. But at low temperatures the loop becomes rect- angular due to a strong increase in the anisotropy. As an example, Fig. 8 shows the M - H loop of the multilayer with t(Tb-Fe) = 204 ~,, t(Pt) = 20 A. and with four bilayers at 50 K. The coercivity is seen to have decreased to 15.5 kOe from the 41 kOe ob- served for the 1500 ,~ thick single layer. This shows
400
I
~ ol '
-6 -4 -2 0 2 4 6
H (I")
Fig. 8. M - H loop of the multilayer with t ( T b - F e ) = 204 ,~, t(Pt) = 20 ,~ and with four bilayers•
the effect of the coupling with the soft interfacial alloy layer• Fig. 9 illustrates the sharp decrease in H c with increasing temperature, for the multilayer men- tioned above.
In conclusion, we have studied the temperature dependence of magnetisation of a single T b 1 6 F e 8 4 film and T b 1 6 F e s a / P t multilayers analysing the data on the basis of mean field theory and extracted some fundamental parameters such as K), Jij- From the temperature dependence of H~ we have calculated the random local anisotropy. Finally, the interfacial alloy is found to have a large magnetisation and is ferromagnetic, which lead us to conclude that it is a F e - P t alloy. Due to exchange coupling between this alloy layer which is magnetically soft, and the T b - F e layer the coercivity is strongly reduced in the multi- layer, this reduction is greater for thinner layers.
Q D
0 I I q
50 100 150
T ( K )
