Journal of Magnetism and Magnetic Materials 104-107 (1992) 157-158 North-Holland
R a n d o m a n i s o t r o p y studies in a m o r p h o u s F e - E r - B - S i alloys H. Lassri and R. Krishnan
Laboratoire de Magndtisme et Matdriaux Magndtiques, C.N.R.S., 92195 Meudon, France
We have studied the magnetization (M) of melt spun amorphous Fes0_~ErxBl2Si 8 alloys with 0 _< x _< 15 under high fields up to 15 T, and have analysed the results at 4 K based on the random magnetic anisotropy (RMA) model. The local anisotropy K L is found to be (5.2_+0.4)× 10 7 erg cm 3 and is independent of x. The RMA field H~ increases from 80 kOe for x = 1.8 to 393 kOe for x = 11 and Hcx goes from 203 to 726 kOe in the same range. For x = 15, where the Er sub-net work moment dominates, the above values are 3 to 4 times higher. The results are discussed.
A m o r p h o u s alloys containing rare earth metals and particularly those with large s p i n - o r b i t coupling pre- sent what is known as r a n d o m magnetic anisotropy (RMA). This p h e n o m e n o n is due to topological disor- der. Harris et al. [1] first proposed the Hamiltonian for the R M A , based on the mean field approximation.
Aharony and Pytte [2] calculated the equation of state for R M A systems and showed that no long-range mag- netic order exists in systems with less than four dimen- sions. The effect of an applied magnetic field in a R M A system was first studied by Chudnovsky et al.
[3,4]. This model enables one to analyze the magnetic behaviour of the alloys presenting R M A and has been used by several authors to interpret their results [5].
The magnetic structure strongly depends on the pa- r a m e t e r A r = A r ( R c / a ) 2 where Ar = D / J o , and R~ i s the spatial correlation of the easy axes (taken as 5 A) and a is the atomic spacing. T h e R M A field H~ is expressed as
H r = 2 K L / M o, (1)
and the c o h e r e n t anisotropy field H~ as
H~ = 2 K J M o, (2)
where K L and K c are the local and c o h e r e n t anisotropy constants. M 0 is the saturated extrapolated value of the magnetization by assuming a field d e p e n d e n c e as H -°5. Finally the exchange field H~x can be written as
Hex = 2 A / M o ( R c ) 2. (3)
W h e n the r a n d o m anisotropy is large each spin is directed almost along the local easy axis at the site and if the inverse is true then some amount of alignment occurs. D e p e n d i n g on the externally applied field strength the nature of the regimes changes and for example for a strong enough field one has
H > H~ = H ¢ / H ~ x .
(4)
Then, an alignment of the spins occurs and one has what one calls a ferromagnet with wandering axes. O u r experimental conditions correspond to this regime.
Rapidly q u e n c h e d a m o r p h o u s alloys (metallic glasses), containing rare earth metals are interesting candidates for studying the above aspects and we de- scribe here some results obtained by us on amorphous F e - E r - B - S i alloys. W e have reported recently the magnetic and M6ssbauer studies on some of these samples [6].
A m o r p h o u s Fes0_~Er~B12Si~ alloys with 0 _<x < 15 were p r e p a r e d by the melt spinning technique in a protective a t m o s p h e r e of argon. T h e surface velocity of the c o p p e r wheel was in the range 35 to 40 m / s . The amorphous state was verified by X-ray diffraction. The exact composition of the samples was d e t e r m i n e d by the electron probe micro-analysis.
T h e magnetization was measured at 4 K under applied fields going up to 15 T.
The approach to saturation in the magnetization can be described in two ways. For an applied field Hap p > He×, the field d e p e n d e n c e follows the H 2 law, whereas when Hap p < He×, which is appropriate for our study, the d e p e n d e n c e is best described by a H 0.5 law. Fig. 1 shows the results for x = 4.8, 6.3 and 11, at 4 K. The deviation of the data points for H > 6 T arises, as we have shown earlier [6], from the fact that the antiferromagnetic interaction between Fe and E r becomes unstable under very high fields. F r o m the straight line portion we calculated the slope ~ M / M o which can be expressed as [3]
M / M o = ~ V ~ ,
(5)
where H~pp is the external field. F r o m the above the field H s was calculated. T h e exchange A was calcu- lated by the m e t h o d based on the m e a n field model, proposed by Hasegawa [7]. D u e to the lack of space, we only briefly mention the following. W e took the values of the interatomic distances from ref. [7] which are reasonable. T h e various exchange interaction con- 0312-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
~o E
115 H e x
110
9G
85 35
I 0
~ ° =4 8
I I I
1 2 3
H - O 5 (10-lkOe~O.5)
Fig. 1. The H -°5 dependence of the magnetization in amor- phous Feso_,Er~B12Si s alloys for three different Er concen-
trations at 4 K.
s t a n t s J~,/, w h e r e i a n d j r e p r e s e n t F e a n d Er, respec- tively, w e r e c a l c u l a t e d from the C u r i e t e m p e r a t u r e a n d the m o d e l p r o p o s e d by H e i m a n et al. [8]. T h e e x c h a n g e c o n s t a n t A d e c r e a s e d from 31.46 × 10 - s to 23.85 × 10 -8 erg cm -1 w h e n x i n c r e a s e d from 1.8 to 11.0.
F r o m t h e s e A values Hex was c a l c u l a t e d using r e l a t i o n (3). Finally, knowing H s a n d He× a n d using r e l a t i o n (4), H r was calculated. Fig. 2 shows at 4 K, t h e p a r a m - e t e r s H~x a n d H r as a f u n c t i o n of the E r c o n t e n t . It is s e e n t h a t He~ > H~ a n d t h a t they b o t h i n c r e a s e rapidly with x. Finally f r o m H~ with t h e h e l p of eq. (1) K L was calculated. It was f o u n d to b e 5 x 10 7 erg cm -3 for all the compositions.
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158 H. Lassri, R. Krishnan / Anisotropy in Fe-Er-B-Si alloys
i I
0 5 10 15
X ( a t %)
Fig. 2. The Er concentration dependence of H ~ and H r in amorphous Fes0 xEr~B12Si s alloys at 4 K.
H i g h field m a g n e t i z a t i o n m e a s u r e m e n t s were per- f o r m e d at Service N a t i o n a l des C h a m p s I n t e n s e s , G r e n o b l e .
R e f e r e n c e s
[1] R. Harris, M. Plischke and M.J. Zuckerman, Phys. Rev.
Lett. 31 (1973) 160.
[2] A. Aharony and E. Pytte, Phys. Rev. Lett. 45 (1980) 1583.
[3] E.M. Chudnovsky and R.A. Serota, J. Phys. C 16 (1983) 4181.
[4] E.M. Chudnovsky, W.M. Saslow and R.A. Serota, Phys.
Rev. B 33 (1986) 251.
[5] D.J. Sellmyer and S. Naris. J. Appl. Phys. 57 (1985) 3584.
[6] R. Krishnan, H. Lassri and J. Teillet, J. Magn. Magn.
Mater. 98 (1991) 155.
[7] R. Hasegawa, J. Appl. Phys. 45 (1974) 3109.
[8] N. Heiman, K. Lee and R. Potter, J. Appl. Phys. 47 (1976) 2634.
