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On the behavior of localized magnetic moments in liquid Cu-Al(Fe) alloys
Journal of Magnetism and Magnetic Materials 2 (1976) 223-225 0 North-Holland Publishing Company
ON THE BEHAVIOR OF LOCALIZED MAGNETIC MOMENTS IN LIQUID Cu-AI (Fe) Alloys E. WACHTEL and A. PANTASIS Max.Planck-Institut fuer Metallforschung, Institut fuer Werkstoffwissenschaften,
Stuttgart, Germany
The magnetic properties of dilute Cu-A1 alloys with 5 at. % Fe were measured in the solid and liquid states. The results are compared to the Scalapino formula for the susceptibility of dilute alloys. The transition from the magnetic to the nonmagnetic state was observed at 41.5 at, % Al.
The susceptibility of dilute CU-Alalloys with 5 at.% Fe was measured in the solid and liquid states. Copper and aluminium are completely miscible in the liquid state and by addition of iron up to 5 at.% the alloy can be still regarded as dilute [ 1). In this case the Anderson model [2] of the s-d interaction is applicable and leads to reasonable results. A comprehensive description of the model is given by Heeger [3]. Gardner and Flynn 141, and Loram, Grassie and Shallow [5] have shown that for dilute binary Cu-Fe and Au-Fe alloys the Anderson model can describe satisfactorily the magnetic properties of these alloys. Our purpose was to study the change in the magnetic properties of the alloys due to the aluminium and the transition from the “magnetic” to “nonmagnetic” impurity state. By regarding the interaction between a 3d electron of the transition metal impurity and an s electron of the host matrix as a small perturbation of the ground state of the impurity atom. Scalapino [6] gives the following expression for the impurity susceptibility:
N*g2*S*(S
Xi =
one obtains: cO
Xi
=7
(Co
1 ’ - ln(T/T&
=N*g2 lS*(s + l)&kB)
which represents a modified Curie law. t
+ lk;
3*k,*T
L
~-
‘ChJ
Tch represents the Kondo [7] characteristic temperature, N is the Avogadro number, k, the Boltzmann constant, S the spin quantum number for the total spin of the 3d electrons in the free impurity atom, ,.+I Bohr’s magneton, pk(EF) the density of states of the s-electrons at the Fermi surface and I the coupling constant. On summing all orders to logarithmic accuracy
I
I
nm
Bw
I Pm0
temQ@mtwYx
Fig. 1. Reciprocal molar susceptibility alloys with 5 at.% Fe.
of liquid Cu-AI (Fe)
I
woo
E. Wachtel, A. PantasisfOnthe behavior of localized magnetic moments
224
?-
6_
6__ If
&him
in
d
%
Fig. 2. Results of the Curie-Weiss approach.
Figure 1 shows the temperature dependence of the reciprocal molar susceptibility for the measured alloys in the liquid state. Some of the curves are displaced by Al/x*. By increasing the ahrminium concentration the temperature dependence decreased and at 41.5 at .% Al, we observe a change to a negative slope which indicates the transition to the nonmagnetic state. By assuming that the magnetic behavior of the alloys with positive slope of the l/x* curves is due to a direct interaction between the Fe impurity atoms, the curves can be fitted to a Currie-Weiss form XA = “/(T - 0,)
(3)
where C’ is the Curie-constant and 8, the paramagnetic Curie temperature. The effective magneton number is then &==,‘N. (R = universal gas constant). ,
(4)
Fis. 3. Measured and calculated values of l/xi at high temperature.
Figure 2 gives the results of this approach. The rise ofthen’ a curve by more than 30 at.% Al and the extreme drop in ep indicate that the magnetic properties of the alloys can not be understood as a pure d-d interaction. Equation (1) gives 1/Xi values which increase nonlinearly with increasing temperature. At high temperatures the difference between these Scalapino-curves and the measured curves become smaller. If we fit the results to equations (1) and(2) (fig. 3) we can calculate the effective magneton number & and the parameters p&+) I and Tch. The results are shown in fig. 4. A condition for the validity of Anderson’s ap preach is that I&EF) II 4 1. As fig. 4 shows, this condition is no more fulfilled for the alloys with more than 40 at.% Al. Between 20 and 40 at.% Al the model has a limited validity, because of the simultaneous increase of \p I I and Tch, l
l
l
E. Wachtel,A. PantasislOnthe behavior of localized magnetic moments
1
225
The comparison of the two theoretical approaches leads to the supposition that the localized magnetic moments in the measured Cu-Al (Fe) alloys are due not only to an s-d interaction but also to an indirect d-d coupling of the impurity atoms.
References [ 1] O.F. Gruber and J.A. Gardner, Phys. Rev. B4, 11 (1971) 3994-4003. [2] P.W. Anderson, Phys. Rev. 124, 1 (1961) 41-53. [3] A.J. Heeger, Sol. Stat. Physics 23 (1969) 283. (41 J.A. Gardner and C.P. Flynn, Phil Msg. 15 (1967) 1235-1254. (51 J.W. Loram, A.D.C. Grassie and G.A. Swallow, Phys. Rev. B2, 7 (1970) 2760-2766. [6] D.J. Scalapino, Phys Rev. Letters 16, 21 (1966) 937-939. [7] J. Kondo, Progr. Theoret. Phys. (Kyoto) 32 (1964) 37. [ 8) H. Rininsland and E. Wachtel, Giessereiforschung 22 (1970) 129.
0
10
Jo
20
alumhium
in at. X
Fig. 4. Results of the Anderson-Scalapino
approach.
i0
ON THE BEHAVIOR OF LOCALIZED MAGNETIC MOMENTS IN LIQUID Cu-AI (Fe) Alloys E. WACHTEL and A. PANTASIS Max.Planck-Institut fuer Metallforschung, Institut fuer Werkstoffwissenschaften,
Stuttgart, Germany
The magnetic properties of dilute Cu-A1 alloys with 5 at. % Fe were measured in the solid and liquid states. The results are compared to the Scalapino formula for the susceptibility of dilute alloys. The transition from the magnetic to the nonmagnetic state was observed at 41.5 at, % Al.
The susceptibility of dilute CU-Alalloys with 5 at.% Fe was measured in the solid and liquid states. Copper and aluminium are completely miscible in the liquid state and by addition of iron up to 5 at.% the alloy can be still regarded as dilute [ 1). In this case the Anderson model [2] of the s-d interaction is applicable and leads to reasonable results. A comprehensive description of the model is given by Heeger [3]. Gardner and Flynn 141, and Loram, Grassie and Shallow [5] have shown that for dilute binary Cu-Fe and Au-Fe alloys the Anderson model can describe satisfactorily the magnetic properties of these alloys. Our purpose was to study the change in the magnetic properties of the alloys due to the aluminium and the transition from the “magnetic” to “nonmagnetic” impurity state. By regarding the interaction between a 3d electron of the transition metal impurity and an s electron of the host matrix as a small perturbation of the ground state of the impurity atom. Scalapino [6] gives the following expression for the impurity susceptibility:
N*g2*S*(S
Xi =
one obtains: cO
Xi
=7
(Co
1 ’ - ln(T/T&
=N*g2 lS*(s + l)&kB)
which represents a modified Curie law. t
+ lk;
3*k,*T
L
~-
‘ChJ
Tch represents the Kondo [7] characteristic temperature, N is the Avogadro number, k, the Boltzmann constant, S the spin quantum number for the total spin of the 3d electrons in the free impurity atom, ,.+I Bohr’s magneton, pk(EF) the density of states of the s-electrons at the Fermi surface and I the coupling constant. On summing all orders to logarithmic accuracy
I
I
nm
Bw
I Pm0
temQ@mtwYx
Fig. 1. Reciprocal molar susceptibility alloys with 5 at.% Fe.
of liquid Cu-AI (Fe)
I
woo
E. Wachtel, A. PantasisfOnthe behavior of localized magnetic moments
224
?-
6_
6__ If
&him
in
d
%
Fig. 2. Results of the Curie-Weiss approach.
Figure 1 shows the temperature dependence of the reciprocal molar susceptibility for the measured alloys in the liquid state. Some of the curves are displaced by Al/x*. By increasing the ahrminium concentration the temperature dependence decreased and at 41.5 at .% Al, we observe a change to a negative slope which indicates the transition to the nonmagnetic state. By assuming that the magnetic behavior of the alloys with positive slope of the l/x* curves is due to a direct interaction between the Fe impurity atoms, the curves can be fitted to a Currie-Weiss form XA = “/(T - 0,)
(3)
where C’ is the Curie-constant and 8, the paramagnetic Curie temperature. The effective magneton number is then &==,‘N. (R = universal gas constant). ,
(4)
Fis. 3. Measured and calculated values of l/xi at high temperature.
Figure 2 gives the results of this approach. The rise ofthen’ a curve by more than 30 at.% Al and the extreme drop in ep indicate that the magnetic properties of the alloys can not be understood as a pure d-d interaction. Equation (1) gives 1/Xi values which increase nonlinearly with increasing temperature. At high temperatures the difference between these Scalapino-curves and the measured curves become smaller. If we fit the results to equations (1) and(2) (fig. 3) we can calculate the effective magneton number & and the parameters p&+) I and Tch. The results are shown in fig. 4. A condition for the validity of Anderson’s ap preach is that I&EF) II 4 1. As fig. 4 shows, this condition is no more fulfilled for the alloys with more than 40 at.% Al. Between 20 and 40 at.% Al the model has a limited validity, because of the simultaneous increase of \p I I and Tch, l
l
l
E. Wachtel,A. PantasislOnthe behavior of localized magnetic moments
1
225
The comparison of the two theoretical approaches leads to the supposition that the localized magnetic moments in the measured Cu-Al (Fe) alloys are due not only to an s-d interaction but also to an indirect d-d coupling of the impurity atoms.
References [ 1] O.F. Gruber and J.A. Gardner, Phys. Rev. B4, 11 (1971) 3994-4003. [2] P.W. Anderson, Phys. Rev. 124, 1 (1961) 41-53. [3] A.J. Heeger, Sol. Stat. Physics 23 (1969) 283. (41 J.A. Gardner and C.P. Flynn, Phil Msg. 15 (1967) 1235-1254. (51 J.W. Loram, A.D.C. Grassie and G.A. Swallow, Phys. Rev. B2, 7 (1970) 2760-2766. [6] D.J. Scalapino, Phys Rev. Letters 16, 21 (1966) 937-939. [7] J. Kondo, Progr. Theoret. Phys. (Kyoto) 32 (1964) 37. [ 8) H. Rininsland and E. Wachtel, Giessereiforschung 22 (1970) 129.
0
10
Jo
20
alumhium
in at. X
Fig. 4. Results of the Anderson-Scalapino
approach.
i0