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Origin of magnetic alignment in heusler alloys
O R I G I N OF M A G N E T I C A L I G N M E N T IN H E U S L E R A L L O Y S MARY BETH STEARNS Ford Research Staff, Dearborn, M1 48121, USA
It is shown that the magnetic alignment in ferromagnetic Heusler alloys is caused by the positive polarization of the d-like conduction electrons at the M n - M n distance. The two other polarizing interactions, s-d exchange and super-exchange, are found to give negative polarization contributions at the Mn-Mn distance.
It is well established [1] that the s-like conduction electron polarization (s-CEP) in Fe and Fe3Si is negative in the region of the nearest neighbor magnetic atoms. Thus, the ferromagnetic alignment in these materials is not due to the s-like conduction electrons. It has been shown [2] to be due to a small number of d-like conduction electrons which are positively polarized in the region of the near neighbor magnetic atoms. This polarization arises from the Coulomb exchange interaction of the itinerant d(i) electrons with the localized d(1) electrons. Since the CEP has an RKKY-like oscillatory behavior, the sign of the polarization of a given type, e.g. s or d(i), electron at a particular distance depends on the number of conduction electrons of that type. The Heusler alloys (X2MnZ) [3] are an excellent system in which to independently observe and separate the effects of the s and d(i) conduction electrons. This is done by observing the behavior of various quantities as the elements X and Z are varied. In varying the X element, which is typically a transition element to the right of Fe in the periodic table, the number of s-like conduction electrons, n~, is essentially constant (about one per X atom) while the relative variation of the number of d(i)-like conduction electrons, n d, is considerably greater. The value of n d decreases with increasing column and increases with increasing row in the periodic table. Thus n a increases from Cu to Ni to Co or from Ni to Pd to Pt. In contrast, when the transition element X is fixed and the Z element (a non-transition element containing only sp valence electrons) is varied, n d remains constant. Whether n s varies appreciably as Z is changed is controversial. There are two points of view: In the charge perturbation type models [4] n s is assumed to vary as the number of outer valence electrons, i.e. as the column of Z in the periodic table. In the alternate approach it is assumed that n s does not change appreciably with
Z. This view assumes that only about one s-like valence electron is contributed to the conduction band and the other valence electrons stay well within the unit cell of the Z atom, screening the nuclear charge. This latter point of view is supported by the behavior [5, 6] of the hyperfine field (hff) at the Inn X atoms and the 2nn Z atoms with respect to the magnetic Mn atoms. The hff values show that for all the Heusler alloys discussed here (those where all the moment, of ~ 4/~B, exists on the Mn atom) the s-conduction electron polarization (s-CEP) is essentially the same and thus quite independent of X or Z. Another expected effect of the Z atoms is that they couple the 3nn Mn atoms through a superexchange interaction. This interaction is usually through the p-like electrons and antiferromagnetic. Whether the s-d(1) or d(i)-d(1) Coulomb exchange or superexchange dominates the alignment of the magnetic Mn atoms can be seen from the behavior of the Curie (or Neel) temperature, T c, of the Heusler alloys. The value of T c is an indication of strength of the CEP and superexchange polarization at one Mn atom caused by all the other Mn atoms. As discussed above, both the s-CEP and the polarization caused by superexchange are considered to be negative. Thus ferromagnetic coupling is due to the d-CEP. Since the d-CEP has an RKKY-Iike oscillatory behavior, at a fixed distance (in this case the 3nn distance of the M n atoms), its magnitude depends on nd. For a small value of n d ( ~ 0.1 per atom) the d-CEP is positive in the region of 3nn Mn atoms. As n d increases, k F (the Fermi wa;ee vector) increases and the first node of the d-CEP moves to smaller distances. This causes the d-CEP to decrease at the M n atoms. Since only the X atoms change n d, Tc should decrease as X varies from Cu to Ni to Pd to Pt. In this picture we expect very little variation of T¢ with the Z element. Since the d(i) electrons have spatial symmetrics very similar to that of the d(1) electrons, the
Journal of Magnetism and Magnetic Materials 15-18 (1980) 301-302 @North Holland
301
M. B. Stearns/Magnetic alignment in Heusler alloys
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TABLE 1 Variation of T¢ values of Heusler alloys with Z for a given X Z
To(K)
V'Mn(#B)
d(A)
Cu2MnZ A1 In Sn
630 500 (530)
4.12 3.95 4.11
5.949 6.206 6.173
Ni2MnZ Ga In Sn Sb
379 323 344 360
4.17 4.4 4.05 3.27
5.825 6.068 6.052 6.000
Pd2MnZ In Ge Sn Sb
142(A.F.) 170 189 247
3.2 4.23 4.4
6.373 6.174 6.380 6.424
Ir2MnZ Ga
24
4.1
6.052
Pt2MnZ Ga
75(A.F.)
6.16
d(i)-d(1) i n t e r a c t i o n is c o n s i d e r a b l y larger t h a n the s-d(1) interaction. T a b l e 1 lists the T c values of the H e u s l e r alloys in a m a n n e r which clearly shows t h a t Tc m a i n l y d e p e n d s on the X e l e m e n t [3]. T h e X e l e m e n t s a r e listed in o r d e r of i n c r e a s i n g nd. F o r X = Cu, the e l e m e n t with fewest d(i) e l e c t r o n s a n d therefore the largest d - C E P at the M n a t o m s , T~ is in the r a n g e 500-630 K. W h i l e for X = Ir a n d Pt, which h a v e the largest n d values, the d - C E P is small o r p e r h a p s negative. This results in T~ values which are small
or a n t i f e r r o m a g n e t i c . T h e T c values of the Ir a n d Pt alloys thus gives a n i n d i c a t i o n of the strength of the p o l a r i z a t i o n f r o m the s~l(1) a n d s u p e r e x c h a n g e i n t e r a c t i o n s at the 3nn distance. W e see that for the CUEMnZ alloys the s - d 0 ) plus s u p e r e x c h a n g e p o l a r i z a t i o n is at least 3-5 times w e a k e r t h a n that due to the d(i)-d(1) interaction. A n analysis of the spin wave s p e c t r u m [7] of Cu2MnA1 i n d i c a t e d that at the 3nn d i s t a n c e the s - C E P was negligible a n d the d - C E P was a b o u t three times the p o l a r i z a t i o n f r o m superexchange. A can b e seen from table 1 there is no c o r r e l a t i o n b e t w e e n T c a n d #Mn or the lattice c o n s t a n t d. T h u s the T¢ a n d hff b e h a v i o r of these alloys strongly s u p p o r t s the view t h a t the M n a t o m s in f e r r o m a g n e t i c H e u s l e r alloys are a l i g n e d b y the i t i n e r a n t d(i) electrons.
References [1] M. B. Stearns, Phys. Rev. 147 (1966) 439; B4 (1971) 4069, 408 I. [2] M. B. Stearns, Phys. Rev. B8 (1973) 4383; B9 (1974) 2311; B13 (1976) 1183; M. B. Stearns and L. A. Feldkamp, Phys. Rev. BI3 (1976) 1198. [3] P. J. Webster, Contemp. Phys. 10 (1969) 559; C. C. M. Campbell, J. Phys. F5 (1951) 1931. [4] E. g., E. Daniel and J. Friedel, J. Phys. Chem. Solids 24 (1963) 1601; B. Caroli and A. Blandin, ibid 27 (1966) 503. [5] A. Blandin and I. A. Campbell, J. Magn. Magn. Mat. 1 (1975) 1. [6] M. B. Stearns, J. Appl. Phys. 50 (1979) 2060. [7] Analysis of data of K. Tajima, Y. Ishikawa, P. J. Webster, M. W. Stringfellow, D. Tocchetti and R. A. Zeabeck, 43 (1977) 483, by: J. R. Reitz and M. B. Stearns, J. Appl. Phys. 50 (1979) 2066.
It is shown that the magnetic alignment in ferromagnetic Heusler alloys is caused by the positive polarization of the d-like conduction electrons at the M n - M n distance. The two other polarizing interactions, s-d exchange and super-exchange, are found to give negative polarization contributions at the Mn-Mn distance.
It is well established [1] that the s-like conduction electron polarization (s-CEP) in Fe and Fe3Si is negative in the region of the nearest neighbor magnetic atoms. Thus, the ferromagnetic alignment in these materials is not due to the s-like conduction electrons. It has been shown [2] to be due to a small number of d-like conduction electrons which are positively polarized in the region of the near neighbor magnetic atoms. This polarization arises from the Coulomb exchange interaction of the itinerant d(i) electrons with the localized d(1) electrons. Since the CEP has an RKKY-like oscillatory behavior, the sign of the polarization of a given type, e.g. s or d(i), electron at a particular distance depends on the number of conduction electrons of that type. The Heusler alloys (X2MnZ) [3] are an excellent system in which to independently observe and separate the effects of the s and d(i) conduction electrons. This is done by observing the behavior of various quantities as the elements X and Z are varied. In varying the X element, which is typically a transition element to the right of Fe in the periodic table, the number of s-like conduction electrons, n~, is essentially constant (about one per X atom) while the relative variation of the number of d(i)-like conduction electrons, n d, is considerably greater. The value of n d decreases with increasing column and increases with increasing row in the periodic table. Thus n a increases from Cu to Ni to Co or from Ni to Pd to Pt. In contrast, when the transition element X is fixed and the Z element (a non-transition element containing only sp valence electrons) is varied, n d remains constant. Whether n s varies appreciably as Z is changed is controversial. There are two points of view: In the charge perturbation type models [4] n s is assumed to vary as the number of outer valence electrons, i.e. as the column of Z in the periodic table. In the alternate approach it is assumed that n s does not change appreciably with
Z. This view assumes that only about one s-like valence electron is contributed to the conduction band and the other valence electrons stay well within the unit cell of the Z atom, screening the nuclear charge. This latter point of view is supported by the behavior [5, 6] of the hyperfine field (hff) at the Inn X atoms and the 2nn Z atoms with respect to the magnetic Mn atoms. The hff values show that for all the Heusler alloys discussed here (those where all the moment, of ~ 4/~B, exists on the Mn atom) the s-conduction electron polarization (s-CEP) is essentially the same and thus quite independent of X or Z. Another expected effect of the Z atoms is that they couple the 3nn Mn atoms through a superexchange interaction. This interaction is usually through the p-like electrons and antiferromagnetic. Whether the s-d(1) or d(i)-d(1) Coulomb exchange or superexchange dominates the alignment of the magnetic Mn atoms can be seen from the behavior of the Curie (or Neel) temperature, T c, of the Heusler alloys. The value of T c is an indication of strength of the CEP and superexchange polarization at one Mn atom caused by all the other Mn atoms. As discussed above, both the s-CEP and the polarization caused by superexchange are considered to be negative. Thus ferromagnetic coupling is due to the d-CEP. Since the d-CEP has an RKKY-Iike oscillatory behavior, at a fixed distance (in this case the 3nn distance of the M n atoms), its magnitude depends on nd. For a small value of n d ( ~ 0.1 per atom) the d-CEP is positive in the region of 3nn Mn atoms. As n d increases, k F (the Fermi wa;ee vector) increases and the first node of the d-CEP moves to smaller distances. This causes the d-CEP to decrease at the M n atoms. Since only the X atoms change n d, Tc should decrease as X varies from Cu to Ni to Pd to Pt. In this picture we expect very little variation of T¢ with the Z element. Since the d(i) electrons have spatial symmetrics very similar to that of the d(1) electrons, the
Journal of Magnetism and Magnetic Materials 15-18 (1980) 301-302 @North Holland
301
M. B. Stearns/Magnetic alignment in Heusler alloys
302
TABLE 1 Variation of T¢ values of Heusler alloys with Z for a given X Z
To(K)
V'Mn(#B)
d(A)
Cu2MnZ A1 In Sn
630 500 (530)
4.12 3.95 4.11
5.949 6.206 6.173
Ni2MnZ Ga In Sn Sb
379 323 344 360
4.17 4.4 4.05 3.27
5.825 6.068 6.052 6.000
Pd2MnZ In Ge Sn Sb
142(A.F.) 170 189 247
3.2 4.23 4.4
6.373 6.174 6.380 6.424
Ir2MnZ Ga
24
4.1
6.052
Pt2MnZ Ga
75(A.F.)
6.16
d(i)-d(1) i n t e r a c t i o n is c o n s i d e r a b l y larger t h a n the s-d(1) interaction. T a b l e 1 lists the T c values of the H e u s l e r alloys in a m a n n e r which clearly shows t h a t Tc m a i n l y d e p e n d s on the X e l e m e n t [3]. T h e X e l e m e n t s a r e listed in o r d e r of i n c r e a s i n g nd. F o r X = Cu, the e l e m e n t with fewest d(i) e l e c t r o n s a n d therefore the largest d - C E P at the M n a t o m s , T~ is in the r a n g e 500-630 K. W h i l e for X = Ir a n d Pt, which h a v e the largest n d values, the d - C E P is small o r p e r h a p s negative. This results in T~ values which are small
or a n t i f e r r o m a g n e t i c . T h e T c values of the Ir a n d Pt alloys thus gives a n i n d i c a t i o n of the strength of the p o l a r i z a t i o n f r o m the s~l(1) a n d s u p e r e x c h a n g e i n t e r a c t i o n s at the 3nn distance. W e see that for the CUEMnZ alloys the s - d 0 ) plus s u p e r e x c h a n g e p o l a r i z a t i o n is at least 3-5 times w e a k e r t h a n that due to the d(i)-d(1) interaction. A n analysis of the spin wave s p e c t r u m [7] of Cu2MnA1 i n d i c a t e d that at the 3nn d i s t a n c e the s - C E P was negligible a n d the d - C E P was a b o u t three times the p o l a r i z a t i o n f r o m superexchange. A can b e seen from table 1 there is no c o r r e l a t i o n b e t w e e n T c a n d #Mn or the lattice c o n s t a n t d. T h u s the T¢ a n d hff b e h a v i o r of these alloys strongly s u p p o r t s the view t h a t the M n a t o m s in f e r r o m a g n e t i c H e u s l e r alloys are a l i g n e d b y the i t i n e r a n t d(i) electrons.
References [1] M. B. Stearns, Phys. Rev. 147 (1966) 439; B4 (1971) 4069, 408 I. [2] M. B. Stearns, Phys. Rev. B8 (1973) 4383; B9 (1974) 2311; B13 (1976) 1183; M. B. Stearns and L. A. Feldkamp, Phys. Rev. BI3 (1976) 1198. [3] P. J. Webster, Contemp. Phys. 10 (1969) 559; C. C. M. Campbell, J. Phys. F5 (1951) 1931. [4] E. g., E. Daniel and J. Friedel, J. Phys. Chem. Solids 24 (1963) 1601; B. Caroli and A. Blandin, ibid 27 (1966) 503. [5] A. Blandin and I. A. Campbell, J. Magn. Magn. Mat. 1 (1975) 1. [6] M. B. Stearns, J. Appl. Phys. 50 (1979) 2060. [7] Analysis of data of K. Tajima, Y. Ishikawa, P. J. Webster, M. W. Stringfellow, D. Tocchetti and R. A. Zeabeck, 43 (1977) 483, by: J. R. Reitz and M. B. Stearns, J. Appl. Phys. 50 (1979) 2066.