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Electronic structure and competition between chemical and magnetic interactions in binary transition metal alloys
Journal of Magnetism and Magnetic Materials 54-57 (1986) 967-968
967
ELECTRONIC STRUCTURE AND COMPETITION BETWEEN CHEMICAL AND MAGNETIC INTERACTIONS IN BINARY TRANSITION METAL ALLOYS A. B I E B E R a n d F. G A U T I E R L.M.S.E.S., 4, rue Blaise Pascal, 67070 Strasbourg, France
The phase stability (ground state) and the short range order, in equilibrium states, for magnetic transition metal alloys (above the Curie temperature) have been investigated using the generalized perturbation method and the static approximation. We show that the experimental trends are accounted for in this theory and we point out that magnetic interactions stabilize ordered structures at low temperatures (in Pt, Ni, Fe . . . . based alloys). 1. Introduction The importance of the interplay between chemical and magnetic interactions in binary transition metal (TM) alloys A~B 1_~ has recently been pointed out both for the phase stability, the short-range order (SRO) and the topology of the phase diagrams [1]. In this paper: i) we summarize the results we obtained, using the electronic theory of alloys in the framework of the itinerant magnetism, about this interplay in the equilibrium states," ii) we show that the trends we obtained for the fcc and bcc alloys, both at 0 K (phase stability) and at high temperature, T > TOM (TcM is the magnetic ordering temperature), agree with the experimental results; iii) we relate the results to the statistical models (Ising-Heisenberg (IH) . . . . ) which are, up to now, the only way to study such effects. We extend the generalized perturbation method [2] to compute the band energy E (in the Hartree-Fock approximation at T = 0 K and in the static approximation for finite temperatures [3]) for each configuration characterized by the set (Px, mx} (Px = 1 if the site is occupied by A, 0 otherwise and ma is the magnetic moment on the cell 7t). E is obtained from a rapidly convergent cluster expansion defined from a reference medium which represents roughly (in the CPA) the completely disordered alloy with moments pointing in all directions. Neglecting the local environment effects [4] (which can be large in some peculiar cases) and using a tight binding canonical " d " band model, this expansion is thus dependent (apart from the off-diagonal disorder) both upon the chemical (8 0 = 2(~ A - ~ B ) / W ) a n d the magnetic (8 i = 2(eil, - ~ij, ) / W ; i = A, B) disorders; 80 is the diagonal disorder when m x = 0 whereas 8~ represents the amount of disorder which occurs from the moment of the atomic species i (~so is the " d " energy level corresponding to i and to o = ~', $) and W is the average bandwidth [1]. The energy E can then be written, apart from a structure independent constant, in terms of pair interactions (PI) v which we can split into chemical (v~) and magnetic ( J ) interactions; the other terms of the expansion (multiplets, biquadratic exchange . . . ) are in general negligible [5]. The magnetic
PI become isotropic above TCM but, although the PI have then the same formal expression as those we use in an 1H model (v~(~, (m x, m r ) = v ~ { , - J ~ rhxrh~, where rhT, is the unit vector in the m x direction), the two models are quite different: 1) the PI vc, and J,, between nth nearest neighbors (nn), are defined from the s a m e reference medium so that they are related and dependent both on concentration and temperature; 2) the thermodynamic quantities and the SRO are obtained from a statistical average over all possible configurations including not only the orientation but also the amplitude fluctuations of mx. However for alloys close to the local moment limit (MnPt 3, FePt 3, FePd3) [3] the chemical SRO is directly given by the IH results [5]. For each pair, four interactions are necessary to describe the energy of the system: the chemical interactions 4J~ = vAB - (v~AA + vB,B ) / 2 , the average magnetic interaction 8k, = jAA + ] f B + 2jAr3 and two magnetic interactions 8./, = jAA + .]sa _ 2jAB and 4jn = JuAA -av,sB, which express the fact that the i - j atoms couple magnetically in different ways. 2. General trends for phase stability and order in magnetic alloys The stability of ordered structures (OS) at 0 K has been successfully predicted, for non magnetic TM alloys, in particular domains of the space (8 0, Nd) [6]. It is strongly modified by magnetism: for example in ferromagnets we must consider separately the two spin subbands ('In = J~ ,, + J ~ ~) and study the stability versus the corresponding band fillings Ndo and disorders 6° = 80 - o(SA -- 8B)/2. Experimentally many L12 (Ni3Fe , Pt3Co, Pd3Fe . . . ) , L10 (CoPt, PtMn . . . . ) and B2 (FeCo, FeRh) type OS, corresponding to large values of Nd, are stabilized by magnetism according to the following mechanism we showed to be valid [5]: 1) the hypothetical alloy with m x = 0 would segregate because it corresponds to a value of Nd which is too large [6]; 2) in the ferromagnetic state the PI [J~a[ for the minority bands is larger than ]J~l[ (8~ > 8 1 ) and stabilizes OS (J~l < 0) since it corresponds to smaller band fillings
0 3 0 4 - 8 8 5 3 / 8 6 / $ 0 3 . 5 0 © Elsevier Science P u b l i s h e r s B.V.
968
A. Bieher, tq Gautier / Binary transition metal alloys
(2Nd ~ < Na). For example for the P t 3 M n alloy (80 = 0.9, 8A = 0.8, 8B = 0.1) we o b t a i n (in meV): 4 J I r = 50, 4 J 1 = - 1 6 2 , 4J2r = 0 , 4J2~ = 5 . 5 , 4afar = 2 . 1 , 4J3s = 1 . 3 , 4J4T = 4.4, 4J4~ = 9.1; according to ref. [7] the most stable OS is then L12. For T > Tc. M m a g n e t i s m increases the range of Nj for which chemical SRO exists (J~ < 0) in qualitative agreement with the previous trends at T = 0 K. For example, whereas segregation is predicted in n o n magnetic alloys for Nd > 8, the SRO ( - J ~ ) increases with magnetism (SA) up to N d = 8.9 for ~0 = 0.4 and 6B = 0.1. However the PI are quantitatively different from those we derive at T = 0 K. Note finally that antiferromagnetic (AF) order also increases the stability range of OS for the same reason since this phase stability is equivalent to that of a q u a t e r n a r y alloy Ao,./2Bo(~ ,.)/2 (o =
~, +) [51. 3. Some examples In N i - F e alloys (80 = 0.4, ~A = 0.8, ~B ~ 0.1) the magnetic m o m e n t s induce the L12 OS at 0 K, SRO (J1 < 0) and small A F interactions k 1. These latter PI decrease with iron c o n c e n t r a t i o n and ,/1 becomes very small for N i F e 3 in agreement with SRO m e a s u r e m e n t s (in NiFe 3, [ J1/J2 [ = 0.4, whereas for N i 3 F e [ J l / J 2 1 = 3 [8]) a n d with the topology of the phase diagram (the order disorder transition t e m p e r a t u r e Too decreases with increasing iron concentration). This decrease of I J~ I with the c o n c e n t r a t i o n in magnetic atoms is necessary to explain this asymmetry since ferromagnetic interactions induce the reverse asymmetry [9]; it is also predicted in other systems in agreement with the asymmetry observed in the phase diagrams ( P t - M , M = Co, Fe, Mn). The series of fcc Pt I ,.M,. systems (where M is a T M of the 1st series) is unique since all these systems present OS at low temperatures. The general trends we o b t a i n e d theoretically are as follows: i) the OS are induced by m a g n e t i s m (see section 2); for example P t 3 M n is L12 a n d Pt3V on the b o r d e r line between L12 a n d DO22 stability regions [6] in agreement with the experimental results [10]; ii) for T > T(, M the SRO ( J1 > 0) decreases with increasing c o n c e n t r a t i o n as in N i - F e alloys; iii) the magnetic interactions between 1st a n d 2nd n n in P t - M n alloys are A F and ferromagnetic (respectively) in agreement with the experimental data: chemical PI (J~ < 0 ) a n d magnetic PI ( k 2 > 0 ) b o t h induce a ferromagnetic L12 ordered structure below Toy) [111.
The series of bcc Fel_,.M ,, alloys (where M = Co, Mn, Cr, V) has also been carefully studied. In the FeCo alloys the B2 order type OS is also induced by magnetism and for T > ToM the PI are strongly concentration d e p e n d e n t ; the magnetic PI between Fe and Co atoms are large so that they induce an enhancement of the SRO parameters at lower temperatures. In the F e - M n and F e - C r alloys we obtain a strong variation of the P1 with concentration in agreement with the change of sign of J1 predicted a n d observed recently at low t e m p e r a t u r e in F e - C r alloys [12]. In the F e - V alloys the B2 type OS is stabilized at low temperature, the PI vary smoothly with c and the magnetic interactions between Fe a n d V atoms are negligible; the SRO is thus depressed by chemical ordering in agreement with the experimental results [13]. In conclusion this short summary shows that the general trends for chemical and magnetic SRO in T M alloys are well accounted for by the present theory a l t h o u g h it is oversimplified and c a n n o t yet give a detailed quantitative agreement with the experimental results. [1] For a general discussion, see F. Gautier, in: High Temperature Alloys: Theory and Design, ed. J. Stiegler, AIME (1985) p. 264. [2] F. Gautier, F. Ducastelle and J. Giner, Phil. Magn. 31, (1975) 1373. F. Ducastelle and F. Gautier, J. Phys. F6 (1976) 2039. [3] For a review, see T. Moriya and Y. Takahashi, Ann. Rev. Mator. Sci. 14 (1984) 1. F. Gautier, in: Magnetism of Metals and Alloys, ed. M. Cyrot (North-Holland, Amsterdam, 1982). [4] Such effects were studied within a simple band model by Y. Kakehashi, J. Magn. Magn. Mat. 37 (1983) 109 and refs. therein. [5] A. Bieber and F. Gautier, to be published. [6] A. Bieber and F. Gautier, Solid State Commun. 38 (1981) 1219 and submitted for publication. [7] J. Kanamori and Y. Kakehashi, J. de Phys. 37, (1977) C7 247. [8] P. Cened6se and D. Gratias, private communication. [9] J.M. Sanchez and C.H. Lin, Phys. Rev. B30 (1984) 1448. [10] Long period structures have been observed in the Pt-V system: see D. Schryvers and S. Amelinckx, Mater. Res. Bull. 20 (1985) 367. [11] A.V. Kolubaev, N.S. Golosov and V.E. Panin, Sov. Phys. Solid State 19 (1978) 1863. [12] I. Mirebeau, M. Hennion and G. Parette, Phys. Rev. Lett. 53 (1984) 687. [13] V. Pierron-Bohnes, I. Mirebeau, E. Balanzat and M.C. Cadeville, J. Phys. F14 (1984) 197. V. Pierron-Bohnes, M.C. Cadeville, A. Bieber and F. Gautier, J. Magn. Magn. Mat. 54-57 (1986) 2 P1 10.
967
ELECTRONIC STRUCTURE AND COMPETITION BETWEEN CHEMICAL AND MAGNETIC INTERACTIONS IN BINARY TRANSITION METAL ALLOYS A. B I E B E R a n d F. G A U T I E R L.M.S.E.S., 4, rue Blaise Pascal, 67070 Strasbourg, France
The phase stability (ground state) and the short range order, in equilibrium states, for magnetic transition metal alloys (above the Curie temperature) have been investigated using the generalized perturbation method and the static approximation. We show that the experimental trends are accounted for in this theory and we point out that magnetic interactions stabilize ordered structures at low temperatures (in Pt, Ni, Fe . . . . based alloys). 1. Introduction The importance of the interplay between chemical and magnetic interactions in binary transition metal (TM) alloys A~B 1_~ has recently been pointed out both for the phase stability, the short-range order (SRO) and the topology of the phase diagrams [1]. In this paper: i) we summarize the results we obtained, using the electronic theory of alloys in the framework of the itinerant magnetism, about this interplay in the equilibrium states," ii) we show that the trends we obtained for the fcc and bcc alloys, both at 0 K (phase stability) and at high temperature, T > TOM (TcM is the magnetic ordering temperature), agree with the experimental results; iii) we relate the results to the statistical models (Ising-Heisenberg (IH) . . . . ) which are, up to now, the only way to study such effects. We extend the generalized perturbation method [2] to compute the band energy E (in the Hartree-Fock approximation at T = 0 K and in the static approximation for finite temperatures [3]) for each configuration characterized by the set (Px, mx} (Px = 1 if the site is occupied by A, 0 otherwise and ma is the magnetic moment on the cell 7t). E is obtained from a rapidly convergent cluster expansion defined from a reference medium which represents roughly (in the CPA) the completely disordered alloy with moments pointing in all directions. Neglecting the local environment effects [4] (which can be large in some peculiar cases) and using a tight binding canonical " d " band model, this expansion is thus dependent (apart from the off-diagonal disorder) both upon the chemical (8 0 = 2(~ A - ~ B ) / W ) a n d the magnetic (8 i = 2(eil, - ~ij, ) / W ; i = A, B) disorders; 80 is the diagonal disorder when m x = 0 whereas 8~ represents the amount of disorder which occurs from the moment of the atomic species i (~so is the " d " energy level corresponding to i and to o = ~', $) and W is the average bandwidth [1]. The energy E can then be written, apart from a structure independent constant, in terms of pair interactions (PI) v which we can split into chemical (v~) and magnetic ( J ) interactions; the other terms of the expansion (multiplets, biquadratic exchange . . . ) are in general negligible [5]. The magnetic
PI become isotropic above TCM but, although the PI have then the same formal expression as those we use in an 1H model (v~(~, (m x, m r ) = v ~ { , - J ~ rhxrh~, where rhT, is the unit vector in the m x direction), the two models are quite different: 1) the PI vc, and J,, between nth nearest neighbors (nn), are defined from the s a m e reference medium so that they are related and dependent both on concentration and temperature; 2) the thermodynamic quantities and the SRO are obtained from a statistical average over all possible configurations including not only the orientation but also the amplitude fluctuations of mx. However for alloys close to the local moment limit (MnPt 3, FePt 3, FePd3) [3] the chemical SRO is directly given by the IH results [5]. For each pair, four interactions are necessary to describe the energy of the system: the chemical interactions 4J~ = vAB - (v~AA + vB,B ) / 2 , the average magnetic interaction 8k, = jAA + ] f B + 2jAr3 and two magnetic interactions 8./, = jAA + .]sa _ 2jAB and 4jn = JuAA -av,sB, which express the fact that the i - j atoms couple magnetically in different ways. 2. General trends for phase stability and order in magnetic alloys The stability of ordered structures (OS) at 0 K has been successfully predicted, for non magnetic TM alloys, in particular domains of the space (8 0, Nd) [6]. It is strongly modified by magnetism: for example in ferromagnets we must consider separately the two spin subbands ('In = J~ ,, + J ~ ~) and study the stability versus the corresponding band fillings Ndo and disorders 6° = 80 - o(SA -- 8B)/2. Experimentally many L12 (Ni3Fe , Pt3Co, Pd3Fe . . . ) , L10 (CoPt, PtMn . . . . ) and B2 (FeCo, FeRh) type OS, corresponding to large values of Nd, are stabilized by magnetism according to the following mechanism we showed to be valid [5]: 1) the hypothetical alloy with m x = 0 would segregate because it corresponds to a value of Nd which is too large [6]; 2) in the ferromagnetic state the PI [J~a[ for the minority bands is larger than ]J~l[ (8~ > 8 1 ) and stabilizes OS (J~l < 0) since it corresponds to smaller band fillings
0 3 0 4 - 8 8 5 3 / 8 6 / $ 0 3 . 5 0 © Elsevier Science P u b l i s h e r s B.V.
968
A. Bieher, tq Gautier / Binary transition metal alloys
(2Nd ~ < Na). For example for the P t 3 M n alloy (80 = 0.9, 8A = 0.8, 8B = 0.1) we o b t a i n (in meV): 4 J I r = 50, 4 J 1 = - 1 6 2 , 4J2r = 0 , 4J2~ = 5 . 5 , 4afar = 2 . 1 , 4J3s = 1 . 3 , 4J4T = 4.4, 4J4~ = 9.1; according to ref. [7] the most stable OS is then L12. For T > Tc. M m a g n e t i s m increases the range of Nj for which chemical SRO exists (J~ < 0) in qualitative agreement with the previous trends at T = 0 K. For example, whereas segregation is predicted in n o n magnetic alloys for Nd > 8, the SRO ( - J ~ ) increases with magnetism (SA) up to N d = 8.9 for ~0 = 0.4 and 6B = 0.1. However the PI are quantitatively different from those we derive at T = 0 K. Note finally that antiferromagnetic (AF) order also increases the stability range of OS for the same reason since this phase stability is equivalent to that of a q u a t e r n a r y alloy Ao,./2Bo(~ ,.)/2 (o =
~, +) [51. 3. Some examples In N i - F e alloys (80 = 0.4, ~A = 0.8, ~B ~ 0.1) the magnetic m o m e n t s induce the L12 OS at 0 K, SRO (J1 < 0) and small A F interactions k 1. These latter PI decrease with iron c o n c e n t r a t i o n and ,/1 becomes very small for N i F e 3 in agreement with SRO m e a s u r e m e n t s (in NiFe 3, [ J1/J2 [ = 0.4, whereas for N i 3 F e [ J l / J 2 1 = 3 [8]) a n d with the topology of the phase diagram (the order disorder transition t e m p e r a t u r e Too decreases with increasing iron concentration). This decrease of I J~ I with the c o n c e n t r a t i o n in magnetic atoms is necessary to explain this asymmetry since ferromagnetic interactions induce the reverse asymmetry [9]; it is also predicted in other systems in agreement with the asymmetry observed in the phase diagrams ( P t - M , M = Co, Fe, Mn). The series of fcc Pt I ,.M,. systems (where M is a T M of the 1st series) is unique since all these systems present OS at low temperatures. The general trends we o b t a i n e d theoretically are as follows: i) the OS are induced by m a g n e t i s m (see section 2); for example P t 3 M n is L12 a n d Pt3V on the b o r d e r line between L12 a n d DO22 stability regions [6] in agreement with the experimental results [10]; ii) for T > T(, M the SRO ( J1 > 0) decreases with increasing c o n c e n t r a t i o n as in N i - F e alloys; iii) the magnetic interactions between 1st a n d 2nd n n in P t - M n alloys are A F and ferromagnetic (respectively) in agreement with the experimental data: chemical PI (J~ < 0 ) a n d magnetic PI ( k 2 > 0 ) b o t h induce a ferromagnetic L12 ordered structure below Toy) [111.
The series of bcc Fel_,.M ,, alloys (where M = Co, Mn, Cr, V) has also been carefully studied. In the FeCo alloys the B2 order type OS is also induced by magnetism and for T > ToM the PI are strongly concentration d e p e n d e n t ; the magnetic PI between Fe and Co atoms are large so that they induce an enhancement of the SRO parameters at lower temperatures. In the F e - M n and F e - C r alloys we obtain a strong variation of the P1 with concentration in agreement with the change of sign of J1 predicted a n d observed recently at low t e m p e r a t u r e in F e - C r alloys [12]. In the F e - V alloys the B2 type OS is stabilized at low temperature, the PI vary smoothly with c and the magnetic interactions between Fe a n d V atoms are negligible; the SRO is thus depressed by chemical ordering in agreement with the experimental results [13]. In conclusion this short summary shows that the general trends for chemical and magnetic SRO in T M alloys are well accounted for by the present theory a l t h o u g h it is oversimplified and c a n n o t yet give a detailed quantitative agreement with the experimental results. [1] For a general discussion, see F. Gautier, in: High Temperature Alloys: Theory and Design, ed. J. Stiegler, AIME (1985) p. 264. [2] F. Gautier, F. Ducastelle and J. Giner, Phil. Magn. 31, (1975) 1373. F. Ducastelle and F. Gautier, J. Phys. F6 (1976) 2039. [3] For a review, see T. Moriya and Y. Takahashi, Ann. Rev. Mator. Sci. 14 (1984) 1. F. Gautier, in: Magnetism of Metals and Alloys, ed. M. Cyrot (North-Holland, Amsterdam, 1982). [4] Such effects were studied within a simple band model by Y. Kakehashi, J. Magn. Magn. Mat. 37 (1983) 109 and refs. therein. [5] A. Bieber and F. Gautier, to be published. [6] A. Bieber and F. Gautier, Solid State Commun. 38 (1981) 1219 and submitted for publication. [7] J. Kanamori and Y. Kakehashi, J. de Phys. 37, (1977) C7 247. [8] P. Cened6se and D. Gratias, private communication. [9] J.M. Sanchez and C.H. Lin, Phys. Rev. B30 (1984) 1448. [10] Long period structures have been observed in the Pt-V system: see D. Schryvers and S. Amelinckx, Mater. Res. Bull. 20 (1985) 367. [11] A.V. Kolubaev, N.S. Golosov and V.E. Panin, Sov. Phys. Solid State 19 (1978) 1863. [12] I. Mirebeau, M. Hennion and G. Parette, Phys. Rev. Lett. 53 (1984) 687. [13] V. Pierron-Bohnes, I. Mirebeau, E. Balanzat and M.C. Cadeville, J. Phys. F14 (1984) 197. V. Pierron-Bohnes, M.C. Cadeville, A. Bieber and F. Gautier, J. Magn. Magn. Mat. 54-57 (1986) 2 P1 10.