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Spin waves in fcc NiCo alloys by neutron spectrometry
345 SPIN WAVES IN FCC Ni-Co ALLOYS BY NEUTRON SPECTROMETRY*
K. M I K K E , J. J A N K O W S K A , A. M O D R Z E J E W S K I and E. F R I K K E E t Institute o[ Nuclear Research, Swierk 05-400 Otwock, Poland
The spin wave stiffness for Ni-Co alloys was investigated by inelastic neutron scattering. Contrary to spin wave resonance data and the rigid band model calculations within RPA, the stiffness constant D does not decrease with Co concentration.
Long wavelength spin waves in ferromagnetic 3d metal alloys obey the quadratic dispersion E = D q 2. The variation of the spin wave stiffness constant D with composition for fcc Ni-Co alloys was experimentally investigated by the spin wave resonance (SWR) technique [1]. The obtained dependence of D on the average number of electrons per atom (e/a) was qualitatively similar to that for N i - F e fcc alloys [2-4]. These data might be interpreted in terms of the Heisenberg model, which is, unfortunately, basically incorrect for itinerant magnetics. Much more interest is therefore devoted to explanations based on band models. Since both N i - F e and Ni-Co alloys follow closely the Slater-Pauling curve, the characteristic quantity determining the properties of these alloys should be the electron concentration. One can then try to apply the rigid band model (RBM) as has been done in [5] and the resulting D (e/a) relation should be independent of the nature of the second c o m p o n e n t in a binary alloy. More recent refined band model calculations of D were based on the coherent potential approximation (CPA) [6-8]. As demonstrated in [6, 7] the use of C P A does not lead, however, to results qualitatively different from RBM. The D (e/a) dependence obtained with C P A is more smoothed-out compared to that for RBM but its character remains essentially unchanged. Thus also for C P A one should not expect any significant differences between N i - F e and N i - C o alloys. The main objective of our measurements was the test of this expected similarity for the spin-wave stiffness constant. Our results are in complete disagreement with these predictions and also with the SWR data. * Partly supported by the Institute of Physics of the Polish Academy of Science. t Netherlands Energy Research Foundation, E.C.N., P e n e n (N.H.) The Netherlands.
Physica 86--88B (1977) 345-346 © North-Holland
Our investigations were made at room temperature for six single crystal samples with Co concentration from 0 to 50at.%. Only the samples with mosaic spreads below 15 min of arc (FWHM) were used. In one c a s e Nio.79Coom the mosaic spread was below 4min. All measurements were performed on a triple-axis spectrometer mostly at the E W A 10 MW reactor at Swierk. A series of runs with improved resolution and statistics was also carried out at the H F R reactor at ECN Petten for the Ni0.s3Co0.17 sample. With moderate resolution employed and large values of D observed, large resolution corrections were thus unavoidable. In order to give us more confidence in our resolution correction procedures, extensive measurements were made for a pure nickel sample as a reference material for which very accurate data are available [9]. Another check was the data obtained with improved resolution at Petten. The values of D for each sample were obtained by fitting the experimental points to the parabolic dispersion relation E = Dq 2. T h e y are displayed as open circles in fig. 1. Different runs, e.g. for different directions, are averaged and displayed as single points since no anisotropy could be noticed. The line through these points is a curve computed on basis of a localized spin-model for the best fit of exchange integrals Jt2/J n = 0.83 -- 0.09 and J=/Jn = 0.49---0.14, where 1 stands for Ni and 2 for Co. Our room temperature data for the N i - F e alloys [3] are shown by crosses. The SWR data for the N i - C o alloys [1] are shown by the solid line marked SWR and the theoretical results by Wakoh [5] are indicated by a dashed line. The proper comparison between D (e/a) for the two alloys should be made for 0 K. H o w e v e r , as expected and experimentally verified [3, 4], if the Curie temperature is much above room temperature the value of D does not change much between room temperature and 0 K. Thus
346
D meV,~.2 600
40(
t
l0
t
9.8
1
I
9.6
I
I
9.4
I
e/e
Fig. I. Spin wave stiffness constant D against electron concentration for Ni-Co alloys (open circles); for Ni-Fe alloys (crosses), for pure Ni [4] (filled circle) and for pure Ni [10] (square). The lower solid l i n e - S W R data [1]; the dashed l i n e - calculations by [5].
in our case only the pure nickel value should be corrected. The values 525 and 550 meV/k 2 were reported for pure Ni at 4.2 K in [4] and in [10] and they are shown by the filled circle and square, respectively. These values, if combined with the rest of our data for Ni-Co, produce nearly a straight line with only a small increase of D with the decreasing electron concentration. This character of the D (e/a) dependence is completely different from the shape of this relation observed by neutron scattering for N i Fe alloys and this is quite contrary to the theoretical predictions summarized above. Our data are also quite different from SWR results for Ni-Co alloys [1] and the discrepancies are much more pronounced than in the case of N i - F e alloys. The problem of adequacy of band-theoretical descriptions of spin waves in 3d metal alloys has been the subject of considerable effort over several years. The lack of success with RBM was ascribed to the oversimplification regarding the role of the second component in the alloy. C P A was thus expected to remove this d e f i c i e n c y - w i t h this aim in mind some rather refined and tedious calculations were performed
recently [8]. Edwards and Hill [6,7] have shown, however, that especially for the case of alloys containing Fe and Co, there are no essential differences between the computations basing on RBM and those using CPA. Their conclusion was that C P A would not help and they pointed out two main deficiencies of the present theories: (1) absence of interatomic interactions, and (2) inaccuracies resulting from the use of RPA. This last factor should be especially important in the case where the concentration of magnetic carriers is high. Thus for Fe and Co it should be more pronounced than for Ni. This argument applies also to Nibased alloys containing Co and Fe where the use of R P A might lead to considerable errors. From this point of view the experimentally established difference in the behaviour of D (e/a) for N i - F e and Ni-Co demonstrates the need of a qualitatively different approach to the theory of spin waves in 3d metal alloys. We wish to express our thanks to Dr. D.M. Edwards for indicating the problem to us. Note added in proof. After this work was completed magnetization data for the same concentration range of Ni-Co alloys were published [l l]. Although the D values derived from these data are systematically lower than neutron scattering results, the variation of D with concentration shows a similar trend.
References [1] M, Hinoul and J. Witters, Solid State Commun. 10 (1972) 749. [2] T. Maeda, H. Yamauchi and H. Watanabe, J. Phys. Soc. Jap. 35 (1973) 1635. [3] K. Mikke, J. Jankowska and A. Modrzejewski, J. Phys. F: Metal Phys. 6 (1976) 631. [4] M. Hennion, B. Hennion, A. Castets and D. Toccheti, Solid State Commun. 17 (1975) 899. [5] S. Wakoh, J. Phys. Soc. Jap. 30 (1971) 1068. [6] D.M. Edwards and D. Hill, J. Phys. F: Metal Phys. 3 (1973) L162. [7] D.M. Edwards and D. Hill, J. Phys. F: Metal Phys. 6 (1976) 607. [8] R. Riedinger and H. Nauciel-Bioch, J. Phys. F: Metal Phys. 5 (1975) 732. [9] H.A. Mook and R.M. Nicklow, Phys. Rev. B7 (1973) 336. [10] H.A. Mook, J.W. Lynn and R.M. Nickiow, Phys. Rev. Lett. 30 (1973) 556. [11] I. Maeda, H. Yamauchi and H. Watanabe, J. Phys. Soc. Jap. 40 (1976) 1559.
K. M I K K E , J. J A N K O W S K A , A. M O D R Z E J E W S K I and E. F R I K K E E t Institute o[ Nuclear Research, Swierk 05-400 Otwock, Poland
The spin wave stiffness for Ni-Co alloys was investigated by inelastic neutron scattering. Contrary to spin wave resonance data and the rigid band model calculations within RPA, the stiffness constant D does not decrease with Co concentration.
Long wavelength spin waves in ferromagnetic 3d metal alloys obey the quadratic dispersion E = D q 2. The variation of the spin wave stiffness constant D with composition for fcc Ni-Co alloys was experimentally investigated by the spin wave resonance (SWR) technique [1]. The obtained dependence of D on the average number of electrons per atom (e/a) was qualitatively similar to that for N i - F e fcc alloys [2-4]. These data might be interpreted in terms of the Heisenberg model, which is, unfortunately, basically incorrect for itinerant magnetics. Much more interest is therefore devoted to explanations based on band models. Since both N i - F e and Ni-Co alloys follow closely the Slater-Pauling curve, the characteristic quantity determining the properties of these alloys should be the electron concentration. One can then try to apply the rigid band model (RBM) as has been done in [5] and the resulting D (e/a) relation should be independent of the nature of the second c o m p o n e n t in a binary alloy. More recent refined band model calculations of D were based on the coherent potential approximation (CPA) [6-8]. As demonstrated in [6, 7] the use of C P A does not lead, however, to results qualitatively different from RBM. The D (e/a) dependence obtained with C P A is more smoothed-out compared to that for RBM but its character remains essentially unchanged. Thus also for C P A one should not expect any significant differences between N i - F e and N i - C o alloys. The main objective of our measurements was the test of this expected similarity for the spin-wave stiffness constant. Our results are in complete disagreement with these predictions and also with the SWR data. * Partly supported by the Institute of Physics of the Polish Academy of Science. t Netherlands Energy Research Foundation, E.C.N., P e n e n (N.H.) The Netherlands.
Physica 86--88B (1977) 345-346 © North-Holland
Our investigations were made at room temperature for six single crystal samples with Co concentration from 0 to 50at.%. Only the samples with mosaic spreads below 15 min of arc (FWHM) were used. In one c a s e Nio.79Coom the mosaic spread was below 4min. All measurements were performed on a triple-axis spectrometer mostly at the E W A 10 MW reactor at Swierk. A series of runs with improved resolution and statistics was also carried out at the H F R reactor at ECN Petten for the Ni0.s3Co0.17 sample. With moderate resolution employed and large values of D observed, large resolution corrections were thus unavoidable. In order to give us more confidence in our resolution correction procedures, extensive measurements were made for a pure nickel sample as a reference material for which very accurate data are available [9]. Another check was the data obtained with improved resolution at Petten. The values of D for each sample were obtained by fitting the experimental points to the parabolic dispersion relation E = Dq 2. T h e y are displayed as open circles in fig. 1. Different runs, e.g. for different directions, are averaged and displayed as single points since no anisotropy could be noticed. The line through these points is a curve computed on basis of a localized spin-model for the best fit of exchange integrals Jt2/J n = 0.83 -- 0.09 and J=/Jn = 0.49---0.14, where 1 stands for Ni and 2 for Co. Our room temperature data for the N i - F e alloys [3] are shown by crosses. The SWR data for the N i - C o alloys [1] are shown by the solid line marked SWR and the theoretical results by Wakoh [5] are indicated by a dashed line. The proper comparison between D (e/a) for the two alloys should be made for 0 K. H o w e v e r , as expected and experimentally verified [3, 4], if the Curie temperature is much above room temperature the value of D does not change much between room temperature and 0 K. Thus
346
D meV,~.2 600
40(
t
l0
t
9.8
1
I
9.6
I
I
9.4
I
e/e
Fig. I. Spin wave stiffness constant D against electron concentration for Ni-Co alloys (open circles); for Ni-Fe alloys (crosses), for pure Ni [4] (filled circle) and for pure Ni [10] (square). The lower solid l i n e - S W R data [1]; the dashed l i n e - calculations by [5].
in our case only the pure nickel value should be corrected. The values 525 and 550 meV/k 2 were reported for pure Ni at 4.2 K in [4] and in [10] and they are shown by the filled circle and square, respectively. These values, if combined with the rest of our data for Ni-Co, produce nearly a straight line with only a small increase of D with the decreasing electron concentration. This character of the D (e/a) dependence is completely different from the shape of this relation observed by neutron scattering for N i Fe alloys and this is quite contrary to the theoretical predictions summarized above. Our data are also quite different from SWR results for Ni-Co alloys [1] and the discrepancies are much more pronounced than in the case of N i - F e alloys. The problem of adequacy of band-theoretical descriptions of spin waves in 3d metal alloys has been the subject of considerable effort over several years. The lack of success with RBM was ascribed to the oversimplification regarding the role of the second component in the alloy. C P A was thus expected to remove this d e f i c i e n c y - w i t h this aim in mind some rather refined and tedious calculations were performed
recently [8]. Edwards and Hill [6,7] have shown, however, that especially for the case of alloys containing Fe and Co, there are no essential differences between the computations basing on RBM and those using CPA. Their conclusion was that C P A would not help and they pointed out two main deficiencies of the present theories: (1) absence of interatomic interactions, and (2) inaccuracies resulting from the use of RPA. This last factor should be especially important in the case where the concentration of magnetic carriers is high. Thus for Fe and Co it should be more pronounced than for Ni. This argument applies also to Nibased alloys containing Co and Fe where the use of R P A might lead to considerable errors. From this point of view the experimentally established difference in the behaviour of D (e/a) for N i - F e and Ni-Co demonstrates the need of a qualitatively different approach to the theory of spin waves in 3d metal alloys. We wish to express our thanks to Dr. D.M. Edwards for indicating the problem to us. Note added in proof. After this work was completed magnetization data for the same concentration range of Ni-Co alloys were published [l l]. Although the D values derived from these data are systematically lower than neutron scattering results, the variation of D with concentration shows a similar trend.
References [1] M, Hinoul and J. Witters, Solid State Commun. 10 (1972) 749. [2] T. Maeda, H. Yamauchi and H. Watanabe, J. Phys. Soc. Jap. 35 (1973) 1635. [3] K. Mikke, J. Jankowska and A. Modrzejewski, J. Phys. F: Metal Phys. 6 (1976) 631. [4] M. Hennion, B. Hennion, A. Castets and D. Toccheti, Solid State Commun. 17 (1975) 899. [5] S. Wakoh, J. Phys. Soc. Jap. 30 (1971) 1068. [6] D.M. Edwards and D. Hill, J. Phys. F: Metal Phys. 3 (1973) L162. [7] D.M. Edwards and D. Hill, J. Phys. F: Metal Phys. 6 (1976) 607. [8] R. Riedinger and H. Nauciel-Bioch, J. Phys. F: Metal Phys. 5 (1975) 732. [9] H.A. Mook and R.M. Nicklow, Phys. Rev. B7 (1973) 336. [10] H.A. Mook, J.W. Lynn and R.M. Nickiow, Phys. Rev. Lett. 30 (1973) 556. [11] I. Maeda, H. Yamauchi and H. Watanabe, J. Phys. Soc. Jap. 40 (1976) 1559.