ISSN 1318-0010
KZLTET 32(3-513)165(1998)
CALCULATION OF THE CURIE TEMPERATURE IN THE
SYSTEM Nd2Fe17-xAlx
IZRAČUN CURIEJEVE TEMPERATURE V SISTEMU Nd2Fe17-xAlx
MATEJ KOMELJ, S. KOBE
Jozef Stefan Institute, Jamova 39, 1000 Ljubljana
Prejem rokopisa - received: 1998-11-16; sprejem za objavo - accepted for publication: 1998-12-07
The ferromagnetic alloy Nd2Fe17 has a low Curie temperature (p330K). By substituting some of the Fe atoms in the crystal lattice with Al atoms the volume of the unit cell is increased and consequently, the Curie temperature increases up to a maximum of p470K. Therefore the alloy Nd2Fe17-xAlx is potentially suitable as a permanent magnet material. From the electronic structure we have predicted the relative changes of the Curie temperature in the spin fluctuation approximation. We have calculated the electronic structure within the framework of the Density Functional Theory and the Local Spin Density Approximation using the LMTO method.
Key words: permanent magnet materials, Curie temperature, density functional theory
Feromagnetna zlitina Nd2Fe17 ima nizko Curiejevo temperaturo (p330K). Z zamenjavo nekaterih atomov Fe v kristalni mreži z atomi Al se poveča prostornina osnovne celice in zato tudi Curiejeva temperatura do največ p470K. To pomeni, da je zlitina Nd2Fe17-xAlx potencialno primerna kot material za izdelavo trajnih magnetov. Iz elektronske strukture smo v okviru približka spinskih fluktuacij napovedali relativne spremembe Curiejeve temperature zaradi prisotnosti Al. Elektronsko strukturo smo izračunali v okviru teorije gostotnih funkcionalov in približka lokalne spinske gostote z uporabo metode LMTO.
Ključne besede: trajno-magnetni materiali, Curiejeva temperatura, teorija gostotnih funkcionalov
1 INTRODUCTION
The R2Fe17 rare- earth intermetallic compounds are, despite their uniaxial magneto- crystalline anisotropy, not suited for permanent magnet materials because of their low Curie temperature (TC). The first efforts to overcome this problem involved attempts to interstitially modify the basic alloys by introducing carbon1 or nitro-gen2 into the material. The unit cell volumes of carbided R2FenCx or nitrided R2FenNx material are expanded by approximately 5% to 7% and, as a result, their Curie temperatures increase by about 400°C. However, the presence of carbon or nitrogen causes difficulties in the manufacture of these new materials3. Hence alternative ways of increasing the volumes of the unit cell and Curie temperatures must be found. One approach is the formation of pseudobinary alloys of the type R2Fen-xMx where M stands for aluminum, silicon or gallium4.
An example is the alloy Nd2Fen with Tc p 330K i.e. slightly above the room temperature, which enables the use of the material for limited practical applications. G. J. Long et al.5 experimentally obtained the dependence of Tc on the aluminum content in the system Nd2Fen-xAlx. The best improvement (TC P 470) was achieved for the alloy with x p 4.
We have calculated the Curie temperatures of Nd2Fe17-xAlx relative to the Tc of Nd2Fen.
2 THEORY
The only reliable theoretical investigations of mag-
netic properties of the crystalline materials are based on
calculation of the electronic structure from first principles within the framework of the density functional the-ory6. This theory is valid only for the description of the electronic ground state of the crystal which is in reality present only at zero temperature. Therefore the Curie temperature can not be derived rigorously without using any approximations. The easiest approach follows the Stoner theory of ferromagnetism from 19367. It is based on the idea that above the Curie temperature not just the exchange interaction but also particular local magnetic moments disappear. This is not true because in the paramagnetic state the local magnetic moments are still present but they are randomly oriented due to thermal excitations. However the Stoner Curie temperature (Ts) serves as the starting point for better approximations. The next step was undertaken by Mohn and Wohlfarth8 who considered also the effects of spin fluctuations. They introduced the characteristic temperature TTS describing the influence of spin fluctuations. The approximate Curie temperature TC is the solution of the equation:
T2 T
— + — - 1 = 0 T2 T
(1)
lsf
Both quantities, Ts and Tsf are obtained from the electronic structure. We have calculated it using the linear-muffin-tin-orbital (LMTO) method9 in the atomic-sphere (ASA) approximation. Another simplification must be performed to describe the exchange- correlation potential between electrons. We have chosen the most common way applying the local spin density approximation (LSDA)10.
KOVINE, ZLITINE, TEHNOLOGIJE 32 (1998) 	3-4	16
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M. KOMELJ, S. KOBE: CALCULATION OF THE CURIE TEMPERATURE..
Figure 1: Rhombohedral crystall structure of Nd2Fej7-xAlx Slika 1: Romboedricna kristalna struktura Nd2Fej7-xAlx
3 RESULTS
All the calculations for the system Nd2Fen-xAlx have been performed using experimentally obtained values3 of the lattice constants. The Nd2Fen compound crystallizes in the rhombohedral Th2Znn type structure which is shown on Figure 1. On the basis of neutron diffraction experiments5 it was found that Al atoms substituted Fe atoms in the crystal lattice of the system Nd2Fen-xAlx, however the aluminum almost completely avoids the 9d site. At compositions up to an x of approximately 6, aluminum prefers the 18h site and occupies the 6c and 18f sites in an approximately random mode. In contrast, at higher aluminum compositions, aluminum strongly prefers the 6c and 18f sites and the aluminum occupancy of the 18h site remains relatively constant at approximately 45%. Since the calculations are limited to the completely periodic structures we have supposed the models for unit cells where the positions of Al atoms were fixed.
We have realized, as demonstrated previously (see for example11), that the Mohn Wohlfarth theory in connection with LSDA does not give the right values for Tc, but the relative changes agree well with the experimental results. This is evident from Figure 2 where the ratio TC(Nd2Fe17-xAlx)/TC(Nd2Fe17) is plotted against the aluminum content x. The agreement between theory and ex-periment5 is the worst for x=4 and 6. This can be explained by the fact that compounds with such aluminum contents in reality do not exhibit long range order and can not be described just by one unit cell. The Curie temperature of Nd2Fe9Al8 is almost three times lower than the TC of the basic alloy because the material exhibits just weak ferromagnetism due to the low Fe content.
4 CONCLUSION
We have carried out the band structure calculations
for the system Nd2Fe17-xAlx using the LMTO ASA9
514
Figure 2: Comparison between theoretically and experimentally5 determined ratio n = TC(Nd2Fe17-xAlx)/TC(Nd2Fe17) as a function of aluminum content x
Slika 2: Primerjava med teoreti~no in eksperimentalno dolo~enim razmerjem n = TC(Nd2Fe17-xAlx)/TC(Nd2Fe17), kot funkcijo vsebnosti aluminija x
which is suitable for the investigations of the properties of ideal crystals. The compounds with x 9 0 do not have a real periodic structure. Our results could be improved by taking into account more than just one unit cell but this would require enormous computational time.
The Mohn Wohlfarth theory8 considers Stoner excitations and spin fluctuations which both destroy magnetization of a ferromagnetic material. A more reliable approach should also include magnons although the use of LSDA10 is the main reason why only the relative changes and not the TC itself can be predicted. The only proper way to theoretically determine Curie temperature would be a real temperature dependent band structure calculation. So far this still remains a challenge for solid state physics.
5 REFERENCES
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3	K. H. J., in Supermagnets, Hard Magnetic Materials, edited by G. J. Long, F. Grandjean (Kluwer, Dordrecht, 1991) p. 553
4F. Weitzer, K. Hiebl, P. Rogl, J. Appl. Phys. 65 (1989) 4963 5G. J. Long, G. K. Marasinghe, S. Mishra, O. A. Pringle, Z. Hu, W. B. Yelon, D. P. Middleton, K. H. J. Buschow, F. Grandjean, J. Appl. Phys. 76 (1994) 5383
6P. Hohenberg, W. Kohn, Phys. Rev., 136 (1964) B864 7E. C. Stoner, Proc. Royal Soc. A, 154 (1936) 656 8P. Mohn, E. P. Wohlfarth, J. Phys. F: Met. Phys., 17 (1987) 2421 9O. K. Andersen, Phys. Rev. B, 12 (1975) 3060 10W. Kohn, L. J. Sham, Phys. Rev., 140 (1965) A1133 11Q. Qi, R. Skomski, J. M. D. Coey, J. Phys.: Condens. Matter, 6 (1994) 3245
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