Moldavian Journal of the Physical Sciences, N2, 2002

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1 Moldavian Journal of the Physical Sciences, N2, 2 LCTRONIC STRUCTURS AND MAGNTIC PROPRTIS O R n+1 Co n+ 2n (n=, 1, 2, and ) COMPOUNDS WITH R=Y AND P. Vlaic,. urzo aculty of Physics, abes-olyai University, Cluj-Napoca, Romania ASTRACT R n+1 Co n+ 2n compounds where R =rare earth or yttrium crystallize in a hexagonal structure having P6/mmm space group. The magnetic behavior of cobalt in compounds with R=Y and is studied by first-principle spin polarized band calculations. The computed magnetizations are compared with those experimentally obtained. The magnetic behavior of cobalt is strongly dependent on nature of R elements and on local environment. INTRODUCTION R n+1 Co n+ 2n compounds where R is a rare earth or yttrium having n=1 (RCo ), n=2 (R Co 11 ), n= (R 2 Co 7 ) and n= (RCo 2 ) are obtained by ordered substitutions of cobalt with boron in a RCo -type structure [1]. RCo compounds crystallize in a hexagonal structure of CaCu -type having P6/mmm space group. The crystalline structure of compounds with n 1 can be imagined as being built up by alternative stacking of one layer of RCo and n layers of RCo 2 unit cells (ig. 1). All these compounds have also P6/mmm space group. In these structures R, Co and atoms are distributed on different crystallographic sites (Table 1) having different number and nature of nearest-neighbors (NN). As the local environment depends on crystallographic site, the cobalt atoms from different positions are expected to have different magnetic contributions. y magnetic measurements only the mean values of cobalt moments may be obtained. The mean cobalt moments, M Co, calculated from saturation magnetizations depend on the nature of R elements and decrease with increasing concentration of boron as shown in ig. 2a for compounds with R=Y or. Reliable values of the saturation moments of cobalt may be obtained only for gadolinium (S-state) or yttrium (non-magnetic element). or non-s-state rare earth compounds due to high anisotropy, the saturation is difficult to be obtained. The compounds with yttrium are ferromagnetic while in case of gadolinium system they are ferrimagnetically ordered. ig. 1 The crystalline structures of R n+1 Co n+ 2n compounds

2 Moldavian Journal of the Physical Sciences, N2, 2 Table 1 Crystallographic characteristics of R n+1 Co n+ 2n compounds Compound RCo RCo R Co 11 R 2 Co 7 RCo 2 Lattice constants Number Coordinates Atoms R=Y R= (type of NN) a (Å) c (Å) Ref. a (Å) c (Å) Ref. x/a y/b z/c R (1a) 6 (Co (2c)) Co (2c) [2] [2] 6 (Co (g)) 1/ 2/ Co (g) (Co (2c)) 1/2 1/2 R (1a) 6 (Co (2c)) R (1b) 6 ( (2d)) 1/2 Co (2c) [] [] 6 (Co (6i)) 1/ 2/ Co (6i) 2 ( (2d)) 1/2.287 (2d) 6 (Co (6i)) 1/ 2/ 1/2 R (1a) 6 (Co (2c)) R (2e) 6 (Co (6i)). Co (2c) 6 (Co (6i)) 1/ 2/ Co (g) [] [] ( (h)) 1/2 1/2 Co (6i) 2 ( (h)) 1/2. (h) 6(Co (g, 6i)) 1/ 2/. R (1a) 6 (Co (2c)) R (1b) 6 ( (h)) 1/2 R (2e) 6 (Co (6i 1 )).2 Co (2c) 6 (Co (6i 1 )) 1/ 2/ Co (6i 1 ) [1] [] 2 ( (2d)) 1/2.1 Co (6i 2 ) 7 2 ( (2d)) 1/2.7 (2d) (Co (6i 1 )) 1/ 2/ 1/2 (h) 6 (Co (6i 2 )) 1/ 2/.262 R (1a) 6 ( (2c)) Co (g).1. [6].7.9 [6] ( (2c)) 1/2 1/2 (2c) 6 (Co (g) ) 1/ 2/ 2. M Co (µ /(Co atom )) (a) Y T C (K) 8 (b) Y n/[(n+1)] n/[(n+1)] ig.2 Dependences of mean cobalt moments at.2 K (a) and Curie temperatures (b) on n/[(n+1)] ratio in (Y,) n+1 Co n+ 2n compounds The aim of this paper is to investigate the correlation between crystallographic and magnetic properties starting from band structure calculations and magnetic measurements. 1

3 Moldavian Journal of the Physical Sciences, N2, 2 MTHOD O CALCULATIONS AND RSULTS The electronic structure is the key to the understanding of the materials properties like the saturation magnetization, Curie temperature and magnetic anisotropy. The band structure calculations were performed by using the ab initio tight binding linear muffin-tin orbital method in the atomic sphere approximation (T-LMTO-ASA) [7]. The calculations were performed by using experimental values of lattice constants. The radii of atomic spheres used in ASA were determined in such a way that the volume of a unit cell to be equal to the total volume of touching spheres centered on each atom. In the form of local density approximation (LDA) the total electronic potential is the sum of external, Coulomb and exchange correlation potentials [8]. The functional form of the exchange correlation energy was the free electron parameterization [9]. Relativistic corrections were included without spin orbit coupling. The total densities of states (DOS) obtained for (Y,) n+1 Co n+ 2n compounds are presented in ig.. According to actual theories [, 11], the values of N( ) for majority and minority spin subbands are the crucial point that affects T C. or both series T C decreases with increasing r-values (ig. 2b), N( ) having also similar behavior for both spin subbands. The partial DOS obtained for Co atoms occupying same crystallographic sites, for a given R element, are almost identical. These atoms have similar DOS since they have similar local environment. The cobalt atoms located on (2c) and (6i) or (6i 1 ) positions have the main contribution to the DOS at the ermi level. Co (g) atoms have an important contribution to N( ) only in case of (Y,)Co compounds where there are no boron atoms. Also, Y, and atoms have only small contributions to the DOS at =. The magnetic moments of different atoms located on various crystallographic sites, obtained from band structure calculations are presented in Table 2. The magnetic moments per formula unit agree reasonably with those experimentally determined, the difference probably being caused by the fact that the saturation has not been attained in all cases. Small magnetic moments were induced on Y d shells due to hybridization with Co d bands. The induced Y d moments are antiparallel oriented with the cobalt ones and decrease with increasing n in R n+1 Co n+ 2n formula. The highest values of Y d moments may be associated with highest number of cobalt atoms as nearest-neighbors. or both R=Y and systems, the cobalt moments are dependent on lattice sites. Co (2c) site has the highest value of magnetic moment since these atoms have in first sphere of coordination 6 Co (6i) atoms. The magnetic moments of Co (6i) atoms are lower than those of Co (2c) ones since they have in first shell of coordination 2 atoms. The lowest values of cobalt moments in boron compounds are obtained for Co (g) positions where in first coordination shell we have boron atoms. The cobalt magnetic moments depend also on the nature of R element. We note that for a given R and for the same number of NN, the cobalt magnetic moments seem to depend also on the interatomic distances. The first attempt to estimate the cobalt magnetic moments of unequivalent sites was made by Ogata [12]. Starting with experimental values of saturation magnetizations, the average Co moments for Y system may be expressed by relation (1), where Μ Co (N) represents the magnetic moment of cobalt atoms Μ Co =[(n+1)μ Co (2)+6Μ Co (1)+2Μ Co ()]/(n+) (1) which have N boron layers just above and/or bellow (N=, 1 and 2). y fitting the above equation with the experimentally observed values and assuming that the magnetic moments of Y and atoms are equal to zero they obtained the following values: Μ Co ()=1.66 µ, Μ Co (1)=. µ and Μ Co (2)= µ, the agreement with our results being quite good. In case of compounds our calculations gave: Μ Co () 1.7 µ, Μ Co (1).8 µ and Μ Co (2).1 µ, also in good agreement with those obtained from band structure calculations. 2

4 Moldavian Journal of the Physical Sciences, N2, 2 DOS ( states / ( ev f.u. spin ) ) YC o YCo DOS (states / ( ev f.u. spin )) Co Co Y Co 11 Co Y 2 Co 7 2 Co YCo 2 Co nergy (ev) nergy ( ev ) ig. The total DOS for (Y,) n+1 Co n+ 2n compounds

5 Moldavian Journal of the Physical Sciences, N2, 2 Table2 The magnetic moments of (Y,) n+1 Co n+ 2n compounds (n=, 1, 2, and ) Compound Atoms R (1a) RCo Co (2c) Co (g) R (1a) R (1b) RCo Co (2c) Co (6i) (2d) -.. R (1a) R (2e) Co (2c) R Co 11 Co (g) Co (6i) (h) R (1a) R (1b) R (2e) R 2 Co 7 Co (2c) Co (6i 1 ) Co (6i 2 ) (2d) (h) R (1a) RCo 2 Co (g) (2c) -.2. M atom (µ ) M total (µ /f.u.) M exp (µ /f.u.) R=Y R= R=Y R= R=Y R= [1] [1] 1.2 [1] [1].8.11 [12] 2.6 [] [1]..6 [1].. [1, 1] [16, 17].98 [12].7 2. [18] 2.81 [12].2 [] 2.8 [] 11. [21] 11. [17] 8. [18] 9.6 [22] 6.9. [19] 6. [2] 6. [2] CONCLUSIONS lectronic structure calculations showed that the (Y,) n+1 Co n+ 2n compounds are ferimagnetically ordered. The values of magnetic moments of cobalt atoms are strongly dependent on local atomic configurations. The highest values of Co atomic moments were obtained for (2c) positions. The magnitude of cobalt moments may be analyzed by extending a mixing model proposed by Kanamori [2] in order to explain the effect of in R-e- system. or example in case of Y Co 11 compound, in ig. we plotted the relative positions of centers of gravity for Y d, Co d and 2p states. The Co (6i) atomic layer is located between the ones containing (h) and Co (2c) atoms. Due to the mixing of d (6i) states with 2p and Y d (1a, 2e) states, the center of gravity for local DOS shifts to lower energy for Y d (1a, 2e) and Co d (6i, g) and to higher energy for 2p. Mixing of Co d (2c) with Y d (1a, 2e) and Co d (6i, g) states shifts the center of gravity for local DOS to lower energy for Y (1a, 2e) and Co d (6i, g) and to higher energy for Co d (2c) states. Due to characteristic sites of atoms, as above mentioned, the electrons flow into Co (6i) and Co (g ) from neighboring atoms because 2p states shift to higher energy. Since the majority spin band is full, the minority spin band occupation increases and the difference between the populations of majority spin band and the minority one diminishes and the magnetic moment of Co (6i) atoms becomes small. The local moments of Co (2c) atoms in compounds with n 1 are larger than that in case of YCo compound. As mentioned above the center of gravity for Co (2c) sites shifts towards higher energy side. Some electrons of Co (2c) sites flow out decreasing the number of electrons with

6 Moldavian Journal of the Physical Sciences, N2, 2 minority spin (majority spin band being full). Therefore, the magnetic moments of Co (2c) sites in compounds with n 1 will become larger compared with that in YCo. The magnetic susceptibility of YCo 2 compound observed experimentally at T K is χ exp =2.9* - emu/f.u. [19]. The spin susceptibility at K estimated from DOS at is 1.6* - emu/f.u., in good agreement with the experimental one. 2p d ((1a), (2e)) d (h) (2e) (1a) (6i) (2e) (1a) (2c) (g) (6i) (g) ig. Schematic representation of mixing between Co d, Y d and 2p states in Y Co 11 compound RRNCS [1] Yu.. Kuzma and N.S. ilonizhko, Kristallografiya 18 (197) 7 [2] J. H. Wernick, J. H. Geller, Acta Crystallogr. 12 (199) 662 [] A.T. Pedziwitar, S.Y. Jiang, W.. Wallace,. urzo and V. Pop, J. Magn. Magn. Mat. 66 (1987) 69 [] A. Kowalczyc, P. Stefanski, I Trans. Magn. (199) 68 [] H. H. A. Smit, R. C. Thiel, K. H. J. uschow, J. Phys., Metal Phys. 18 (1988) [6] H. Ido, M. Nanjo, M. Yamada, J. Appl. Phys. 7 (199) [7] O.K. Anderson, Phys. Rev. 12 (197) 6 [8] R.O. Jones, D. Gunnarsson, Rev. Mod. Phys. 61 (1989) 689 [9] V. Von arth, L. Heiden, J. Phys. C: Solid State Phys. (1972) 1629 [] D. Gunnarsson, J. Phys 6 (1976) 87 [11] P. Mohn,. P. Wohlfarth, J. Phys 17 (1987) 221 [12] H. Ogata, H. Ido, H. Yamauchi, J. Appl. Phys. 7 (199) 911 [1] A. Szajek, J. Magn. Magn. Mater. 18 (1998), 22 [1] H. Yamada, K. Terao, H. Nakazawa, I. Kitagawa, N. Suzuki, H. Ido, J. Magn. Magn. Mat.18(1998)9 [1] R. Lemaire, Cobalt 2 (1966) 12 [16]. urzo, V. Pop, R. allou, J. Magn. Magn. Mat. 17/18 (1996) 61 [17]. urzo, V. Pop, C. C. orodi, R. allou, I Trans. Magn. (199) 628 [18] R. allou,. urzo, V. Pop, A. Pentek, J. Appl. Phys. 7 (199) 69 [19] R. allou,. urzo, V. Pop, J. Magn. Magn. Mat. 1-1 (199) 9 [] N. M. Hong, P. N. Minh and N. P. Thuy, Solid State Commun. 8 (1992) 211 [21] A. Kowalczyc, P. Stefanski, I Trans. Magn. (199) 68 [22] A. Kowalczyc, J. Magn. Magn. Mat. 17 (1997) 279 [2] S. K. Malik, A. M. Umarji, G. K. Sheny, J. Appl. Phys. 7 (198) 22 [2] J. Kanamori, Proc. th Int. Workshop on Rare-arth Magnets, Kyoto, (1989) 1