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Magnetocrystalline anisotropy of RCo5 intermetallics: itinerant-electron contribution
Journal of Magnetism and Magnetic Materials 226}230 (2001) 1011}1013
Magnetocrystalline anisotropy of RCo intermetallics: itinerant-electron contribution L. Steinbeck *, M. Richter , H. Eschrig IFW Dresden, PO Box 270016, 01171 Dresden, Germany
Abstract The itinerant-state magnetocrystalline anisotropy energies (MAE) of RCo (R"Y, La, Pr, Nd, Sm, Gd) have been determined by relativistic density-functional calculations in local spin density approximation, with additionally taking into account orbital polarization. The calculated MAEs are found to be strongly a!ected by changes of the lattice geometry (c/a ratio and volume) resulting from (a) uniaxial strain in YCo and (b) the lanthanide contraction along the RCo series. 2001 Elsevier Science B.V. All rights reserved. Keywords: Anisotropy energy; Density functional calculations; Rare earth}transition metal compounds
The magnetocrystalline anisotropy (MA) of ferromagnetic rare-earth (R) transition-metal (T) intermetallics arises mainly from (a) the interaction of the partially "lled aspherical R 4f shell with the crystal "eld and (b) the coupling of the direction of the T 3d magnetization (mainly carried by the spin) to the orbital moment, and, thus, to the anisotropic crystal environment, by spinorbit (SO) interaction [1]. The 3d orbital moment, which is not completely quenched in the metal due to the presence of intra-atomic Coulomb correlations (Hund's second rule) and SO interaction, acquires an anisotropy, because of the anisotropy of the hybridization. This gives rise to a dependence of the SO splitting on the magnetization direction. The strong uniaxial MA of SmCo is dominated by the 4f contribution at low temperatures, but 3d and 4f MA are of comparable size at room temperature. The two cannot in general be separated in magnetization measurements. Inelastic neutron scattering provides independent information on the 4f MA but is di$cult and in many cases impossible for ferromagnetic RT intermetallics. Therefore, it is usually assumed that the 3d MA is the same as that of the isostructural Y (La, Lu) compound. However, in many cases the lattice
* Corresponding author. Tel.: #49-351-4659-382; fax: #49351-4659-490. E-mail address: [email protected] (L. Steinbeck).
geometry of RT systems varies considerably as a function of the rare earth, cf. the volume decrease and c/a ratio change for RCo along the R series (Table 1), as a conse quence of the lanthanide contraction. This will, in general, change band structure, orbital moment anisotropy (OMA) and MAE. Moreover, in RT compound "lms [2,3], the lattice geometry is expected to be modi"ed in comparison with the bulk system, because of the strain induced by the lattice mismatch between "lm and substrate. We calculated the itinerant-electron MAE of YCo at various c/a ratios keeping (a) the lattice para meter a and (b) the volume constant, and the MAE of RCo for a number of light rare earths (R"Y, La, Pr, Nd, Sm, Gd). The MA energies were determined by means of the force theorem from density-functional (DF) calculations in the local spin density approximation (LSDA), performed with the fully relativistic version [4] of the optimized LCAO method [5]. In order to take the intra-atomic Coulomb correlations in the 3d shell into account, we introduce a correction to LSDA, the orbital polarization (OP) [6]. For YCo we obtain a MAE of 0.58 meV/f.u. with SO only and 4.4 meV/f.u., in much better agreement with the experimental value of 3.8 meV/f.u. [7], if the OP correction is included. The MAE increases linearly with the c/a ratio if the latter is varied at constant lattice parameter a (Fig. 1), because the reduction of hybridization in c direction enhances the OMA and, thus, the MAE. If the c/a ratio is varied
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 1 1 8 9 - 6
1012
L. Steinbeck et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1011}1013
Table 1 Experimental lattice parameters a and c and c/a ratios of RCo used for the present calculations R
a (a.u.)
c (a.u.)
c/a
Y [9] La [10] Pr [11] Nd [11] Sm [12] Gd [11]
9.313 9.6538 9.4592 9.4592 9.4563 9.3792
7.544 7.4961 7.5477 7.5165 7.5004 7.4966
0.8101 0.7765 0.7979 0.7946 0.7932 0.7993
Fig. 2. Magnetocrystalline anisotropy energy E and orbital moment anisotropy of RCo (R " La, Nd, Sm, Pr, Gd, Y), * calculated at the experimental lattice parameters and plotted as a function of the c/a ratio. Fig. 1. Calculated magnetocrystalline anisotropy energy of YCo as a function of the c/a ratio (see text).
at constant volume (Fig. 1), the ensuing MAE change is much smaller, re#ecting the di!erent and partially compensating behavior of the OMAs of the two inequivalent Co sites in this case. We "nd a surprisingly large variation of the MAE of RCo along the R series (upper part of Fig. 2). The OMA (lower part of Fig. 2) diminishes by about 30% between LaCo and YCo while the orbital moment (not shown) is lowered by about 20%. This results in a strong variation of the MAE between LaCo and YCo . Experimentally, the T sublattice MA can be directly measured only for the Y and La compound, where the 4f shell is empty. The MAE of 4.4 meV/f.u., obtained from magnetization measurements on LaCo [8], is only slightly larger than that of YCo . This is in contrast to the large variation obtained in the calculation, which is predominantly a lattice geometry e!ect, since a calculation for LaCo at the lattice parameters of YCo yields only a slight increase of the MAE in comparison with YCo . The large variation of the calculated MAE results from relatively small changes of height and position of the large peak appearing in the band-"lling dependence of the MAE (Fig. 3) just below the correct number of valence electrons, q"48. In summary, our DF calculations of the MA energies of strained YCo and RCo compounds show that vari ation of the lattice geometry (c/a ratio and volume) [9}12] induces slight changes of the band structure, which, because of the pronounced dependence of the MAE on the position of the Fermi level, strongly a!ect the MAE. This gives rise to a large variation of the
Fig. 3. Calculated magnetocrystalline anisotropy energy of YCo and LaCo as a function of band "lling.
calculated MAE of RCo along the R series, in contrast to the commonly assumed independence of the Co sublattice MA on the R constituent and to the experimental MAE of LaCo . This work was supported by the German Bundesministerium fuK r Bildung und Forschung, project 13N7443. References [1] [2] [3] [4]
M. Richter, J. Phys. D 31 (1998) 1017. E.E. Fullerton et al., J. Appl. Phys. 81 (1997) 5637. D.J. Keavney et al., Phys. Rev. B 57 (1998) 5291. M. Richter, H. Eschrig, Solid State Commun. 72 (1989) 263. [5] H. Eschrig, Optimized LCAO Method and the Electronic Structure of Extended Systems, Springer, Berlin, 1989.
L. Steinbeck et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1011}1013 [6] O. Eriksson, M.S.S. Brooks, B. Johansson, Phys. Rev. B 41 (1990) 7311. [7] J.M. Alameda, D. Givord, R. Lemaire, Q. Lu, J. Appl. Phys. 52 (1981) 2079. [8] M.I. Bartashevich, T. Goto, M. Yamaguchi, I. Yamamoto, J. Alloys Compounds 219 (1995) 25. [9] H.R. Kirchmayr, E. Burzo, in: H.P.J. Wijn (Ed.), Landolt}BoK rnstein Numerical Data and Functional
1013
Relationships in Science and Technology, New Series, Group III, Vol. 19d2, Springer, Berlin, 1990. [10] O. Moze, L. Pareti, A. Paoluzi, K.H.J. Buschow, Phys. Rev. B 53 (1996) 11550. [11] A.V. Andreev, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, Vol. 8, Elsevier, Amsterdam, 1995, pp. 59}187. [12] K.H.J. Buschow, Rep. Prog. Phys. 40 (1977) 1179.
Magnetocrystalline anisotropy of RCo intermetallics: itinerant-electron contribution L. Steinbeck *, M. Richter , H. Eschrig IFW Dresden, PO Box 270016, 01171 Dresden, Germany
Abstract The itinerant-state magnetocrystalline anisotropy energies (MAE) of RCo (R"Y, La, Pr, Nd, Sm, Gd) have been determined by relativistic density-functional calculations in local spin density approximation, with additionally taking into account orbital polarization. The calculated MAEs are found to be strongly a!ected by changes of the lattice geometry (c/a ratio and volume) resulting from (a) uniaxial strain in YCo and (b) the lanthanide contraction along the RCo series. 2001 Elsevier Science B.V. All rights reserved. Keywords: Anisotropy energy; Density functional calculations; Rare earth}transition metal compounds
The magnetocrystalline anisotropy (MA) of ferromagnetic rare-earth (R) transition-metal (T) intermetallics arises mainly from (a) the interaction of the partially "lled aspherical R 4f shell with the crystal "eld and (b) the coupling of the direction of the T 3d magnetization (mainly carried by the spin) to the orbital moment, and, thus, to the anisotropic crystal environment, by spinorbit (SO) interaction [1]. The 3d orbital moment, which is not completely quenched in the metal due to the presence of intra-atomic Coulomb correlations (Hund's second rule) and SO interaction, acquires an anisotropy, because of the anisotropy of the hybridization. This gives rise to a dependence of the SO splitting on the magnetization direction. The strong uniaxial MA of SmCo is dominated by the 4f contribution at low temperatures, but 3d and 4f MA are of comparable size at room temperature. The two cannot in general be separated in magnetization measurements. Inelastic neutron scattering provides independent information on the 4f MA but is di$cult and in many cases impossible for ferromagnetic RT intermetallics. Therefore, it is usually assumed that the 3d MA is the same as that of the isostructural Y (La, Lu) compound. However, in many cases the lattice
* Corresponding author. Tel.: #49-351-4659-382; fax: #49351-4659-490. E-mail address: [email protected] (L. Steinbeck).
geometry of RT systems varies considerably as a function of the rare earth, cf. the volume decrease and c/a ratio change for RCo along the R series (Table 1), as a conse quence of the lanthanide contraction. This will, in general, change band structure, orbital moment anisotropy (OMA) and MAE. Moreover, in RT compound "lms [2,3], the lattice geometry is expected to be modi"ed in comparison with the bulk system, because of the strain induced by the lattice mismatch between "lm and substrate. We calculated the itinerant-electron MAE of YCo at various c/a ratios keeping (a) the lattice para meter a and (b) the volume constant, and the MAE of RCo for a number of light rare earths (R"Y, La, Pr, Nd, Sm, Gd). The MA energies were determined by means of the force theorem from density-functional (DF) calculations in the local spin density approximation (LSDA), performed with the fully relativistic version [4] of the optimized LCAO method [5]. In order to take the intra-atomic Coulomb correlations in the 3d shell into account, we introduce a correction to LSDA, the orbital polarization (OP) [6]. For YCo we obtain a MAE of 0.58 meV/f.u. with SO only and 4.4 meV/f.u., in much better agreement with the experimental value of 3.8 meV/f.u. [7], if the OP correction is included. The MAE increases linearly with the c/a ratio if the latter is varied at constant lattice parameter a (Fig. 1), because the reduction of hybridization in c direction enhances the OMA and, thus, the MAE. If the c/a ratio is varied
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 1 1 8 9 - 6
1012
L. Steinbeck et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1011}1013
Table 1 Experimental lattice parameters a and c and c/a ratios of RCo used for the present calculations R
a (a.u.)
c (a.u.)
c/a
Y [9] La [10] Pr [11] Nd [11] Sm [12] Gd [11]
9.313 9.6538 9.4592 9.4592 9.4563 9.3792
7.544 7.4961 7.5477 7.5165 7.5004 7.4966
0.8101 0.7765 0.7979 0.7946 0.7932 0.7993
Fig. 2. Magnetocrystalline anisotropy energy E and orbital moment anisotropy of RCo (R " La, Nd, Sm, Pr, Gd, Y), * calculated at the experimental lattice parameters and plotted as a function of the c/a ratio. Fig. 1. Calculated magnetocrystalline anisotropy energy of YCo as a function of the c/a ratio (see text).
at constant volume (Fig. 1), the ensuing MAE change is much smaller, re#ecting the di!erent and partially compensating behavior of the OMAs of the two inequivalent Co sites in this case. We "nd a surprisingly large variation of the MAE of RCo along the R series (upper part of Fig. 2). The OMA (lower part of Fig. 2) diminishes by about 30% between LaCo and YCo while the orbital moment (not shown) is lowered by about 20%. This results in a strong variation of the MAE between LaCo and YCo . Experimentally, the T sublattice MA can be directly measured only for the Y and La compound, where the 4f shell is empty. The MAE of 4.4 meV/f.u., obtained from magnetization measurements on LaCo [8], is only slightly larger than that of YCo . This is in contrast to the large variation obtained in the calculation, which is predominantly a lattice geometry e!ect, since a calculation for LaCo at the lattice parameters of YCo yields only a slight increase of the MAE in comparison with YCo . The large variation of the calculated MAE results from relatively small changes of height and position of the large peak appearing in the band-"lling dependence of the MAE (Fig. 3) just below the correct number of valence electrons, q"48. In summary, our DF calculations of the MA energies of strained YCo and RCo compounds show that vari ation of the lattice geometry (c/a ratio and volume) [9}12] induces slight changes of the band structure, which, because of the pronounced dependence of the MAE on the position of the Fermi level, strongly a!ect the MAE. This gives rise to a large variation of the
Fig. 3. Calculated magnetocrystalline anisotropy energy of YCo and LaCo as a function of band "lling.
calculated MAE of RCo along the R series, in contrast to the commonly assumed independence of the Co sublattice MA on the R constituent and to the experimental MAE of LaCo . This work was supported by the German Bundesministerium fuK r Bildung und Forschung, project 13N7443. References [1] [2] [3] [4]
M. Richter, J. Phys. D 31 (1998) 1017. E.E. Fullerton et al., J. Appl. Phys. 81 (1997) 5637. D.J. Keavney et al., Phys. Rev. B 57 (1998) 5291. M. Richter, H. Eschrig, Solid State Commun. 72 (1989) 263. [5] H. Eschrig, Optimized LCAO Method and the Electronic Structure of Extended Systems, Springer, Berlin, 1989.
L. Steinbeck et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1011}1013 [6] O. Eriksson, M.S.S. Brooks, B. Johansson, Phys. Rev. B 41 (1990) 7311. [7] J.M. Alameda, D. Givord, R. Lemaire, Q. Lu, J. Appl. Phys. 52 (1981) 2079. [8] M.I. Bartashevich, T. Goto, M. Yamaguchi, I. Yamamoto, J. Alloys Compounds 219 (1995) 25. [9] H.R. Kirchmayr, E. Burzo, in: H.P.J. Wijn (Ed.), Landolt}BoK rnstein Numerical Data and Functional
1013
Relationships in Science and Technology, New Series, Group III, Vol. 19d2, Springer, Berlin, 1990. [10] O. Moze, L. Pareti, A. Paoluzi, K.H.J. Buschow, Phys. Rev. B 53 (1996) 11550. [11] A.V. Andreev, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, Vol. 8, Elsevier, Amsterdam, 1995, pp. 59}187. [12] K.H.J. Buschow, Rep. Prog. Phys. 40 (1977) 1179.