- Email: [email protected]
Magnetism of FeRh1−xPdx system — band calculation
Journal of Magnetism and Magnetic Materials NO-144 (1995) 79-80
ELSEVIER
Magnetismof FeRh,-xPd, system- bandcalculation S. Yuasa a, H. Miyajima ay*, Y. Otani a, A. Sakuma b aDegarfment of ?hysics, Faculty ofkienre and Technology, Keio University, Hiyoshi 344-1, Kohoku, Yokohama 223, Japan Mugnetic & Electric Materials Reseurch Lab., Hitachi Mefals, Ltd., Mikajiri 52!W, Kumagayu, Saitama 360, Japan
Abstract The first-principle spin-polarized energy band calculations were performed using the LMTO method in order to determine the total energy and the local moments of the body-centered tetragonal FeRh, -$d, alloys as a function of the axial ratio c/a from 0.8 to 1.358. The calculations show that there are competing ferromagnetic and antiferromagnetic states in FeRh alloy with c/u = 1 and in FeRh,,SPd,,5 alloy with c/a = 1.238. The first-order magnetic transitions can therefore be induccj at finite temperatures as have been observed experirentally in both alloys.
1.1ntrnducti0n The ordered bee FeRh alloy with CsCI-type structure is known to exhibit a first-order phase transition from the low-temperature antiferromagnetic (AF) to the high-temprature ferromagnetic (FM) state above room temperature [I]. First qualitative insight on the mechanism of the AF-FM transition had been given by Moriya and Usaml [2]. Quantitative spin-polarized band calculations have been also performed in order to study the electric structure as well as the energy state of the bee FeRh alloy [3-61. Moruzzi aud Marcus [6] used the augmented spherical wave (ASW) method and succeeded in explaining the magnetic properties of the bee FeRh alloy. We separately performed the first-principle band calculation based on the linearized muffin-tin orbital (LMTO) method for the bee FeRh 1_ x Pd, to explain the ground-state properties 171. Apart from the calculation, we have found following facts from a series of experimental studies of the bodycentered tetragonal (bet) FeRh,-,Pd, alloys with relatively lower symmetry compared to the bee structure [8]. The substitution of Pd for Rh stabi!izes the ordered bet structure of CuAu-type in the composition range 0.225 5 x 2 1, and the competing AF and FM states appear around x = 0.5. The bet FeRh, -XPd, alloys with OS3
* Corresponding author. Fax: +81-45-563-1761; [email protected].
0304.8853/95/$09.50
email: miya-
In this work, we performed Ule first-principle spinpolarized band calculation to evaluate the total energy and the local moments of the bet FeRh,-,Pd, as a function of the axial ratio c/a. We will present some of the results, and will discuss on the effect of the Pd-substitution and the tetragonal lattice distortion. 2. Results and discussion The LMTO method with atomic sphere approximation (ASA) 19,101 has been employed to perform a semi-relativistic band calculation in the framework of the local spin density functional theory. The exchange-correlation term takes the form introduced by von Barth and Hedin Ill] with parameters given by Janak [12]. The competing magnetic free energy of the AF and FM states decides the character of the first-order phase transition. In the case of the bet FeRh,,Pd,, alloy, the observed AF-PM first-order transition around 380 K indicates that the stable phase at the ground state is antiferro-
Fig. 1. Total energy of the hct FeRh,,Pd,, alloy with the axial ratio C/II = 1.238 in the ferromagnetic (e) and antiferromagnetic (0) states as a function of the Wiper-Seitz
8 1995 Elsevier Science B.V. All rights reserved
SSDI 0304~8853(94)01136-2
radius rw.
80
S. Yuasa et al. / Jorcmnl of Magnetism and Magnetic Materials 140-144 (1995) 79-80
agreement with the experimental value (Fig. 2a). The structure is the ordered CsCl type bee. As for the FeRho.sPd,,s and FePd alloys, however, the stable values of c/a are much smaller than the experimentally obtained values. Such a discrepancy between the calculation and the experiment may be caused by the pronounced spherical muff&tin potential as in the case of tetragonal HeusIer alloys [13]. When the axial ratio was fixed to the experimental value, the observed magnetic properties could be reproduced by the calculations, Energetically competing AF and FM states take place in the bee FeRh (c/a = 1) and the bet FeRh0.5Pd0,5 (c/a = 1.2381, while the ferromagnetic state is relatively stable in the bet FePd (c/a = 1.358). Finally we give a brief comment on the effects of the Pd substitution and the tetragonal lattice distortion on the electric structure of the bet FeRh,-,Pd, alloys. The substitution of Pd for Rh hardly changes the shape of the DOS both in the FM and AF states but it removes about 0.06 electrons from the Fe atom when the value of x is increased from 0 to 1. This indeed lowers the position of the Fermi level. The tetragonal lattice distortion from bee to bet structure influences the crystal symmetry, which destroys the degeneracy at the Fermi level, resulting in the split of the minority spin band around the Fermi level as in the case of the bet MnAl [14]. The combination of these two effects may lead to a suppression of the spin polarization with an increase of c/a.
IrliglclL
FeRh,,Pd, ,..a:,.
me ma of the bet FeRh,,Fd,,,!
References [I] M. Fallot, Ann. Phys. 10 (1938) 291. [2] T. Moriya and K. Usami, Solid State Commun. 23 (1977) 935. [3] M.A. Kahn, J. Phys. F 9 (1979) 457. [4] C. Koenig, J. Phys. F 12 (1982) 1123. 151 H. Hasegawa, J. Magn. Magn. Mater. 66 (1987) 175. [6] V.L. Moruui and P.M. Marcus, Phys. Rev. B 46 (1992) 2864. [7]
[8] [9] [lo] Fig. 2. Total energy of (a) alloys as a function of the represent the ferromagnetic tively. The arrows indicate
FeRh, (b) FeRh,,Pd,,s axial ratio c/u, where and antiferromagnetic the experimental values
and (c) FePd (a) and (0) states, respecof c/u.
[ll] [12] [13]
S. Yuasa, Y. Otani, H. Miyajima and A. Sakuma, J. Magn. SW. Jpn. 18 (1994) 235 (in Japanese). H. Miyajima, S. Yuasa and Y. Otani, Jpn. I. Appl. Phys. 32 (Suppl. 32-3) (1993) 232. O.K. Andersen, Phys. Rev. B 12 (1975) 3060. H.L. Skriver, The LMTO Method, eds. M. Cardona, P, Fulde and H.J. Queisser (Springer, Berlin, 1984). U. von Barth and H. Hedin, J. Phys. C 5 (1972) 1629, J.F. Janak, Solid State Commun. 25 (1978) 53. S. Fujii, S. Ishida and S. Asano, J. Phys. Sot. Jpn. 58 (19R9)
3657. 1141 A. Sakuma, 1.
Phys. Sot. Jpn. 63 (1994) 1422.
ELSEVIER
Magnetismof FeRh,-xPd, system- bandcalculation S. Yuasa a, H. Miyajima ay*, Y. Otani a, A. Sakuma b aDegarfment of ?hysics, Faculty ofkienre and Technology, Keio University, Hiyoshi 344-1, Kohoku, Yokohama 223, Japan Mugnetic & Electric Materials Reseurch Lab., Hitachi Mefals, Ltd., Mikajiri 52!W, Kumagayu, Saitama 360, Japan
Abstract The first-principle spin-polarized energy band calculations were performed using the LMTO method in order to determine the total energy and the local moments of the body-centered tetragonal FeRh, -$d, alloys as a function of the axial ratio c/a from 0.8 to 1.358. The calculations show that there are competing ferromagnetic and antiferromagnetic states in FeRh alloy with c/u = 1 and in FeRh,,SPd,,5 alloy with c/a = 1.238. The first-order magnetic transitions can therefore be induccj at finite temperatures as have been observed experirentally in both alloys.
1.1ntrnducti0n The ordered bee FeRh alloy with CsCI-type structure is known to exhibit a first-order phase transition from the low-temperature antiferromagnetic (AF) to the high-temprature ferromagnetic (FM) state above room temperature [I]. First qualitative insight on the mechanism of the AF-FM transition had been given by Moriya and Usaml [2]. Quantitative spin-polarized band calculations have been also performed in order to study the electric structure as well as the energy state of the bee FeRh alloy [3-61. Moruzzi aud Marcus [6] used the augmented spherical wave (ASW) method and succeeded in explaining the magnetic properties of the bee FeRh alloy. We separately performed the first-principle band calculation based on the linearized muffin-tin orbital (LMTO) method for the bee FeRh 1_ x Pd, to explain the ground-state properties 171. Apart from the calculation, we have found following facts from a series of experimental studies of the bodycentered tetragonal (bet) FeRh,-,Pd, alloys with relatively lower symmetry compared to the bee structure [8]. The substitution of Pd for Rh stabi!izes the ordered bet structure of CuAu-type in the composition range 0.225 5 x 2 1, and the competing AF and FM states appear around x = 0.5. The bet FeRh, -XPd, alloys with OS3
* Corresponding author. Fax: +81-45-563-1761; [email protected].
0304.8853/95/$09.50
email: miya-
In this work, we performed Ule first-principle spinpolarized band calculation to evaluate the total energy and the local moments of the bet FeRh,-,Pd, as a function of the axial ratio c/a. We will present some of the results, and will discuss on the effect of the Pd-substitution and the tetragonal lattice distortion. 2. Results and discussion The LMTO method with atomic sphere approximation (ASA) 19,101 has been employed to perform a semi-relativistic band calculation in the framework of the local spin density functional theory. The exchange-correlation term takes the form introduced by von Barth and Hedin Ill] with parameters given by Janak [12]. The competing magnetic free energy of the AF and FM states decides the character of the first-order phase transition. In the case of the bet FeRh,,Pd,, alloy, the observed AF-PM first-order transition around 380 K indicates that the stable phase at the ground state is antiferro-
Fig. 1. Total energy of the hct FeRh,,Pd,, alloy with the axial ratio C/II = 1.238 in the ferromagnetic (e) and antiferromagnetic (0) states as a function of the Wiper-Seitz
8 1995 Elsevier Science B.V. All rights reserved
SSDI 0304~8853(94)01136-2
radius rw.
80
S. Yuasa et al. / Jorcmnl of Magnetism and Magnetic Materials 140-144 (1995) 79-80
agreement with the experimental value (Fig. 2a). The structure is the ordered CsCl type bee. As for the FeRho.sPd,,s and FePd alloys, however, the stable values of c/a are much smaller than the experimentally obtained values. Such a discrepancy between the calculation and the experiment may be caused by the pronounced spherical muff&tin potential as in the case of tetragonal HeusIer alloys [13]. When the axial ratio was fixed to the experimental value, the observed magnetic properties could be reproduced by the calculations, Energetically competing AF and FM states take place in the bee FeRh (c/a = 1) and the bet FeRh0.5Pd0,5 (c/a = 1.2381, while the ferromagnetic state is relatively stable in the bet FePd (c/a = 1.358). Finally we give a brief comment on the effects of the Pd substitution and the tetragonal lattice distortion on the electric structure of the bet FeRh,-,Pd, alloys. The substitution of Pd for Rh hardly changes the shape of the DOS both in the FM and AF states but it removes about 0.06 electrons from the Fe atom when the value of x is increased from 0 to 1. This indeed lowers the position of the Fermi level. The tetragonal lattice distortion from bee to bet structure influences the crystal symmetry, which destroys the degeneracy at the Fermi level, resulting in the split of the minority spin band around the Fermi level as in the case of the bet MnAl [14]. The combination of these two effects may lead to a suppression of the spin polarization with an increase of c/a.
IrliglclL
FeRh,,Pd, ,..a:,.
me ma of the bet FeRh,,Fd,,,!
References [I] M. Fallot, Ann. Phys. 10 (1938) 291. [2] T. Moriya and K. Usami, Solid State Commun. 23 (1977) 935. [3] M.A. Kahn, J. Phys. F 9 (1979) 457. [4] C. Koenig, J. Phys. F 12 (1982) 1123. 151 H. Hasegawa, J. Magn. Magn. Mater. 66 (1987) 175. [6] V.L. Moruui and P.M. Marcus, Phys. Rev. B 46 (1992) 2864. [7]
[8] [9] [lo] Fig. 2. Total energy of (a) alloys as a function of the represent the ferromagnetic tively. The arrows indicate
FeRh, (b) FeRh,,Pd,,s axial ratio c/u, where and antiferromagnetic the experimental values
and (c) FePd (a) and (0) states, respecof c/u.
[ll] [12] [13]
S. Yuasa, Y. Otani, H. Miyajima and A. Sakuma, J. Magn. SW. Jpn. 18 (1994) 235 (in Japanese). H. Miyajima, S. Yuasa and Y. Otani, Jpn. I. Appl. Phys. 32 (Suppl. 32-3) (1993) 232. O.K. Andersen, Phys. Rev. B 12 (1975) 3060. H.L. Skriver, The LMTO Method, eds. M. Cardona, P, Fulde and H.J. Queisser (Springer, Berlin, 1984). U. von Barth and H. Hedin, J. Phys. C 5 (1972) 1629, J.F. Janak, Solid State Commun. 25 (1978) 53. S. Fujii, S. Ishida and S. Asano, J. Phys. Sot. Jpn. 58 (19R9)
3657. 1141 A. Sakuma, 1.
Phys. Sot. Jpn. 63 (1994) 1422.