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Metamagnetic transition in Mg(Co,Ni)2 with the hexagonal C14-type Laves phase structure
ARTICLE IN PRESS
Physica B 363 (2005) 32–35 www.elsevier.com/locate/physb
Metamagnetic transition in MgðCo; NiÞ2 with the hexagonal C14-type Laves phase structure H. Yamada, H. Shimizu Faculty of Science, Shinshu University, Matsumoto 390-8621, Japan Received 25 February 2005; received in revised form 1 March 2005; accepted 1 March 2005
Abstract A magnetic field-induced metamagnetic transition from the paramagnetic state to the ferromagnetic one is predicted to take place in MgðCo1x Nix Þ2 with the hexagonal C14-type Laves phase structure, by performing first-principle band structure calculations. It is shown that the system becomes paramagnetic at xX0:21 and shows a metamagnetic transition associated with a magnetization jump of about 1mB per 3d transition-metal atom. r 2005 Elsevier B.V. All rights reserved. PACS: 75.30.Kz; 75.10.Lp; 75.50.Cc Keywords: Metamagnetic transition; MgðCo; NiÞ2 ; C14-type Laves phase compound; Electronic structure
Itinerant-electron metamagnetism is now one of the current topics in magnetism. By applying a magnetic field, a metamagnetic transition (MT) takes place from the paramagnetic state to the ferromagnetic one at low temperature, which originates from the special shape of the densityof-states (DOS) curve near the Fermi level [1]. It is well known that a field-induced metamagnetic transition may take place when the Fermi level lies at a minimum or very close to a sharp peak of the DOS curve. Such an MT in the itinerant-electron Corresponding author. Tel.: +81 263 37 2461;
fax: +81 263 37 3071. E-mail address: [email protected] (H. Yamada).
system is actually observed in Co-compounds YCo2 and LuCo2 with the cubic (C15-type) Laves phase structure and others. However, no compounds with the hexagonal (C14-type) Laves structure have so far been reported to show such an MT. In this paper, MgðCo1x Nix Þ2 with the C14-type structure is found to show the MT at xX0:21; by performing first-principle band structure calculations. MgCo2 with the C14-type structure is ferromagnetic [2,3]. First-principle band structure calculations have been carried out [4], where the total energies are calculated for the ferromagnetic, antiferromagnetic, and paramagnetic states for this compound with the C14-type and C15-type
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.03.001
ARTICLE IN PRESS H. Yamada, H. Shimizu / Physica B 363 (2005) 32–35
33
structures. The ferromagnetic state with 1:3mB per Co atom in the C14-type structure is found to be the most stable one. A sharp minimum of the DOS curve in the paramagnetic state of MgCo2 with the C14-type structure exists at about 0.2 eV above E F ; as seen in Fig. 1(a) of Ref. [4]. When E F lies on such a sharp minimum of the DOS, an MT may take place. This is realized if some Co atoms in MgCo2 are replaced by Ni atoms, as the number of delectrons in Ni is larger than that in Co by one, and E F will shift towards the higher energy side. In the present work, band structure calculations are carried out for MgðCo1x Nix Þ2 by the selfconsistent linearized muffin-tin orbital (LMTO) method with the atomic sphere approximation (ASA), in the framework of the local spin density functional formalism with the exchange correlation potential given by von Barth and Hedin [5], where Co and Ni are treated as virtual atoms with the atomic number averaged over the concentration. Self-consistent calculations are carried out at 1 133 inequivalent k-points in the irreducible 24 Brillouin zone. The basis set with angular momenta up to l max ¼ 3 is taken. The ratio between atomic spheres of Mg and the virtual 3d transitionmetal (TM) atoms is taken as ð32 Þ1=2 ; which is
determined by the touching rigid spheres of atoms. The c=a ratio of the lattice parameters in the C14type structure is kept to an ideal ratio ð83 Þ1=2 : Fig. 1 shows the calculated local DOS curves for x ¼ 0:25: Bold solid and dotted curves are local DOS of the TM atom at 6h and 2a sites, and the thin curve is that of the Mg atom at the 4f site. E F comes to the minimum of the DOS curves of Co, as has been expected. The total energy EðMÞ is calculated as a function of the magnetic moment M, by using a fixed-spin-moment method, combined with the LMTO-ASA. Numerical calculations are carried out at x ¼ 0; 0.05, 0.10, 0.15, 0.20 and 0.25 for MgðCo1x Nix Þ2 : Fig. 2 shows the calculated results of the magnetic energy DEðMÞ ¼ EðMÞ Eð0Þ as a function of the magnetic moment M. It is found that the critical concentration between the ferromagnetic and paramagnetic states is a little larger than x ¼ 0:20: Above this critical value, the paramagnetic state becomes more stable than the ferromagnetic one. However, even at x ¼ 0:25; there exists a ferromagnetic solution with 1.0, 0.9, and 0:1mB on TM atoms at 6h and 2a sites and on the Mg atoms, respectively. This ferromagnetic state will be stabilized by the magnetic field. That is, a metamagnetic transition will take place at a
Fig. 1. Local DOS curves of MgðCo0:75 Ni0:25 Þ2 with the C14type structure calculated at the lattice constant observed in MgCo2 : The Fermi level E F is at E ¼ 0:
Fig. 2. Magnetic energies DEðMÞ as a function of magnetic moment M per formula unit (one Mg atom and two TM atoms) at x ¼ 0:0; 0.05, 0.10, 0.15, 0.20, and 0.25 for MgðCo1x Nix Þ2 with the C14-type structure.
ARTICLE IN PRESS 34
H. Yamada, H. Shimizu / Physica B 363 (2005) 32–35 Table 1 Estimated values of the Landau coefficients a, b, and c for MgðCo1x Nix Þ2 with the C14-type structure x
a ðT=ðmB =f:u:ÞÞ
b ðT=ðmB =f:u:Þ3 Þ
c ðT=ðmB =f:u:Þ5 Þ
0.10 0.15 0.20 0.25
0:689 103 0:981 103 1:210 103 1:291 103
0:745 103 0:949 103 1:132 103 1:211 103
0:114 103 0:152 103 0:194 103 0:228 103
Fig. 3. Local DOS curves of MgðCo0:75 Ni0:25 Þ2 with the C14type structure in the ferromagnetic state. The Fermi level E F is at E ¼ 0:
certain magnetic field. Fig. 3 shows the local DOS curves for MgðCo0:75 Ni0:25 Þ2 in the ferromagnetic state. Bold, dotted and thin curves denote those of TM atoms at 6h and 2a sites and the Mg atoms, respectively. The magnetic energy DEðMÞ is given by DEðMÞ ¼ 12 aM 2 þ 14 bM 4 þ 16 cM 6 ,
(1)
where a, b, and c are Landau coefficients. These Landau coefficients are roughly estimated by fitting the calculated DEðMÞ shown in Fig. 2 to the form of Eq. (1). The estimated values of a, b, and c at x ¼ 0:10; 0.15, 0.20, and 0.25 are listed in Table 1. It should be mentioned that the absolute values of b for these compounds are much larger than those for LuðCo; AlÞ2 and LuðCo; GaÞ2 with the C15-type structure [6]. The MT takes place for a40; bo0; c40; and 3=16oac=b2 o9=20 [7]. The values of ac=b2 estimated from Table 1 are shown in Fig. 4. At x ¼ 0:21; the value of ac=b2 becomes 3/16. At this concentration, the ferromagnetic state becomes unstable even at low temperature and an MT takes place from the paramagnetic state to the ferromagnetic one under a certain magnetic field. In the region of 5=28oac=b2 o3=16; on the other hand, the ferromagnetic state is stable at low temperature. However, a first-order transition from the
Fig. 4. Estimated values of a, b, and c for MgðCo1x Nix Þ2 at x ¼ 0:10; 0.15, 0.20, and 0.25.
ferromagnetic state to the paramagnetic one occurs at the Curie temperature T C : A first-order transition at T C will be seen in the concentration range 0:18oxo0:21; as estimated from Fig. 4. The jump of magnetization DM at T C is given by ð3jbj=4cÞ1=2 [8], which is 2:1mB =f:u: at x ¼ 0:2: By the Clausius–Clapeyron relation, the isothermal magnetic entropy change DSm is given by qT C DS m ¼ DM, (2) qB where B is the magnetic field. qT C =qB in Eq. (2) is proportional to jbjDM 3 [8]. The values of DM and jbj are so large that a strong magnetocaloric effect is expected near x ¼ 0:2: Unfortunately, the numerical values of T C and DS m for the present system cannot be obtained without the observed value of the characteristic temperature T max where the paramagnetic susceptibility reaches a maximum
ARTICLE IN PRESS H. Yamada, H. Shimizu / Physica B 363 (2005) 32–35
[8]. It is highly desirable that measurements of T max for MgðCo1x Nix Þ2 are performed near x ¼ 0:2: In this paper, it has been shown by band structure calculations that MgðCo1x Nix Þ2 with the C14-type structure shows an MT at xX0:21: The change of M at the critical field of MT is about 1mB per TM atom, which is larger than that of YCo2 and LuCo2 with the C15-type structure [1]. This fact will promote the studies for pseudobinary compounds MgðCo1x Nix Þ2 with the C14type structure, as a potential material for magnetic sensors and magnetic refrigerators.
35
References [1] T. Goto, K. Fukamichi, H. Yamada, Physica B 300 (2001) 167. [2] K.H.J. Buschow, Solid State Commun. 17 (1975) 891. [3] K.H.J. Buschow, H. Krop, E. Dormann, J. Magn. Magn. Mater 23 (1981) 257. [4] H. Yamada, H. Shimizu, J. Alloys Compounds 388 (2005) 15. [5] U. von Barth, L. Hedin, J. Phys. C 5 (1972) 1629. [6] K. Fukamichi, T. Yokoyama, H. Saito, T. Goto, H. Yamada, Phys. Rev. B 64 (2001) 134401. [7] H. Yamada, Phys. Rev. B 47 (1993) 11211. [8] H. Yamada, T. Goto, Phys. Rev. B 68 (2003) 184417.
Physica B 363 (2005) 32–35 www.elsevier.com/locate/physb
Metamagnetic transition in MgðCo; NiÞ2 with the hexagonal C14-type Laves phase structure H. Yamada, H. Shimizu Faculty of Science, Shinshu University, Matsumoto 390-8621, Japan Received 25 February 2005; received in revised form 1 March 2005; accepted 1 March 2005
Abstract A magnetic field-induced metamagnetic transition from the paramagnetic state to the ferromagnetic one is predicted to take place in MgðCo1x Nix Þ2 with the hexagonal C14-type Laves phase structure, by performing first-principle band structure calculations. It is shown that the system becomes paramagnetic at xX0:21 and shows a metamagnetic transition associated with a magnetization jump of about 1mB per 3d transition-metal atom. r 2005 Elsevier B.V. All rights reserved. PACS: 75.30.Kz; 75.10.Lp; 75.50.Cc Keywords: Metamagnetic transition; MgðCo; NiÞ2 ; C14-type Laves phase compound; Electronic structure
Itinerant-electron metamagnetism is now one of the current topics in magnetism. By applying a magnetic field, a metamagnetic transition (MT) takes place from the paramagnetic state to the ferromagnetic one at low temperature, which originates from the special shape of the densityof-states (DOS) curve near the Fermi level [1]. It is well known that a field-induced metamagnetic transition may take place when the Fermi level lies at a minimum or very close to a sharp peak of the DOS curve. Such an MT in the itinerant-electron Corresponding author. Tel.: +81 263 37 2461;
fax: +81 263 37 3071. E-mail address: [email protected] (H. Yamada).
system is actually observed in Co-compounds YCo2 and LuCo2 with the cubic (C15-type) Laves phase structure and others. However, no compounds with the hexagonal (C14-type) Laves structure have so far been reported to show such an MT. In this paper, MgðCo1x Nix Þ2 with the C14-type structure is found to show the MT at xX0:21; by performing first-principle band structure calculations. MgCo2 with the C14-type structure is ferromagnetic [2,3]. First-principle band structure calculations have been carried out [4], where the total energies are calculated for the ferromagnetic, antiferromagnetic, and paramagnetic states for this compound with the C14-type and C15-type
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.03.001
ARTICLE IN PRESS H. Yamada, H. Shimizu / Physica B 363 (2005) 32–35
33
structures. The ferromagnetic state with 1:3mB per Co atom in the C14-type structure is found to be the most stable one. A sharp minimum of the DOS curve in the paramagnetic state of MgCo2 with the C14-type structure exists at about 0.2 eV above E F ; as seen in Fig. 1(a) of Ref. [4]. When E F lies on such a sharp minimum of the DOS, an MT may take place. This is realized if some Co atoms in MgCo2 are replaced by Ni atoms, as the number of delectrons in Ni is larger than that in Co by one, and E F will shift towards the higher energy side. In the present work, band structure calculations are carried out for MgðCo1x Nix Þ2 by the selfconsistent linearized muffin-tin orbital (LMTO) method with the atomic sphere approximation (ASA), in the framework of the local spin density functional formalism with the exchange correlation potential given by von Barth and Hedin [5], where Co and Ni are treated as virtual atoms with the atomic number averaged over the concentration. Self-consistent calculations are carried out at 1 133 inequivalent k-points in the irreducible 24 Brillouin zone. The basis set with angular momenta up to l max ¼ 3 is taken. The ratio between atomic spheres of Mg and the virtual 3d transitionmetal (TM) atoms is taken as ð32 Þ1=2 ; which is
determined by the touching rigid spheres of atoms. The c=a ratio of the lattice parameters in the C14type structure is kept to an ideal ratio ð83 Þ1=2 : Fig. 1 shows the calculated local DOS curves for x ¼ 0:25: Bold solid and dotted curves are local DOS of the TM atom at 6h and 2a sites, and the thin curve is that of the Mg atom at the 4f site. E F comes to the minimum of the DOS curves of Co, as has been expected. The total energy EðMÞ is calculated as a function of the magnetic moment M, by using a fixed-spin-moment method, combined with the LMTO-ASA. Numerical calculations are carried out at x ¼ 0; 0.05, 0.10, 0.15, 0.20 and 0.25 for MgðCo1x Nix Þ2 : Fig. 2 shows the calculated results of the magnetic energy DEðMÞ ¼ EðMÞ Eð0Þ as a function of the magnetic moment M. It is found that the critical concentration between the ferromagnetic and paramagnetic states is a little larger than x ¼ 0:20: Above this critical value, the paramagnetic state becomes more stable than the ferromagnetic one. However, even at x ¼ 0:25; there exists a ferromagnetic solution with 1.0, 0.9, and 0:1mB on TM atoms at 6h and 2a sites and on the Mg atoms, respectively. This ferromagnetic state will be stabilized by the magnetic field. That is, a metamagnetic transition will take place at a
Fig. 1. Local DOS curves of MgðCo0:75 Ni0:25 Þ2 with the C14type structure calculated at the lattice constant observed in MgCo2 : The Fermi level E F is at E ¼ 0:
Fig. 2. Magnetic energies DEðMÞ as a function of magnetic moment M per formula unit (one Mg atom and two TM atoms) at x ¼ 0:0; 0.05, 0.10, 0.15, 0.20, and 0.25 for MgðCo1x Nix Þ2 with the C14-type structure.
ARTICLE IN PRESS 34
H. Yamada, H. Shimizu / Physica B 363 (2005) 32–35 Table 1 Estimated values of the Landau coefficients a, b, and c for MgðCo1x Nix Þ2 with the C14-type structure x
a ðT=ðmB =f:u:ÞÞ
b ðT=ðmB =f:u:Þ3 Þ
c ðT=ðmB =f:u:Þ5 Þ
0.10 0.15 0.20 0.25
0:689 103 0:981 103 1:210 103 1:291 103
0:745 103 0:949 103 1:132 103 1:211 103
0:114 103 0:152 103 0:194 103 0:228 103
Fig. 3. Local DOS curves of MgðCo0:75 Ni0:25 Þ2 with the C14type structure in the ferromagnetic state. The Fermi level E F is at E ¼ 0:
certain magnetic field. Fig. 3 shows the local DOS curves for MgðCo0:75 Ni0:25 Þ2 in the ferromagnetic state. Bold, dotted and thin curves denote those of TM atoms at 6h and 2a sites and the Mg atoms, respectively. The magnetic energy DEðMÞ is given by DEðMÞ ¼ 12 aM 2 þ 14 bM 4 þ 16 cM 6 ,
(1)
where a, b, and c are Landau coefficients. These Landau coefficients are roughly estimated by fitting the calculated DEðMÞ shown in Fig. 2 to the form of Eq. (1). The estimated values of a, b, and c at x ¼ 0:10; 0.15, 0.20, and 0.25 are listed in Table 1. It should be mentioned that the absolute values of b for these compounds are much larger than those for LuðCo; AlÞ2 and LuðCo; GaÞ2 with the C15-type structure [6]. The MT takes place for a40; bo0; c40; and 3=16oac=b2 o9=20 [7]. The values of ac=b2 estimated from Table 1 are shown in Fig. 4. At x ¼ 0:21; the value of ac=b2 becomes 3/16. At this concentration, the ferromagnetic state becomes unstable even at low temperature and an MT takes place from the paramagnetic state to the ferromagnetic one under a certain magnetic field. In the region of 5=28oac=b2 o3=16; on the other hand, the ferromagnetic state is stable at low temperature. However, a first-order transition from the
Fig. 4. Estimated values of a, b, and c for MgðCo1x Nix Þ2 at x ¼ 0:10; 0.15, 0.20, and 0.25.
ferromagnetic state to the paramagnetic one occurs at the Curie temperature T C : A first-order transition at T C will be seen in the concentration range 0:18oxo0:21; as estimated from Fig. 4. The jump of magnetization DM at T C is given by ð3jbj=4cÞ1=2 [8], which is 2:1mB =f:u: at x ¼ 0:2: By the Clausius–Clapeyron relation, the isothermal magnetic entropy change DSm is given by qT C DS m ¼ DM, (2) qB where B is the magnetic field. qT C =qB in Eq. (2) is proportional to jbjDM 3 [8]. The values of DM and jbj are so large that a strong magnetocaloric effect is expected near x ¼ 0:2: Unfortunately, the numerical values of T C and DS m for the present system cannot be obtained without the observed value of the characteristic temperature T max where the paramagnetic susceptibility reaches a maximum
ARTICLE IN PRESS H. Yamada, H. Shimizu / Physica B 363 (2005) 32–35
[8]. It is highly desirable that measurements of T max for MgðCo1x Nix Þ2 are performed near x ¼ 0:2: In this paper, it has been shown by band structure calculations that MgðCo1x Nix Þ2 with the C14-type structure shows an MT at xX0:21: The change of M at the critical field of MT is about 1mB per TM atom, which is larger than that of YCo2 and LuCo2 with the C15-type structure [1]. This fact will promote the studies for pseudobinary compounds MgðCo1x Nix Þ2 with the C14type structure, as a potential material for magnetic sensors and magnetic refrigerators.
35
References [1] T. Goto, K. Fukamichi, H. Yamada, Physica B 300 (2001) 167. [2] K.H.J. Buschow, Solid State Commun. 17 (1975) 891. [3] K.H.J. Buschow, H. Krop, E. Dormann, J. Magn. Magn. Mater 23 (1981) 257. [4] H. Yamada, H. Shimizu, J. Alloys Compounds 388 (2005) 15. [5] U. von Barth, L. Hedin, J. Phys. C 5 (1972) 1629. [6] K. Fukamichi, T. Yokoyama, H. Saito, T. Goto, H. Yamada, Phys. Rev. B 64 (2001) 134401. [7] H. Yamada, Phys. Rev. B 47 (1993) 11211. [8] H. Yamada, T. Goto, Phys. Rev. B 68 (2003) 184417.