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Orbital polarization effect on electronic structure and Fermi surface in ferromagnetic UGa2
Physica B 281&282 (2000) 771}772
Orbital polarization e!ect on electronic structure and Fermi surface in ferromagnetic UGa 2 Hiroshi Yamagami!,*, Tetsuo Honma", Etsuji Yamamoto", Yoshinori Haga", Shingo Araki#, Dai Aoki#, Yoshihiko Inada#, Rikio Settai#, Yoshichika O1 nuki",# !Graduate School of Science, Tohoku University, Sendai, 980-8578, Japan "Advanced Science Research Center, Japan Atomic Energy Institute, Tokai, Ibaraki 319-1195, Japan #Graduate School of Science, Osaka University, Toyonaka, 560-0043, Japan
Abstract A self-consistent band calculation including an orbital polarization is performed for ferromagnetic UGa on the basis 2 of an all-electron fully-relativistic spin-polarized LAPW (RSPLAPW) method with exchange-correlation potentials in a local density approximation (LDA). The obtained magnetic moment is composed of the spin of about !2.0 l and the B orbital moment of about 4.9 l . Accordingly, it can be interpreted as if the con"guration were a localized 5f2, though the B f character contains about 2.5 as valence electrons. From the band structure, the Fermi surface is constructed in order to analyze frequencies observed by the de Haas}van Alphen (dHvA) e!ect. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: 5f-Magnetism; Relativistic LAPW method; UGa ; Fermi surface 2
Uranium compound UGa has the AlB -type hexag2 2 onal crystal structure, and exhibits ferromagnetic ordering below ¹ "120 K [1]. The magnetic moment at the # U site was observed by the neutron di!raction as about 3.0k along the [1 1 21 0] easy-axis [2]. The dHvA experiB ment has been done recently, indicating a main Fermi surface of UGa is a multiple-connected one [3]. Ab 2 initio electronic structure calculations for UGa were 2 done by treating the 5f states as band states and as localized states with 5f3 or 5f2 con"guration [4]. In this paper, the orbital polarization (OP) technique [5] is applied to the 5f-itinerant band theory, thereby calculating the electronic band structure, magnetic moments and the Fermi surface for the ferromagnetic UGa . 2 The self-consistent calculations are performed by the RSPLAPW method based on the spin-polarized coupled
* Corresponding author. Tel.: #81-22-217-7756; fax: #8122-217-7746. E-mail address: [email protected] (H. Yamagami)
Dirac equation (SPCDE) [6]. The orbital dependent potential < "I ¸ lK is added to the SPCDE at the 03" 03" z z U site, where lK denotes the angular momentum operator z and ¸ is the projection of the orbital moment along the z z-axis. The parameter I was taken to be equal to 03" 2.6 mRy [5]. The spin polarization is considered by the exchange-correlation potentials in a LDA. The densities and potentials are constructed in the mu$n-tin-approximation. The lattice constants for UGa are set to experi2 mental values of a"4.2130 As and c"4.0171 As . As a result, the spin moment at the U site is obtained as !2.03 l , which is composed of the d-component of B 0.05 l and the f-component of !1.98 l . The orbital B B moment is enhanced to 4.94 l , and the d- and f-comB ponent contain 0.19 l and 4.75 l , respectively. The B B total magnetic moment is 2.91 l , comparable to the B experimental value. Judging from the magnetic properties, it can be interpreted as if the con"guration were a localized 5f2, through the f electrons are occupied as valence electrons by about 2.5 within the U mu$n}tin sphere. In the band structure, the 5f bands are split far from the Fermi level due to the OP, and thus it causes the
0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 2 1 7 - X
772
H. Yamagami et al. / Physica B 281&282 (2000) 771}772
Fig. 2. Angular dependence of dHvA frequencies in UGa . The 2 theoretical results are shown by solid lines, and the experimental results are indicated by open circles.
Fig. 1. Fermi surface of ferromagnetic UGa using the fully2 relativistic spin-polarized LAPW method with the orbital polarization. (a) and (b) are plotted at the center of the A point in the Brillouin zone, and (c) and (d) are centered at the C point.
small speci"c heat coe$cient c of 9.23 mJ/mol K2. It is in good agreement with the experimental value of 10.0 mJ/mol K2. Five bands, i.e. the 9}13th band in counting from the bottom of Ga}4s valence band, cross the Fermi level, and the Fermi surfaces made from the 10th to 13th band are presented in Fig. 1. The hole sheet of the 9th band, which can not be shown in Fig. 1 for lack of space, forms a small rugby-ball-like Fermi surface centered at the A point in the Brillouin zone (BZ). Note that the magnetic BZ for UGa is a c-base-centered orthorombic, but we assume 2 here that the hexagonal symmetry is conserved in the Fermi surface. Fig. 2 shows an angular dependence of dHvA frequencies as functions of the "eld direction. The theoretical
results obtained from the Fermi surfaces are indicated by solid lines. Each of the branches named by alphabets originates from the corresponding orbit in Fig. 1, where l comes from the hole sheet of the 9th band. The dHvA frequencies observed with a high-quality single crystal are shown by open circles, and the experimental branches are labeled by Greek letters. The observed branches a, b, c and d correspond to l, k, h and e, respectively. The OP e!ect is relevant not only to the magnetic properties, but also to the Fermi surface. Acknowledgements This research was supported in part by Grant-in-Aid for Encouragement of Young Scientists. References [1] A.V. Andreev et al., J. Phys. (Paris) Colloq. 40 (1979) C4-18. [2] A.C. Lawson et al., J. Magn. Magn. Mater. 50 (1985) 83. [3] I. Sakamoto et al., J. Alloys Compounds 275}277 (1998) 505. [4] M. Divis\ et al., Phys. Rev. B 53 (1996) 9658. [5] O. Eriksson et al., J. Phys.: Condens. Matter 1 (1989) 4005. [6] H. Yamagami, J. Phys. Soc. Japan 67 (1998) 3176.
Orbital polarization e!ect on electronic structure and Fermi surface in ferromagnetic UGa 2 Hiroshi Yamagami!,*, Tetsuo Honma", Etsuji Yamamoto", Yoshinori Haga", Shingo Araki#, Dai Aoki#, Yoshihiko Inada#, Rikio Settai#, Yoshichika O1 nuki",# !Graduate School of Science, Tohoku University, Sendai, 980-8578, Japan "Advanced Science Research Center, Japan Atomic Energy Institute, Tokai, Ibaraki 319-1195, Japan #Graduate School of Science, Osaka University, Toyonaka, 560-0043, Japan
Abstract A self-consistent band calculation including an orbital polarization is performed for ferromagnetic UGa on the basis 2 of an all-electron fully-relativistic spin-polarized LAPW (RSPLAPW) method with exchange-correlation potentials in a local density approximation (LDA). The obtained magnetic moment is composed of the spin of about !2.0 l and the B orbital moment of about 4.9 l . Accordingly, it can be interpreted as if the con"guration were a localized 5f2, though the B f character contains about 2.5 as valence electrons. From the band structure, the Fermi surface is constructed in order to analyze frequencies observed by the de Haas}van Alphen (dHvA) e!ect. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: 5f-Magnetism; Relativistic LAPW method; UGa ; Fermi surface 2
Uranium compound UGa has the AlB -type hexag2 2 onal crystal structure, and exhibits ferromagnetic ordering below ¹ "120 K [1]. The magnetic moment at the # U site was observed by the neutron di!raction as about 3.0k along the [1 1 21 0] easy-axis [2]. The dHvA experiB ment has been done recently, indicating a main Fermi surface of UGa is a multiple-connected one [3]. Ab 2 initio electronic structure calculations for UGa were 2 done by treating the 5f states as band states and as localized states with 5f3 or 5f2 con"guration [4]. In this paper, the orbital polarization (OP) technique [5] is applied to the 5f-itinerant band theory, thereby calculating the electronic band structure, magnetic moments and the Fermi surface for the ferromagnetic UGa . 2 The self-consistent calculations are performed by the RSPLAPW method based on the spin-polarized coupled
* Corresponding author. Tel.: #81-22-217-7756; fax: #8122-217-7746. E-mail address: [email protected] (H. Yamagami)
Dirac equation (SPCDE) [6]. The orbital dependent potential < "I ¸ lK is added to the SPCDE at the 03" 03" z z U site, where lK denotes the angular momentum operator z and ¸ is the projection of the orbital moment along the z z-axis. The parameter I was taken to be equal to 03" 2.6 mRy [5]. The spin polarization is considered by the exchange-correlation potentials in a LDA. The densities and potentials are constructed in the mu$n-tin-approximation. The lattice constants for UGa are set to experi2 mental values of a"4.2130 As and c"4.0171 As . As a result, the spin moment at the U site is obtained as !2.03 l , which is composed of the d-component of B 0.05 l and the f-component of !1.98 l . The orbital B B moment is enhanced to 4.94 l , and the d- and f-comB ponent contain 0.19 l and 4.75 l , respectively. The B B total magnetic moment is 2.91 l , comparable to the B experimental value. Judging from the magnetic properties, it can be interpreted as if the con"guration were a localized 5f2, through the f electrons are occupied as valence electrons by about 2.5 within the U mu$n}tin sphere. In the band structure, the 5f bands are split far from the Fermi level due to the OP, and thus it causes the
0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 2 1 7 - X
772
H. Yamagami et al. / Physica B 281&282 (2000) 771}772
Fig. 2. Angular dependence of dHvA frequencies in UGa . The 2 theoretical results are shown by solid lines, and the experimental results are indicated by open circles.
Fig. 1. Fermi surface of ferromagnetic UGa using the fully2 relativistic spin-polarized LAPW method with the orbital polarization. (a) and (b) are plotted at the center of the A point in the Brillouin zone, and (c) and (d) are centered at the C point.
small speci"c heat coe$cient c of 9.23 mJ/mol K2. It is in good agreement with the experimental value of 10.0 mJ/mol K2. Five bands, i.e. the 9}13th band in counting from the bottom of Ga}4s valence band, cross the Fermi level, and the Fermi surfaces made from the 10th to 13th band are presented in Fig. 1. The hole sheet of the 9th band, which can not be shown in Fig. 1 for lack of space, forms a small rugby-ball-like Fermi surface centered at the A point in the Brillouin zone (BZ). Note that the magnetic BZ for UGa is a c-base-centered orthorombic, but we assume 2 here that the hexagonal symmetry is conserved in the Fermi surface. Fig. 2 shows an angular dependence of dHvA frequencies as functions of the "eld direction. The theoretical
results obtained from the Fermi surfaces are indicated by solid lines. Each of the branches named by alphabets originates from the corresponding orbit in Fig. 1, where l comes from the hole sheet of the 9th band. The dHvA frequencies observed with a high-quality single crystal are shown by open circles, and the experimental branches are labeled by Greek letters. The observed branches a, b, c and d correspond to l, k, h and e, respectively. The OP e!ect is relevant not only to the magnetic properties, but also to the Fermi surface. Acknowledgements This research was supported in part by Grant-in-Aid for Encouragement of Young Scientists. References [1] A.V. Andreev et al., J. Phys. (Paris) Colloq. 40 (1979) C4-18. [2] A.C. Lawson et al., J. Magn. Magn. Mater. 50 (1985) 83. [3] I. Sakamoto et al., J. Alloys Compounds 275}277 (1998) 505. [4] M. Divis\ et al., Phys. Rev. B 53 (1996) 9658. [5] O. Eriksson et al., J. Phys.: Condens. Matter 1 (1989) 4005. [6] H. Yamagami, J. Phys. Soc. Japan 67 (1998) 3176.