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Electronic band structure of La4Sb3 and La4Bi3
Journal of Magnetism and Magnetic Materials 52 (1985) 307-309 North-Holland, Amsterdam
307
E L E C T R O N I C B A N D S T R U C T U R E OF La4Sb 3 A N D La4Bi 3
Katsuhiko TAKEGAHARA, Hisatomo HARIMA and Tadao K A S U Y A Department of Physics, Tohoku University, Sendai 980, Japan
The self-consistent APW band calculations for La4Sb 3 and La4Bi 3 have been done. A narrow gap appears between the conduction bands derived dominantly from the L a d states and the valence bands derived mostly from the p states of pnictogens mixed with the L a d states. In Sm4Bi 3 the 4f level is expected to be in this gap, but closes to the bottom of conduction band.
A m o n g the rare earth pnictides with the anti-Th3P 4 type crystal structure, LaaSb 3 and LaaBi 3 have recently attracted particular interest as a proper reference material for the study of the dense Kondo state found in Sm4As3, the anomalous magnetic properties in Sm4Sb 3 and the valence fluctuating state in Sm4Bi 3 [1]. In this paper, the one electron energy band structure for both compounds are calculated by a self-consistent A P W method. We construct the one electron potential by using the local density approximation and taking relativistic effects into account except the spin-orbit interaction. La4X 3 (X = Sb and Bi) crystallize in the anti-Th3P 4 type structure which is based on a body-centered cubic lattice [2]. The space group is T6-I43d, with sixteen La in 16(c):u, u, u ; . . . ; and twelve X in 12(a): 3 / 8 , 0, 1 / 4 ; . . . . where u = 1/12. The radius of the La muffin tin sphere is determined in such a way that the La spheres contact each other. The radius of the X muffin tin sphere is determined in such a way that the radius of La sphere is subtracted from the nearest neighbor L a - X distance. Thus, the La and X muffin tin spheres occupy 43.4 and 20.5% of the total volume of the crystal, respectively. Calculated results for the band structure of LanSb 3 and La4Bi 3 along the principal symmetry axes in the Brillouin zone are shown in figs. 1 and 2. In order to show the character of the wave function of the Bloch states, calculated results for the total and partial densities of states of LaaBi 3 are shown in fig. 3. Calculated densities of states of La4Sb 3 are very similar to those of La4Bi 3 and thus are not shown. Calculated results for the density of states at the Fermi energy and several quantities for both compounds are listed in table 1. In table 1, calculated results for the electron distribu0304-8853/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
tions in the La and X muffin tin spheres both for the starting and final potentials are shown. The results show that about 0.16 or 0.17 electrons are transferred from a La sphere to X spheres in the course of the self-consistent calculation. Since the starting potential is constructed from the charge densities of the neutral atoms, the results show a tendency of the charge transfer occurring in La4X3, though a quantitative description of the charge transfer is difficult because a clear-cut definition of the boundary of each atom in the compound is not possible. In the band structure shown in fig. 2, we do not show that the lowest bands arise from the Bi 5d and 6s
LFI4SB \~'-~~ ~ 0°4
/
EF ~0o3 C£2
~Oo2 /
0ol
~
:~2.~
F
H
N
P
N
Fig. 1. Self-consistent energy band structure of ga4Sb 3.
308
K. Takegahara et al. / Electronic band structure of La 4 Sb
and La 4 Bi
LR4BI3
LR4BI3
EF
300.0
250°0
@°4 EF
200°0
-- 1 5 0 o 0
°0°3
E F
dE3 >n"
m
ioooo
>~3 0C
50.0
t~Oo2 z
z LJ
Oo
0ol
0.2
0.3
0.4
ENERGY ( R Y D . )
Oo LR4BI3
H
P
F
H
N
P
N
Fig. 2. Self-consistent energy band structure of La4Bi 3.
EF
300.0
F ,
250°0
o
200.0
states and the La 5p states, which lie at - 1 . 2 9 6 , - 0 . 4 6 5 --0.409 and - 0 . 9 1 4 - 0 . 8 7 3 Ryd, respectively. In La4Sb 3 (fig. 1), these bands lie at - 0 . 9 0 1 - - 0 . 8 4 8 Ryd for the La 5p states and at - 0 . 3 5 6 - 0 . 2 8 2 Ryd for the Sb 5s states. The Sb 4d states are treated as the frozen core states. In the La atom, the low-lying one electron states are the 5d and 6s states and in the Bi atom they are the 6p states. As is seen from figs. 2 and 3, the low-lying bands from the 1st to the 18th consist mainly of the Bi p states mixed with the La d states. The total width of these valence bands is 0.2 Ryd both for LaaBi 3 and La4Sb 3. This width is nearly the same as that of the valence bands of La monopnictides [3] but is narrower than that of Th3P 4 in which the width of the valence band is 0:35 Ryd [4]. Between the 18th and the 19th bands, the narrow gap appears with the width of 0.01 Ryd for LanSb 3 and 0.0042 Ryd for La4Bi 3. The conduction bands starting from the 19th band are derived dominantly from the La d states. At the F, H and P points in the Brillouin zone, the degenerated states are very close to the Fermi energy. From figs. 1 and 2, it is seen that the F~ state at the Fermi level shifts down about 0.2 eV in LaaBi 3. This is due to the downward shift of the La 6s state in LaaBi 3. As is seen from table 1, the f component of the density of states at the Fermi energy is about 10% of the total density of states. The occupied f character electron is 0.18 per La atom. At the F point, the f dominant states, in which the f character is more than 60%, lie
150.0 w I00.0 o
5OoO
Oo
O,l
A4B[3 300.0
0.4
0,2 0°3 ENEROY (RYD°)
EF I
I
9 9 25o°o
200.0
--
I50.0
I00.0
50.0 z
O°
0.1
0°2 0°3 ENEROY ( R Y D . )
0.4
Fig. 3. Density of states of La4Bi 3 up to the 32nd band. Solid curves show the total density of states and hatched parts show the partial densities of states. (a) La f component; (b) La d component; (c) Bi p component.
K. Takegahara et al. / Electronic band structure of La 4Sb3 and La 4 Bi ~
Table 1 Calculated results for some physical quantities
Lattice constant (,~)
La4Sb 3
La4Bi 3
9.6485
9.790
Electrons in a La muffin tin sphere starting potential 55.93 final potential 55.76
55.99 55.83
Electrons in an X muffin tin sphere starting potential 49.86 final potential 50.09
81.78 81.94
Fermi energy (Ryd)
0.3610
0.3606
Density of states at the Fermi energy (states/Ryd F.U.) La 4 f 7.97 7.49 La 4 d 34.61 36.30 La 4 p 1.77 1.91 X3 P 5.06 4.67 total 77.01 76.32 y (m J / K 2 mol) 13.33 13.21 Charge content within the muffin tin radii (per F.U.) La 4 f 0.738 0.732 La 4 d 4.677 4.830 La 4 p 0.891 0.931 X3 p 7.274 6.847 Total charge (per F.U.) 21.0 21.0
309
In Sm4Bi 3, Sm is expected to be di- and trivalent in the ratio of 3 to 1. T h e n the Fermi level lies in the gap. The gap is expected to be wider because the La d c o n d u c t i o n b a n d s are lifed up at least one eV. Furthermore, the 4f level in the gap with b o t h occupied a n d unoccupied states widens the gap further by the mixing effects. Experimental facts show that Sm4Bi 3 is rather like semimetal or degenerated semiconductor. This m e a n s that the 4f level is very close to the b o t t o m of the c o n d u c t i o n b a n d because it becomes a trivalent metal with pressure. Both Sm4Sb 3 a n d S m 4 A s 3 are trivalent metals but the resistivity for S m n S b 3 is unusually large. This means that the unoccupied 4f level is very close to the Fermi energy. These calculations may be done by the tight binding model using the i n f o r m a t i o n in the present calculation. W e t h a n k Profs. A. Yanase a n d A. Hasegawa for providing us with a c o m p u t e r p r o g r a m of the A P W m e t h o d a n d for helpful discussions. Various useful discussions with A. Ochiai on the experimental results are gratefully acknowledged. This work was partly supp o r t e d by the G r a n t - i n - A i d for Scientific Research from the Ministry of Education, Science a n d Culture of Japan.
References between 0.413 a n d 0.528 Ryd for La4Sb3 and between 0.431 a n d 0.518 Ryd for La4Bi 3. These widths are caused by the d - f hybridization. Few experimental results a b o u t L a 4 X 3 are reported except for the lattice constant. Recently, Ochiai et al. [5] m e a s u r e d the t e m p e r a t u r e d e p e n d e n c e of the electrical resistivity a n d the Hall resistivity. T h e electrical resistivity shows the metallic type b e h a v i o r but the Hall resistivity changes the sign as the t e m p e r a t u r e increases. Calculated b a n d structures do not contradict the measured ones.
[1] A. Ochiai, T. Suzuki and T. Kasuya, J. Magn. Magn. Mat, 52 (1985) 13. [2] F. Hulliger and H.R, Ott, J. Less-Common Metals 55 (1977) 103. [3] A. Hasegawa, J. Phys. C 13 (1980) 6147. [4] T. Suzuki, S. Takagi, N. Niitsuma, K. Takegahara, T. Kasuya, A. Yanese, T. Sakakibara, M. Date, P.J. Markowski and Z. Henkie, in: High Field Magnetism, ed. M. Date (North-Holland, Amsterdam, 1983)p. 183. [5] A. Ochiai, Y. Nakabayashi, Y.S. Kwon. K. Takeuchi, K. Takegahara, T. Suzuki and T. Kasuya, J. Magn. Magn. Mat. 52 (1985) 304.
307
E L E C T R O N I C B A N D S T R U C T U R E OF La4Sb 3 A N D La4Bi 3
Katsuhiko TAKEGAHARA, Hisatomo HARIMA and Tadao K A S U Y A Department of Physics, Tohoku University, Sendai 980, Japan
The self-consistent APW band calculations for La4Sb 3 and La4Bi 3 have been done. A narrow gap appears between the conduction bands derived dominantly from the L a d states and the valence bands derived mostly from the p states of pnictogens mixed with the L a d states. In Sm4Bi 3 the 4f level is expected to be in this gap, but closes to the bottom of conduction band.
A m o n g the rare earth pnictides with the anti-Th3P 4 type crystal structure, LaaSb 3 and LaaBi 3 have recently attracted particular interest as a proper reference material for the study of the dense Kondo state found in Sm4As3, the anomalous magnetic properties in Sm4Sb 3 and the valence fluctuating state in Sm4Bi 3 [1]. In this paper, the one electron energy band structure for both compounds are calculated by a self-consistent A P W method. We construct the one electron potential by using the local density approximation and taking relativistic effects into account except the spin-orbit interaction. La4X 3 (X = Sb and Bi) crystallize in the anti-Th3P 4 type structure which is based on a body-centered cubic lattice [2]. The space group is T6-I43d, with sixteen La in 16(c):u, u, u ; . . . ; and twelve X in 12(a): 3 / 8 , 0, 1 / 4 ; . . . . where u = 1/12. The radius of the La muffin tin sphere is determined in such a way that the La spheres contact each other. The radius of the X muffin tin sphere is determined in such a way that the radius of La sphere is subtracted from the nearest neighbor L a - X distance. Thus, the La and X muffin tin spheres occupy 43.4 and 20.5% of the total volume of the crystal, respectively. Calculated results for the band structure of LanSb 3 and La4Bi 3 along the principal symmetry axes in the Brillouin zone are shown in figs. 1 and 2. In order to show the character of the wave function of the Bloch states, calculated results for the total and partial densities of states of LaaBi 3 are shown in fig. 3. Calculated densities of states of La4Sb 3 are very similar to those of La4Bi 3 and thus are not shown. Calculated results for the density of states at the Fermi energy and several quantities for both compounds are listed in table 1. In table 1, calculated results for the electron distribu0304-8853/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
tions in the La and X muffin tin spheres both for the starting and final potentials are shown. The results show that about 0.16 or 0.17 electrons are transferred from a La sphere to X spheres in the course of the self-consistent calculation. Since the starting potential is constructed from the charge densities of the neutral atoms, the results show a tendency of the charge transfer occurring in La4X3, though a quantitative description of the charge transfer is difficult because a clear-cut definition of the boundary of each atom in the compound is not possible. In the band structure shown in fig. 2, we do not show that the lowest bands arise from the Bi 5d and 6s
LFI4SB \~'-~~ ~ 0°4
/
EF ~0o3 C£2
~Oo2 /
0ol
~
:~2.~
F
H
N
P
N
Fig. 1. Self-consistent energy band structure of ga4Sb 3.
308
K. Takegahara et al. / Electronic band structure of La 4 Sb
and La 4 Bi
LR4BI3
LR4BI3
EF
300.0
250°0
@°4 EF
200°0
-- 1 5 0 o 0
°0°3
E F
dE3 >n"
m
ioooo
>~3 0C
50.0
t~Oo2 z
z LJ
Oo
0ol
0.2
0.3
0.4
ENERGY ( R Y D . )
Oo LR4BI3
H
P
F
H
N
P
N
Fig. 2. Self-consistent energy band structure of La4Bi 3.
EF
300.0
F ,
250°0
o
200.0
states and the La 5p states, which lie at - 1 . 2 9 6 , - 0 . 4 6 5 --0.409 and - 0 . 9 1 4 - 0 . 8 7 3 Ryd, respectively. In La4Sb 3 (fig. 1), these bands lie at - 0 . 9 0 1 - - 0 . 8 4 8 Ryd for the La 5p states and at - 0 . 3 5 6 - 0 . 2 8 2 Ryd for the Sb 5s states. The Sb 4d states are treated as the frozen core states. In the La atom, the low-lying one electron states are the 5d and 6s states and in the Bi atom they are the 6p states. As is seen from figs. 2 and 3, the low-lying bands from the 1st to the 18th consist mainly of the Bi p states mixed with the La d states. The total width of these valence bands is 0.2 Ryd both for LaaBi 3 and La4Sb 3. This width is nearly the same as that of the valence bands of La monopnictides [3] but is narrower than that of Th3P 4 in which the width of the valence band is 0:35 Ryd [4]. Between the 18th and the 19th bands, the narrow gap appears with the width of 0.01 Ryd for LanSb 3 and 0.0042 Ryd for La4Bi 3. The conduction bands starting from the 19th band are derived dominantly from the La d states. At the F, H and P points in the Brillouin zone, the degenerated states are very close to the Fermi energy. From figs. 1 and 2, it is seen that the F~ state at the Fermi level shifts down about 0.2 eV in LaaBi 3. This is due to the downward shift of the La 6s state in LaaBi 3. As is seen from table 1, the f component of the density of states at the Fermi energy is about 10% of the total density of states. The occupied f character electron is 0.18 per La atom. At the F point, the f dominant states, in which the f character is more than 60%, lie
150.0 w I00.0 o
5OoO
Oo
O,l
A4B[3 300.0
0.4
0,2 0°3 ENEROY (RYD°)
EF I
I
9 9 25o°o
200.0
--
I50.0
I00.0
50.0 z
O°
0.1
0°2 0°3 ENEROY ( R Y D . )
0.4
Fig. 3. Density of states of La4Bi 3 up to the 32nd band. Solid curves show the total density of states and hatched parts show the partial densities of states. (a) La f component; (b) La d component; (c) Bi p component.
K. Takegahara et al. / Electronic band structure of La 4Sb3 and La 4 Bi ~
Table 1 Calculated results for some physical quantities
Lattice constant (,~)
La4Sb 3
La4Bi 3
9.6485
9.790
Electrons in a La muffin tin sphere starting potential 55.93 final potential 55.76
55.99 55.83
Electrons in an X muffin tin sphere starting potential 49.86 final potential 50.09
81.78 81.94
Fermi energy (Ryd)
0.3610
0.3606
Density of states at the Fermi energy (states/Ryd F.U.) La 4 f 7.97 7.49 La 4 d 34.61 36.30 La 4 p 1.77 1.91 X3 P 5.06 4.67 total 77.01 76.32 y (m J / K 2 mol) 13.33 13.21 Charge content within the muffin tin radii (per F.U.) La 4 f 0.738 0.732 La 4 d 4.677 4.830 La 4 p 0.891 0.931 X3 p 7.274 6.847 Total charge (per F.U.) 21.0 21.0
309
In Sm4Bi 3, Sm is expected to be di- and trivalent in the ratio of 3 to 1. T h e n the Fermi level lies in the gap. The gap is expected to be wider because the La d c o n d u c t i o n b a n d s are lifed up at least one eV. Furthermore, the 4f level in the gap with b o t h occupied a n d unoccupied states widens the gap further by the mixing effects. Experimental facts show that Sm4Bi 3 is rather like semimetal or degenerated semiconductor. This m e a n s that the 4f level is very close to the b o t t o m of the c o n d u c t i o n b a n d because it becomes a trivalent metal with pressure. Both Sm4Sb 3 a n d S m 4 A s 3 are trivalent metals but the resistivity for S m n S b 3 is unusually large. This means that the unoccupied 4f level is very close to the Fermi energy. These calculations may be done by the tight binding model using the i n f o r m a t i o n in the present calculation. W e t h a n k Profs. A. Yanase a n d A. Hasegawa for providing us with a c o m p u t e r p r o g r a m of the A P W m e t h o d a n d for helpful discussions. Various useful discussions with A. Ochiai on the experimental results are gratefully acknowledged. This work was partly supp o r t e d by the G r a n t - i n - A i d for Scientific Research from the Ministry of Education, Science a n d Culture of Japan.
References between 0.413 a n d 0.528 Ryd for La4Sb3 and between 0.431 a n d 0.518 Ryd for La4Bi 3. These widths are caused by the d - f hybridization. Few experimental results a b o u t L a 4 X 3 are reported except for the lattice constant. Recently, Ochiai et al. [5] m e a s u r e d the t e m p e r a t u r e d e p e n d e n c e of the electrical resistivity a n d the Hall resistivity. T h e electrical resistivity shows the metallic type b e h a v i o r but the Hall resistivity changes the sign as the t e m p e r a t u r e increases. Calculated b a n d structures do not contradict the measured ones.
[1] A. Ochiai, T. Suzuki and T. Kasuya, J. Magn. Magn. Mat, 52 (1985) 13. [2] F. Hulliger and H.R, Ott, J. Less-Common Metals 55 (1977) 103. [3] A. Hasegawa, J. Phys. C 13 (1980) 6147. [4] T. Suzuki, S. Takagi, N. Niitsuma, K. Takegahara, T. Kasuya, A. Yanese, T. Sakakibara, M. Date, P.J. Markowski and Z. Henkie, in: High Field Magnetism, ed. M. Date (North-Holland, Amsterdam, 1983)p. 183. [5] A. Ochiai, Y. Nakabayashi, Y.S. Kwon. K. Takeuchi, K. Takegahara, T. Suzuki and T. Kasuya, J. Magn. Magn. Mat. 52 (1985) 304.