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Electronic band structures and unoccupied densities of states for Lu compounds
PHYSICALIt
Physica B 186-188 (1993) 850-852 North-Holland
E l e c t r o n i c b a n d structures and u n o c c u p i e d d e n s i t i e s o f states for Lu c o m p o u n d s Katsuhiko Takegahara ~ Education Center for Information Processing, Tohoku University, Sendai, Japan
The band structures for Lu intermetallic compounds ( L u P d 3, L u A I 3 and LuAI2) and Lu and Sr pnictides (LuAs, L u 4 A s 3 and Sr4As3) are calculated up to 14-20eV above the Fermi level by a self-consistent APW method. The agreement between the calculated density of states curves and the observed BIS spectra is quite good for intermetallic compounds, although some discrepancies are found for pnictides.
Bremsstrahlung isochromat spectroscopy (BIS) is an important tool to study the density of states ( D O S ) above the Fermi level (Ev). In a previous paper [1], we reported the results of self-consistent A P W band calculation for Y b A s and Yb4As 3 and compared the calculated unoccupied D O S curves with the observed BIS spectra [2]. In Y b A s , the total D O S curve except for 4f state is in good agreement with the observed BIS spectra but the discrepancy appears in YbaAs 3 due to the valence fluctuation. H o w e v e r , there is an ambiguity in determining E v of Yb compounds in the local density approximation. In this paper, we present a systematic comparison of calculated D O S curves of Lu compounds and observed BIS spectra, which gives a clear picture of the trends in the unoccupied spd states above E~. A m o n g many Lu compounds, BIS measurements were m a d e on LuPd 3 [3], LuAI 3 [4] and L u A i 2 [5]. T h e n we p e r f o r m e d the self-consistent A P W band calculations for these compounds with the local density approximation ( L D A ) . The eigenvalues and the wave functions are calculated with about 100 plane waves per atom and the angular m o m e n t u m up to 7. T h e n the eigenvalues were found to converge well within 0.05 eV. Using the final self-consistent charge density, the eigenvalue and wave function are calculated at the symmetry points and axes. The calculated total and partial D O S curves with a Gaussian broadening of 0.7 eV ( F W H M ) are shown in figs. 1-3. This broadening width corresponds to the experimental resolution of BIS. O t h e r details of the method of Correspondence to: K. Takegahara, Aomori Public College, Aomori 030, Japan. ' Present address: Aomori Public College, Aomori, Japan.
calculations are the same as those described in the previous paper [1]. We compare the calculated unoccupied D O S curves with the BIS spectra. The BIS spectrum of LuPd 3 observed up to 13 eV is dominated by two peaks at about 3 and 7 eV above E~ [3]. F r o m fig. 1, the former peak is due to mixed states between the Lu 5d and the Pd 4d states and the latter the Lu 5d state.
LuPd 3 15.0
EF
A
I ~ ' ~ ~ I ~ ~ ' ~ I ~ ~ * ' I ' '
12.0
"
total
-
',
Lu-f
-
9.0 6 . 0
>~
'* .,
3.0 o.o 7~' i L,...~,_~, ~ , ~ t . ~ 0.0 "q 0.0
-- i
i
, u
-0 . 0
6 . 0
-q L.~ i -
~ l J ~ J ~ l
J I E . L u - s
ilillllJ
li]ii
-
till
F
Pd-d ',
-
0.0
d,
~
0.0
-
0.0
-]~i
i
I i
3.0 -
I i
Li
I
12~I.~11
i I ni
i i
I
-
I
I i I i
SI
!
[ I i--
out
--
o o - - ~ ~ 1 ' ~ ' ~ -5.0
0.0
5.0
10.0
15.0
Energy (eV) Fig. 1. Broadened densities of states for LuPd 3. Solid curves show the total density of states and hatched parts show the partial densities of states. Notation 'out' means the component at the outer region of muffin-tin spheres.
0921-4526/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
K. Takegahara I Band structures of Lu compounds LuAI
8.0
3
EF
I ' '' '
' ' 'l ' ' '
' I ' '' 'I ' ' '
-- t o t a l 6.0 ~- Lu-f
~ >
I
4.0 2.0
,~
0.0
0.0
-~
0.0
-
Lu-d
5
J''' '
-q
Lu-s
o o 3 LI: ---
:~
.-
0.0
=
0.0
' ......
Al-p :
~ ~l-~
,
-- o u t
',
_~ 0.0
',
~_~...,...,_..
-I0.0
_
''
~
,-
'
-5.0
0.0 5.0 Energy (eV)
10.0
Fig. 2. Broadened total and partial densities of states for LuAl 3. Symbols are as for fig. 1.
In the BIS spectrum of LuAI 3 [4], the intensity at E r is very small and gradually increases with a shoulder at 1.5 eV. T h e r e are two broad peaks at 5.5 and 10 eV. T h e experimental BIS spectrum is taken with the p h o t o n energy of 1486.6 eV and thus the d and f states have large scattering cross section in this energy re-
gion. Thus the observed BIS spectrum is considered to consist of the Lu 5d and AI 3d states as shown in fig. 2. Actually, the Lu d and A I d densities of states are small in the vicinity of E r. In the BIS spectrum of LuA1 z, two peaks around 5 and 7 eV and a weak peak at 2 eV are observed [5]. F r o m fig. 3, these peaks are considered to be due to the Lu 5d state. As m e n t i o n e d in the previous paper [1], the BIS spectrum of Y b A s in the high-energy region should be c o m p a r e d with the unoccupied D O S curve of L u A s because Yb is stable trivalent in YbAs. The calculated D O S for L u A s is shown in fig. 4. Except for the 4f level, overall feature is very similar to those of Y b A s but E r rises about 1 eV. In the BIS spectrum, the large peak is observed at 5.5 eV and another peak at 10.2 eV [2]. F r o m fig. 4, the former peak is due to the Lu 5d state and the latter the antibonding bands between the Lu 5d and As 4p states. H o w e v e r , the calculated 5d peak position is at about 1.5 eV lower energy side than the observed one. This feature is similar to that of the early transition metals in which the d bans are almost e m p t y [6]. Finally, we note the study on the BIS spectrum of Yb4ms3, in which the large peak due to the Yb 5d state is observed at 7.5 eV [2]. Yb4As 3 is a valence fluctuating c o m p o u n d , the ratio of Yb 2÷ and Yb 3÷ ions being 3:1. Thus we calculated band structures of the trivalent system LuaAs 3 and the divalent system
LuAs
12
LuA
8.0
,,,,
, , , l , , , , l , , , ~ l , , , ,
2.0 -
*~ -~
0.0
~O
0.0 0,0
', I
- I,Jll
ii
l l ] i t l
i
= o
0.0 0.0
,
Lu-p
,~,
i
, I
i iii
I
-
, I , , ~
, , ~
.
i ,,
0
,~
i ,,
~
~ r t , ,,
, i
total
2.0
~-,~,
'
Al-d
',
A
[Jl
~
' ' ; ' : ~
-10.0
.
-5.0
,
m
~ . L ~
I I-
z.0 i i La
° ° °" h [--] 0.0
-
l-p 1,-, s ,
L tn
0
0
iillilllT~,,,n~~J
tJ~
_~
L,
,i
I I i tJ~LL.a.~
I , , ~1
o
o o -i,,,,i,
"~
0.0
,
0.0
I
,
Lu-s
~ ~A.~,
t.-I
, ,,
j
~ J I , , ,
,As-p
, L,~~_.._..~,fammrt~..._..~...:.
-
0.0
--
L t t i I L , i ,J --
--, .-
Lu-d
,
i : j i I , , L LJ
0.0
H
0.0
--
"~
EF
, , ,
4.0 >
--
-
I i,
6
-
~
-
0.0
total Lu-f
',
>~'~ 4.0-_ ~-
8.0
EF
6.0 -
851
I , t , ~
~
~llk,,
,.I
~ , ,
As-s
,~I
,I
I I I I I J i t
out
~
0.0 5.0 10.0 Energy (eV)
15.0
Fig. 3. Broadened total and partial densities of states for LuAl 2. Symbols are as for fig. 1.
o
-5.0
0.0
5.0 10.0 15.0 Energy (eV)
20.0
Fig. 4. Total and partial densities of states for LuAs. Symbols are as for fig. 1.
852
K. Takegahara / Band structures of Lu compounds
Sr4A %. In both compounds, the unoccupied DOS has a large peak due to the Lu 5d and Sr 4d states around 3.7 and 6.7 eV, respectively. If the Lu and Sr valence are assumed to be the mean valence of Yb, 2.25, the Fermi level is modified to be located in the gap. Then the Lu 5d and Sr 4d peaks are at 4.5 and 5.7 eV above the modified EF, respectively. The discrepancy between calculated and observed peak position is considered to be the same feature of LuAs. Our conclusion is that the agreement between calculated one-particle DOS curves and BIS spectra of the intermetallic compounds is good. This is because the Lu 5d state has rather extended properties due to the strong hybridization with other states and thus the LDA is applicable. On the other hand, the main origin of disagreement found in Yb pnictides may be due to inadequate treatment of the self-interaction term [7], because of relatively localized property of Lu 5d states.
We thank Professor O, Sakai for valuable comments and critical reading of the manuscript. The numerical
computation was partly performed at the Computer Center of the Institute for Molecular Science. References [1] K. Takagahara and Y. Kaneta, J. Phys. Soc. Jpn. 60 (1991) 4009. [2] Y. Saitoh, S. Suga, H. Matsubara, Y. Tsukikawa, Y. Mori, A. Oyamada, A. Ochiai, T. Suzuki and T. Kasuya, J. Phys. Soc. Jpn. 60 (1991) 4005. [3] C. Laubschat, G. Kaindl, E.V. Sampathkumaran and W.D. Schneider, Solid State Commun. 49 (1984) 339. [4] S.-J. Oh, S. Suga, A. Kakizaki, M. Taniguchi, T. Ishii, J.-S. Kang, J.W. Allen, O. Gunnarsson, N.E. Christensen, A. Fujimori, T. Suzuki, T. Kasuya, T. Miyahara, H. Kato, K. Sch6nhammer, M.S. Torikachvili and M.B. Maple, Phys. Rev. B 37 (1988) 2861. [5] S.-J. Oh, J.W. Allen, M.S. Torikachvili and M.B. Maple, J. Magn. Magn. Mater. 52 (1985) 183. [6] W. Speier, J.C. Fuggle, R. Zeller, B. Ackermann, K. Szot, F.U. Hillebrecht and M. Campagna, Phys. Rev. B 30 (1984) 6921. [7] T. Kasuya, O. Sakai, J. Tanaka, H. Kitazawa and T~ Suzuki, J. Magn. Magn. Mater. 63&64 (1987) 9.
Physica B 186-188 (1993) 850-852 North-Holland
E l e c t r o n i c b a n d structures and u n o c c u p i e d d e n s i t i e s o f states for Lu c o m p o u n d s Katsuhiko Takegahara ~ Education Center for Information Processing, Tohoku University, Sendai, Japan
The band structures for Lu intermetallic compounds ( L u P d 3, L u A I 3 and LuAI2) and Lu and Sr pnictides (LuAs, L u 4 A s 3 and Sr4As3) are calculated up to 14-20eV above the Fermi level by a self-consistent APW method. The agreement between the calculated density of states curves and the observed BIS spectra is quite good for intermetallic compounds, although some discrepancies are found for pnictides.
Bremsstrahlung isochromat spectroscopy (BIS) is an important tool to study the density of states ( D O S ) above the Fermi level (Ev). In a previous paper [1], we reported the results of self-consistent A P W band calculation for Y b A s and Yb4As 3 and compared the calculated unoccupied D O S curves with the observed BIS spectra [2]. In Y b A s , the total D O S curve except for 4f state is in good agreement with the observed BIS spectra but the discrepancy appears in YbaAs 3 due to the valence fluctuation. H o w e v e r , there is an ambiguity in determining E v of Yb compounds in the local density approximation. In this paper, we present a systematic comparison of calculated D O S curves of Lu compounds and observed BIS spectra, which gives a clear picture of the trends in the unoccupied spd states above E~. A m o n g many Lu compounds, BIS measurements were m a d e on LuPd 3 [3], LuAI 3 [4] and L u A i 2 [5]. T h e n we p e r f o r m e d the self-consistent A P W band calculations for these compounds with the local density approximation ( L D A ) . The eigenvalues and the wave functions are calculated with about 100 plane waves per atom and the angular m o m e n t u m up to 7. T h e n the eigenvalues were found to converge well within 0.05 eV. Using the final self-consistent charge density, the eigenvalue and wave function are calculated at the symmetry points and axes. The calculated total and partial D O S curves with a Gaussian broadening of 0.7 eV ( F W H M ) are shown in figs. 1-3. This broadening width corresponds to the experimental resolution of BIS. O t h e r details of the method of Correspondence to: K. Takegahara, Aomori Public College, Aomori 030, Japan. ' Present address: Aomori Public College, Aomori, Japan.
calculations are the same as those described in the previous paper [1]. We compare the calculated unoccupied D O S curves with the BIS spectra. The BIS spectrum of LuPd 3 observed up to 13 eV is dominated by two peaks at about 3 and 7 eV above E~ [3]. F r o m fig. 1, the former peak is due to mixed states between the Lu 5d and the Pd 4d states and the latter the Lu 5d state.
LuPd 3 15.0
EF
A
I ~ ' ~ ~ I ~ ~ ' ~ I ~ ~ * ' I ' '
12.0
"
total
-
',
Lu-f
-
9.0 6 . 0
>~
'* .,
3.0 o.o 7~' i L,...~,_~, ~ , ~ t . ~ 0.0 "q 0.0
-- i
i
, u
-0 . 0
6 . 0
-q L.~ i -
~ l J ~ J ~ l
J I E . L u - s
ilillllJ
li]ii
-
till
F
Pd-d ',
-
0.0
d,
~
0.0
-
0.0
-]~i
i
I i
3.0 -
I i
Li
I
12~I.~11
i I ni
i i
I
-
I
I i I i
SI
!
[ I i--
out
--
o o - - ~ ~ 1 ' ~ ' ~ -5.0
0.0
5.0
10.0
15.0
Energy (eV) Fig. 1. Broadened densities of states for LuPd 3. Solid curves show the total density of states and hatched parts show the partial densities of states. Notation 'out' means the component at the outer region of muffin-tin spheres.
0921-4526/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
K. Takegahara I Band structures of Lu compounds LuAI
8.0
3
EF
I ' '' '
' ' 'l ' ' '
' I ' '' 'I ' ' '
-- t o t a l 6.0 ~- Lu-f
~ >
I
4.0 2.0
,~
0.0
0.0
-~
0.0
-
Lu-d
5
J''' '
-q
Lu-s
o o 3 LI: ---
:~
.-
0.0
=
0.0
' ......
Al-p :
~ ~l-~
,
-- o u t
',
_~ 0.0
',
~_~...,...,_..
-I0.0
_
''
~
,-
'
-5.0
0.0 5.0 Energy (eV)
10.0
Fig. 2. Broadened total and partial densities of states for LuAl 3. Symbols are as for fig. 1.
In the BIS spectrum of LuAI 3 [4], the intensity at E r is very small and gradually increases with a shoulder at 1.5 eV. T h e r e are two broad peaks at 5.5 and 10 eV. T h e experimental BIS spectrum is taken with the p h o t o n energy of 1486.6 eV and thus the d and f states have large scattering cross section in this energy re-
gion. Thus the observed BIS spectrum is considered to consist of the Lu 5d and AI 3d states as shown in fig. 2. Actually, the Lu d and A I d densities of states are small in the vicinity of E r. In the BIS spectrum of LuA1 z, two peaks around 5 and 7 eV and a weak peak at 2 eV are observed [5]. F r o m fig. 3, these peaks are considered to be due to the Lu 5d state. As m e n t i o n e d in the previous paper [1], the BIS spectrum of Y b A s in the high-energy region should be c o m p a r e d with the unoccupied D O S curve of L u A s because Yb is stable trivalent in YbAs. The calculated D O S for L u A s is shown in fig. 4. Except for the 4f level, overall feature is very similar to those of Y b A s but E r rises about 1 eV. In the BIS spectrum, the large peak is observed at 5.5 eV and another peak at 10.2 eV [2]. F r o m fig. 4, the former peak is due to the Lu 5d state and the latter the antibonding bands between the Lu 5d and As 4p states. H o w e v e r , the calculated 5d peak position is at about 1.5 eV lower energy side than the observed one. This feature is similar to that of the early transition metals in which the d bans are almost e m p t y [6]. Finally, we note the study on the BIS spectrum of Yb4ms3, in which the large peak due to the Yb 5d state is observed at 7.5 eV [2]. Yb4As 3 is a valence fluctuating c o m p o u n d , the ratio of Yb 2÷ and Yb 3÷ ions being 3:1. Thus we calculated band structures of the trivalent system LuaAs 3 and the divalent system
LuAs
12
LuA
8.0
,,,,
, , , l , , , , l , , , ~ l , , , ,
2.0 -
*~ -~
0.0
~O
0.0 0,0
', I
- I,Jll
ii
l l ] i t l
i
= o
0.0 0.0
,
Lu-p
,~,
i
, I
i iii
I
-
, I , , ~
, , ~
.
i ,,
0
,~
i ,,
~
~ r t , ,,
, i
total
2.0
~-,~,
'
Al-d
',
A
[Jl
~
' ' ; ' : ~
-10.0
.
-5.0
,
m
~ . L ~
I I-
z.0 i i La
° ° °" h [--] 0.0
-
l-p 1,-, s ,
L tn
0
0
iillilllT~,,,n~~J
tJ~
_~
L,
,i
I I i tJ~LL.a.~
I , , ~1
o
o o -i,,,,i,
"~
0.0
,
0.0
I
,
Lu-s
~ ~A.~,
t.-I
, ,,
j
~ J I , , ,
,As-p
, L,~~_.._..~,fammrt~..._..~...:.
-
0.0
--
L t t i I L , i ,J --
--, .-
Lu-d
,
i : j i I , , L LJ
0.0
H
0.0
--
"~
EF
, , ,
4.0 >
--
-
I i,
6
-
~
-
0.0
total Lu-f
',
>~'~ 4.0-_ ~-
8.0
EF
6.0 -
851
I , t , ~
~
~llk,,
,.I
~ , ,
As-s
,~I
,I
I I I I I J i t
out
~
0.0 5.0 10.0 Energy (eV)
15.0
Fig. 3. Broadened total and partial densities of states for LuAl 2. Symbols are as for fig. 1.
o
-5.0
0.0
5.0 10.0 15.0 Energy (eV)
20.0
Fig. 4. Total and partial densities of states for LuAs. Symbols are as for fig. 1.
852
K. Takegahara / Band structures of Lu compounds
Sr4A %. In both compounds, the unoccupied DOS has a large peak due to the Lu 5d and Sr 4d states around 3.7 and 6.7 eV, respectively. If the Lu and Sr valence are assumed to be the mean valence of Yb, 2.25, the Fermi level is modified to be located in the gap. Then the Lu 5d and Sr 4d peaks are at 4.5 and 5.7 eV above the modified EF, respectively. The discrepancy between calculated and observed peak position is considered to be the same feature of LuAs. Our conclusion is that the agreement between calculated one-particle DOS curves and BIS spectra of the intermetallic compounds is good. This is because the Lu 5d state has rather extended properties due to the strong hybridization with other states and thus the LDA is applicable. On the other hand, the main origin of disagreement found in Yb pnictides may be due to inadequate treatment of the self-interaction term [7], because of relatively localized property of Lu 5d states.
We thank Professor O, Sakai for valuable comments and critical reading of the manuscript. The numerical
computation was partly performed at the Computer Center of the Institute for Molecular Science. References [1] K. Takagahara and Y. Kaneta, J. Phys. Soc. Jpn. 60 (1991) 4009. [2] Y. Saitoh, S. Suga, H. Matsubara, Y. Tsukikawa, Y. Mori, A. Oyamada, A. Ochiai, T. Suzuki and T. Kasuya, J. Phys. Soc. Jpn. 60 (1991) 4005. [3] C. Laubschat, G. Kaindl, E.V. Sampathkumaran and W.D. Schneider, Solid State Commun. 49 (1984) 339. [4] S.-J. Oh, S. Suga, A. Kakizaki, M. Taniguchi, T. Ishii, J.-S. Kang, J.W. Allen, O. Gunnarsson, N.E. Christensen, A. Fujimori, T. Suzuki, T. Kasuya, T. Miyahara, H. Kato, K. Sch6nhammer, M.S. Torikachvili and M.B. Maple, Phys. Rev. B 37 (1988) 2861. [5] S.-J. Oh, J.W. Allen, M.S. Torikachvili and M.B. Maple, J. Magn. Magn. Mater. 52 (1985) 183. [6] W. Speier, J.C. Fuggle, R. Zeller, B. Ackermann, K. Szot, F.U. Hillebrecht and M. Campagna, Phys. Rev. B 30 (1984) 6921. [7] T. Kasuya, O. Sakai, J. Tanaka, H. Kitazawa and T~ Suzuki, J. Magn. Magn. Mater. 63&64 (1987) 9.