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Fermi surface of low carrier compound CeBi
ELSEVIER
Physica B 230-232 (1997) 192-194
Fermi surface of low carrier compound CeBi K. Morita a, T. Goto a'*, S. Nakamura a, Y. Haga b, T. Suzuki c, Y. Kaneta d, O.
Sakai c
aDepartment of Physics, Niigata University, Niigata 950-21, Japan bAdvanced Science Research Center, Japan Atomic Energy Research Institute, Tokai 319-11, Japan CDepartment of Physics, Tohoku University, Sendai 980-77, Japan dDepartment of Quantum Engineering and Systems Science, University of Tokyo, Tokyo 113, Japan Abstract
Fermi surface of low carrier compound CeBi has been investigated by the acoustic dHvA measurement of ultrasonic waves. The Fermi surfaces observed in the ferromagnetic phase of CeBi consist of the hole surfaces fl~, fig, f13 and f14 located at F point and the electron surfaces ~, 7 at X points. The angular variation of the dHvA frequencies in CeBi is reproduced by the result of the band calculation based on the p-f mixing effect. Keywords: CeBi; Fermi surface; de Haas-van Alphen effect
Cerium monopnictides, CeX (X = Bi, Sb, As, P), with the rock-salt structure are characterized by low carrier electron systems. The various magnetic properties of CeBi and CeSb are ascribed to the p - f mixing effect [1], where the strong mixing between the p-hole bands and the localized 4f-electronic state plays an important role. The multiplet (J = -52) of C e 3 + ion in CeBi splits into the l " 7 ground state and the Fs excited one at As = 8 K in a cubic crystalline electric field (CEF) potential [2]. This small CEF splitting in CeBi is caused by the mixing effect of the F8 excited state to the p-hole band with F8 (J = 3) character of Bi. Below TN = 25.2 K, CeBi shows the antiferromagnetic order with a type-I structure ( + - ), consisting of a stacking structure of (00 1) plane [3]. The investigation of the Fermi surface of CeBi and CeSb is very important, because the p-hole band with the F8 symmetry, in particular, is strongly modified by the mixing effect to the 4f-state with Fs. Actually, the de H a a s - v a n Alphen (dHvA) ef-
* Corresponding author.
fect of oscillatory magnetization and the acoustic dHvA effect of sound velocity on CeSb have detected the heavy f14 hole surface [4, 5], which was predicted by the theoretical investigation based on the p - f mixing model. In the case of CeBi, the dHvA measurement of the oscillatory magnetization has been done so far [6], but the observation of f14 still remained to be solved. In the present paper we have done the acoustic dHvA measurement on CeBi by longitudinal sound wave. The piezoelectoric plates of LiNbO3 for sound wave generation and detector were bonded on cleaved (001) planes of CeBi. The elastic constant is obtained by C = pv 2. Here density p = 8.44 g/cm3 was estimated by the lattice parameter a = 6.500 A of CeBi [2]. A 3He evaporating refrigerator with a sample orienting system of two-circle goniometer was used for the low-temperature measurement down to 0.4 K. In Fig. 1, we show the elastic constant C11 of the longitudinal sound wave propagating along [001] direction as a function of the applied field along [100] direction at 0.55K. The antiferromagnetic phase AF ( + + - - ) changes into the
0921-4526/97/$17.00 Copyright © 1997 Elsevier ScienceB.V. All rights reserved Pll S092 1-4526(96)0058 7-X
193
K: Morita et al. /Physica B 230 232 (1997) 192-194 i
i
+
i
i
CeBi H//[100] ullkll[O01] T=0.55K
1.514
-i
1.512
.9o O~
3 ....
I ....
I ....
I ....
:
..
I
eeel
1.510 ,O
j1.508
~) 0
1.506 210
40
'
610
S 10 15 dHvA Frequency[106Oe] '
80
'
ft. lO
20
1;0
120
Magnetic Field [kOe]
Fig. 1. The field dependence of the elastic constant Cll of CeBi measured by the longitudinal sound wave propagating along [001] direction at 0.55 K. The magnetic field is applied along [100] direction. Inset shows the F FT spectrum of the oscillation in the ferromagnetic phase above 52 kOe.
CeBi
5oo400
Cll mode u//k//[001] FFT : 80~120kOe (Ho=96kOe)
E
r-
-45-30-lS [101]
0 15 [001]
30
45 60 [111]
75
90 [110]
Field Angle [degree]
Fig. 3. The field angular dependence of the dHvA frequency of CeBi. Closed circles are the result by the present acoustic dHvA measurement and open circles by the oscillatory magnetization of Kitazawa. The solid lines mean the result of the energy-band calculation by the LMTO method.
?
:'-" 200
o '~
5
" -
11011 IOOl]
~
-j ~. lO0- +
~ ~
11111 [11Ol
~
o,
llool 0
5 '
1'0
1'5
20 '
25
ClHvA Frequency [I0 s Oe]
Fig. 2. A view of the FFT spectra for the quantum oscillation of C1; in CeBi. The discontinuity of the spectrum in [111] and [1011 directions is due to a reorientation of ferromagnetic moment.
ferrimagnetic AF' ( + + + - ) phase at 17 kOe. In high magnetic field above 52 kOe the ferromagnetic phase F ( + ) was observed. As one can see in Fig. 1, the quantum oscillation of Cll has been observed in the F phase. We performed the fast Fourier transformation (FFT) for the quantum oscillation of Cll in the field range from 80 to 120 kOe. A view of the F F T spectra in the plane of the dHvA frequency and the applied field direction is shown in Fig. 2. As one can see in inset of Figs. 1 and 2, the hole surfaces /31, f12, /33, and /34 are clearly observed. The electron surfaces ~ and ? are
also found. In the case of the ct surface the higher harmonic oscillations up to 4a are detected. It should be noted that the spectrum in Fig. 2 changes discontinuously in the field directions along [1 1 I] and [101] axes because of a reorientation of ferromagnetic moment along the fourfold crystal axis. In Fig. 3, the field angular dependence of the dHvA frequency obtained by our result are shown by closed circles. The open circles indicate the result of the oscillatory magnetization by Kitazawa et al. [6]. The solid lines in Fig. 3 is the result of the energy-band calculation by the linear muffin-tin orbital (LMTO) method in the ferromagnetic F phase. The closed orbits of fll~" /32, f13 and fl+ are identified as the hole surface centered at F point. The energy-band calculation based on the p - f mixing model show that the hole surfaces of f14 and f13 at F point are considerably enlarged along [001] direction parallel to the ferromagnetic moment. The characteristic angular dependence of fl¢ and f13 in Fig. 3 is reproduced by the anisotropic shape of the fl¢ and f13 surfaces in the energy-band calculation. The isotropic angular dependence of the dHvA frequency of f12 and fll means mostly spherical shape of fiE and fll surfaces. The orbits of c~and
194
K. Morita et al. / Physica B 230-232 (1997) 192-194
Table 1 Cyclotron effective mass of CeBi obtained by the acoustic dHvA effect and the effective mass by the energy-band calculation. The magnetic field was applied along 1-001] direction. The mass enhancement factor being the ratio of the experiment to the band theory is also listed m*/mo
ct 7(low) 7(high) fll f12 f13 //4
Experiment
Calculated
Enhancement
0.34 1.3 1.0 0.29 0.81 0.86 2.0
0.173 0.525 0.531 0.165 0.222 0.529 0.550
2.0 2.5 1.9 1.8 3.6 1.6 3.6
7 correspond to the closed electron Fermi surfaces centered at X points. In the ferromagnetic F phase with the magnetic moment parallel to [001] axis, the 7 surface locates in kx-k r plane and the ~ surface exists on kz axis. The angular dependence of c~and 7 in Fig. 3 are consistent with the ellipsoidal shape elongated to the tetragonal axis of X points. The splitting of the hole surfaces of ill, f12, f13 and f14 at F point is caused by the p - f mixing, while the splitting of the electron surfaces 7~owand ~higlais due to the d - f Coulomb interaction. We have estimated the carrier number n = 0.03/Ce ion of CeBi, which is larger than n = 0.02/Ce ion of CeSb [4]. The cyclotron effective masses of CeBi were determined by the temperature dependence of the
oscillation intensity of the elastic constant Cll. In Table 1 we show the effective masses for the orbits in the field along [001] axis. The orbit of the f14 surface in CeBi under the field along [001] has the effective mass 2.0mo, which is considerably smaller than 4.3mo for f14 in CeSb [5]. The effective masses obtained by the energy-band calculation are also listed in Table 1. The mass enhancement factor, which is the ratio of the cyclotron mass to the mass of the energy-band calculation, is values of 1.6-3.6. In conclusion, we measured the acoustic dHvA effect of CeBi by the longitudinal sound wave. The quantum oscillation of the hole surfaces ill, f12, f13, f14 and the electron surfaces ~, 7 was detected clearly. The field angular dependence of the dHvA frequency of CeBi is reproduced by the energyband calculation based on the p - f mixing model.
References [ll H. Takahashi and T. Kasuya, J. Phys. C 18 (1985) 2697, 2709, 2721, 2731, 2745, 2755. I-2] H. Heer, A. Furrer, W. H~ilg and O. Vogt, J. Phys. C 12 (1979) 5207. 1-3] J. Rossat-Mignod, P. Burlet, S. Quezel, J. M. Effantin, D. Delac6te, H. Bartholin, O. Vogt and D. Ravot, J. Magn. Magn. Mater. 31-34 (1983) 398. 1-4] H. Aoki, G. W. Crabtree, W. Joss and F. Hulliger, J. Magn. Magn. Mater. 52 (1991) 169. 1-51 R. Senai, T. Goto, S. Sakatsume, Y. S. Kwon, T. Suzuki, Y. Kaneta and O. Sakai, J. Phys. Soc. Japan. 63 (1994) 3026. 1-6"1 T. Kasuya, O. Sakai, J. Tanaka, H. Kitazawa and T. Suzuki, J. Magn. Magn. Mater. 63&64 (1987) 9.
Physica B 230-232 (1997) 192-194
Fermi surface of low carrier compound CeBi K. Morita a, T. Goto a'*, S. Nakamura a, Y. Haga b, T. Suzuki c, Y. Kaneta d, O.
Sakai c
aDepartment of Physics, Niigata University, Niigata 950-21, Japan bAdvanced Science Research Center, Japan Atomic Energy Research Institute, Tokai 319-11, Japan CDepartment of Physics, Tohoku University, Sendai 980-77, Japan dDepartment of Quantum Engineering and Systems Science, University of Tokyo, Tokyo 113, Japan Abstract
Fermi surface of low carrier compound CeBi has been investigated by the acoustic dHvA measurement of ultrasonic waves. The Fermi surfaces observed in the ferromagnetic phase of CeBi consist of the hole surfaces fl~, fig, f13 and f14 located at F point and the electron surfaces ~, 7 at X points. The angular variation of the dHvA frequencies in CeBi is reproduced by the result of the band calculation based on the p-f mixing effect. Keywords: CeBi; Fermi surface; de Haas-van Alphen effect
Cerium monopnictides, CeX (X = Bi, Sb, As, P), with the rock-salt structure are characterized by low carrier electron systems. The various magnetic properties of CeBi and CeSb are ascribed to the p - f mixing effect [1], where the strong mixing between the p-hole bands and the localized 4f-electronic state plays an important role. The multiplet (J = -52) of C e 3 + ion in CeBi splits into the l " 7 ground state and the Fs excited one at As = 8 K in a cubic crystalline electric field (CEF) potential [2]. This small CEF splitting in CeBi is caused by the mixing effect of the F8 excited state to the p-hole band with F8 (J = 3) character of Bi. Below TN = 25.2 K, CeBi shows the antiferromagnetic order with a type-I structure ( + - ), consisting of a stacking structure of (00 1) plane [3]. The investigation of the Fermi surface of CeBi and CeSb is very important, because the p-hole band with the F8 symmetry, in particular, is strongly modified by the mixing effect to the 4f-state with Fs. Actually, the de H a a s - v a n Alphen (dHvA) ef-
* Corresponding author.
fect of oscillatory magnetization and the acoustic dHvA effect of sound velocity on CeSb have detected the heavy f14 hole surface [4, 5], which was predicted by the theoretical investigation based on the p - f mixing model. In the case of CeBi, the dHvA measurement of the oscillatory magnetization has been done so far [6], but the observation of f14 still remained to be solved. In the present paper we have done the acoustic dHvA measurement on CeBi by longitudinal sound wave. The piezoelectoric plates of LiNbO3 for sound wave generation and detector were bonded on cleaved (001) planes of CeBi. The elastic constant is obtained by C = pv 2. Here density p = 8.44 g/cm3 was estimated by the lattice parameter a = 6.500 A of CeBi [2]. A 3He evaporating refrigerator with a sample orienting system of two-circle goniometer was used for the low-temperature measurement down to 0.4 K. In Fig. 1, we show the elastic constant C11 of the longitudinal sound wave propagating along [001] direction as a function of the applied field along [100] direction at 0.55K. The antiferromagnetic phase AF ( + + - - ) changes into the
0921-4526/97/$17.00 Copyright © 1997 Elsevier ScienceB.V. All rights reserved Pll S092 1-4526(96)0058 7-X
193
K: Morita et al. /Physica B 230 232 (1997) 192-194 i
i
+
i
i
CeBi H//[100] ullkll[O01] T=0.55K
1.514
-i
1.512
.9o O~
3 ....
I ....
I ....
I ....
:
..
I
eeel
1.510 ,O
j1.508
~) 0
1.506 210
40
'
610
S 10 15 dHvA Frequency[106Oe] '
80
'
ft. lO
20
1;0
120
Magnetic Field [kOe]
Fig. 1. The field dependence of the elastic constant Cll of CeBi measured by the longitudinal sound wave propagating along [001] direction at 0.55 K. The magnetic field is applied along [100] direction. Inset shows the F FT spectrum of the oscillation in the ferromagnetic phase above 52 kOe.
CeBi
5oo400
Cll mode u//k//[001] FFT : 80~120kOe (Ho=96kOe)
E
r-
-45-30-lS [101]
0 15 [001]
30
45 60 [111]
75
90 [110]
Field Angle [degree]
Fig. 3. The field angular dependence of the dHvA frequency of CeBi. Closed circles are the result by the present acoustic dHvA measurement and open circles by the oscillatory magnetization of Kitazawa. The solid lines mean the result of the energy-band calculation by the LMTO method.
?
:'-" 200
o '~
5
" -
11011 IOOl]
~
-j ~. lO0- +
~ ~
11111 [11Ol
~
o,
llool 0
5 '
1'0
1'5
20 '
25
ClHvA Frequency [I0 s Oe]
Fig. 2. A view of the FFT spectra for the quantum oscillation of C1; in CeBi. The discontinuity of the spectrum in [111] and [1011 directions is due to a reorientation of ferromagnetic moment.
ferrimagnetic AF' ( + + + - ) phase at 17 kOe. In high magnetic field above 52 kOe the ferromagnetic phase F ( + ) was observed. As one can see in Fig. 1, the quantum oscillation of Cll has been observed in the F phase. We performed the fast Fourier transformation (FFT) for the quantum oscillation of Cll in the field range from 80 to 120 kOe. A view of the F F T spectra in the plane of the dHvA frequency and the applied field direction is shown in Fig. 2. As one can see in inset of Figs. 1 and 2, the hole surfaces /31, f12, /33, and /34 are clearly observed. The electron surfaces ~ and ? are
also found. In the case of the ct surface the higher harmonic oscillations up to 4a are detected. It should be noted that the spectrum in Fig. 2 changes discontinuously in the field directions along [1 1 I] and [101] axes because of a reorientation of ferromagnetic moment along the fourfold crystal axis. In Fig. 3, the field angular dependence of the dHvA frequency obtained by our result are shown by closed circles. The open circles indicate the result of the oscillatory magnetization by Kitazawa et al. [6]. The solid lines in Fig. 3 is the result of the energy-band calculation by the linear muffin-tin orbital (LMTO) method in the ferromagnetic F phase. The closed orbits of fll~" /32, f13 and fl+ are identified as the hole surface centered at F point. The energy-band calculation based on the p - f mixing model show that the hole surfaces of f14 and f13 at F point are considerably enlarged along [001] direction parallel to the ferromagnetic moment. The characteristic angular dependence of fl¢ and f13 in Fig. 3 is reproduced by the anisotropic shape of the fl¢ and f13 surfaces in the energy-band calculation. The isotropic angular dependence of the dHvA frequency of f12 and fll means mostly spherical shape of fiE and fll surfaces. The orbits of c~and
194
K. Morita et al. / Physica B 230-232 (1997) 192-194
Table 1 Cyclotron effective mass of CeBi obtained by the acoustic dHvA effect and the effective mass by the energy-band calculation. The magnetic field was applied along 1-001] direction. The mass enhancement factor being the ratio of the experiment to the band theory is also listed m*/mo
ct 7(low) 7(high) fll f12 f13 //4
Experiment
Calculated
Enhancement
0.34 1.3 1.0 0.29 0.81 0.86 2.0
0.173 0.525 0.531 0.165 0.222 0.529 0.550
2.0 2.5 1.9 1.8 3.6 1.6 3.6
7 correspond to the closed electron Fermi surfaces centered at X points. In the ferromagnetic F phase with the magnetic moment parallel to [001] axis, the 7 surface locates in kx-k r plane and the ~ surface exists on kz axis. The angular dependence of c~and 7 in Fig. 3 are consistent with the ellipsoidal shape elongated to the tetragonal axis of X points. The splitting of the hole surfaces of ill, f12, f13 and f14 at F point is caused by the p - f mixing, while the splitting of the electron surfaces 7~owand ~higlais due to the d - f Coulomb interaction. We have estimated the carrier number n = 0.03/Ce ion of CeBi, which is larger than n = 0.02/Ce ion of CeSb [4]. The cyclotron effective masses of CeBi were determined by the temperature dependence of the
oscillation intensity of the elastic constant Cll. In Table 1 we show the effective masses for the orbits in the field along [001] axis. The orbit of the f14 surface in CeBi under the field along [001] has the effective mass 2.0mo, which is considerably smaller than 4.3mo for f14 in CeSb [5]. The effective masses obtained by the energy-band calculation are also listed in Table 1. The mass enhancement factor, which is the ratio of the cyclotron mass to the mass of the energy-band calculation, is values of 1.6-3.6. In conclusion, we measured the acoustic dHvA effect of CeBi by the longitudinal sound wave. The quantum oscillation of the hole surfaces ill, f12, f13, f14 and the electron surfaces ~, 7 was detected clearly. The field angular dependence of the dHvA frequency of CeBi is reproduced by the energyband calculation based on the p - f mixing model.
References [ll H. Takahashi and T. Kasuya, J. Phys. C 18 (1985) 2697, 2709, 2721, 2731, 2745, 2755. I-2] H. Heer, A. Furrer, W. H~ilg and O. Vogt, J. Phys. C 12 (1979) 5207. 1-3] J. Rossat-Mignod, P. Burlet, S. Quezel, J. M. Effantin, D. Delac6te, H. Bartholin, O. Vogt and D. Ravot, J. Magn. Magn. Mater. 31-34 (1983) 398. 1-4] H. Aoki, G. W. Crabtree, W. Joss and F. Hulliger, J. Magn. Magn. Mater. 52 (1991) 169. 1-51 R. Senai, T. Goto, S. Sakatsume, Y. S. Kwon, T. Suzuki, Y. Kaneta and O. Sakai, J. Phys. Soc. Japan. 63 (1994) 3026. 1-6"1 T. Kasuya, O. Sakai, J. Tanaka, H. Kitazawa and T. Suzuki, J. Magn. Magn. Mater. 63&64 (1987) 9.