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Fermi surface and cyclotron mass of extremely low carrier system CeAs
PHYSICA
Physica B 186-188 (1993) 153-155 North-Holland
Fermi surface and cyclotron mass of extremely low carrier system CeAs N. Takeda, Y.S. Kwon, Y. Haga, N. Sato, T. Suzuki and T. Komatsubara Department of Physics, Faculty of Science, Tohoku University, Sendai 980, Japan The Fermi surface and the cyclotron mass of a semimetallic compound, CeAs, were determined by use of the dHvA effect. We have found that the cyclotron mass of the hole surface decreases with increasing magnetic field. CeAs is a dense Kondo system with low carrier concentration of 0.0024/formula unit.
1. Introduction
The heavy fermion system with low carrier concentration has attracted much attention because it contradicts a naive picture of the Kondo state. Ce-monopnictides are a typical system. CeAs is a semimetallic compound with a NaC1 crystal structure, and is in the antiferromagnetic state below 7.7 K. The 4f-state in CeAs splits into the FT-doublet ground state and the Fs-quartet excited state, and the excitation energy is about 150 K [1]. The electrical resistivity shows a - I n T dependence at high temperatures, and has two peaks at about 50K and the N6el temperature [2]. The magnetic moment in the antiferromagnetic state is 0.68/za, which nearly equals the 0.71/z B expected from the F7 doublet [3]. There is almost no shrinking of the magnetic moment. A dense Kondo-like behavior of the electrical resistivity at high temperatures is explained qualitatively by the p - f mixing between the valence band and the excited F8 state, and the Kondo temperature of the F7 state is much lower than that of the F8 state [2]. In this sense, CeAs is different from the usual dense Kondo systems. In this paper, we report the Fermi surface and the cyclotron mass by use of the de H a a s - v a n Alphen (dHvA) effect.
in fields up to 8T. The dHvA oscillation in the (1 0 0 ) direction and corresponding Fourier spectrum are shown in fig. 1. Figure 2 shows the extremal crosssectional areas of the Fermi surface as a function of the magnetic field direction. The angular dependence is similar to that of LaSb [4]. The a - and a'-branches
,,I
.... 4O
I ....
t ....
45
i
50
55
'Z
55
. . . .
i
,
;
70
,
,
]
75
H (kOel
0 4
"~
60
CeAs H//<100> T=0.54K
03
J
02
ct
Em
o ~.
2. Experimental results
a'
The dHvA effect was measured with a 3He cryostat
2,8
4
6
8
F [MG]
Correspondence to: N. Takeda, Department of Physics, Faculty of Science, Tohoku University, Sendai 980, Japan.
Fig. 1. The dHvA oscillations and corresponding Fourier spectrum in the (1 0 0) direction.
0921-4526/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
154
N. Takeda et al. / Fermi surface and cyclotron mass of CeAs
{I00}
0.8
{110}
]
'
I
I
'
i
]
1
CeAs
3
y2
mj
or'
8
CeAs
t
0.
"
H//<100>
l ff
o
,
30
<11o>
60
<1 O>
90
<111>
Field Direction
++
0.5
e.
30
<110>
(degrees)
0.5
Fig. 2. The extremal cross-sectional areas of the Fermi surface as a function of the magnetic field direction. Solid lines indicate the calculated result of the three ellipsoids centered at X-points and the sphere centered at the F-point.
0.4 I
0.3
are electron surfaces, which are three ellipsoids centered at X-points. Two principal radii of the ellipsoid, kll and k±, which are parallel and perpendicular to the F - X line, are 0.20/~ and 0.045 •. The/3-branch is a nearly spherical hole surface with a radius of 0.068/~. The cyclotron mass of a and/3 are determined to be 0.35rn o and 0.47m 0 at 5.6T, respectively. Figure 3 shows a mass plot in the (1 00> direction. The magnetic field dependence of the cyclotron mass of the /3-branch has been measured at different magnetic fields, and is shown in fig. 4. The magnetic field is defined by H = 2[1/H 1 + 1/H2] l, where H a and H 2 are the end points of the magnetic field interval used
-2
[
1
+
! ,
0
-3
,
20
l
,
40
I
~
BO
I
aO
r
r
r
[
i
CeAs H//<100> -
~
~
5 m *=0. 3 5 m e
I
o
I
J
J
I
L
100
for a fast Fourier transform (FFF). The cyclotron mass decreases with increasing magnetic field up to 30%.
-4
-5
I
Fig. 4. The field dependence of the cyclotron mass of/3 in the <100) direction.
;K oJ I
<(
,
H (KOe]
B ~ _ m ":0.47mo
I
,
0.5
,
,
r
1
,
,
,
.5
T (Iq
Fig. 3. A mass plot of ~ and/3 in the (1 00) direction. The magnetic field is 5.6T. X = 2~r2m*ckBT/ehH.
N. Takeda et al. I Fermi surface and cyclotron mass o f CeAs
155
3. Discussion
following form:
The dependence of the cyclotron mass on the magnetic field is also observed in metallic dense Kondo compounds. Wassermann et al. [5] obtained a simple expression for the field dependence of the cyclotron mass,
{ m * ( H ) - 1}-~/2 = {m*(0) - 1}-~/2{1 + ( J h / T A ) } . (2)
m*/m
1 + 2 D n f T A / N ( T A + Jh) 2
b =
(1)
= m*(H),
where m b is a band mass, 2D is the conduction band width, nf is the mean occupancy, TA is the Kondo temperature, N is the degeneracy (2J + 1) and h = glzBH. Chapmann et al. [6] rewrote eq. (1) in the
1.01
0.8
~
0.6
i
% 0.4
0.2
0
CeAs
L
References
H//<100>
mb---0.17mo
20
40
6O
80
We assume that the band mass of CeAs is not so different from that of LaSb, 0.17m 0 [4]. Following Chapmann et al., we show, in fig. 5, the left-hand side of eq. (2) plotted as a function of H. m*(0) is determined from the intercept at H = 0 to be 1.6m 0. This value is not so large, but, the mass enhancement amounts to about 10. T A is calculated from the gradient of fig. 5 to be 2.3 K using g = 10/7 and J = 1/2 for the Fy-doublet. It is important to compare the field dependence with the electronic specific heat coefficient. Although the specific heat was measured above 1.5 K [2], it is difficult to extrapolate to 0 K in order to estimate the electronic specific heat coefficient. It is necessary to measure the specific heat below 1 K. The carrier numbers of electrons and holes are 0.0024 electrons/formula unit (f.u.) and 0.00058 holes/f.u. The hole number is about 1/4 of that of electrons. Since CeAs is a semimetallic compound with an equal number of electrons and holes, there should exist another hole surface which corresponds to the y-branch of LaSh. It is expected that such a hole surface has a large cyclotron mass.
100
H {KOe]
Fig. 5. The linear relationship of the left-hand side of eq. (2) as a function of H.
[1] H. Heer, A. Furrer, W. Halg and O. Vogt, J. Phys. C: Solid State Phys. 2 (1979) 5207. [2] T. Suzuki, Y.S. Kwon, S. Ozeki, Y. Haga and T. Kasuya, J. Magn. Magn. Mater. 90&91 (1990) 493. [3] B. Rainford, K.C. Tarberfield, G. Busch and O. Vogt, J. Phys. C. (Proc. Phys. Soc.) 1 (1968) 679. [4] A. Hasegawa, J. Phys. Soc. Jpn. 54 (1985) 677. [5] A. Wassermann, M. Springford and A.C. Hewson, J. Phys: Condens. Matter 1 (1989) 2669. [6] S.B. Chapmann, M. Hunt, P. Meeson and M. Springford, Physica B 163 (1990) 361.
Physica B 186-188 (1993) 153-155 North-Holland
Fermi surface and cyclotron mass of extremely low carrier system CeAs N. Takeda, Y.S. Kwon, Y. Haga, N. Sato, T. Suzuki and T. Komatsubara Department of Physics, Faculty of Science, Tohoku University, Sendai 980, Japan The Fermi surface and the cyclotron mass of a semimetallic compound, CeAs, were determined by use of the dHvA effect. We have found that the cyclotron mass of the hole surface decreases with increasing magnetic field. CeAs is a dense Kondo system with low carrier concentration of 0.0024/formula unit.
1. Introduction
The heavy fermion system with low carrier concentration has attracted much attention because it contradicts a naive picture of the Kondo state. Ce-monopnictides are a typical system. CeAs is a semimetallic compound with a NaC1 crystal structure, and is in the antiferromagnetic state below 7.7 K. The 4f-state in CeAs splits into the FT-doublet ground state and the Fs-quartet excited state, and the excitation energy is about 150 K [1]. The electrical resistivity shows a - I n T dependence at high temperatures, and has two peaks at about 50K and the N6el temperature [2]. The magnetic moment in the antiferromagnetic state is 0.68/za, which nearly equals the 0.71/z B expected from the F7 doublet [3]. There is almost no shrinking of the magnetic moment. A dense Kondo-like behavior of the electrical resistivity at high temperatures is explained qualitatively by the p - f mixing between the valence band and the excited F8 state, and the Kondo temperature of the F7 state is much lower than that of the F8 state [2]. In this sense, CeAs is different from the usual dense Kondo systems. In this paper, we report the Fermi surface and the cyclotron mass by use of the de H a a s - v a n Alphen (dHvA) effect.
in fields up to 8T. The dHvA oscillation in the (1 0 0 ) direction and corresponding Fourier spectrum are shown in fig. 1. Figure 2 shows the extremal crosssectional areas of the Fermi surface as a function of the magnetic field direction. The angular dependence is similar to that of LaSb [4]. The a - and a'-branches
,,I
.... 4O
I ....
t ....
45
i
50
55
'Z
55
. . . .
i
,
;
70
,
,
]
75
H (kOel
0 4
"~
60
CeAs H//<100> T=0.54K
03
J
02
ct
Em
o ~.
2. Experimental results
a'
The dHvA effect was measured with a 3He cryostat
2,8
4
6
8
F [MG]
Correspondence to: N. Takeda, Department of Physics, Faculty of Science, Tohoku University, Sendai 980, Japan.
Fig. 1. The dHvA oscillations and corresponding Fourier spectrum in the (1 0 0) direction.
0921-4526/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
154
N. Takeda et al. / Fermi surface and cyclotron mass of CeAs
{I00}
0.8
{110}
]
'
I
I
'
i
]
1
CeAs
3
y2
mj
or'
8
CeAs
t
0.
"
H//<100>
l ff
o
,
30
<11o>
60
<1 O>
90
<111>
Field Direction
++
0.5
e.
30
<110>
(degrees)
0.5
Fig. 2. The extremal cross-sectional areas of the Fermi surface as a function of the magnetic field direction. Solid lines indicate the calculated result of the three ellipsoids centered at X-points and the sphere centered at the F-point.
0.4 I
0.3
are electron surfaces, which are three ellipsoids centered at X-points. Two principal radii of the ellipsoid, kll and k±, which are parallel and perpendicular to the F - X line, are 0.20/~ and 0.045 •. The/3-branch is a nearly spherical hole surface with a radius of 0.068/~. The cyclotron mass of a and/3 are determined to be 0.35rn o and 0.47m 0 at 5.6T, respectively. Figure 3 shows a mass plot in the (1 00> direction. The magnetic field dependence of the cyclotron mass of the /3-branch has been measured at different magnetic fields, and is shown in fig. 4. The magnetic field is defined by H = 2[1/H 1 + 1/H2] l, where H a and H 2 are the end points of the magnetic field interval used
-2
[
1
+
! ,
0
-3
,
20
l
,
40
I
~
BO
I
aO
r
r
r
[
i
CeAs H//<100> -
~
~
5 m *=0. 3 5 m e
I
o
I
J
J
I
L
100
for a fast Fourier transform (FFF). The cyclotron mass decreases with increasing magnetic field up to 30%.
-4
-5
I
Fig. 4. The field dependence of the cyclotron mass of/3 in the <100) direction.
;K oJ I
<(
,
H (KOe]
B ~ _ m ":0.47mo
I
,
0.5
,
,
r
1
,
,
,
.5
T (Iq
Fig. 3. A mass plot of ~ and/3 in the (1 00) direction. The magnetic field is 5.6T. X = 2~r2m*ckBT/ehH.
N. Takeda et al. I Fermi surface and cyclotron mass o f CeAs
155
3. Discussion
following form:
The dependence of the cyclotron mass on the magnetic field is also observed in metallic dense Kondo compounds. Wassermann et al. [5] obtained a simple expression for the field dependence of the cyclotron mass,
{ m * ( H ) - 1}-~/2 = {m*(0) - 1}-~/2{1 + ( J h / T A ) } . (2)
m*/m
1 + 2 D n f T A / N ( T A + Jh) 2
b =
(1)
= m*(H),
where m b is a band mass, 2D is the conduction band width, nf is the mean occupancy, TA is the Kondo temperature, N is the degeneracy (2J + 1) and h = glzBH. Chapmann et al. [6] rewrote eq. (1) in the
1.01
0.8
~
0.6
i
% 0.4
0.2
0
CeAs
L
References
H//<100>
mb---0.17mo
20
40
6O
80
We assume that the band mass of CeAs is not so different from that of LaSb, 0.17m 0 [4]. Following Chapmann et al., we show, in fig. 5, the left-hand side of eq. (2) plotted as a function of H. m*(0) is determined from the intercept at H = 0 to be 1.6m 0. This value is not so large, but, the mass enhancement amounts to about 10. T A is calculated from the gradient of fig. 5 to be 2.3 K using g = 10/7 and J = 1/2 for the Fy-doublet. It is important to compare the field dependence with the electronic specific heat coefficient. Although the specific heat was measured above 1.5 K [2], it is difficult to extrapolate to 0 K in order to estimate the electronic specific heat coefficient. It is necessary to measure the specific heat below 1 K. The carrier numbers of electrons and holes are 0.0024 electrons/formula unit (f.u.) and 0.00058 holes/f.u. The hole number is about 1/4 of that of electrons. Since CeAs is a semimetallic compound with an equal number of electrons and holes, there should exist another hole surface which corresponds to the y-branch of LaSh. It is expected that such a hole surface has a large cyclotron mass.
100
H {KOe]
Fig. 5. The linear relationship of the left-hand side of eq. (2) as a function of H.
[1] H. Heer, A. Furrer, W. Halg and O. Vogt, J. Phys. C: Solid State Phys. 2 (1979) 5207. [2] T. Suzuki, Y.S. Kwon, S. Ozeki, Y. Haga and T. Kasuya, J. Magn. Magn. Mater. 90&91 (1990) 493. [3] B. Rainford, K.C. Tarberfield, G. Busch and O. Vogt, J. Phys. C. (Proc. Phys. Soc.) 1 (1968) 679. [4] A. Hasegawa, J. Phys. Soc. Jpn. 54 (1985) 677. [5] A. Wassermann, M. Springford and A.C. Hewson, J. Phys: Condens. Matter 1 (1989) 2669. [6] S.B. Chapmann, M. Hunt, P. Meeson and M. Springford, Physica B 163 (1990) 361.