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De Haas–van Alphen effect in GdAs
Physica B 281&282 (2000) 750}751
De Haas}van Alphen e!ect in GdAs Y. Nakanishi!,*, F. Takahashi!, T. Sakon!, M. Yoshida!, D.X. Li", T. Suzuki", M. Motokawa! !Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan "Graduated School of Science, Tohoku University, Sendai 980-8578, Japan
Abstract We have for the "rst time observed de Haas}van Alphen e!ect in GdAs below the NeH el temperature in magnetic "elds up to 15 T. The Fermi surface consists of three ellipsoidal electron surfaces and a spherical surface. We have also determined the corresponding e!ective masses and mean free paths. Furthermore, by analyzing the angular dependence of Fermi surface, the number of carriers belonging to each Fermi surface is estimated. It is consistent with that measured by the Hall e!ect. In GdX as the lattice constant is increased, the number of carriers decreases. On the other hand, however, GdAs has less carrier concentration compared to that of GdSb. ( 2000 Published by Elsevier Science B.V. All rights reserved. Keywords: Gd-monopnictides; de Haas}van Alphen e!ect; Carrier concentration
Rare-earth (RE) monopnictides attract both experimentalists and theorists for their much interesting physical phenomena. In the series from GdN to GdSb, the corresponding conductivity changes from a semiconductor-like to a metallic. For their magnetic properties, GdN shows a ferromagnet, whereas the others are antiferromagnetic. In order to investigate the properties of Fermi surface, the de Haas}van Alphen (dHvA) e!ect has an advantage in the sense that we can obtain the direct information about conduction electrons. So far, in Gd monopnictides, GdSb is the only compound in which this was successfully observed. Since it was very di$cult to grow a high-quality single crystal due to the high melting temperature and high vapor pressure, only a few studies have been done in the past. Moreover, their electronic structure and mechanism of conductivity have not been analyzed enough. However, recently high-quality single crystal of GdAs was successfully grown so we could observe clear dHvA signals for it. In this paper we report the shape of Fermi surface, cyclotron e!ective masses and carrier densities. GdAs with NaCl crystal structure is an antiferromagnet below 18.7 K [1], however, the spin * Corresponding author. Tel.: #81-22-215-2017; fax: #8122-215-2016. E-mail address: [email protected] (Y. Nakanishi)
structure has not been determined so far. Among the RX (R; rare-earth) systems, Gd monopnictides are the most simple series, that is, Gd3` ion appearing in GdX has a 4f 7 con"guration and is an S-state ion with spin 7 and no 2 orbital momentum, So the crystalline electric "eld (CEF) e!ects in GdX are considered to be fairly weak. Actually, the magnetization of GdAs increases linearly and saturates at 17 T and no change of the magnetic structure occurs. There is less anisotropy due to the weak CEF e!ects [1]. Single crystals of GdAs are grown by the mineralization method in tungsten crucibles. This is described in detail elsewhere [2]. The dHvA e!ects for GdAs were measured by the "eld modulation method. A top loading type of 3He cryostat and a superconducting magnet up to 15 T were used for the measurement. The amplitude of the modulation "eld was 70 Oe and the frequency was 323 Hz. The temperature was changed from 0.5 to 4.2 K by controlling the vapor pressure of helium. The "eld directions are in the M1 0 0N and M1 1 0N planes. They were analyzed by Fast-Fourier Transform (FFT), and the angular dependence of these frequencies are plotted. Demagnetization "eld must be taken into account in the induced ferromagnetic ordered phase. We used the following correction for conduction electrons as e!ective "elds: H "H#4p(1!N)M, %&&
0921-4526/00/$ - see front matter ( 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 0 3 0 - 3
Y. Nakanishi et al. / Physica B 281&282 (2000) 750}751
Fig. 1. The extremal cross-sectional areas of Fermi surface as a function of the direction of magnetic "elds. The a-, a@-, aAbranch are assumed to be three ellipsoids centered at the Xpoints. The b-branch is assumed to be a sphere centered at the C-points. Table 1 The cyclotron mass in the principal axis. The value in parentheses is that of LaSb for comparison [4] Branch F(¹)
mH(m ) 0
[1 0 0]
[1 1 0]
[1 1 1]
[1 0 0]
[1 1 0]
[1 1 1]
a
246.4
331.84
382.1
0.24
*
b
434.88
*
452.8
0.20 (0.14) 0.26 (0.15)
* (0.17)
0.22 (0.23)
Table 2 q in the [1 0 0] axis
¹"4.2 K ¹"0.5 K
a-branch (s)
b-branch (s)
2.33]10~13 3.69]10~13
0.90]10~13 1.65]10~13
where H, H , N, M denote external "eld, e!ective mag%&& netic "elds, a demagnetization coe$cient (in this sample N is 0.34 and is assumed to be constant even if the magnetic "eld direction is changed for the sake of simplicity) and the magnetization of GdAs, respectively. Fig. 1 shows the angular dependence of the extremal crosssectional area of the Fermi surface for GdAs. The shape of the Fermi surface is very similar to that of LaSb [3]. So the oscillations are caused by an electron pocket at the X-point, two hole pockets at the C-point [4]. The e!ective cyclotron masses are listed in Table 1. By analyzing the "eld dependence of FFT spectrum, the relaxation times q of a- and b-branch were estimated and listed in Table 2. The q of a-branch is more than two times larger than that of b-branch. In this measurement we could not
751
Fig. 2. The lattice constant dependence of the carrier number in rare-earth As.
observe c-branch clearly. The e!ective cyclotron masses of b-branch are also similar to those of LaSb, however, those of a-branch are half as small as LaSb's [3]. Analyzing the angular dependence of Fermi surface we estimated the carrier number. The carrier numbers of aand b-branch are determined to be 2.27]1020 (/cm3) (0.0115/Gd) and 0.516]1020 (/cm3) (0.0026/Gd), respectively. These values are mostly consistent with those measured by the Hall e!ect [3]. Since GdAs is a semimetallic compound with an equal number of electrons and holes, there should exist another hole surface which corresponds to the c-branch of LaSb and its carrier number is considered to be 1.76]1020 (/cm3) (0.0089/Gd). Fig. 2 shows the lattice constant dependence of the carrier number. So far, LaAs, CeAs and YbAs have been successfully used to measure dHvA e!ect and determine the shapes of Fermi surfaces and the carrier numbers. The carrier number increases linearly on decreasing the lattice constant. This behavior is di!erent from that of rare-earth Sb. Thus, it is considered that the Fermi surfaces of rare-earth As compounds cannot be in#uenced much compared to those of rare-earth Sb due to the interactions between the carriers and the localized spins of the 4f electrons in rare earth. We also studied the magnetic "eld dependence of Fermi surfaces of GdAs. However, in the present study they were negligibly small, within about 3% in 4.5}15 T for both a- and b-branch. The change of the Fermi surface is considered to be small with change in the magnetic ordering as the external "eld increases.
References [1] D.X. Li, Dr. thesis, Tohoku University, 1995. [2] D.X. Li, Y. Haga, H. Shida, Y.S. Kwon, T. Suzuki, Phys. Rev. B 54 (1996) 10 483. [3] R. Settai, T. Goto, S. Sakatsume, Y.S. Kwon, T. Suzuki, T. Kasuya, Physica B 186}188 (1993) 176. [4] A. Hasegawa, J. Phys. Soc. Japan 54 (1985) 677.
De Haas}van Alphen e!ect in GdAs Y. Nakanishi!,*, F. Takahashi!, T. Sakon!, M. Yoshida!, D.X. Li", T. Suzuki", M. Motokawa! !Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan "Graduated School of Science, Tohoku University, Sendai 980-8578, Japan
Abstract We have for the "rst time observed de Haas}van Alphen e!ect in GdAs below the NeH el temperature in magnetic "elds up to 15 T. The Fermi surface consists of three ellipsoidal electron surfaces and a spherical surface. We have also determined the corresponding e!ective masses and mean free paths. Furthermore, by analyzing the angular dependence of Fermi surface, the number of carriers belonging to each Fermi surface is estimated. It is consistent with that measured by the Hall e!ect. In GdX as the lattice constant is increased, the number of carriers decreases. On the other hand, however, GdAs has less carrier concentration compared to that of GdSb. ( 2000 Published by Elsevier Science B.V. All rights reserved. Keywords: Gd-monopnictides; de Haas}van Alphen e!ect; Carrier concentration
Rare-earth (RE) monopnictides attract both experimentalists and theorists for their much interesting physical phenomena. In the series from GdN to GdSb, the corresponding conductivity changes from a semiconductor-like to a metallic. For their magnetic properties, GdN shows a ferromagnet, whereas the others are antiferromagnetic. In order to investigate the properties of Fermi surface, the de Haas}van Alphen (dHvA) e!ect has an advantage in the sense that we can obtain the direct information about conduction electrons. So far, in Gd monopnictides, GdSb is the only compound in which this was successfully observed. Since it was very di$cult to grow a high-quality single crystal due to the high melting temperature and high vapor pressure, only a few studies have been done in the past. Moreover, their electronic structure and mechanism of conductivity have not been analyzed enough. However, recently high-quality single crystal of GdAs was successfully grown so we could observe clear dHvA signals for it. In this paper we report the shape of Fermi surface, cyclotron e!ective masses and carrier densities. GdAs with NaCl crystal structure is an antiferromagnet below 18.7 K [1], however, the spin * Corresponding author. Tel.: #81-22-215-2017; fax: #8122-215-2016. E-mail address: [email protected] (Y. Nakanishi)
structure has not been determined so far. Among the RX (R; rare-earth) systems, Gd monopnictides are the most simple series, that is, Gd3` ion appearing in GdX has a 4f 7 con"guration and is an S-state ion with spin 7 and no 2 orbital momentum, So the crystalline electric "eld (CEF) e!ects in GdX are considered to be fairly weak. Actually, the magnetization of GdAs increases linearly and saturates at 17 T and no change of the magnetic structure occurs. There is less anisotropy due to the weak CEF e!ects [1]. Single crystals of GdAs are grown by the mineralization method in tungsten crucibles. This is described in detail elsewhere [2]. The dHvA e!ects for GdAs were measured by the "eld modulation method. A top loading type of 3He cryostat and a superconducting magnet up to 15 T were used for the measurement. The amplitude of the modulation "eld was 70 Oe and the frequency was 323 Hz. The temperature was changed from 0.5 to 4.2 K by controlling the vapor pressure of helium. The "eld directions are in the M1 0 0N and M1 1 0N planes. They were analyzed by Fast-Fourier Transform (FFT), and the angular dependence of these frequencies are plotted. Demagnetization "eld must be taken into account in the induced ferromagnetic ordered phase. We used the following correction for conduction electrons as e!ective "elds: H "H#4p(1!N)M, %&&
0921-4526/00/$ - see front matter ( 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 0 3 0 - 3
Y. Nakanishi et al. / Physica B 281&282 (2000) 750}751
Fig. 1. The extremal cross-sectional areas of Fermi surface as a function of the direction of magnetic "elds. The a-, a@-, aAbranch are assumed to be three ellipsoids centered at the Xpoints. The b-branch is assumed to be a sphere centered at the C-points. Table 1 The cyclotron mass in the principal axis. The value in parentheses is that of LaSb for comparison [4] Branch F(¹)
mH(m ) 0
[1 0 0]
[1 1 0]
[1 1 1]
[1 0 0]
[1 1 0]
[1 1 1]
a
246.4
331.84
382.1
0.24
*
b
434.88
*
452.8
0.20 (0.14) 0.26 (0.15)
* (0.17)
0.22 (0.23)
Table 2 q in the [1 0 0] axis
¹"4.2 K ¹"0.5 K
a-branch (s)
b-branch (s)
2.33]10~13 3.69]10~13
0.90]10~13 1.65]10~13
where H, H , N, M denote external "eld, e!ective mag%&& netic "elds, a demagnetization coe$cient (in this sample N is 0.34 and is assumed to be constant even if the magnetic "eld direction is changed for the sake of simplicity) and the magnetization of GdAs, respectively. Fig. 1 shows the angular dependence of the extremal crosssectional area of the Fermi surface for GdAs. The shape of the Fermi surface is very similar to that of LaSb [3]. So the oscillations are caused by an electron pocket at the X-point, two hole pockets at the C-point [4]. The e!ective cyclotron masses are listed in Table 1. By analyzing the "eld dependence of FFT spectrum, the relaxation times q of a- and b-branch were estimated and listed in Table 2. The q of a-branch is more than two times larger than that of b-branch. In this measurement we could not
751
Fig. 2. The lattice constant dependence of the carrier number in rare-earth As.
observe c-branch clearly. The e!ective cyclotron masses of b-branch are also similar to those of LaSb, however, those of a-branch are half as small as LaSb's [3]. Analyzing the angular dependence of Fermi surface we estimated the carrier number. The carrier numbers of aand b-branch are determined to be 2.27]1020 (/cm3) (0.0115/Gd) and 0.516]1020 (/cm3) (0.0026/Gd), respectively. These values are mostly consistent with those measured by the Hall e!ect [3]. Since GdAs is a semimetallic compound with an equal number of electrons and holes, there should exist another hole surface which corresponds to the c-branch of LaSb and its carrier number is considered to be 1.76]1020 (/cm3) (0.0089/Gd). Fig. 2 shows the lattice constant dependence of the carrier number. So far, LaAs, CeAs and YbAs have been successfully used to measure dHvA e!ect and determine the shapes of Fermi surfaces and the carrier numbers. The carrier number increases linearly on decreasing the lattice constant. This behavior is di!erent from that of rare-earth Sb. Thus, it is considered that the Fermi surfaces of rare-earth As compounds cannot be in#uenced much compared to those of rare-earth Sb due to the interactions between the carriers and the localized spins of the 4f electrons in rare earth. We also studied the magnetic "eld dependence of Fermi surfaces of GdAs. However, in the present study they were negligibly small, within about 3% in 4.5}15 T for both a- and b-branch. The change of the Fermi surface is considered to be small with change in the magnetic ordering as the external "eld increases.
References [1] D.X. Li, Dr. thesis, Tohoku University, 1995. [2] D.X. Li, Y. Haga, H. Shida, Y.S. Kwon, T. Suzuki, Phys. Rev. B 54 (1996) 10 483. [3] R. Settai, T. Goto, S. Sakatsume, Y.S. Kwon, T. Suzuki, T. Kasuya, Physica B 186}188 (1993) 176. [4] A. Hasegawa, J. Phys. Soc. Japan 54 (1985) 677.