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Microwave studies of low carrier state in Yb4As3
Physica B 246—247 (1998) 460—463
Microwave studies of low carrier state in Yb As 4 3 H. Matsui!,*, T. Yasuda!, A. Ochiai", H. Harima#, H. Aoki$, T. Suzuki$, N. Toyota! ! Research Institute for Advanced Science and Technology, Osaka Prefecture University, Gakuenchou 1-2, Sakai 599-8570, Japan " Department of Material Science and Technology, Niigata University, Niigata 950-21, Japan # Institute for Scientific and Industrial Research, Osaka University, Osaka 567, Japan $ Department of Physics, Tohoku University, Sendai 980-77, Japan
Abstract To observe the cyclotron resonance (CR) in Yb As , we have performed the microwave experiments with the cavity 4 3 perturbation and the simple transmission techniques. The CR mass is evaluated as 0.72 m which is consistent with the 0 theoretical value of about 0.7 m obtained by the recent band structure calculations for LuYb As . It can be concluded 0 3 3 that the observed CR originates from the light 4p-holes of As ions centered at the ! point. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Yb As ; Cyclotron resonance; ESR; Low carrier-density 4 3
The extremely low carrier-density system of Yb As indicates various unusual properties [1]. 4 3 The carrier density is estimated to be 0.001 per Yb3` by Hall effect. This system shows a structural phase transition from the high-temperature cubic structure with anti-Th P type to low-temperature 3 4 rhombohedral one at about ¹ "300 K. Below ¹ , S S the rhombohedral structure is formed by shrinking along a trigonal short S1 1 1T direction among four equivalent S1 1 1T axes and the domains are induced without a uniaxial applied pressure. Furthermore, the low temperature phase is accompanied by the charge ordering in which the Yb3` ion chains are aligned along the short S1 1 1T direction.
* Corresponding author. Fax: #81 722 54 9935; e-mail: [email protected].
The specific heat coefficient c amounts to 200 mJ/mol K2 and electrical resistivity exhibits a ¹2 dependence below 100 K [1]. It has remained an unsettled question what is the origin of the heavy fermion-like behaviors. Neutron inelastic scattering measurements by Kohgi et al. [2] have recently clarified that the one-dimensional Yb3` chains are formed along short S1 1 1T and the low energy spin excitations are induced on these S"1 2 one-dimensional Heisenberg antiferromagnetic chains along short S1 1 1T [3,4]. Moreover, the measurements of specific heat, magnetic susceptibility [5—8] and optical reflection [9] on Yb (As X ) (X"P, Sb) indicate that the large 4 1~y y 3 c value of Yb As originates not from the mass4 3 enhancements of conduction electrons as seen in the usual heavy fermion systems, but from spin excitations. The temperature change of the electronic
0921-4526/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved PII S 0 9 2 1 - 4 5 2 6 ( 9 7 ) 0 0 9 6 1 - 7
H. Matsui et al. / Physica B 246—247 (1998) 460—463
structures has been observed by high resolution photoemission measurements due to the stabilization of Yb3` state on the short S1 1 1T [10]. Therefore, these results suggest that the thermal and magnetic properties are caused basically by the one-dimensional spin excitations. In order to determine the mass of the conduction electrons in Yb As , the cyclotron resonance (CR) 4 3 experiments have been performed by the MVNA vector network analyzer (ABmm) within the microwave frequency regions (16—110 GHz) at temperature down to 0.55 K in magnetic fields applied perpendicular to (1 0 0) up to 10 T [11]. We have measured the relative changes of amplitude for transmitting waves as a function of magnetic field at fixed frequency and different temperatures. The single crystal of Yb As has been prepared 4 3 by the flux method [1]. A small sample (1]0.5]0.5 mm3) is used for the cavity perturbation experiments with rectangular cavities made by Cu. The TE and TE modes are induced at 101 102 18.36 and 25.43 GHz. It is important to note that the responses for an AC electric field of microwave can be separated from that for an AC magnetic field by these two modes. The simple transmission experiments have been carried out with a large sample (3]4]0.5 mm3). Fig. 1 shows the transmission amplitude of 18.36 GHz by cavity perturbation as a function of magnetic field. The sample is positioned at the center of the cavity where the AC electric field is maximum. Therefore, the contribution of electric dipole transition is dominant in this TE . The 101 absorption appeared at H "0.47 T originates CR from the CR which depends on the temperatures strongly. The relaxation time q is 6.2]10~11 s at 0.55 K through the relation of *H/H "2uq CR where *H is the full width at half maximum. It can be considered that the domain has little influence on the CR at 0.47 T. The absorption at 0.66 T which is observed below 1.4 K can be attributed to the electron spin resonance (ESR) from the comparison to the results of TE and simple trans102 mission as mentioned below. The magnetic dipole transition contributes dominantly to the absorption of TE at 102 25.43 GHz. As shown in Fig. 2, an antisymmetric absorption is observed and the temperature
461
Fig. 1. Cavity transmission at 18.36 GHz for different temperatures.
Fig. 2. Cavity transmission at 25.43 GHz for different temperatures.
dependence is small. The CR signal can not be detected in TE . 102 Fig. 3 shows the magnetic field dependence of transmission without any cavity for various frequencies. With increasing the microwave frequencies, the intensity of transmitting wave decreases according to the losses in the guide walls and the skin depth effect of the sample. The CR can only observe at a frequency of 20.05 GHz and a resonant frequency is 0.56 T where the position is denoted by a dotted line in Fig. 3. The small shoulder at 0.7 T originates from the ESR. Another resonance for
462
H. Matsui et al. / Physica B 246—247 (1998) 460—463
Fig. 3. Transmission for various frequencies at 1.5 K.
in Fig. 3 is marked by solid circle and squares. The dotted line indicates the CR with the mass of 0.72 m [11]. The solid line is a fitting result leading 0 to g"2.04. Although the origin of the ESR is not clear, it can be expected that it corresponds to the conduction electrons, impurities or Yb3` ions which are not positioned on short S1 1 1T. The band structure calculations for cubic Yb As were carried out by LAPW method [12]. 4 3 Recently, more rigorous band structure calculations in the charge ordering state have been performed for LuYb As , in which Yb atoms along 3 3 short S1 1 1T are replaced by Lu atoms [13]. The LuYb As becomes a semimetal with small 4p-hole 3 3 pockets of As ions centered at the ! point and a 5d-electron pocket of Yb along the P axis. The cyclotron mass is calculated to be about 0.7 m for 0 the 4p-hole by the band structure calculations. The calculated value is very close to our experimental CR mass mentioned above. The 5d-electron with one-dimensional dispersion has a large CR mass compared to the 4p-hole and is affected strongly by the domains. Furthermore, the Hall coefficient is positive and the hole contributes to the transport phenomena dominantly [1]. Therefore, these results lead to the conclusion that the observed CR with 0.72 m comes from the 4p-holes centered at 0 the ! point. This conclusion is consistent with the recent measurements of specific heat [5—8], neutron inelastic scattering [2] and optical reflection [9], which show that the conduction electrons are not enhanced as seen in the usual heavy fermion systems. This work is supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan.
Fig. 4. Resonant frequency versus resonant magnetic field.
various frequencies can be attributed to the ESR which is represented by the arrows. In Fig. 4 we summarize the results of resonant frequency vs. resonant magnetic field obtained in this study. The open circle, square and triangle are obtained by the TE in Fig. 1 and TE in 101 102 Fig. 2. The resonance observed by the transmission
References [1] A. Ochiai, T. Suzuki, T. Kasuya, J. Phys. Soc. Japan 59 (1990) 4129. [2] M. Kohgi, K. Iwasa, A. Ochiai, T. Suzuki, J.-M. Mignot, B. Gillon, A. Goukassov, J. Schweizer, K. Kakurai, M. Nishi, A. Donni, T. Osakabe, Physica B 230—232 (1997) 638. [3] P. Fulde, B. Schmidt, P. Thalmeier, Europhys. Lett. 31 (1995) 323. [4] B. Schmidt, P. Thalmeier, P. Fulde, Europhys. Lett. 35 (1996) 109.
H. Matsui et al. / Physica B 246—247 (1998) 460—463 [5] A. Ochiai, E. Hotta, Y. Haga, T. Suzuki, O. Nakamura, J. Magn. Magn. Mater. 140—144 (1995) 1249. [6] H. Aoki, A. Ochiai, T. Suzuki, R. Helfrich, F. Steglich, Physica B 230—232 (1997) 698. [7] A. Ochiai, H. Aoki, T. Suzuki, R. Helfrich, F. Steglich, Physica B 230—232 (1997) 708. [8] R. Helfrich, M. Koppen, M. Lang, F. Steglich, A. Ochiai, Proc. ICM/SCES 1997, to be published.
463
[9] R. Pittini, M. Ikezawa, A. Ochiai, H. Aoki, T. Suzuki, Proc. ICM/SCES 1997, to be published. [10] S. Suga et al., to be published. [11] H. Matsui, A. Ochiai, H. Harima, H. Aoki, T. Suzuki, T. Yasuda, N. Toyota, J. Phys. Soc. Jpn. 66 (1997) 3729. [12] K. Takegahara, Y. Kaneta, J. Phys. Soc. Japan 60 (1991) 4009. [13] H. Harima, J. Phys. Soc. Jpn. 67 (1997) 37.
Microwave studies of low carrier state in Yb As 4 3 H. Matsui!,*, T. Yasuda!, A. Ochiai", H. Harima#, H. Aoki$, T. Suzuki$, N. Toyota! ! Research Institute for Advanced Science and Technology, Osaka Prefecture University, Gakuenchou 1-2, Sakai 599-8570, Japan " Department of Material Science and Technology, Niigata University, Niigata 950-21, Japan # Institute for Scientific and Industrial Research, Osaka University, Osaka 567, Japan $ Department of Physics, Tohoku University, Sendai 980-77, Japan
Abstract To observe the cyclotron resonance (CR) in Yb As , we have performed the microwave experiments with the cavity 4 3 perturbation and the simple transmission techniques. The CR mass is evaluated as 0.72 m which is consistent with the 0 theoretical value of about 0.7 m obtained by the recent band structure calculations for LuYb As . It can be concluded 0 3 3 that the observed CR originates from the light 4p-holes of As ions centered at the ! point. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Yb As ; Cyclotron resonance; ESR; Low carrier-density 4 3
The extremely low carrier-density system of Yb As indicates various unusual properties [1]. 4 3 The carrier density is estimated to be 0.001 per Yb3` by Hall effect. This system shows a structural phase transition from the high-temperature cubic structure with anti-Th P type to low-temperature 3 4 rhombohedral one at about ¹ "300 K. Below ¹ , S S the rhombohedral structure is formed by shrinking along a trigonal short S1 1 1T direction among four equivalent S1 1 1T axes and the domains are induced without a uniaxial applied pressure. Furthermore, the low temperature phase is accompanied by the charge ordering in which the Yb3` ion chains are aligned along the short S1 1 1T direction.
* Corresponding author. Fax: #81 722 54 9935; e-mail: [email protected].
The specific heat coefficient c amounts to 200 mJ/mol K2 and electrical resistivity exhibits a ¹2 dependence below 100 K [1]. It has remained an unsettled question what is the origin of the heavy fermion-like behaviors. Neutron inelastic scattering measurements by Kohgi et al. [2] have recently clarified that the one-dimensional Yb3` chains are formed along short S1 1 1T and the low energy spin excitations are induced on these S"1 2 one-dimensional Heisenberg antiferromagnetic chains along short S1 1 1T [3,4]. Moreover, the measurements of specific heat, magnetic susceptibility [5—8] and optical reflection [9] on Yb (As X ) (X"P, Sb) indicate that the large 4 1~y y 3 c value of Yb As originates not from the mass4 3 enhancements of conduction electrons as seen in the usual heavy fermion systems, but from spin excitations. The temperature change of the electronic
0921-4526/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved PII S 0 9 2 1 - 4 5 2 6 ( 9 7 ) 0 0 9 6 1 - 7
H. Matsui et al. / Physica B 246—247 (1998) 460—463
structures has been observed by high resolution photoemission measurements due to the stabilization of Yb3` state on the short S1 1 1T [10]. Therefore, these results suggest that the thermal and magnetic properties are caused basically by the one-dimensional spin excitations. In order to determine the mass of the conduction electrons in Yb As , the cyclotron resonance (CR) 4 3 experiments have been performed by the MVNA vector network analyzer (ABmm) within the microwave frequency regions (16—110 GHz) at temperature down to 0.55 K in magnetic fields applied perpendicular to (1 0 0) up to 10 T [11]. We have measured the relative changes of amplitude for transmitting waves as a function of magnetic field at fixed frequency and different temperatures. The single crystal of Yb As has been prepared 4 3 by the flux method [1]. A small sample (1]0.5]0.5 mm3) is used for the cavity perturbation experiments with rectangular cavities made by Cu. The TE and TE modes are induced at 101 102 18.36 and 25.43 GHz. It is important to note that the responses for an AC electric field of microwave can be separated from that for an AC magnetic field by these two modes. The simple transmission experiments have been carried out with a large sample (3]4]0.5 mm3). Fig. 1 shows the transmission amplitude of 18.36 GHz by cavity perturbation as a function of magnetic field. The sample is positioned at the center of the cavity where the AC electric field is maximum. Therefore, the contribution of electric dipole transition is dominant in this TE . The 101 absorption appeared at H "0.47 T originates CR from the CR which depends on the temperatures strongly. The relaxation time q is 6.2]10~11 s at 0.55 K through the relation of *H/H "2uq CR where *H is the full width at half maximum. It can be considered that the domain has little influence on the CR at 0.47 T. The absorption at 0.66 T which is observed below 1.4 K can be attributed to the electron spin resonance (ESR) from the comparison to the results of TE and simple trans102 mission as mentioned below. The magnetic dipole transition contributes dominantly to the absorption of TE at 102 25.43 GHz. As shown in Fig. 2, an antisymmetric absorption is observed and the temperature
461
Fig. 1. Cavity transmission at 18.36 GHz for different temperatures.
Fig. 2. Cavity transmission at 25.43 GHz for different temperatures.
dependence is small. The CR signal can not be detected in TE . 102 Fig. 3 shows the magnetic field dependence of transmission without any cavity for various frequencies. With increasing the microwave frequencies, the intensity of transmitting wave decreases according to the losses in the guide walls and the skin depth effect of the sample. The CR can only observe at a frequency of 20.05 GHz and a resonant frequency is 0.56 T where the position is denoted by a dotted line in Fig. 3. The small shoulder at 0.7 T originates from the ESR. Another resonance for
462
H. Matsui et al. / Physica B 246—247 (1998) 460—463
Fig. 3. Transmission for various frequencies at 1.5 K.
in Fig. 3 is marked by solid circle and squares. The dotted line indicates the CR with the mass of 0.72 m [11]. The solid line is a fitting result leading 0 to g"2.04. Although the origin of the ESR is not clear, it can be expected that it corresponds to the conduction electrons, impurities or Yb3` ions which are not positioned on short S1 1 1T. The band structure calculations for cubic Yb As were carried out by LAPW method [12]. 4 3 Recently, more rigorous band structure calculations in the charge ordering state have been performed for LuYb As , in which Yb atoms along 3 3 short S1 1 1T are replaced by Lu atoms [13]. The LuYb As becomes a semimetal with small 4p-hole 3 3 pockets of As ions centered at the ! point and a 5d-electron pocket of Yb along the P axis. The cyclotron mass is calculated to be about 0.7 m for 0 the 4p-hole by the band structure calculations. The calculated value is very close to our experimental CR mass mentioned above. The 5d-electron with one-dimensional dispersion has a large CR mass compared to the 4p-hole and is affected strongly by the domains. Furthermore, the Hall coefficient is positive and the hole contributes to the transport phenomena dominantly [1]. Therefore, these results lead to the conclusion that the observed CR with 0.72 m comes from the 4p-holes centered at 0 the ! point. This conclusion is consistent with the recent measurements of specific heat [5—8], neutron inelastic scattering [2] and optical reflection [9], which show that the conduction electrons are not enhanced as seen in the usual heavy fermion systems. This work is supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan.
Fig. 4. Resonant frequency versus resonant magnetic field.
various frequencies can be attributed to the ESR which is represented by the arrows. In Fig. 4 we summarize the results of resonant frequency vs. resonant magnetic field obtained in this study. The open circle, square and triangle are obtained by the TE in Fig. 1 and TE in 101 102 Fig. 2. The resonance observed by the transmission
References [1] A. Ochiai, T. Suzuki, T. Kasuya, J. Phys. Soc. Japan 59 (1990) 4129. [2] M. Kohgi, K. Iwasa, A. Ochiai, T. Suzuki, J.-M. Mignot, B. Gillon, A. Goukassov, J. Schweizer, K. Kakurai, M. Nishi, A. Donni, T. Osakabe, Physica B 230—232 (1997) 638. [3] P. Fulde, B. Schmidt, P. Thalmeier, Europhys. Lett. 31 (1995) 323. [4] B. Schmidt, P. Thalmeier, P. Fulde, Europhys. Lett. 35 (1996) 109.
H. Matsui et al. / Physica B 246—247 (1998) 460—463 [5] A. Ochiai, E. Hotta, Y. Haga, T. Suzuki, O. Nakamura, J. Magn. Magn. Mater. 140—144 (1995) 1249. [6] H. Aoki, A. Ochiai, T. Suzuki, R. Helfrich, F. Steglich, Physica B 230—232 (1997) 698. [7] A. Ochiai, H. Aoki, T. Suzuki, R. Helfrich, F. Steglich, Physica B 230—232 (1997) 708. [8] R. Helfrich, M. Koppen, M. Lang, F. Steglich, A. Ochiai, Proc. ICM/SCES 1997, to be published.
463
[9] R. Pittini, M. Ikezawa, A. Ochiai, H. Aoki, T. Suzuki, Proc. ICM/SCES 1997, to be published. [10] S. Suga et al., to be published. [11] H. Matsui, A. Ochiai, H. Harima, H. Aoki, T. Suzuki, T. Yasuda, N. Toyota, J. Phys. Soc. Jpn. 66 (1997) 3729. [12] K. Takegahara, Y. Kaneta, J. Phys. Soc. Japan 60 (1991) 4009. [13] H. Harima, J. Phys. Soc. Jpn. 67 (1997) 37.