- Email: [email protected]
Electron-strain interaction in YCu2
Physica B 169 (1991) 495-496 North-Holland
ELECTRON-STRAIN
Rikio SETTAI,
INTERACTION
Terutaka
IN YCu2
GOTO, Tadao FUJIMURA
and Yoshichika
ONUKI"
*Research Institute for Scientific Measurements, Tohoku University, Sendai Institute of Material Science, University of Tsukuba, Tsukuba 305, Japan
980, Japan
with the the elastic properties of the intermetallic compound YCu investigated We have The longitudinal 2c11 as w;bL orthorhombic crystal class by means of the ultrasonic measurements. dependencies. as the transverse C44, C66 modes exhibit the softening in the temperature relationship between those softenings and the acoustic de Haas-van Alphen oscillatory amplitude are discussed.
Intermetallic compounds RCu2, where R are the rare earth elements, exhibit the various magnetism at low temperatures[l,2]. Especially CeCu2 is recognized as a heavy Fermion compound exhibiting the antiferromagnetism below TN=3.5K specific heat coefficient with a large In order to examine the c-f y=82mJ/mol.K2[3]. mixing effect in CeCu2, the de Haas-van Alphen measurements have been performed by (dHvA) magnetic and acoustic means the of Those results have been compared methods[4,5]. to the ones on the reference compound YCu2 with where the 4f electrons do y=6.5mJ/mol.K2[6], not exist. In the present paper, we show the elastic properties of YCu2 focusing on the interaction between the conduction electron and the elastic strain. For the sound velocity measurements, the apparatus based on the phase comparison method have been used. The relative velocity change of the sound wave with the frequency of 30MHz was detected with the resolution of one part in 107. Because the crystal structure of YCu2 belongs to the2;rthorhombic with the space group symmetry D2h (Imma), the longitudinal Cl13 C22' C33 and the transverse C44, C55, C66 modes are available. As was shown in Fig.1, the temperature dependencies of the elastic constant C44 and C66 modes exhibit pronounced softenings below room temperature. The Cl1 mode also shows a softening below about 80K. Those behaviors of the elastic instability in modes may be related to the band ?%n_aTnedll?? coupling mechanism between the elastic strain and the appropriate conduction band electrons. In order to examine the electron-strain interaction in YCu2 I we have performed the acoustic dHvA measurements corresponding to the
quantum oscillations of the elastic constants. From the second derivative of the LifshitzKosevich free energy with respect to the elastic strain ET, one gets the two oscillatory terms of the elastic constants.
T (Kl
Fig.1 dependencies of Temperature constants C44, C55, C66 in YCu2.
the
elastic
R. Settai et al. I Electron-strain interaction in Ku,
496
(1)
Here RT, RD and RS are the reduction factors of the finite temperature, impurity scattering and spin contributions, respectively, SS was
0.2
0.1
0.3
0.4
dHvA Frequency (10' Oe) 4.0.
defined in reference[7]. In Fig.2, we present the angular variation of the Fourier spectra of the transverse Ch4, C55 and C66 modes in the compound of YCu2 with the Dingle temperature relative 1.3K. The measured at TD=0.5K intensity are the oscillatory variation Of governed by the curvature factor, A"=a*A/aks', The extremal orbit. individual for the are spectra of Fourier amplitude absolute related to the derivative of the areas of the a2F/aEr2 and orbits, extremal (aF/asF)Z, namely, the deformation potential, which means the coupling between the conduction electrons of the orbits and the elastic strain. Here, F defined as, dHvA frequency denotes the F=(ch/2ne)A. The 8 branch is commonly observed On the other in the transverse modes in Fig.2. hand, the c( and 6 branches, are detected only in the C4,+ and C66 modes, which show the temperature the in softenings elastic Before jumping to the conclusion dependencies. to the detailed description of the band JahnTeller mechanism in YCu,, we have to compare to calculations[8]. results of the i band the Nevertheless we could propose that the acoustic dHvA effect is a nice probe to determine the in quantative interaction electron-strain manner.
REFERENCES
(1) Y.Hashimoto, b-
0.1
(2) 0.2 dHvA Frequency
0.3
0.4
(IO' De)
(3)
(4)
(5)
(6) b 0.1
(7) 0.2
0.3
0.4
dHvA Frequency (10' Oe)
Fig.2 Angular variation of the Fourier Spectra of the acoustic dHvA oscillations in Ch4, C55, C66 modes in YCu2
(8)
H.Fujii and T.Okamoto, J. Phys. Sot. Jpn. 47 (1979) 67. K.Andres, E.Bucher, J.P.Maita and A.S.Cooper, Phys. Rev. Lett. 28 (1972) 1652. E.Gartz, E.Bauer, B.Barbara, S.Zemirli, F.Steglich, C.D.Bredl and W.Lieke, J. Phys. F: Met. Phys. 15 (1986) 1975 K.Satoh, I.Umehara, A.Fukuda, Y.Kurosawa and Y.Onuki, submitted to Proc. of Int. Conf. Magnetic Phase Transition. R.Settai, H.Matsui, Y.Ohe, T.Goto, S.Sakatsume, Y.Onuki, F.Iga, M.Kasaya, submitted to Proc. of Int. Conf. Magnetic Phase Transition. N.H.Luong, J.J.M.Franse and T.D.Hein, J. Mag. Mag. Mat. 50 (1985) 153. D.Shoenberg, Magnetic oscillations in metals (CAMBRIDGE UNIVERSITY PRESS, 1984) H.Harima, S.Miyahara and A.Yanase, submitted to Santa Fe Conf. (1989).
ELECTRON-STRAIN
Rikio SETTAI,
INTERACTION
Terutaka
IN YCu2
GOTO, Tadao FUJIMURA
and Yoshichika
ONUKI"
*Research Institute for Scientific Measurements, Tohoku University, Sendai Institute of Material Science, University of Tsukuba, Tsukuba 305, Japan
980, Japan
with the the elastic properties of the intermetallic compound YCu investigated We have The longitudinal 2c11 as w;bL orthorhombic crystal class by means of the ultrasonic measurements. dependencies. as the transverse C44, C66 modes exhibit the softening in the temperature relationship between those softenings and the acoustic de Haas-van Alphen oscillatory amplitude are discussed.
Intermetallic compounds RCu2, where R are the rare earth elements, exhibit the various magnetism at low temperatures[l,2]. Especially CeCu2 is recognized as a heavy Fermion compound exhibiting the antiferromagnetism below TN=3.5K specific heat coefficient with a large In order to examine the c-f y=82mJ/mol.K2[3]. mixing effect in CeCu2, the de Haas-van Alphen measurements have been performed by (dHvA) magnetic and acoustic means the of Those results have been compared methods[4,5]. to the ones on the reference compound YCu2 with where the 4f electrons do y=6.5mJ/mol.K2[6], not exist. In the present paper, we show the elastic properties of YCu2 focusing on the interaction between the conduction electron and the elastic strain. For the sound velocity measurements, the apparatus based on the phase comparison method have been used. The relative velocity change of the sound wave with the frequency of 30MHz was detected with the resolution of one part in 107. Because the crystal structure of YCu2 belongs to the2;rthorhombic with the space group symmetry D2h (Imma), the longitudinal Cl13 C22' C33 and the transverse C44, C55, C66 modes are available. As was shown in Fig.1, the temperature dependencies of the elastic constant C44 and C66 modes exhibit pronounced softenings below room temperature. The Cl1 mode also shows a softening below about 80K. Those behaviors of the elastic instability in modes may be related to the band ?%n_aTnedll?? coupling mechanism between the elastic strain and the appropriate conduction band electrons. In order to examine the electron-strain interaction in YCu2 I we have performed the acoustic dHvA measurements corresponding to the
quantum oscillations of the elastic constants. From the second derivative of the LifshitzKosevich free energy with respect to the elastic strain ET, one gets the two oscillatory terms of the elastic constants.
T (Kl
Fig.1 dependencies of Temperature constants C44, C55, C66 in YCu2.
the
elastic
R. Settai et al. I Electron-strain interaction in Ku,
496
(1)
Here RT, RD and RS are the reduction factors of the finite temperature, impurity scattering and spin contributions, respectively, SS was
0.2
0.1
0.3
0.4
dHvA Frequency (10' Oe) 4.0.
defined in reference[7]. In Fig.2, we present the angular variation of the Fourier spectra of the transverse Ch4, C55 and C66 modes in the compound of YCu2 with the Dingle temperature relative 1.3K. The measured at TD=0.5K intensity are the oscillatory variation Of governed by the curvature factor, A"=a*A/aks', The extremal orbit. individual for the are spectra of Fourier amplitude absolute related to the derivative of the areas of the a2F/aEr2 and orbits, extremal (aF/asF)Z, namely, the deformation potential, which means the coupling between the conduction electrons of the orbits and the elastic strain. Here, F defined as, dHvA frequency denotes the F=(ch/2ne)A. The 8 branch is commonly observed On the other in the transverse modes in Fig.2. hand, the c( and 6 branches, are detected only in the C4,+ and C66 modes, which show the temperature the in softenings elastic Before jumping to the conclusion dependencies. to the detailed description of the band JahnTeller mechanism in YCu,, we have to compare to calculations[8]. results of the i band the Nevertheless we could propose that the acoustic dHvA effect is a nice probe to determine the in quantative interaction electron-strain manner.
REFERENCES
(1) Y.Hashimoto, b-
0.1
(2) 0.2 dHvA Frequency
0.3
0.4
(IO' De)
(3)
(4)
(5)
(6) b 0.1
(7) 0.2
0.3
0.4
dHvA Frequency (10' Oe)
Fig.2 Angular variation of the Fourier Spectra of the acoustic dHvA oscillations in Ch4, C55, C66 modes in YCu2
(8)
H.Fujii and T.Okamoto, J. Phys. Sot. Jpn. 47 (1979) 67. K.Andres, E.Bucher, J.P.Maita and A.S.Cooper, Phys. Rev. Lett. 28 (1972) 1652. E.Gartz, E.Bauer, B.Barbara, S.Zemirli, F.Steglich, C.D.Bredl and W.Lieke, J. Phys. F: Met. Phys. 15 (1986) 1975 K.Satoh, I.Umehara, A.Fukuda, Y.Kurosawa and Y.Onuki, submitted to Proc. of Int. Conf. Magnetic Phase Transition. R.Settai, H.Matsui, Y.Ohe, T.Goto, S.Sakatsume, Y.Onuki, F.Iga, M.Kasaya, submitted to Proc. of Int. Conf. Magnetic Phase Transition. N.H.Luong, J.J.M.Franse and T.D.Hein, J. Mag. Mag. Mat. 50 (1985) 153. D.Shoenberg, Magnetic oscillations in metals (CAMBRIDGE UNIVERSITY PRESS, 1984) H.Harima, S.Miyahara and A.Yanase, submitted to Santa Fe Conf. (1989).