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Optical conductivity of a non-Fermi-liquid material YbRh2Si2
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) 36–37
Optical conductivity of a non-Fermi-liquid material YbRh2 Si2 S. Kimuraa,b,*, T. Nishib, J. Sichelschmidtc, V. Voevodinc, J. Ferstlc, C. Geibelc, F. Steglichc a
b
UVSOR Facility, Institute for Molecular Science, Okazaki 444-8585, Japan Department of Structural Molecular Science, The Graduate University for Advanced Studies, Okazaki 444-8585, Japan c Max Planck Institute for Chemical Physics of Solids, Nothnitzer Str. 40, Dresden D-01187, Germany .
Abstract The temperature-dependent electronic structure of YbRh2 Si2 has been investigated by the optical conductivity ðsðoÞÞ measurement in the photon energy range of 10 meV–30 eV at several temperatures of 2.7–300 K: The sðoÞ spectrum as well as the electronic structure changes at two temperatures of 80 and 20 K: At 80 K; the heavy quasiparticles develop and at 20 K; the non-Fermi liquid behavior appears in the sðoÞ spectra. The behavior of YbRh2 Si2 is compared to some Landau Fermi-liquid materials. r 2003 Elsevier B.V. All rights reserved. PACS: 71.27.+a; 78.20.e Keywords: Non-Fermi liquid; Optical conductivity; YbRh2 Si2
YbRh2 Si2 shows a non-Fermi liquid (NFL) behavior in the wide temperature range of 0.1–10 K at ambient pressure and zero magnetic field [1]. Then the material is suitable for the investigation of the fundamental properties of NFL. In this study, we measured reflectivity spectra in the temperature range of 2.7–300 K and in the photon energy range of 0.01–30 eV: We investigate the NFL properties in the optical conductivity ðsðoÞÞ spectra as well as whether the sðoÞ spectrum differs from that of Landau Fermi-liquid (LFL) materials or not. The material was grown by an indium flux method. The c-plane of the tetragonal structure of the sample with a size of 0:8 0:8 0:1 mm3 was measured. The optical spectra in _o ¼ 0:01–1:5 eV was detected at eight temperatures of 2.7–300 K by using conventional FTIR spectrometers with black body light sources in Dresden and Okazaki. The spectrum in the photon energy range of _o ¼ 1:2–30 eV was obtained only at 300 K using the synchrotron radiation in Okazaki. The sðoÞ spectra
*Corresponding author. UVSOR Facility, Institute for Molecular Science, Okazaki 444-8585, Japan. Tel.: +81-56455-7202; fax: +81-564-54-7079. E-mail address: [email protected] (S. Kimura).
were obtained from the Kramers-Kronig analysis of the reflectivity spectra in _o ¼ 0:01–30 eV: The temperature dependence of sðoÞ spectrum is shown in Fig. 1. Two characteristic structures appear, one is a dip structure at around _o ¼ 0:02 eV; the other a broad peak at _o ¼ 0:2 eV: In the former structure, the extrapolation to 0 eV of the sðoÞ at 300 K seems to correspond to the sDC value. The sðoÞ curve seems to be roughly explained by a Drude model but a broad interband transition component due to the cf hybridization as discussed later appears at around 0:2 eV: However, at low temperature, the temperature dependence is the opposite to the sDC : This indicates that a steep rise sðoÞ structure close to the sDC should appear below 0:01 eV: The structure clearly originates from the creation of heavy quasiparticles due to the cf hybridization (so-called ‘‘coherent part’’). On the other hand, the structure corresponding to the latter grows up with decreasing temperature. The structure is commonly observed in dense-Kondo systems such as Ce- and Ybbased compounds, i.e., the origin is the interband transition between the bonding and antibonding cf hybridization states (‘‘incoherent part’’) [2]. The temperature dependence of the peak intensity of the incoherent part is shown in Fig. 2(a). The figure
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.11.031
ARTICLE IN PRESS S. Kimura et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 36–37
(a) Fig. 1. Temperature dependence of optical conductivity ðsðoÞÞ spectrum of YbRh2 Si2 : The direct current conductivities ðsDC Þ at 300, 20 and 2:7 K are also plotted. The sDC at 160 and 80 K are similar to that at 300 K:
indicates that the incoherent part rapidly increases with decreasing temperature from 300 to 80 K; slightly increases from 80 to 20 K and becomes almost constant below 20 K: The increase of the incoherent part indicates the growth of the cf hybridization, i.e., the cf hybridization rapidly and slightly grows up above 80 K and between 80 and 20 K; respectively, and becomes constant below 20 K: The 80 K is consistent with the temperature at which the electric resistivity turns down with decreasing temperature [1] and also the temperature dependence of the 29 Si Knight shift changes [3]. In addition, the constant cf hybridization intensity is consistent with a characteristic spin-fluctuation temperature ðB15 KÞ determined by the NMR. Next, the temperature dependence of the tail of the coherent part at around 0:02 eV is discussed. In general, the sðoÞ due to carriers is explained by the Drude model as the following, sðoÞ ¼ o2P t=4pð1 þ o2 t2 Þ: Here, oP is the plasma frequency and t the relaxation time. At frequencies ðo1 Þ being sufficiently higher than 1=t; o1 tc1: Then sðo1 Þ ¼ o2P =ð4po21 tÞp1=t: Since rp1=tpT n (n ¼ 2 for LFL, o2 for NFL), sðo1 ÞpT n : In the case of YbRh2 Si2 ; n ¼ 1:
37
(b)
Fig. 2. Temperature dependence of sðoÞ at two photon energies of 0:17 eV (a) and 0:02 eV (b) of YbRh2 Si2 : The temperature dependences of sð_o ¼ 0:17 eVÞ and sð_o ¼ 0:02 eVÞ indicate that of the cf hybridization intensity and that of the Drude tail of the heavy quasiparticles, respectively. The T-linear part, which is the evidence of the NFL character, appears below 20 K in the inset of (b).
The temperature dependence of sðoÞ at _o ¼ 0:02 eV is shown in Fig. 2(b). We recognize that the sð_o ¼ 0:02 eVÞ pT is realized below 20 K in the inset of the figure. This is consistent with the appearance of NFL character below 20 K in the electric resistivity and the specific heat [1]. This work was partially supported by a Grants-in-Aid for Scientific Research from MEXT of Japan and was a joint study program of the Institute for Molecular Science (2002).
References [1] O. Trovarelli, et al., Phys. Rev. Lett. 85 (2000) 626. [2] P. Wachter, Handbook on the Physics and Chemistry of Rare Earths, Vol. 19, North-Holland, Amsterdam, 1993 (Chapter 132). [3] K. Ishida, et al., Phys. Rev. Lett. 89 (2002) 107202.
Journal of Magnetism and Magnetic Materials 272–276 (2004) 36–37
Optical conductivity of a non-Fermi-liquid material YbRh2 Si2 S. Kimuraa,b,*, T. Nishib, J. Sichelschmidtc, V. Voevodinc, J. Ferstlc, C. Geibelc, F. Steglichc a
b
UVSOR Facility, Institute for Molecular Science, Okazaki 444-8585, Japan Department of Structural Molecular Science, The Graduate University for Advanced Studies, Okazaki 444-8585, Japan c Max Planck Institute for Chemical Physics of Solids, Nothnitzer Str. 40, Dresden D-01187, Germany .
Abstract The temperature-dependent electronic structure of YbRh2 Si2 has been investigated by the optical conductivity ðsðoÞÞ measurement in the photon energy range of 10 meV–30 eV at several temperatures of 2.7–300 K: The sðoÞ spectrum as well as the electronic structure changes at two temperatures of 80 and 20 K: At 80 K; the heavy quasiparticles develop and at 20 K; the non-Fermi liquid behavior appears in the sðoÞ spectra. The behavior of YbRh2 Si2 is compared to some Landau Fermi-liquid materials. r 2003 Elsevier B.V. All rights reserved. PACS: 71.27.+a; 78.20.e Keywords: Non-Fermi liquid; Optical conductivity; YbRh2 Si2
YbRh2 Si2 shows a non-Fermi liquid (NFL) behavior in the wide temperature range of 0.1–10 K at ambient pressure and zero magnetic field [1]. Then the material is suitable for the investigation of the fundamental properties of NFL. In this study, we measured reflectivity spectra in the temperature range of 2.7–300 K and in the photon energy range of 0.01–30 eV: We investigate the NFL properties in the optical conductivity ðsðoÞÞ spectra as well as whether the sðoÞ spectrum differs from that of Landau Fermi-liquid (LFL) materials or not. The material was grown by an indium flux method. The c-plane of the tetragonal structure of the sample with a size of 0:8 0:8 0:1 mm3 was measured. The optical spectra in _o ¼ 0:01–1:5 eV was detected at eight temperatures of 2.7–300 K by using conventional FTIR spectrometers with black body light sources in Dresden and Okazaki. The spectrum in the photon energy range of _o ¼ 1:2–30 eV was obtained only at 300 K using the synchrotron radiation in Okazaki. The sðoÞ spectra
*Corresponding author. UVSOR Facility, Institute for Molecular Science, Okazaki 444-8585, Japan. Tel.: +81-56455-7202; fax: +81-564-54-7079. E-mail address: [email protected] (S. Kimura).
were obtained from the Kramers-Kronig analysis of the reflectivity spectra in _o ¼ 0:01–30 eV: The temperature dependence of sðoÞ spectrum is shown in Fig. 1. Two characteristic structures appear, one is a dip structure at around _o ¼ 0:02 eV; the other a broad peak at _o ¼ 0:2 eV: In the former structure, the extrapolation to 0 eV of the sðoÞ at 300 K seems to correspond to the sDC value. The sðoÞ curve seems to be roughly explained by a Drude model but a broad interband transition component due to the cf hybridization as discussed later appears at around 0:2 eV: However, at low temperature, the temperature dependence is the opposite to the sDC : This indicates that a steep rise sðoÞ structure close to the sDC should appear below 0:01 eV: The structure clearly originates from the creation of heavy quasiparticles due to the cf hybridization (so-called ‘‘coherent part’’). On the other hand, the structure corresponding to the latter grows up with decreasing temperature. The structure is commonly observed in dense-Kondo systems such as Ce- and Ybbased compounds, i.e., the origin is the interband transition between the bonding and antibonding cf hybridization states (‘‘incoherent part’’) [2]. The temperature dependence of the peak intensity of the incoherent part is shown in Fig. 2(a). The figure
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.11.031
ARTICLE IN PRESS S. Kimura et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 36–37
(a) Fig. 1. Temperature dependence of optical conductivity ðsðoÞÞ spectrum of YbRh2 Si2 : The direct current conductivities ðsDC Þ at 300, 20 and 2:7 K are also plotted. The sDC at 160 and 80 K are similar to that at 300 K:
indicates that the incoherent part rapidly increases with decreasing temperature from 300 to 80 K; slightly increases from 80 to 20 K and becomes almost constant below 20 K: The increase of the incoherent part indicates the growth of the cf hybridization, i.e., the cf hybridization rapidly and slightly grows up above 80 K and between 80 and 20 K; respectively, and becomes constant below 20 K: The 80 K is consistent with the temperature at which the electric resistivity turns down with decreasing temperature [1] and also the temperature dependence of the 29 Si Knight shift changes [3]. In addition, the constant cf hybridization intensity is consistent with a characteristic spin-fluctuation temperature ðB15 KÞ determined by the NMR. Next, the temperature dependence of the tail of the coherent part at around 0:02 eV is discussed. In general, the sðoÞ due to carriers is explained by the Drude model as the following, sðoÞ ¼ o2P t=4pð1 þ o2 t2 Þ: Here, oP is the plasma frequency and t the relaxation time. At frequencies ðo1 Þ being sufficiently higher than 1=t; o1 tc1: Then sðo1 Þ ¼ o2P =ð4po21 tÞp1=t: Since rp1=tpT n (n ¼ 2 for LFL, o2 for NFL), sðo1 ÞpT n : In the case of YbRh2 Si2 ; n ¼ 1:
37
(b)
Fig. 2. Temperature dependence of sðoÞ at two photon energies of 0:17 eV (a) and 0:02 eV (b) of YbRh2 Si2 : The temperature dependences of sð_o ¼ 0:17 eVÞ and sð_o ¼ 0:02 eVÞ indicate that of the cf hybridization intensity and that of the Drude tail of the heavy quasiparticles, respectively. The T-linear part, which is the evidence of the NFL character, appears below 20 K in the inset of (b).
The temperature dependence of sðoÞ at _o ¼ 0:02 eV is shown in Fig. 2(b). We recognize that the sð_o ¼ 0:02 eVÞ pT is realized below 20 K in the inset of the figure. This is consistent with the appearance of NFL character below 20 K in the electric resistivity and the specific heat [1]. This work was partially supported by a Grants-in-Aid for Scientific Research from MEXT of Japan and was a joint study program of the Institute for Molecular Science (2002).
References [1] O. Trovarelli, et al., Phys. Rev. Lett. 85 (2000) 626. [2] P. Wachter, Handbook on the Physics and Chemistry of Rare Earths, Vol. 19, North-Holland, Amsterdam, 1993 (Chapter 132). [3] K. Ishida, et al., Phys. Rev. Lett. 89 (2002) 107202.