Physica B 259—261 (1999) 275—276
Charge fluctuation in Yb (As Sb ) \V V Y. Nemoto *, H. Aoki , T. Goto , A. Ochiai, T. Suzuki Graduate School of Science and Technology, Niigata University, Ikarashi Ninocho 8050, Niigata 950-2181, Japan Material Science and Technology, Niigata University, Niigata 950-2181, Japan The Institute for Solid State Physics, The University of Tokyo, Tokyo 106-8666, Japan
Abstract We present ultrasonic velocity and attenuation measurements of the Sb-substituted compounds Yb (As Sb ) , \V V x"0, 0.12, 0.24, 0.29. The results of our experiments reveal that the one-dimensional charge ordering of Yb> along [1 1 1] direction in Yb As changes into a charge glass order in Yb (As Sb ) . 1999 Elsevier Science B.V. All rights reserved. Keywords: Yb (As Sb ) ; Elastic constant; Charge ordering; Charge glass \V V
Mixed valence compound Yb As with very low car rier density undergoes a structural phase transition at ¹ "292 K from a cubic lattice with the space group ¹ to a trigonal lattice with C associated with the charge ordering of Yb> and Yb> ions . Ultrasonic measurements  showed that the transverse elastic constant C with ! symmetry exhibits a large softening of 18% below 400 K down to ¹ "292 K, whereas no softening has been found near ¹ in the bulk modulus C "(C #2C )/3 with ! symmetry and the trans verse mode (C !C )/2 with ! symmetry. Thus, it is reasonable to assume that the order parameter Q , Q , WX XV Q with ! symmetry corresponding to the charge flucVW tuation mode gives rise to the one-dimensional linear chain of Yb> ions along the body diagonal [1 1 1] direction in the trigonal phase. In order to examine the charge ordering in the Sbsubstituted compounds Yb (As Sb ) , the electric \V V resistivity, the magnetic susceptibility and the Hall coefficient have been measured . The charge ordering temperature ¹ decreases with increasing Sb concentration x. In this work, we present ultrasonic velocity and attenuation measurements on the compounds Yb (As Sb ) , \V V x"0, 0.12, 0.24, 0.29. * Corresponding author. Tel.: #81-25-262-6136; fax: #8125-262-6135; e-mail: [email protected]
Fig. 1 displays the temperature dependence of the transverse elastic constant C for Yb (As Sb ) , \V V x"0, 0.12, 0.24, 0.29. The elastic constant C"ov is easily obtained from the density o. Below 400 K the C mode of Yb As exhibits a remarkable softening of 18% towards ¹ "292 K. The ultrasonic echo suddenly vanishes due to discontinuous increase of the ultrasonic attenuation indicating the first-order phase transition . The charge ordering of Yb (As Sb ) shifts to lower temperature side at ¹ "231 K and C shows more pronounced softening of 34% below 350 K down to ¹ "231 K. For both compounds of Yb (As Sb ) \V V with x"0, 0.12, the temperature dependence of C above ¹ can be well fitted by the Curie-Wiess law ¹!¹ , C "C (1) ¹!H
obtained from the free energy F assuming a bilinear coupling of the order parameter Q , Q , Q and the WX XV VW elastic strain e , e , e . In the case of Yb (As Sb ) WX XV VW the charge ordering temperature shifts to lower side at ¹ "120 K. The softening of C below 340 K is reduced to 25%. The temperature dependence of C in Yb (As Sb ) above ¹ deviates from the Curie—Weiss law of Eq. (1). In Yb (As Sb ) the transition temperature ¹ becomes unclear and the softening of C below 350 K has a tendency to further reduce. In this sample it
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 9 2 5 - 9
Y. Nemoto et al. / Physica B 259—261 (1999) 275—276
elastic constant C for Yb (As Sb ) . The observed pronounced ultrasonic dispersion indicates that the relaxation of the charge fluctuation in Yb (As Sb ) is of thermal activation type. Assuming the charge fluctuation with a single relaxation time q(E), attenuation a reads S
G(E)uq(E) *C dE . a " S 2ov 1#uq(E)
Fig. 1. Temperature dependence of the elastic constant C for Yb (As Sb ) , x"0, 0.12, 0.24, 0.29. \V V
Fig. 2. Temperature dependence of the ultrasonic attenuation up to 102 MHz and of the longitudinal elastic constant C for Yb (As Sb ) . The inset shows different kind of fits of the relaxation time q.
is remarkable that an additional weak softening between 200 and 90 K appears in the longitudinal mode C and in the transverse mode (C !C )/2 which is not ob served for the compounds with x"0, 0.12 and 0.24. Furthermore, the difference of the temperature variation among elastic modes changes to be small. Fig. 2 shows the temperature dependence of the ultrasonic attenuation up to 102 MHz and of the longitudinal
Here, *C is a variation of the elastic constant between, before and after a chrage relaxation, u is a frequency of the sound wave. In the present analysis we adopt a Gaussian type as a distribution function G(E) for the activation energy E. As shown in the inset of Fig. 2 fits of the relaxation time q"q exp(E/k¹) yields a characteristic time q with 10\—10\ s and a center of the activation energy distribution E with 0.037—0.039 eV. At low tem peratures the charge fluctuation time gets as slow as 10\ s. In the case of mixed valence compounds of Sm X (X"S, Se, Te) with Th P structure, there is no charge ordering of Sm> and Sm>. At low temperatures specific heats of Sm Se and Sm Te show a broad maximum and the magnetization curve does a pronounced hysteresis of the field-cooling and zero-fieldcooling process reflecting the metastable state for spin glass ordering in Sm Te . We measured the ultra sonic properties for Sm Se  and Sm Te , the elastic constants C , (C —C )/2 and C exhibit the same temperature dependence and the remarkable ultrasonic dispersion around 150 K indicating the random distribution of Sm> and Sm>. These ultrasonic results for Sm Se and Sm Te resembles well the one for the sub stituted compound of Yb (As Sb ) . Thus, the present results of our experiments reveal that the onedimensional charge ordering of Yb> linear chains in Yb As changes into a charge glass order in Yb (As Sb ) . References  A. Ochiai, T. Suzuki, T. Kasuya, J. Phys. Soc. Japan 59 (1990) 4129.  T. Goto, Y. Nemoto, S. Nakamura, A. Ochiai, T. Suzuki, Physica B 230—232 (1997) 702.  H. Aoki, A. Ochiai, T. Suzuki, R. Helfrich, F. Steglich, Physica B 230—232 (1997) 698.  T. Tayama, K. Tenya, H. Amitsuka, T. Sakakibara, A. Ochiai, T. Suzuki, J. Phys. Soc. Japan 65 (1996) 3467.  A. Tamaki, T. Goto, S. Kunii, T. Suzuki, T. Fujimura, T. Kasuya, J. Phys. C 18 (1985) 5849.