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Specific heat of CeRu2Si2 studied by constant volume dilution
Physica B 259—261 (1999) 73—74
Specific heat of CeRu Si studied by constant volume dilution K. Matsuhira*, T. Sakakibara, K. Tenya, H. Amitsuka Division of Physics, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan
Abstract In order to study the inter-site effects in CeRu Si , we have done a series of diluting experiments under constant volume condition using the pseudo-ternary system Ce (La Y ) Ru Si . Comparing with impurity Kondo model, \V V we found that there is a non-trivial peak structure in the specific heat of CeRu Si caused by certain inter-site effect. This peak structure becomes weak with increasing x and seems to disappear at x&0.2 where metamagnetism also vanishes. 1999 Elsevier Science B.V. All rights reserved. Keywords: CeRu Si ; Specific heat; Dilution effect
The non-magnetic heavy fermion compound CeRu Si has been attracting much interest since it exhibits metamagnetism in the magnetization process in field (H &77 kOe) applied along the tetragonal c-axis [1,2]. + The metamagnetic behavior is considered to be specific to the Kondo lattice system, though its origin is not fully understood yet. In order to study the inter-site effect in CeRu Si , we have done a series of diluting experiments under constant-volume condition [3]. Since the Kondo temperature ¹ (&22 K) of this system is strongly vol) ume dependent [4], we prepared the pseudo-ternary system Ce (La Y ) Ru Si ; the unit cell volume is \V V intended to be fixed constant so that ¹ does not change ) much with x. In this paper, we report the results of the specific heat (C ) measurements. It is well known that . C of CeRu Si exhibits a broad peak at &10 K [5]. The . peak value of C is, however, substantially larger than . what is expected for S" impurity Kondo model (IKM) [5,6]. We mainly focus on this broad peak of C , and . discuss the possible origin by making a careful comparison with IKM. The samples prepared are Ce (La Y ) Ru Si \V V and LaRu Si . In the sample preparation, the starting elements were Ce (4N), La(4N), Y(3N), Ru (3N) and Si
* Corresponding author. Tel.: 81-11-706-3500; fax: 81-11-7465444; e-mail: [email protected].
(5N). Polycrystalline buttons were obtained in an Ar plasma-jet furnace. Single crystals were grown by the Czochralski method in a tri-arc furnace under purified Ar atmosphere. Specific heat measurements were done by a conventional adiabatic method at temperatures from 1.6 K up to 20 K. The 4f electronic specific heat C (¹) K. has been estimated by carefully subtracting the lattice and the non-f electronic contributions from the total specific heat using LaRu Si and x"1 as non-magnetic references [3]. The peak value of C slightly decreased with dilution. . At x"0.15, however, it is still much larger than that of IKM (&1550 mJ/K mol at ¹&¹ /2.2). Thus, there ) should be some extra contributions to C in Ce . \V (La Y ) Ru Si , for which we first consider the fol V lowing single-site mechanism. (i) Because volume thermal expansion coefficients a of CeRu Si has an extraordi4 narily large peak at &9 K, the difference between C and C (constant volume) is not negligible [7]; C is . 4 4 the quantity that should be compared with IKM. (ii) There would be a contribution of T-linear specific heat due to the Kondo effect via higher CEF levels [8]. Let us analyze the specific heat in consideration of these effects. From our results of volume thermal expansion coefficients, C !C (C ) is estimated by thermodynamic K. K4 K4 relation [3]. The estimated C and C !C of x"0 K4 K. K4 and x"0.15 are shown in Fig. 1. The maximum of C of x"0 and x"0.15 is still larger than that of S" K4
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 8 1 7 - 5
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K. Matsuhira et al. / Physica B 259—261 (1999) 73—74
Fig. 1. C /¹, C and C !C of x"0 (closed symbols) K4 K4 K. K4 and x"0.15 (open symbols). Those of IKM with ¹ "22 K ) (dashed line) are also shown. Solid (g"0.175), dashed (g"0.075) and dot-dashed (g"0) lines indicate specific heat calculated by the resonance level model using DOS in Fig. 2.
IKM with ¹ "22 K. As the magnetic entropy of the ) diluted sample given by integration of C /¹ is still K4 growing faster than that of IKM at ¹&20 K, there should be a Kondo contribution from the higher CEF levels. We tentatively estimated this T-linear contribution as &18 mJ/K mol by assuming an entropy balance; we made the magnetic entropy at ¹"20 K equal to the IKM with T-linear correction in C (dot-dashed line in 4 Fig. 1). Although this estimation procedure is rather arbitrary, we could reproduce the C for the sample of K4 x"0.2 by the single-site Kondo effect alone. Importantly, there still remains a peak structure in C of the K4 pure system over the single-site Kondo effect at around 8 K, which we believe to come from certain inter-site effect. This peak structure becomes weak with dilution, and disappears at x&0.2 where metamagnetism also vanished [3]. In the following, we show that the resonance level model [9] modified to incorporate a pseudo-gap well explains the specific heat behavior. The total density of state (DOS) is assumed to be given by a summation of two Lorentzians: o (e) with width D("¹ ) centered at ) e ("0) and o (e) with width W centered at e $E . We $ $ choose E "19 K to reproduce the peak of C at 8 K. 4 The weight for o (e) is represented by a parameter g. Good fitting parameters for x"0 (x"0.15) are obtained to be g"0.175 (g"0.075) and ¼"3.8 K. The calculated results are also shown in Fig. 1; the T-liner contribution from the higher CEF levels is already cor-
Fig. 2. Model DOS for the calculation of the specific heat with g"0 (dot-dashed line), 0.075 (dashed-line) and 0.175 (Solid line).
rected in the results. The DOS is shown in Fig. 2. As a deformation of the lattice periodicity is caused by dilution, the pseudo-gap structure is destroyed with dilution and the DOS structure becomes a simple Lorentz shape (gP0). Although this present model is a simple phenomenological one, we may well expect that a certain pseudo-gap structure exists in the quasi-particle band of CeRu Si , and plays a crucial role on the occurrence of metamagnetism. Recently, an interesting model for metamagnetism is proposed by Satoh and Ohkawa [10]. In this model the magnetic correlation changes from antiferromagnetic at zero field to ferromagnetic at around H . The pseudo+ gap structure plays a critical role on the change of magnetic correlation. Further experimental study would be needed to confirm this prediction.
References [1] P. Haen et al., J. Low Temp. Phys. 67 (1987) 391. [2] J. Flouquet et al., Physica B 215 (1995) 77. [3] K. Matsuhira et al., J. Phys. Soc. Jpn. 66 (1997) 2851. [4] J.-M. Mignot et al., J. Magn. Magn. Mater. 76 & 77 (1988) 97. [5] M.J. Besnus et al., Solid State Commun. 55 (1985) 779. [6] H.-U. Desgranges, K.D. Schotte, Phys. Lett. 91A (1982) 240. [7] A. Lacerda et al., Phys. Rev. B 40 (1989) 8759. [8] S.P. Strong, A.J. Millis, Phys. Rev. B 50 (1994) 12611. [9] K.D. Schotte, U. Schotte, Phys. Lett. 55A (1975) 38. [10] H. Satoh, F.J. Ohkawa, Phys. Rev. B 57 (1998) 5891.
Specific heat of CeRu Si studied by constant volume dilution K. Matsuhira*, T. Sakakibara, K. Tenya, H. Amitsuka Division of Physics, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan
Abstract In order to study the inter-site effects in CeRu Si , we have done a series of diluting experiments under constant volume condition using the pseudo-ternary system Ce (La Y ) Ru Si . Comparing with impurity Kondo model, \V V we found that there is a non-trivial peak structure in the specific heat of CeRu Si caused by certain inter-site effect. This peak structure becomes weak with increasing x and seems to disappear at x&0.2 where metamagnetism also vanishes. 1999 Elsevier Science B.V. All rights reserved. Keywords: CeRu Si ; Specific heat; Dilution effect
The non-magnetic heavy fermion compound CeRu Si has been attracting much interest since it exhibits metamagnetism in the magnetization process in field (H &77 kOe) applied along the tetragonal c-axis [1,2]. + The metamagnetic behavior is considered to be specific to the Kondo lattice system, though its origin is not fully understood yet. In order to study the inter-site effect in CeRu Si , we have done a series of diluting experiments under constant-volume condition [3]. Since the Kondo temperature ¹ (&22 K) of this system is strongly vol) ume dependent [4], we prepared the pseudo-ternary system Ce (La Y ) Ru Si ; the unit cell volume is \V V intended to be fixed constant so that ¹ does not change ) much with x. In this paper, we report the results of the specific heat (C ) measurements. It is well known that . C of CeRu Si exhibits a broad peak at &10 K [5]. The . peak value of C is, however, substantially larger than . what is expected for S" impurity Kondo model (IKM) [5,6]. We mainly focus on this broad peak of C , and . discuss the possible origin by making a careful comparison with IKM. The samples prepared are Ce (La Y ) Ru Si \V V and LaRu Si . In the sample preparation, the starting elements were Ce (4N), La(4N), Y(3N), Ru (3N) and Si
* Corresponding author. Tel.: 81-11-706-3500; fax: 81-11-7465444; e-mail: [email protected].
(5N). Polycrystalline buttons were obtained in an Ar plasma-jet furnace. Single crystals were grown by the Czochralski method in a tri-arc furnace under purified Ar atmosphere. Specific heat measurements were done by a conventional adiabatic method at temperatures from 1.6 K up to 20 K. The 4f electronic specific heat C (¹) K. has been estimated by carefully subtracting the lattice and the non-f electronic contributions from the total specific heat using LaRu Si and x"1 as non-magnetic references [3]. The peak value of C slightly decreased with dilution. . At x"0.15, however, it is still much larger than that of IKM (&1550 mJ/K mol at ¹&¹ /2.2). Thus, there ) should be some extra contributions to C in Ce . \V (La Y ) Ru Si , for which we first consider the fol V lowing single-site mechanism. (i) Because volume thermal expansion coefficients a of CeRu Si has an extraordi4 narily large peak at &9 K, the difference between C and C (constant volume) is not negligible [7]; C is . 4 4 the quantity that should be compared with IKM. (ii) There would be a contribution of T-linear specific heat due to the Kondo effect via higher CEF levels [8]. Let us analyze the specific heat in consideration of these effects. From our results of volume thermal expansion coefficients, C !C (C ) is estimated by thermodynamic K. K4 K4 relation [3]. The estimated C and C !C of x"0 K4 K. K4 and x"0.15 are shown in Fig. 1. The maximum of C of x"0 and x"0.15 is still larger than that of S" K4
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 8 1 7 - 5
74
K. Matsuhira et al. / Physica B 259—261 (1999) 73—74
Fig. 1. C /¹, C and C !C of x"0 (closed symbols) K4 K4 K. K4 and x"0.15 (open symbols). Those of IKM with ¹ "22 K ) (dashed line) are also shown. Solid (g"0.175), dashed (g"0.075) and dot-dashed (g"0) lines indicate specific heat calculated by the resonance level model using DOS in Fig. 2.
IKM with ¹ "22 K. As the magnetic entropy of the ) diluted sample given by integration of C /¹ is still K4 growing faster than that of IKM at ¹&20 K, there should be a Kondo contribution from the higher CEF levels. We tentatively estimated this T-linear contribution as &18 mJ/K mol by assuming an entropy balance; we made the magnetic entropy at ¹"20 K equal to the IKM with T-linear correction in C (dot-dashed line in 4 Fig. 1). Although this estimation procedure is rather arbitrary, we could reproduce the C for the sample of K4 x"0.2 by the single-site Kondo effect alone. Importantly, there still remains a peak structure in C of the K4 pure system over the single-site Kondo effect at around 8 K, which we believe to come from certain inter-site effect. This peak structure becomes weak with dilution, and disappears at x&0.2 where metamagnetism also vanished [3]. In the following, we show that the resonance level model [9] modified to incorporate a pseudo-gap well explains the specific heat behavior. The total density of state (DOS) is assumed to be given by a summation of two Lorentzians: o (e) with width D("¹ ) centered at ) e ("0) and o (e) with width W centered at e $E . We $ $ choose E "19 K to reproduce the peak of C at 8 K. 4 The weight for o (e) is represented by a parameter g. Good fitting parameters for x"0 (x"0.15) are obtained to be g"0.175 (g"0.075) and ¼"3.8 K. The calculated results are also shown in Fig. 1; the T-liner contribution from the higher CEF levels is already cor-
Fig. 2. Model DOS for the calculation of the specific heat with g"0 (dot-dashed line), 0.075 (dashed-line) and 0.175 (Solid line).
rected in the results. The DOS is shown in Fig. 2. As a deformation of the lattice periodicity is caused by dilution, the pseudo-gap structure is destroyed with dilution and the DOS structure becomes a simple Lorentz shape (gP0). Although this present model is a simple phenomenological one, we may well expect that a certain pseudo-gap structure exists in the quasi-particle band of CeRu Si , and plays a crucial role on the occurrence of metamagnetism. Recently, an interesting model for metamagnetism is proposed by Satoh and Ohkawa [10]. In this model the magnetic correlation changes from antiferromagnetic at zero field to ferromagnetic at around H . The pseudo+ gap structure plays a critical role on the change of magnetic correlation. Further experimental study would be needed to confirm this prediction.
References [1] P. Haen et al., J. Low Temp. Phys. 67 (1987) 391. [2] J. Flouquet et al., Physica B 215 (1995) 77. [3] K. Matsuhira et al., J. Phys. Soc. Jpn. 66 (1997) 2851. [4] J.-M. Mignot et al., J. Magn. Magn. Mater. 76 & 77 (1988) 97. [5] M.J. Besnus et al., Solid State Commun. 55 (1985) 779. [6] H.-U. Desgranges, K.D. Schotte, Phys. Lett. 91A (1982) 240. [7] A. Lacerda et al., Phys. Rev. B 40 (1989) 8759. [8] S.P. Strong, A.J. Millis, Phys. Rev. B 50 (1994) 12611. [9] K.D. Schotte, U. Schotte, Phys. Lett. 55A (1975) 38. [10] H. Satoh, F.J. Ohkawa, Phys. Rev. B 57 (1998) 5891.