We have recently shown that CeRhSn exhibits non-Fermi liquid temperaturę dependences in its low-temperature physical properties. Here we suggest that the non-Fermi liquid behavior observed in CeRhSn may be due to the existence of a Griffiths phase in the vicinity of a quantum critical point, based on electrical resistivity, magnetic susceptibility, and specific heat measurements. For CeRhSn, the low-temperature scaling of bulk
properties (C/T oc y oc T _1+A, where A < 1) is masked by an anomaly at about 6 K, which is of magnetic origin

Ho, P.-C.

Maple, M. B.

Zawada, T.

Ślebarski, Andrzej

Acta Physica Polonica B

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             Title: Non-fermi liquid scaling in CeRhSn  Author: Andrzej Ślebarski, T. Zawada, M.B. Maple, P.-C. Ho  Citation style: Ślebarski Andrzej, Zawada T., Maple M.B., Ho P.-C. (2003). Non-fermi liquid scaling in CeRhSn."Acta Physica Polonica B"(Vol. 34, no. 2 (2003), s. 1295-1298).   N O N -FERM I LIQUID SCALING IN CeRhSn*A. S l e b a r s k i ,  T . Z a w a d aInstitute of Physics, University of Silesia Uniwersytecka 4, 40-007 Katowice, PolandM .B . M a p l e  a n d  P .-C . H oDepartment of Physics and Institute for Pure and Applied Physical Sciences University of California, San Diego, La Jolla, CA 92093-0360, USA(Received July 10, 2002)We have recently shown that CeRhSn exhibits non-Fermi liquid tem­perature dependences in its low-temperature physical properties. Here we suggest that the non-Fermi liquid behavior observed in CeRhSn may be due to the existence of a Griffiths phase in the vicinity of a quantum crit­ical point, based on electrical resistivity, magnetic susceptibility, and spe­cific heat measurements. For CeRhSn, the low-temperature scaling of bulk properties (C /T  oc y oc T _1+A, where A < 1) is masked by an anomaly at about 6 K, which is of magnetic origin.PACS numbers: 71.27.+a, 71.30.Mb, 75.20.Hr, 72.15.QmTheoretical models of the non-Fermi liquid (NFL) behavior based on single im purity mechanisms include a multichannel Kondo effect of magnetic [1,2] or electric origin [3] and a conventional Kondo effect with a distribution of Kondo tem peratures due to  chemical disorder [4,5]. Theoretical models which incorporate interionic interactions include fluctuations of an order param eter in the vicinity of a second-order phase transition at 0 K (quantum  critical point (QCP)) [6-12] and an inhomogeneous Griffiths phase [13]. The Griffiths phase [14] consists of magnetic clusters in a param agnetic phase and forms as a result of the com petition between the Kondo effect and the RKKY interaction in the presence of disorder. Castro Neto et a l ,  [13] conclude th a t the specific heat and magnetic susceptibility follow a power law 7  =  C ( T ) / T  ex x (T ) c* T -1+A (where A <  1), due to the existence of a Griffiths phase close to a QCP. We recently investigated the compound* Presented a t th e  International Conference on Strongly Correlated Electron Systems, (SCES02), Cracow, Poland, July 10-13, 2002.CeRhSn which exhibits NFL behavior [15-17]. The electrical resistivity and magnetic susceptibility have power law tem perature dependences at low tem peratures with small exponents p(T )  oc T 0-75 and x (T ) oc T -0 -5, and y  =  C ( T ) / T  oc — In T  (the la tte r over a lim ited tem perature range). Experim ental comparisons to the theory of Castro Neto et al., have been m ade and will be discussed below.The specific heat da ta  for non-annealed CeRhSn (sample (a)) and for CeRhSn samples annealed for 4 days (sample (6)) and 8 days (sample (c)) are displayed as C / T  versus In T  in Fig. 1. The high tem perature spe­cific heat d a ta  are very similar for all the samples investigated [16] while, a t tem peratures lower then about 6.2 K, the magnetic contribution to  the specific heat is strongly dependent on the amount of atomic disorder. As­suming th a t the crystalline electric field ground sta te  is a doublet, the to tal m agnetic entropy per formula unit of CeRhSn is 7?ln2 =  5.76 Jm ol-1 K - 2 . The small peak in the specific heat of CeRhSn observed at Tn represents an extremallv small fraction ~ (T \ /11 \u 2 which is respectively ~  0.12, 0.06, and0.02 of entropy i? In 2 at the phase transition for sample (a), (6), and (c). At present, we do not know whether the observed anomalies reflect long-range order of the small magnetic moments or whether they should be attribu ted  to  the other correlation effects, e.g., spin-glass behavior. We have not seen any magnetic order within a limit for an ordered moment of about 0.25 P b , using a high-resolution neutron spectrom eter [16]. Some type of static m agnetic order in CeRhSn with tiny ordered moments less than  0.1 p B is probably due to  subtle structural defects.Fig. 1 reveals th a t C / T  varies as T - ” below 2 K for sample (a) and (6) (see Table I), while it varies as T - ” between 1.5 K and 5 K for CeRhSn an­nealed for 8 days (sample (c)). The best fit of the expression C (T )  / T  =  c T ^ n to  the da ta  yields n  =  0.54 for sample (a), n  =  0.39 for sample (6) andTABLE IComparison of electrical resistivity Ap, magnetic susceptibility x, and specific heatC  data for CeRhSn polycrystalline samples: unannealed (a), annealed for 4 days (6), and for 8 days (c).CeRhSn A p  = Ap(0)[l + (T /T o)n] X oc y - l + A C /T oc T -1+AAp(  0) T0 n T-range A T -range A T -range[pOcm] [K] M M M(a) 47.50 6.8 0.73 1.8-25 0.60 1.8-6 0.46 0.6-2(6) 32.0 3.6 0.75 1.8-25 0.65 1.8-6 0.61 0.6-2(c) 30.38 3.5 0.71 1.8-25 0.49 0.4-4.2 0.65 1.5-5T ( K )0 5 10 15T ( K )Fig. 1. Upper part: Specific heat C  divided by T, C /T ,  versus ln T  for three CeRhSn samples (sample (a) unannealed; samples (6) and (c) annealed for 4 and 8 days, respectively) [16]. The C / T  data were fitted by the formula C (T ) /T  = c T ^ n in the range T  < 2K for samples (a) and (6), and in the range 1.5 < T  < 5K for sample (c). The fits are represented by solid lines. The values of c are, respectively: 246.4 mJmol-1K-3 , 235.9mJmol-1K-3 , and 195.8mJmol-1K-3 for samples (a), (6), and (c). The n values are listed in Table I. Lower part: Magnetic susceptibility X versus T  on a double logarithmic plot and the incremental electrical resistivity ú p  = p(CeRhSn) —p(LaRhSn) versus T  for a CeRhSn sample annealed for 8 days (sample (c)). The solid line represents the fit of the expression Ap(T) = A p(0) [1 +  a(T /T k)”] to the data with n = 0.74, A p(0) =  32.2 gilcm, a = 13.9 and Tk = 145K (Tk is the Kondo temperature). The straight line represents the relation x oc T ^ n.n  =  0.35 for sample (c). A noticeable deviation of the C / T  d a ta  from linearity in logT at T  < 1.5 K (sample (c)) is not expected for a NFL. How­ever, a number of systems have been reported (e.g., Ce(Ruo.7Rho.3)2SÍ2 [18], U(Pto.94Pdo.o6)3 [19]) UCU3AI2 [20]) which show NFL behavior coexistent with magnetic order. These systems show m agnetic behavior in the middleor even above the tem perature range where C /T  cx ln T  or T ^ n , and do not fit the picture of the QCP [8]. It is possible th a t the NFL tem perature dependences of p (T ),  x (T ), and C (T )  for disordered CeRhSn in the low- tem perature region are related to the proximity of a magnetically ordered sta te  th a t depends on the degree of atomic order. The param eters obtained from the best fits (Table I) are consistent with the presence of a Griffiths phase a t very low tem peratures i.e. C / T  cx x  cx T -1+A, with A < 1.Two of us (AS and TZ) would like to thank  the Polish S tate Commit­tee for Scientific Research (KBN) for financial support from project No. 5 P03B07920. Research at UCSD was supported by the U.S. Departm ent of Energy under G rant No. DE-FG03-86ER-15230. ‘REFERENCES(1] P. Nozieres, A. Blandin, J. Phys. 41, 193 (1983).(2] A.M. Tsvelik, J. Phys. C 1 8 , 159 (1985).(3] D.L. Cox, Phys. Rev. Lett. 59, 1240 (1987).(4] O.O. Bernal, D.E. M acLaug h lin , H.G. Lukefahr, B. Andraka, Phys. Rev. Lett. 75, 2023 (1995).(5] E. Miranda, V. D obrosavljevic, G. Kotliar, J. Phys. Condens. Matter 8, 9871 (1996).(6] T. Moriya, Spin Fluctuations in Itinerant Magnetism, Springer, Berlin 1985.(7] B. Andraka, A.M. Tsvelik, Phys. Rev. Lett. 6 7 ,  2886 (1991).(8] A.J. Mills, Phys. Rev. B 4 8 , 7183 (1993).(9] M.A. Continentino, Phys. Rev. B 4 7 ,  11587 (1993).[10] A.M. Tsvelik, M. Reizer, Phys. Rev. B 4 8 , 9887 (1993).[11] T. Moriya, T. Takimoto, J. Phys. Soc. Jpn. 6 4 ,  960 (1995).[12] S. Sachdev, N. Read, R. Oppermann, Phys. Rev. B 5 2 ,  10286 (1995).[13] A.H. Castro Neto, G. Castilla, B.A. Jones, Phys. Rev. Lett. 81, 3531 (1998).[14] R.B. Griffiths, Phys. Rev. Lett. 2 3, 17 (1969).[15] A. Slebarski, A. Jezierski, M.B. Maple, A. Zygmunt, Acta Phys. Pol. B  32, 3331 (2001).[16] A. Slebarski, M.B. Maple, E.J. Freeman, C. Sirvent, M . Radlowska, A. Jezier­ski, E. Granado, Q. Huang, J.W. Lynn, Phil. Mag. B 8 2 , 943 (2002).[17] A. Slebarski, N.A. Frederick, M.B. Maple, Phil. Mag. B , to be published.[18] T. Taniguchi, Y. Tabata, H. Tanabe, Y. M iyako, J. Magn. Magn. Mater. 1 7 7 ,419 (1998).[19] J.S. Kim, B. Andraka, G.R. Stewart, Phys. Rev. B 4 5 ,  12081 (1992).[20] H. Nakotte, K. Prokes, E.B. Brück, K.H.J. Buschow, F.R. de Boer, A.V. An­dreev, M.C. Aronson, A. Lacerda, M.S. T orikachvili, R.A. Robinson, M.A.M. Bourke, A.J. Schultz, Phys. Rev. B 5 4 ,  12176 (1996).

Non-fermi liquid scaling in CeRhSn

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Non-fermi liquid scaling in CeRhSn

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