Pressure dependence of the Néel and the superconducting transition temperature of CeCo(In0.9Cd0.1)5 studied by thermal expansion

We present low-temperature thermal expansion measurements on the nominally 10% Cd doped CeCoIn5. While the superconducting transition temperature is monotonically suppressed, an antiferromagnetic phase evolves in CeCoIn5 by Cd-doping. For the uniaxial pressure dependence of the Néel temperature along c, we find ðqTN=qpÞkc 1⁄4 0:206K=GPa. The magnetic field dependence (for Bkc) of TN is stronger compared to CeRhIn5. As no traces of a superconducting transition are resolved in thermal expansion along the c-axis, we estimate a lower limit of the in-plane pressure dependence to ðqT c=qpÞ?c 1⁄4 0:38K=GPa. r 2007 Elsevier B.V. All rights reserved. PACS: 75.30. m; 75.30.Kz; 75.50.Ee; 74.25.Bt; 74.62.Yb; 74.70.Tx


Introduction
The tetragonal CeMIn 5 ðM ¼ Co; Rh; IrÞ family of heavy fermion compounds is ideally suited to study the interplay of magnetic and superconducting (SC) ground states. While CeRhIn 5 orders antiferromagnetically (AFM) below T N ¼ 3:8 K [1], CeIrIn 5 [2], and CeCoIn 5 [3] superconduct below T c ¼ 0:4 and 2.3 K, respectively. The observed non-Fermi liquid behavior in the Co-115 close to the upper critical field of the superconductivity is believed to originate from a magnetic quantum critical point which coincides with the upper critical field for superconductivity [4,5]. By doping Cd on the In-sites, CeCoIn 5 can be driven to an AFM ground state and shows superconductivity below T c % 1:3 K. In a wide range of concentration and pressure, both, SC and AFM coexist [6].

Results
Here, we present thermal expansion measurements on CeCo(In 0.9 Cd 0.1 ) 5 , which orders AFM commensurate with the crystal lattice at T N % 3 K [7]. The magnetic intensity below T c % 1:3 K, where superconductivity is observed in electrical resistivity and specific heat, changes only marginal which points to a coexistence of AFM and SC [8]. The nominally 10% Cd-doped sample can be considered to be shifted by 1.6 GPa with respect to CeRhIn 5 derived from the temperature pressure phase diagram for the latter [6].
The uniaxial thermal expansion coefficient along the c-direction a kc was obtained by means of a high resolution capacitive dilatometer adapted to a 3 He/ 4 He dilution refrigerator. Its relative resolution of up to 10 À11 allows to study pressure dependences of the Ne´el temperature and the SC transition temperature most sensitively.
Previous specific heat studies showed that T c is monotonically suppressed by Cd doping and vanishes at x % 0:15. Simultaneously, antiferromagnetism appears at x % 0:05 and the Ne´el temperature increases as x increases. In Fig. 1, the magnetic contribution to the specific heat is shown, measured in a commercial physical property measurement system (PPMS, quantum design). A lambda-like anomaly, indicative for a second order phase transition is detected at T N . A second, much smaller anomaly marks the onset of superconductivity. In the right part of Fig. 1, the thermal expansion parallel to the c-direction vs. temperature is plotted. The Ne´el temperature T N % 3 K is in good agreement with the aforementioned results of CðTÞ. An SC phase transition, however, could not be resolved at lower temperatures.
Assuming a scattering of Da % 0:2 Â 10 À6 =K of the data at T c % 1:3 K, a lower limit of the uniaxial pressure dependence along c can be estimated with the Ehrenfest relation ðqT c =qpÞ ¼ V m T c ðDa=DCÞ (V m : molar volume) to ðqT c =qpÞ kc ¼ 0:040 K=GPa, whereas the jump anomaly DC has been estimated by an equal-area construction in CðTÞ=T. The hydrostatic pressure dependence of the SC transition temperature can be derived from the temperature pressure phase diagram [6,9] and is evaluated to ð0:8 AE 0:2Þ K=GPa. This leads to the conclusion, that the uniaxial in-plane pressure dependence has to be at least ðqT N =qpÞ ?c ¼ 0:38 K=GPa and accordingly a jump anomaly in the thermal expansion of a ?c ¼ 1:9 Â 10 À6 =K is expected. Further measurements are needed to confirm this prediction.
The crystal structure of the CeMIn 5 family which consists of an alternating series of CeIn 3 and MIn 2 , stacked along c, gives rise to extended 2D behavior in the physical properties. Thus, an anisotropy of the pressure dependences is expected which indeed has been observed in the isostructural compound CeRhIn 5 [10] and in undoped CeCoIn 5 . For the latter, the uniaxial pressure dependence of the SC transition temperature along c is ðqT c =qpÞ kc ¼ 0:18 K=GPa while in-plane ðqT c =qpÞ ?c ¼ 0:3 K=GPa has been found [11].
We now turn to the analysis of the antiferromagnetic phase transition. In Fig. 2, a kc is shown for various magnetic fields of B ¼ 0, 2, 4, and 7 T ðBkcÞ. The anomaly marks the temperature below which the system orders AFM. The uniaxial pressure dependence of the Ne´el temperature along c for B ¼ 0 T yields ðqT N =qpÞ kc ¼ 0:206 K=GPa. In magnetic fields (Bkc), T N is shifted to lower temperatures, similar to CeRhIn 5 , but with an about ten times stronger field dependence compared to the latter [12]. Hence, the antiferromagnetic ground state is much less stable than that of CeRhIn 5 toward external magnetic fields. Since the orientation of the magnetic moments of the Cd-doped CeCoIn 5 is not yet clarified, the origin of this difference remains unclear.

Summary
To summarize, we have studied the heavy fermion compound CeCo(In 0.9 Cd 0.1 ) 5 by low-temperature thermal expansion measurements. While the results for the Ne´el temperature are in agreement with specific heat data, no sign of the SC phase transition could be resolved. We assign this to the anisotropy of the uniaxial pressure dependences in this family of compounds. A rough estimation in terms of the Ehrenfest relation leads to an expected jump anomaly of Da ?c % 1:9 Â 10 À6 =K which needs to be verified experimentally in future measurements. The pressure dependence of the Ne´el temperature yields ðqT c =qpÞ kc ¼ 0:206 K=GPa. The suppression of T N in external magnetic fields (Bkc) is significantly stronger than for CeRhIn 5 . Fig. 1. Temperature dependence of the magnetic contribution to the specific heat C mag (left) and the uniaxial thermal expansion coefficient a kc along the tetragonal c-direction for CeCo(In 0.9 Cd 0.1 ) 5 . Fig. 2. Uniaxial thermal expansion coefficient a kc along the tetragonal cdirection for various magnetic fields for CeCo(In 0.9 Cd 0.1 ) 5 .