- Email: [email protected]
Heat capacity of CeCu2Si2 under hydrostatic pressure
ARTICLE IN PRESS
Physica B 378–380 (2006) 415–416 www.elsevier.com/locate/physb
Heat capacity of CeCu2Si2 under hydrostatic pressure E. Lengyel, G. Sparn, M. Nicklas, H.S. Jeevan, C. Geibel, F. Steglich Max Planck Institute for Chemical Physics of Solids,No¨thnitzerstr. 40, 01187 Dresden, Germany
Abstract We present low temperature ð0:4 KoTo2 KÞ heat capacity measurements under hydrostatic pressure (po2:1 GPa) and in magnetic fields (Bp8 T) on a single crystal of the heavy-fermion compound CeCu2Si2. At ambient pressure, our A=S type single crystal orders antiferromagnetically (AFM) at T N 0:7 K and superconducts below a slightly lower temperature T c 0:5 K. Application of only a small pressure (p 0:1 GPa) suppresses the long-range AFM order and rapidly shifts the superconducting transition temperature to T c 0:62 K. Upon further increasing pressure T c ðpÞ reveals a shallow minimum at p 1:6 GPa from where it starts to increase again, indicating the entrance into the high-pressure superconducting region. r 2006 Elsevier B.V. All rights reserved. PACS: 71.27.þa; 74.62.Fj; 75.20.Hr Keywords: Heavy Fermion; Heat capacity; Hydrostatic pressure
CeCu2Si2, the first discovered heavy-fermion superconductor (SC) [1], shows a fascinating interplay between magnetism and superconductivity. Systematic investigations on the ternary chemical Ce–Cu–Si phase diagram revealed the existence of four different ground states in the narrow homogeneity range of the 1:2:2 phase [2]. The Curich samples become superconducting (S type), the Cudeficient samples exhibit a magnetic phase (A type), while a higher Cu deficiency produces a sample (X type) showing neither the A phase nor superconductivity down to the lowest accessible temperature. In an intermediate range, in between the S and the A type samples, one can find a so-called A/S type CeCu2Si2 which exhibits an AFM phase transition at a transition temperature T N and upon further cooling becomes superconducting at a SC transition temperature T c (T c oT N ). Recent neutrondiffraction studies on CeCu2Si2 have identified the A phase as an incommensurate (IC) spin-density-wave phase with a rather low magnetic moment of about 0:1 mB per Ce atom [3].
Corresponding author. Tel.: +49 351 4646 2424; fax: +49 351 4646 2402. E-mail address: [email protected] (E. Lengyel).
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.01.145
Several Ce-based heavy-fermion (HF) SC show a generic phase diagram where the AFM order is suppressed to zero temperature by increasing the hybridization between the Ce 4f-electrons and the conduction electrons leading to the appearance of an antiferromagnetic quantum critical point (AFM QCP) (e.g., CePd2Si2) [4]. In these materials SC appears around this AFM QCP. In contrast to this generic picture, CeCu2Si2 shows a broad SC region which extends up to higher hybridization strengths, far away from the AFM QCP. High-pressure studies on the nonstoichiometric compound CeCu2 ðSi1x Gex Þ2 (xa0; 1), where disorder by doping on the Si/Ge site plays a crucial role in destroying the Cooper pairs and in reducing the SC transition temperature T c , have made clear the origin of this anomalous phase diagram [5]. It was found that in addition to the SC dome located close to the AFM QCP there exists a second SC dome at the high-pressure side, associated with a weakly first-order valence transition of Ce. However, in the stoichiometric compounds CeCu2Si2 and CeCu2Ge2 the two SC regions seem to merge into a single, wide SC region. It is suggested that SC in the lowpressure regime is mediated by spin-density fluctuations while in the high-pressure regime, away from the magnetically ordered phase, charge–density fluctuations are responsible for the electron pairing [5].
ARTICLE IN PRESS E. Lengyel et al. / Physica B 378–380 (2006) 415–416
416
C / T (J/molK2)
1.2 1.0
p (GPa) 0 0.06 0.26 0.73 1.07 1.39 1.96
0.7 TN, Tc (K)
1.4
TN 0.6 Tc 0.5 0
0.5
1.0
1.5
2.0
p (GPa)
0.8 0.6 0.4 0.4
0.8
1.2
1.6
T (K) Fig. 1. Specific heat of CeCu2Si2 as C=T versus T for pressures as indicated in the figure. The inset shows the evolution of the Ne´el temperature T N and of the SC transition temperature T c function of pressure.
Large single crystals of CeCu2Si2, with well-defined ground-state properties, became recently available. The single crystals are grown in aluminum-oxide crucibles by a modified Bridgman technique, using Cu excess as flux medium [6]. Powder X-ray diffraction patterns confirmed the proper tetragonal ThCr2Si2 structure with lattice parameters a 0:4102 nm and c 0:9930 nm at room temperature. Measurements of the heat capacity under hydrostatic pressure have been performed in a 3He cryostat by a quasiadiabatic heat-pulse technique. Measurements at low pressure (po1:1 GPa) were carried out in a CuBe piston-cylinder pressure cell, while for the high-pressure range (pX1:1 GPa) we utilized a double layer NiCrAl– CuBe type piston-cylinder pressure cell. For the entire experiment, Flourinert FC72 was used as a pressure transmitting medium. For our measurements we have chosen a large A/S type single crystal with a mass of about 400 mg. The applied magnetic field was oriented parallel to the c-axis. The low-temperature specific heat of the A/S type single crystal of CeCu2Si2 is displayed in Fig. 1 as C=T versus T at various pressures and in zero magnetic field. As it is shown in the ambient pressure data, the system undergoes two subsequent phase transitions, a magnetic one at T N 0:7 K, which indicates the entrance into the IC AFM state and a transition to a superconducting state, at T c 0:5 K. A small increase in pressure, of about 0.06 GPa, is enough to shift the two-phase transitions very close to each other to T N 0:62 K and T c 0:60 K.
Further increasing pressure leads to the increase of the SC transition temperature. Once T c becomes greater than the AFM transition temperature the presence of the AFM order cannot be detected anymore, except by application of a magnetic field high enough to suppress SC in the system (e.g., at p 0:09 GPa for B ¼ 2 T we find T N 0:41 K). This behavior, in good agreement with the results obtained by mSR measurements [7], could be interpreted in favor of the competition between AFM and SC order in this compound. On increasing the pressure to higher values (see inset in Fig. 1), the SC transition temperature reaches a maximum value of T c 0:63 K at about p 0:26 GPa and decreases then slightly up to p 1:6 GPa, from where it starts to increase again, marking the entrance into the second SC region. The effect of pressure on Ce-based HF compounds is to increase the hybridization strength of the 4f-electrons with the conduction electrons. A high enough pressure leads to a partial delocalization of the 4f-electrons, replacing the HF state by a mixed valence state. The transition from the HF state to the mixed valence state might be a first-order phase transition accompanied by a symmetry-conserving collapse of the unit-cell volume [8]. The effective mass of the quasiparticles is a good measure of such an effect. Our experiments show that for the lowpressure range, pp1:6 GPa,C=T, taken at T ¼ 0:9 K, decreases with dðlnðC=TÞÞ=dp 0:39=GPa while for the high-pressure region 1:6ppp2:1 GPa dðlnðC=TÞÞ=dp 0:21=GPa. The reduction of dðlnðC=TÞÞ=dp, at p 1:6 GPa, in the region where the SC transition temperature starts to increase, might indicate a smooth transition from the HF state to a metallic state with an increased electronic density of states. The existence of a broad region of SC with different electronic properties in different pressure regions supports the existence of two distinct pairing mechanisms in the two merging SC regions of CeCu2Si2. This work was partly supported by the SFB 463. We thank Prof. T. Matsumoto for supplying the NiCrAl alloy for the pressure cell. References [1] [2] [3] [4] [5] [6] [7] [8]
F. Steglich, et al., Phys. Rev Lett. 43 (1979) 1892. R. Modler, et al., Physica B 206 & 207 (1995) 586. O. Stockert, et al., Phys. Rev. Lett. 92 (2004) 136401. F.M. Grosche, et al., J. Phys.: Condens. Matter 13 (2001) 2845. H.Q. Yuan, et al., Science 302 (2003) 2104. H.S. Jeevan, unpublished. R. Feyerherm, et al., Phys. Rev. B 56 (1997) 699. J. Roehler, et al., J. Magn. Magn. Mater. 76 & 77 (1988) 340.
Physica B 378–380 (2006) 415–416 www.elsevier.com/locate/physb
Heat capacity of CeCu2Si2 under hydrostatic pressure E. Lengyel, G. Sparn, M. Nicklas, H.S. Jeevan, C. Geibel, F. Steglich Max Planck Institute for Chemical Physics of Solids,No¨thnitzerstr. 40, 01187 Dresden, Germany
Abstract We present low temperature ð0:4 KoTo2 KÞ heat capacity measurements under hydrostatic pressure (po2:1 GPa) and in magnetic fields (Bp8 T) on a single crystal of the heavy-fermion compound CeCu2Si2. At ambient pressure, our A=S type single crystal orders antiferromagnetically (AFM) at T N 0:7 K and superconducts below a slightly lower temperature T c 0:5 K. Application of only a small pressure (p 0:1 GPa) suppresses the long-range AFM order and rapidly shifts the superconducting transition temperature to T c 0:62 K. Upon further increasing pressure T c ðpÞ reveals a shallow minimum at p 1:6 GPa from where it starts to increase again, indicating the entrance into the high-pressure superconducting region. r 2006 Elsevier B.V. All rights reserved. PACS: 71.27.þa; 74.62.Fj; 75.20.Hr Keywords: Heavy Fermion; Heat capacity; Hydrostatic pressure
CeCu2Si2, the first discovered heavy-fermion superconductor (SC) [1], shows a fascinating interplay between magnetism and superconductivity. Systematic investigations on the ternary chemical Ce–Cu–Si phase diagram revealed the existence of four different ground states in the narrow homogeneity range of the 1:2:2 phase [2]. The Curich samples become superconducting (S type), the Cudeficient samples exhibit a magnetic phase (A type), while a higher Cu deficiency produces a sample (X type) showing neither the A phase nor superconductivity down to the lowest accessible temperature. In an intermediate range, in between the S and the A type samples, one can find a so-called A/S type CeCu2Si2 which exhibits an AFM phase transition at a transition temperature T N and upon further cooling becomes superconducting at a SC transition temperature T c (T c oT N ). Recent neutrondiffraction studies on CeCu2Si2 have identified the A phase as an incommensurate (IC) spin-density-wave phase with a rather low magnetic moment of about 0:1 mB per Ce atom [3].
Corresponding author. Tel.: +49 351 4646 2424; fax: +49 351 4646 2402. E-mail address: [email protected] (E. Lengyel).
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.01.145
Several Ce-based heavy-fermion (HF) SC show a generic phase diagram where the AFM order is suppressed to zero temperature by increasing the hybridization between the Ce 4f-electrons and the conduction electrons leading to the appearance of an antiferromagnetic quantum critical point (AFM QCP) (e.g., CePd2Si2) [4]. In these materials SC appears around this AFM QCP. In contrast to this generic picture, CeCu2Si2 shows a broad SC region which extends up to higher hybridization strengths, far away from the AFM QCP. High-pressure studies on the nonstoichiometric compound CeCu2 ðSi1x Gex Þ2 (xa0; 1), where disorder by doping on the Si/Ge site plays a crucial role in destroying the Cooper pairs and in reducing the SC transition temperature T c , have made clear the origin of this anomalous phase diagram [5]. It was found that in addition to the SC dome located close to the AFM QCP there exists a second SC dome at the high-pressure side, associated with a weakly first-order valence transition of Ce. However, in the stoichiometric compounds CeCu2Si2 and CeCu2Ge2 the two SC regions seem to merge into a single, wide SC region. It is suggested that SC in the lowpressure regime is mediated by spin-density fluctuations while in the high-pressure regime, away from the magnetically ordered phase, charge–density fluctuations are responsible for the electron pairing [5].
ARTICLE IN PRESS E. Lengyel et al. / Physica B 378–380 (2006) 415–416
416
C / T (J/molK2)
1.2 1.0
p (GPa) 0 0.06 0.26 0.73 1.07 1.39 1.96
0.7 TN, Tc (K)
1.4
TN 0.6 Tc 0.5 0
0.5
1.0
1.5
2.0
p (GPa)
0.8 0.6 0.4 0.4
0.8
1.2
1.6
T (K) Fig. 1. Specific heat of CeCu2Si2 as C=T versus T for pressures as indicated in the figure. The inset shows the evolution of the Ne´el temperature T N and of the SC transition temperature T c function of pressure.
Large single crystals of CeCu2Si2, with well-defined ground-state properties, became recently available. The single crystals are grown in aluminum-oxide crucibles by a modified Bridgman technique, using Cu excess as flux medium [6]. Powder X-ray diffraction patterns confirmed the proper tetragonal ThCr2Si2 structure with lattice parameters a 0:4102 nm and c 0:9930 nm at room temperature. Measurements of the heat capacity under hydrostatic pressure have been performed in a 3He cryostat by a quasiadiabatic heat-pulse technique. Measurements at low pressure (po1:1 GPa) were carried out in a CuBe piston-cylinder pressure cell, while for the high-pressure range (pX1:1 GPa) we utilized a double layer NiCrAl– CuBe type piston-cylinder pressure cell. For the entire experiment, Flourinert FC72 was used as a pressure transmitting medium. For our measurements we have chosen a large A/S type single crystal with a mass of about 400 mg. The applied magnetic field was oriented parallel to the c-axis. The low-temperature specific heat of the A/S type single crystal of CeCu2Si2 is displayed in Fig. 1 as C=T versus T at various pressures and in zero magnetic field. As it is shown in the ambient pressure data, the system undergoes two subsequent phase transitions, a magnetic one at T N 0:7 K, which indicates the entrance into the IC AFM state and a transition to a superconducting state, at T c 0:5 K. A small increase in pressure, of about 0.06 GPa, is enough to shift the two-phase transitions very close to each other to T N 0:62 K and T c 0:60 K.
Further increasing pressure leads to the increase of the SC transition temperature. Once T c becomes greater than the AFM transition temperature the presence of the AFM order cannot be detected anymore, except by application of a magnetic field high enough to suppress SC in the system (e.g., at p 0:09 GPa for B ¼ 2 T we find T N 0:41 K). This behavior, in good agreement with the results obtained by mSR measurements [7], could be interpreted in favor of the competition between AFM and SC order in this compound. On increasing the pressure to higher values (see inset in Fig. 1), the SC transition temperature reaches a maximum value of T c 0:63 K at about p 0:26 GPa and decreases then slightly up to p 1:6 GPa, from where it starts to increase again, marking the entrance into the second SC region. The effect of pressure on Ce-based HF compounds is to increase the hybridization strength of the 4f-electrons with the conduction electrons. A high enough pressure leads to a partial delocalization of the 4f-electrons, replacing the HF state by a mixed valence state. The transition from the HF state to the mixed valence state might be a first-order phase transition accompanied by a symmetry-conserving collapse of the unit-cell volume [8]. The effective mass of the quasiparticles is a good measure of such an effect. Our experiments show that for the lowpressure range, pp1:6 GPa,C=T, taken at T ¼ 0:9 K, decreases with dðlnðC=TÞÞ=dp 0:39=GPa while for the high-pressure region 1:6ppp2:1 GPa dðlnðC=TÞÞ=dp 0:21=GPa. The reduction of dðlnðC=TÞÞ=dp, at p 1:6 GPa, in the region where the SC transition temperature starts to increase, might indicate a smooth transition from the HF state to a metallic state with an increased electronic density of states. The existence of a broad region of SC with different electronic properties in different pressure regions supports the existence of two distinct pairing mechanisms in the two merging SC regions of CeCu2Si2. This work was partly supported by the SFB 463. We thank Prof. T. Matsumoto for supplying the NiCrAl alloy for the pressure cell. References [1] [2] [3] [4] [5] [6] [7] [8]
F. Steglich, et al., Phys. Rev Lett. 43 (1979) 1892. R. Modler, et al., Physica B 206 & 207 (1995) 586. O. Stockert, et al., Phys. Rev. Lett. 92 (2004) 136401. F.M. Grosche, et al., J. Phys.: Condens. Matter 13 (2001) 2845. H.Q. Yuan, et al., Science 302 (2003) 2104. H.S. Jeevan, unpublished. R. Feyerherm, et al., Phys. Rev. B 56 (1997) 699. J. Roehler, et al., J. Magn. Magn. Mater. 76 & 77 (1988) 340.