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Pressure-induced transition in a heavy fermion YbPd2Si2
ARTICLE IN PRESS Journal of Physics and Chemistry of Solids 69 (2008) 2301– 2306
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Pressure-induced transition in a heavy fermion YbPd2Si2 Sergey V. Ovsyannikov a,b,, Vladimir V. Shchennikov b, Tetsuya Fujiwara c, Yoshiya Uwatoko a a b c
The Institute of Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8581 Chiba, Japan High Pressure Group, Institute of Metal Physics of Russian Academy of Sciences, Urals Division, GSP-170, 18 S. Kovalevskaya Street, 620041 Yekaterinburg, Russian Federation Faculty of Sciences, Yamaguchi University, 753-8512 Yamaguchi, Japan
article info PACS: 72.20.Pa 05.70.Fh 52.77.Fv 81.70.–q 73.61.Ey 71.22.+i 61.50.Ks 81.40.Vw Keywords: A. Intermetallic compounds C. High pressure D. Electrical conductivity D. Phase transitions D. Transport properties
abstract We report the results of a room-temperature investigation of the thermoelectric and the dilatometric properties of a heavy fermion system YbPd2Si2 (itterbium–palladium–silicon, 1–2–2) at high pressure P up to 22 GPa; YbPd2Si2 is a less-studied representative of the RM2X2 family (R ¼ Ce, Yb, U; M ¼ transition metal; X ¼ Si, Ge) with the tetragonal ThCr2Si2-type structure of the I4/mmm space group. Around P670.5 GPa, a phase transition in Yb–Pd–Si was registered by the drastic changes in the pressure dependencies of the electrical resistance R, the thermopower (Seebeck effect) S, a temperature difference along a sample DT, and a sample’s thickness Dx (related to compressibility). Both a nature of the found phase transition and a presumable P–T phase diagram of YbPd2Si2 are discussed. & 2008 Elsevier Ltd. All rights reserved.
1. Introduction Heavy fermion systems—intermetallic compounds on a basis of rare-earth and actinide elements—attract steady attention due to the unusual properties and rich phase diagrams. One of the main peculiarities of these systems is the abnormally high values of the coefficient of the electron heat capacity, g, owing to a narrow band with a high density of states near the Fermi level. Also they are model systems for investigation of novel physical phenomena, for example: (i) unconventional magnetically mediated superconductivity (contrary to the phonon-mediated one in a conventional superconductor) [1], (ii) recently proposed new types of superconducting pairing interaction based on ‘‘spatially extended density fluctuations’’ possible around a quantum phase transition with a volume collapse but with no change in lattice symmetry [2], and (iii) coexistence of unconventional superconductivity with a weak magnetism [3]. One of the oldest and promising series of heavy fermion systems is ‘‘1–2–2’’, RM2X2 (R ¼ Ce, Yb, U; M ¼ transition metal; X ¼ Si, Ge). A discovery of the heavy fermion superconductivity in its member—CeCu2Si2—below Tc0.5 K [1] motivated further Corresponding author at: High Pressure Group, Institute of Metal Physics of Russian Academy of Sciences, Urals Division, GSP-170, 18 S. Kovalevskaya Street, Yekaterinburg 620041, Russian Federation. Tel./fax: +81 47136 3333. E-mail addresses: [email protected], [email protected] (S.V. Ovsyannikov), [email protected] (V.V. Shchennikov).
0022-3697/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2008.04.007
investigations of these materials, and in particular, a synthesis and search inside the ‘‘1–2–2’’ series itself. Thus, properties of Ce and Yb members of the ‘‘1–2–2’’ family were studied by a range of techniques under variation in both temperature and pressure (probing of the P–T diagram); for example, CePd2Si2 [4–7], CePd2Ge2 [8], CeRh2Si2 [9], CeRu2Ge2 [10], CeCu2Si2 [11,12], CeCu2Ge2 [13,14], CeNi2Si2 [14], CeNi2Ge2 [15], YbRu2Si2 [16,17], YbRu2Ge2 [18], YbCu2Si2 [19,20], YbCu2Ge2 [21], YbNi2Si2 [22], YbNi2Ge2 [23], Yb(Fe,Co)2(Si,Ge)2 [21,24–26], YbPd2Si2 [27–36], YbPd2Ge2 [37], YbIr2Si2 [38], YbMn2Ge2 [39], and some others. U-based compounds are less studied, although they exhibit interesting properties [40,41]. Application of high pressure varies the density of materials and thus changes the intensity configuration of different electronic and magnetic interactions, resulting in different states [4]. Because of a very high sensitivity of properties (especially, superconductivity) to the quality of samples, experimental data may be, to some extent, contradictory that leads to diverging interpretations. Hence, to understand the physics of these systems and the association of found states to certain interactions, the behaviour of each of them seems to be important. For example, a typical P–T phase diagram of the heavy fermion systems proposed in Ref. [4] and including the magnetically mediated superconductivity along with the heavy fermion state and the magnetic metal (long-range magnetic order) still has not been verified for most compounds because of the non-observation of superconductivity. To date, only a few compounds of the RM2X2 family
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manifested a superconducting state, such as CeCu2Si2 (below Tc0.5 K) [1], CeCu2Ge2 (Tc0.6 K at P7.5 GPa) [13], CePd2Si2 (Tc1 K at P2.3 GPa) [4], CeRh2Si2 (Tc0.35 K at P1 GPa) [9], CeNi2Ge2 (Tc0.22 K at P1.5 GPa) [15], YbPd2Ge2 (Tc1.17 K) [37], URh2Si2 (Tc1.3 K) [41], and probably some others. Another Ybbased system manifesting a ‘‘filamentary’’ superconductivity below Tc1.2 K at P40.74 GPa is YbInCu4 [42]. A search for superconductivity in others is complicated both by difficulties in accessing a millikelvin T range and by imperfection of samples, as for realisation of a superconducting state, a carrier mean free path should exceed a superconducting coherence length [4]. At ambient conditions, a moderate heavy fermion system— YbPd2Si2 (g ¼ 203 mJ/(mole K2) [30])—as well as the majority of members of the RM2X2 family adopt the tetragonal ThCr2Si2-type structure with the space group I4/mmm [43]; the lattice parameters of YbPd2Si2 are as follows: a ¼ 4.099 A˚ and b ¼ 9.870 A˚ [44] (Fig. 1). For a number of compounds, this lattice was found to be stable against high-pressure application, for example, up to P60 GPa in CeCu2(Si,Ge)2 [14]. However, recently, a new type of structural transformation has been discovered in this family—an isostructural transformation with a volume collapse; thus, the lattice parameters (a, c) of CeCu2Ge2 dropped by 0.7% at T ¼ 10 K near P15 GPa [45]. In the present work we undertake a high-pressure study of YbPd2Si2 single crystal up to P22 GPa in order to probe a stability of the ambient state, and to investigate P dependencies of the electronic properties. We employ an original automated highpressure set-up designed for registration of phase transformation in solids [46]; the set-up permits simultaneous registration of
Fig. 1. A typical crystal structure of many compounds of the RM2X2 series (R ¼ Ce, Yb; M ¼ transition metal, X ¼ Si, Ge) including YbPd2Si2. The structure is a bodycentred tetragonal lattice of the ThCr2Si2 structural type, space group I4/mmm [43]; the lattice parameters for YbPd2Si2 are as follows: a ¼ 4.099 A˚ and c ¼ 9.870 A˚ [44].
several parameters of a sample and environment, such as an applied force (pressure), (thermo-) electrical signal from a sample, a change in a sample’s thickness Dh, a temperature difference along a sample DT, and others. A high efficiency of this setup was proved by a discovery of the new ‘‘hidden’’ semimetal highpressure phases in ZnTe [47] and GaAs [48], which have not yet been detected by conventional structural techniques.
2. Experimental techniques Measurements of the thermopower (Seebeck effect) S and the electrical resistance R under high quasi-hydrostatic pressure P were performed in the synthetic diamond anvils of the Bridgman type characterised by a high electrical conductivity [49]. A gasket made of the lithographic stone (soft CaCO3-based material) [50] served as a pressure-transmitting medium (Fig. 2). A disc-shaped sample of size 200 200 20–30 mm3 was placed into a hole 200 mm in diameter drilled in the gasket [48,51]. The ratio of the thickness of the gasket to the working diameter of the anvils was lower than 0.055, indicating a quasi-hydrostatic character of compression [52]. The majority of S(P) and R(P) data that are obtained by this technique agree well with those available from hydrostatic studies up to P2–9 GPa [53]. Applied force was measured by a digital dynamometer with the resistive-strain sensors. Pressure values were determined with an uncertainty less than 10% (including possible P gradients) from a calibration curve based on the known pressure-induced phase transitions in Bi, GaP, ZnS, and others [46]. The synthetic diamond anvils were used both as the electrical outputs to a sample and as a heater–cooler pair (the upper anvil was heated) [54,55]. To account for a possible contribution into S from the anvils themselves, we measured Pb samples (SE–1.27 mV/K) in the same conditions. S values were measured in two regimes: at fixed P from a linear dependence of the thermoelectric voltage on a temperature difference DT along a sample and at fixed DT (or density of a thermal flux q) under gradual variation in P [56–58]. The relative errors in R and S determination did not exceed 5% and 20%, respectively. The single-crystalline samples of YbPd2Si2 were grown by a flux method and were preliminarily characterised by a conventional X-ray technique. Pressure-driven contraction of a sample placed inside the lithographic stone container (Fig. 2) was measured with the assistance of an electronic dilatometer (sensitivity 7.5 V/mm) connected together with a mechanical one [46]. An overall output
Fig. 2. A scheme of sample location in a high-pressure cell: (1) sample, (2) gasket made of lithographic stone (soft CaCO3-based material) [50], (3) anvil insets (made of synthetic diamonds) in high-pressure plungers, (4) supporting hard-alloy matrices (plungers). A ring-like bulge of gasket 2 provides a supporting pressure Ps (up to 10 GPa) around the tips of anvils; high quasi-hydrostatic pressure P (from 0 up to 30 GPa) is created in a central part of the gasket around a sample [48,51]. The arrows show acting forces.
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a phase transformation. The bends in the Dh(P) and DT(P) curves near P6 GPa evidence a change in the mechanical properties of a sample, so it seems natural to relate them to alteration of the sample compressibility, which is often concurrent with structural transformations. Near this P value, the S(P) dependencies also exhibit a bend (clearly seen for the 3rd and 4th cycles in Fig. 4a). A return transition is seen more distinctly by an abrupt variation in S beyond P3 GPa (Fig. 4a). So, by the changes in all properties, we register a reversible phase transformation near P6 GPa on pressurisation and near P3 GPa on decompression (Fig. 4).
4. Discussion
Fig. 3. A displacement of the plungers of the high-pressure cell (Fig. 2) under pressure P: (1) a gasket without a sample, (2) a gasket with YbPd2Si2. On a background of elastic contraction of the plungers and deformation of a lithographic stone container, one can distinguish a change in a contraction regime of sample (2), marked by the arrow. Curve 1 was obtained for the first cycle of pressurisation, and a plastic deformation of a lithographic stone gasket is seen on the beginning of pressurisation. Curve 2 was gathered on the fifth cycle of pressurisation and exhibits only elastic effects.
signal from the dilatometer included an elastic contraction of the plungers and a pressure chamber, and a deformation of the lithographic stone container as well (Fig. 3). So, in order to pick out a contribution from a sample itself, the above linear effects (obviously the same for different samples) arising from both a chamber and a container were excluded. Thus, a residual small signal exhibited volumetric anomalies of a sample and qualitatively evidences a change in the material compressibility. A pressure dependence of a temperature difference DT can also point to a change in the sample compressibility, as at nearly stationary conditions DT ¼ qh/l, where h is a thickness of a sample along a thermal flow, q is a density of thermal flow, and l is the thermal conductivity [46].
3. Results The typical pressure dependencies of the thermopower S, of the electrical resistance R, of the sample contraction Dh, and of a temperature difference along the sample DT for single-crystalline YbPd2Si2 are presented in Fig. 4. Negative sign of the thermopower at ambient conditions agrees with the data of Ref. [19] reporting on the Seebeck coefficients for the number of Yb-based heavy fermion systems as follows: S(7–35) mV/K; the ambient thermopower for YbPd2Si2 was found to be SE18 mV/K [44]. The pressure-driven decrease in an absolute value of the Seebeck effect (Fig. 4a) also coincides with a reported behaviour of S(P) for other Yb-based compounds [59]; for example, at room temperature the thermopower of YbCu2Si2 changed from S28 mV/K to 2 mV/K when the pressure increased from ambient to P9.6 GPa [19]. Similar behaviour of S(P) was also noticed for Ce-based systems, for which the room-temperature thermopower moved from a small negative value to a positive one [59]. In our case for all P cycles, we notice a reversible n–p inversion in the thermopower (Fig. 4a). The P-driven decrease in |S| and R might be induced by an increase in electron concentration (Fig. 4a, b) owing to reduction in a sample’s volume. All the dependencies obtained, such as S(P), R(P), DT(P), and Dh(P) (Fig. 4), exhibit the peculiarities evidencing
Fig. 5 shows a typical dependence of the thermopower versus the electrical resistance taken at the same P values. From the d[ln(S)]/d[ln(R)] ratio, we determine a degree of the power dependence—S(R) as follows: SR0.2 and SR7 for low (Po6 GPa) and high-pressure (P46 GPa) regions, respectively. For two-band conductivity with light and heavy electrons, the equation for the thermoelectric power of a metal may be given as follows [60]: 2 p2 k T 3 1 dN d ðÞ S¼ (1) 3jej 2Z Nd ðÞ d ¼Z where k is the Boltzmann constant, T is the temperature, e and e are the electron charge and energy, respectively, Z is the reduced Fermi energy Z ¼ eF/kT, and Nd(e) is the density of states of a heavy d-band. For example, for parabolic electronic band the reduced Fermi energy is Zn– 2/3 (where n is the electron concentration) and assuming that R1/n, a relationship between S and R is as the follows: SR2/3. Behaviour of the thermopower in the high-pressure region (P46 GPa) may be explained by a contribution of the second term in Eq. (1). For an almost empty d-band, this positive contribution causes a rapid decrease in a negative value of S [60]. So, the change in a slope of the S(P) curve (Fig. 4a) might evidence a redistribution of electrons of s-, d-, and f-bands. One probable explanation of the transition found by S(P), R(P), DT(P), and Dh(P) (Fig. 4) is a structural transformation. However, to date no precedent has been reported for the RM2X2 family on a transition of the ThCr2Si2-type structure [43] to a lattice of different symmetry; in the studies undertaken on the number of its representatives such as CeCu2Si2 [14,61], CeCu2Ge2 [14,45,62], CeNi2Ge2 [14], YbCu2Si2 [63], and others, the initial structure is maintained in the same or wider P range. So, probably, in our sample YbPd2Si2, the symmetry of the initial lattice is also retained, while a nature of the transformation may be subtle. The isostructural transformation in the ThCr2Si2-type structure with a volume-collapse effect DV was found only in CeCu2Ge2 and at lowtemperature conditions (T ¼ 10 K) [45]; meanwhile, it might be a characteristic feature for this series of compounds. Because of negligibility of the volume effect (in CeCu2Ge2 DV is less than 0.5% [45]), its direct observation by structural techniques is a challenging task. Thus, through each series of the pressure dependence of the lattice volume Vo(P) for CeCu2Ge2, the DV effect was not evident, while only after superposition of three series, a clear profile of the effect has appeared [45]. One can find resembling weak anomalies in Vo(P) or in a(P) and c(P) curves for other Yb- and Ce-based compounds. For example, the a(P) and c(P) curves for YbCu2Si2 [63] exhibited a number of obvious anomalies (including a change in compressibility), and in a Vo(P) dependence one can notice a step near P12 GPa, similar to the one for CeCu2Ge2 [45]; this DV effect (seen at room temperature) corresponded to a maximum of magnetic-ordering temperature, but it was not noticed in Ref. [63].
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Fig. 4. The pressure P dependencies of the thermoelectric power (Seebeck effect) S (a), of the electrical resistance R (b), of a relative sample’s contraction (relative compressibility) Dh (c), and of a temperature difference along a sample DT (inset in plot c) of YbPd2Si2 single crystal at T ¼ 293 K. The big open symbols correspond to a pressurisation cycle, while the small closed ones to decompression.
Fig. 5. The thermopower S versus the electrical resistance R for YbPd2Si2 by the data from Fig. 4. The big symbols correspond to a pressurisation cycle, while the small ones correspond to decompression. The bends correspond to the pressure values P6 and 3 GPa for the pressurisation and decompression cycles, respectively.
Another probable explanation of the transformation found (Fig. 4) is a pressure-driven valence transition, which may be concurrent with a tiny volume collapse DV due to an abrupt change in an ionic radius of the unstable valence Yb [64] (Fig. 1). In the majority of heavy fermion compounds, a valence of Yb varies between 2+ and 3+ limits. Yb2+ has a filled 4f shell and thus has no magnetic moment contrary to magnetic Yb3+ [65]. The last circumstance explains both the differences in properties between compounds with Yb2+ and Yb3+, and the anomalies of properties of materials with a non-integer (intermediate) valence. At ambient conditions a ‘‘mean valence’’ of Yb in YbPd2Si2 was found to be 2.89 [66]. Application of external pressure can potentially shift this ‘‘mean valence’’ to a trivalent limit. The results presented in Ref. [65] qualitatively demonstrated an increase in the Yb valence in YbPd2Si2 under P4–5 GPa; meanwhile neither a trivalent state was achieved nor a P–T boundary of this transition was found. In YbInCu4, YbMn2Ge2, and other compounds, a pressure-driven valence transition has been already established, exhibiting a hysteresis in the T values of direct and return transformations [42,67]. A spin transition under P is also able to induce an isostructural transition with DV effect but without pressure hysteresis [68].
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It is known that d- and f-electrons can contribute to the formation of covalent bonds in a lattice, such as s- and p-ones, and the strength of these bonds is expected to be stronger [69]. This is a reason of a pressure-induced isostructural-phase transition established both in the octahedral-bonded rare-earth chalcogenides with the NaCl structure (partial transition from d2sp3 to d2sf3 electronic configuration) and in other compounds (partial transition from sp3 to sf3 configuration—in tetrahedral bonded lattices and from dsp2 to dsf2 in quadratic lattices) [70]. A change in occupancy of f-levels leads to peculiarities in structural, electronic, and magnetic properties of materials. In an example of Yb, Sm, and Eu chalcogenides, it was shown that an isostructural valence phase transition happens just after a softening of the NaCl lattice [70]. So, an increase in the ‘‘mean valence’’ and a following growth in an electron concentration could explain our S(P) and R(P) dependencies (Fig. 4a, b). Meanwhile, it seems surprising that a potentially small variation in the ‘‘mean valence’’ (2.9-3) can result in such drastic variation in properties. One of the possible explanations might be as follows: the initially non-magnetic material acquires magnetic properties because of reduction in the Pb–Pd distances along the a- or c-axes (Fig. 1) below some critical value. We could not find in the literature a law relating the Pd–Pd distances along the a- and c-axes in RPd2X2 to the magnetic properties (anti- and ferromagnetism), like the one for the Mn–Mn distances in RMn2X2 [71]; the latter reported on a critical value of the distance separating the regions of anti- and ferromagnetism for RMn2X2 if the Mn–Mn distance along the a-axis is correspondingly shorter or longer than a critical one. In the case of resembling material CePd2Si2 (a ¼ 4.2318 A˚ and b ¼ 9.9035 A˚) [59], it was found that a pressure-driven reduction in a cell volume and increase in the c/a ratio lead to a suppression of the antiferromagnetic state [72]. This fact agrees with the absence of magnetism at ambient conditions in YbPd2Si2; however, it does not hint at prospective modification of a dominant Pd–Pd exchange interaction under further reduction in the distances. The volume-collapse effect was shown to be an important indicator of possibility of existence of a superconducting state near the quantum transition [2]. So, according to Ref. [2], one of the necessary conditions for ‘‘spatially extended density fluctuations’’ superconductivity is a low-lying temperature endpoint of the transition—‘‘well below room temperature’’. Thus, if the feature we found is a valence transition with the DV effect, then probably YbPd2Si2 cannot form a superconducting state near this quantum transition at low temperatures [2]. A search for a pressure-driven superconductivity in YbPd2Si2 would help to clarify this general problem. Notice that at similar P values other Yb-based compounds exhibit a transition into the magnetically ordered Kondo lattice at cryogenic temperatures (T1–3 K), near P8–10 GPa in YbIr2Si2 [73], YbRh2Si2 [74], and YbCu2Si2 [63], and near P5 GPa in YbNi2Ge2 [23]; meanwhile, no features were detected at room temperature. However, the data for YbPd2Si2 from Ref. [75] hint at a different image: possible magnetic ordering below T ¼ 0.5 K at P ¼ 1 GPa. Moreover, Ref. [64] reported on an observation of an unknown weak magnetic phase below T1.4 K at ambient pressure. These findings point that a P–T diagram of YbPd2Si2 may be peculiar. Accounting for a sensitivity of the heavy fermion compounds to external influences, a small non-hydrostaticity in a pressure medium potentially could lead to a change in a pressurisation routine, distinguishing low- and high-pressure regimes. In Ref. [61] it was demonstrated that a moderate non-stoichiometricity (CeCu1.8Si2) results in an increase in the compressibility along the c-axis under pressurisation to P13–15 GPa, and then the c parameter shrinks in a similar manner as the one in the
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stoichiometric compound. The effect of non-stoichiometricity resulted in an obvious bend in a c(P) curve [61]—the resembling feature we observe in our Dh(P) dependencies curves (Fig. 4c).
5. Conclusion By the changes in the thermoelectric and the dilatometric properties, a phase transition in YbPd2Si2 was established at room temperature near P670.5 GPa. If this is a structural transition to a lattice with a different symmetry, it would be the first precedent for the RM2X2 family. One possible alternative explanation is a valence transition that should lead to the tiny volume-collapse effect (DV) because of a difference in the ionic radii of Yb3+ and Yb2+ ions (Fig. 1) [65]. As for the latter variant, it seems surprising that a potentially small variation in the ‘‘mean valence’’ (2.9 [66]-3) could result in such drastic variations in the properties (Fig. 4). However, this valence transition might be concurrent with the acquiring of magnetic properties by the initially non-magnetic material due to reduction in the Pb–Pd distances below some critical value. Note added in proof Recently, in a compound adopting the same ThCr2Si2-type structure, namely, a heavy fermion UMn2Ge2, a pressure-induced structural transition to a lattice of a different symmetry was detected near 16 GPa at room temperature [76]. The high-pressure phase was not refined. This finding supports our discussion about a possibility of a structural transformation in YbPd2Si2 near 6 GPa. Acknowledgements The authors thank Mr. A. Mezenin (IMP) for assistance in the experiment. The work was supported by the JSPS (P05312) and RFBR (Grant no. 07-08-00338).
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Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs
Pressure-induced transition in a heavy fermion YbPd2Si2 Sergey V. Ovsyannikov a,b,, Vladimir V. Shchennikov b, Tetsuya Fujiwara c, Yoshiya Uwatoko a a b c
The Institute of Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8581 Chiba, Japan High Pressure Group, Institute of Metal Physics of Russian Academy of Sciences, Urals Division, GSP-170, 18 S. Kovalevskaya Street, 620041 Yekaterinburg, Russian Federation Faculty of Sciences, Yamaguchi University, 753-8512 Yamaguchi, Japan
article info PACS: 72.20.Pa 05.70.Fh 52.77.Fv 81.70.–q 73.61.Ey 71.22.+i 61.50.Ks 81.40.Vw Keywords: A. Intermetallic compounds C. High pressure D. Electrical conductivity D. Phase transitions D. Transport properties
abstract We report the results of a room-temperature investigation of the thermoelectric and the dilatometric properties of a heavy fermion system YbPd2Si2 (itterbium–palladium–silicon, 1–2–2) at high pressure P up to 22 GPa; YbPd2Si2 is a less-studied representative of the RM2X2 family (R ¼ Ce, Yb, U; M ¼ transition metal; X ¼ Si, Ge) with the tetragonal ThCr2Si2-type structure of the I4/mmm space group. Around P670.5 GPa, a phase transition in Yb–Pd–Si was registered by the drastic changes in the pressure dependencies of the electrical resistance R, the thermopower (Seebeck effect) S, a temperature difference along a sample DT, and a sample’s thickness Dx (related to compressibility). Both a nature of the found phase transition and a presumable P–T phase diagram of YbPd2Si2 are discussed. & 2008 Elsevier Ltd. All rights reserved.
1. Introduction Heavy fermion systems—intermetallic compounds on a basis of rare-earth and actinide elements—attract steady attention due to the unusual properties and rich phase diagrams. One of the main peculiarities of these systems is the abnormally high values of the coefficient of the electron heat capacity, g, owing to a narrow band with a high density of states near the Fermi level. Also they are model systems for investigation of novel physical phenomena, for example: (i) unconventional magnetically mediated superconductivity (contrary to the phonon-mediated one in a conventional superconductor) [1], (ii) recently proposed new types of superconducting pairing interaction based on ‘‘spatially extended density fluctuations’’ possible around a quantum phase transition with a volume collapse but with no change in lattice symmetry [2], and (iii) coexistence of unconventional superconductivity with a weak magnetism [3]. One of the oldest and promising series of heavy fermion systems is ‘‘1–2–2’’, RM2X2 (R ¼ Ce, Yb, U; M ¼ transition metal; X ¼ Si, Ge). A discovery of the heavy fermion superconductivity in its member—CeCu2Si2—below Tc0.5 K [1] motivated further Corresponding author at: High Pressure Group, Institute of Metal Physics of Russian Academy of Sciences, Urals Division, GSP-170, 18 S. Kovalevskaya Street, Yekaterinburg 620041, Russian Federation. Tel./fax: +81 47136 3333. E-mail addresses: [email protected], [email protected] (S.V. Ovsyannikov), [email protected] (V.V. Shchennikov).
0022-3697/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2008.04.007
investigations of these materials, and in particular, a synthesis and search inside the ‘‘1–2–2’’ series itself. Thus, properties of Ce and Yb members of the ‘‘1–2–2’’ family were studied by a range of techniques under variation in both temperature and pressure (probing of the P–T diagram); for example, CePd2Si2 [4–7], CePd2Ge2 [8], CeRh2Si2 [9], CeRu2Ge2 [10], CeCu2Si2 [11,12], CeCu2Ge2 [13,14], CeNi2Si2 [14], CeNi2Ge2 [15], YbRu2Si2 [16,17], YbRu2Ge2 [18], YbCu2Si2 [19,20], YbCu2Ge2 [21], YbNi2Si2 [22], YbNi2Ge2 [23], Yb(Fe,Co)2(Si,Ge)2 [21,24–26], YbPd2Si2 [27–36], YbPd2Ge2 [37], YbIr2Si2 [38], YbMn2Ge2 [39], and some others. U-based compounds are less studied, although they exhibit interesting properties [40,41]. Application of high pressure varies the density of materials and thus changes the intensity configuration of different electronic and magnetic interactions, resulting in different states [4]. Because of a very high sensitivity of properties (especially, superconductivity) to the quality of samples, experimental data may be, to some extent, contradictory that leads to diverging interpretations. Hence, to understand the physics of these systems and the association of found states to certain interactions, the behaviour of each of them seems to be important. For example, a typical P–T phase diagram of the heavy fermion systems proposed in Ref. [4] and including the magnetically mediated superconductivity along with the heavy fermion state and the magnetic metal (long-range magnetic order) still has not been verified for most compounds because of the non-observation of superconductivity. To date, only a few compounds of the RM2X2 family
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manifested a superconducting state, such as CeCu2Si2 (below Tc0.5 K) [1], CeCu2Ge2 (Tc0.6 K at P7.5 GPa) [13], CePd2Si2 (Tc1 K at P2.3 GPa) [4], CeRh2Si2 (Tc0.35 K at P1 GPa) [9], CeNi2Ge2 (Tc0.22 K at P1.5 GPa) [15], YbPd2Ge2 (Tc1.17 K) [37], URh2Si2 (Tc1.3 K) [41], and probably some others. Another Ybbased system manifesting a ‘‘filamentary’’ superconductivity below Tc1.2 K at P40.74 GPa is YbInCu4 [42]. A search for superconductivity in others is complicated both by difficulties in accessing a millikelvin T range and by imperfection of samples, as for realisation of a superconducting state, a carrier mean free path should exceed a superconducting coherence length [4]. At ambient conditions, a moderate heavy fermion system— YbPd2Si2 (g ¼ 203 mJ/(mole K2) [30])—as well as the majority of members of the RM2X2 family adopt the tetragonal ThCr2Si2-type structure with the space group I4/mmm [43]; the lattice parameters of YbPd2Si2 are as follows: a ¼ 4.099 A˚ and b ¼ 9.870 A˚ [44] (Fig. 1). For a number of compounds, this lattice was found to be stable against high-pressure application, for example, up to P60 GPa in CeCu2(Si,Ge)2 [14]. However, recently, a new type of structural transformation has been discovered in this family—an isostructural transformation with a volume collapse; thus, the lattice parameters (a, c) of CeCu2Ge2 dropped by 0.7% at T ¼ 10 K near P15 GPa [45]. In the present work we undertake a high-pressure study of YbPd2Si2 single crystal up to P22 GPa in order to probe a stability of the ambient state, and to investigate P dependencies of the electronic properties. We employ an original automated highpressure set-up designed for registration of phase transformation in solids [46]; the set-up permits simultaneous registration of
Fig. 1. A typical crystal structure of many compounds of the RM2X2 series (R ¼ Ce, Yb; M ¼ transition metal, X ¼ Si, Ge) including YbPd2Si2. The structure is a bodycentred tetragonal lattice of the ThCr2Si2 structural type, space group I4/mmm [43]; the lattice parameters for YbPd2Si2 are as follows: a ¼ 4.099 A˚ and c ¼ 9.870 A˚ [44].
several parameters of a sample and environment, such as an applied force (pressure), (thermo-) electrical signal from a sample, a change in a sample’s thickness Dh, a temperature difference along a sample DT, and others. A high efficiency of this setup was proved by a discovery of the new ‘‘hidden’’ semimetal highpressure phases in ZnTe [47] and GaAs [48], which have not yet been detected by conventional structural techniques.
2. Experimental techniques Measurements of the thermopower (Seebeck effect) S and the electrical resistance R under high quasi-hydrostatic pressure P were performed in the synthetic diamond anvils of the Bridgman type characterised by a high electrical conductivity [49]. A gasket made of the lithographic stone (soft CaCO3-based material) [50] served as a pressure-transmitting medium (Fig. 2). A disc-shaped sample of size 200 200 20–30 mm3 was placed into a hole 200 mm in diameter drilled in the gasket [48,51]. The ratio of the thickness of the gasket to the working diameter of the anvils was lower than 0.055, indicating a quasi-hydrostatic character of compression [52]. The majority of S(P) and R(P) data that are obtained by this technique agree well with those available from hydrostatic studies up to P2–9 GPa [53]. Applied force was measured by a digital dynamometer with the resistive-strain sensors. Pressure values were determined with an uncertainty less than 10% (including possible P gradients) from a calibration curve based on the known pressure-induced phase transitions in Bi, GaP, ZnS, and others [46]. The synthetic diamond anvils were used both as the electrical outputs to a sample and as a heater–cooler pair (the upper anvil was heated) [54,55]. To account for a possible contribution into S from the anvils themselves, we measured Pb samples (SE–1.27 mV/K) in the same conditions. S values were measured in two regimes: at fixed P from a linear dependence of the thermoelectric voltage on a temperature difference DT along a sample and at fixed DT (or density of a thermal flux q) under gradual variation in P [56–58]. The relative errors in R and S determination did not exceed 5% and 20%, respectively. The single-crystalline samples of YbPd2Si2 were grown by a flux method and were preliminarily characterised by a conventional X-ray technique. Pressure-driven contraction of a sample placed inside the lithographic stone container (Fig. 2) was measured with the assistance of an electronic dilatometer (sensitivity 7.5 V/mm) connected together with a mechanical one [46]. An overall output
Fig. 2. A scheme of sample location in a high-pressure cell: (1) sample, (2) gasket made of lithographic stone (soft CaCO3-based material) [50], (3) anvil insets (made of synthetic diamonds) in high-pressure plungers, (4) supporting hard-alloy matrices (plungers). A ring-like bulge of gasket 2 provides a supporting pressure Ps (up to 10 GPa) around the tips of anvils; high quasi-hydrostatic pressure P (from 0 up to 30 GPa) is created in a central part of the gasket around a sample [48,51]. The arrows show acting forces.
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a phase transformation. The bends in the Dh(P) and DT(P) curves near P6 GPa evidence a change in the mechanical properties of a sample, so it seems natural to relate them to alteration of the sample compressibility, which is often concurrent with structural transformations. Near this P value, the S(P) dependencies also exhibit a bend (clearly seen for the 3rd and 4th cycles in Fig. 4a). A return transition is seen more distinctly by an abrupt variation in S beyond P3 GPa (Fig. 4a). So, by the changes in all properties, we register a reversible phase transformation near P6 GPa on pressurisation and near P3 GPa on decompression (Fig. 4).
4. Discussion
Fig. 3. A displacement of the plungers of the high-pressure cell (Fig. 2) under pressure P: (1) a gasket without a sample, (2) a gasket with YbPd2Si2. On a background of elastic contraction of the plungers and deformation of a lithographic stone container, one can distinguish a change in a contraction regime of sample (2), marked by the arrow. Curve 1 was obtained for the first cycle of pressurisation, and a plastic deformation of a lithographic stone gasket is seen on the beginning of pressurisation. Curve 2 was gathered on the fifth cycle of pressurisation and exhibits only elastic effects.
signal from the dilatometer included an elastic contraction of the plungers and a pressure chamber, and a deformation of the lithographic stone container as well (Fig. 3). So, in order to pick out a contribution from a sample itself, the above linear effects (obviously the same for different samples) arising from both a chamber and a container were excluded. Thus, a residual small signal exhibited volumetric anomalies of a sample and qualitatively evidences a change in the material compressibility. A pressure dependence of a temperature difference DT can also point to a change in the sample compressibility, as at nearly stationary conditions DT ¼ qh/l, where h is a thickness of a sample along a thermal flow, q is a density of thermal flow, and l is the thermal conductivity [46].
3. Results The typical pressure dependencies of the thermopower S, of the electrical resistance R, of the sample contraction Dh, and of a temperature difference along the sample DT for single-crystalline YbPd2Si2 are presented in Fig. 4. Negative sign of the thermopower at ambient conditions agrees with the data of Ref. [19] reporting on the Seebeck coefficients for the number of Yb-based heavy fermion systems as follows: S(7–35) mV/K; the ambient thermopower for YbPd2Si2 was found to be SE18 mV/K [44]. The pressure-driven decrease in an absolute value of the Seebeck effect (Fig. 4a) also coincides with a reported behaviour of S(P) for other Yb-based compounds [59]; for example, at room temperature the thermopower of YbCu2Si2 changed from S28 mV/K to 2 mV/K when the pressure increased from ambient to P9.6 GPa [19]. Similar behaviour of S(P) was also noticed for Ce-based systems, for which the room-temperature thermopower moved from a small negative value to a positive one [59]. In our case for all P cycles, we notice a reversible n–p inversion in the thermopower (Fig. 4a). The P-driven decrease in |S| and R might be induced by an increase in electron concentration (Fig. 4a, b) owing to reduction in a sample’s volume. All the dependencies obtained, such as S(P), R(P), DT(P), and Dh(P) (Fig. 4), exhibit the peculiarities evidencing
Fig. 5 shows a typical dependence of the thermopower versus the electrical resistance taken at the same P values. From the d[ln(S)]/d[ln(R)] ratio, we determine a degree of the power dependence—S(R) as follows: SR0.2 and SR7 for low (Po6 GPa) and high-pressure (P46 GPa) regions, respectively. For two-band conductivity with light and heavy electrons, the equation for the thermoelectric power of a metal may be given as follows [60]: 2 p2 k T 3 1 dN d ðÞ S¼ (1) 3jej 2Z Nd ðÞ d ¼Z where k is the Boltzmann constant, T is the temperature, e and e are the electron charge and energy, respectively, Z is the reduced Fermi energy Z ¼ eF/kT, and Nd(e) is the density of states of a heavy d-band. For example, for parabolic electronic band the reduced Fermi energy is Zn– 2/3 (where n is the electron concentration) and assuming that R1/n, a relationship between S and R is as the follows: SR2/3. Behaviour of the thermopower in the high-pressure region (P46 GPa) may be explained by a contribution of the second term in Eq. (1). For an almost empty d-band, this positive contribution causes a rapid decrease in a negative value of S [60]. So, the change in a slope of the S(P) curve (Fig. 4a) might evidence a redistribution of electrons of s-, d-, and f-bands. One probable explanation of the transition found by S(P), R(P), DT(P), and Dh(P) (Fig. 4) is a structural transformation. However, to date no precedent has been reported for the RM2X2 family on a transition of the ThCr2Si2-type structure [43] to a lattice of different symmetry; in the studies undertaken on the number of its representatives such as CeCu2Si2 [14,61], CeCu2Ge2 [14,45,62], CeNi2Ge2 [14], YbCu2Si2 [63], and others, the initial structure is maintained in the same or wider P range. So, probably, in our sample YbPd2Si2, the symmetry of the initial lattice is also retained, while a nature of the transformation may be subtle. The isostructural transformation in the ThCr2Si2-type structure with a volume-collapse effect DV was found only in CeCu2Ge2 and at lowtemperature conditions (T ¼ 10 K) [45]; meanwhile, it might be a characteristic feature for this series of compounds. Because of negligibility of the volume effect (in CeCu2Ge2 DV is less than 0.5% [45]), its direct observation by structural techniques is a challenging task. Thus, through each series of the pressure dependence of the lattice volume Vo(P) for CeCu2Ge2, the DV effect was not evident, while only after superposition of three series, a clear profile of the effect has appeared [45]. One can find resembling weak anomalies in Vo(P) or in a(P) and c(P) curves for other Yb- and Ce-based compounds. For example, the a(P) and c(P) curves for YbCu2Si2 [63] exhibited a number of obvious anomalies (including a change in compressibility), and in a Vo(P) dependence one can notice a step near P12 GPa, similar to the one for CeCu2Ge2 [45]; this DV effect (seen at room temperature) corresponded to a maximum of magnetic-ordering temperature, but it was not noticed in Ref. [63].
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Fig. 4. The pressure P dependencies of the thermoelectric power (Seebeck effect) S (a), of the electrical resistance R (b), of a relative sample’s contraction (relative compressibility) Dh (c), and of a temperature difference along a sample DT (inset in plot c) of YbPd2Si2 single crystal at T ¼ 293 K. The big open symbols correspond to a pressurisation cycle, while the small closed ones to decompression.
Fig. 5. The thermopower S versus the electrical resistance R for YbPd2Si2 by the data from Fig. 4. The big symbols correspond to a pressurisation cycle, while the small ones correspond to decompression. The bends correspond to the pressure values P6 and 3 GPa for the pressurisation and decompression cycles, respectively.
Another probable explanation of the transformation found (Fig. 4) is a pressure-driven valence transition, which may be concurrent with a tiny volume collapse DV due to an abrupt change in an ionic radius of the unstable valence Yb [64] (Fig. 1). In the majority of heavy fermion compounds, a valence of Yb varies between 2+ and 3+ limits. Yb2+ has a filled 4f shell and thus has no magnetic moment contrary to magnetic Yb3+ [65]. The last circumstance explains both the differences in properties between compounds with Yb2+ and Yb3+, and the anomalies of properties of materials with a non-integer (intermediate) valence. At ambient conditions a ‘‘mean valence’’ of Yb in YbPd2Si2 was found to be 2.89 [66]. Application of external pressure can potentially shift this ‘‘mean valence’’ to a trivalent limit. The results presented in Ref. [65] qualitatively demonstrated an increase in the Yb valence in YbPd2Si2 under P4–5 GPa; meanwhile neither a trivalent state was achieved nor a P–T boundary of this transition was found. In YbInCu4, YbMn2Ge2, and other compounds, a pressure-driven valence transition has been already established, exhibiting a hysteresis in the T values of direct and return transformations [42,67]. A spin transition under P is also able to induce an isostructural transition with DV effect but without pressure hysteresis [68].
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It is known that d- and f-electrons can contribute to the formation of covalent bonds in a lattice, such as s- and p-ones, and the strength of these bonds is expected to be stronger [69]. This is a reason of a pressure-induced isostructural-phase transition established both in the octahedral-bonded rare-earth chalcogenides with the NaCl structure (partial transition from d2sp3 to d2sf3 electronic configuration) and in other compounds (partial transition from sp3 to sf3 configuration—in tetrahedral bonded lattices and from dsp2 to dsf2 in quadratic lattices) [70]. A change in occupancy of f-levels leads to peculiarities in structural, electronic, and magnetic properties of materials. In an example of Yb, Sm, and Eu chalcogenides, it was shown that an isostructural valence phase transition happens just after a softening of the NaCl lattice [70]. So, an increase in the ‘‘mean valence’’ and a following growth in an electron concentration could explain our S(P) and R(P) dependencies (Fig. 4a, b). Meanwhile, it seems surprising that a potentially small variation in the ‘‘mean valence’’ (2.9-3) can result in such drastic variation in properties. One of the possible explanations might be as follows: the initially non-magnetic material acquires magnetic properties because of reduction in the Pb–Pd distances along the a- or c-axes (Fig. 1) below some critical value. We could not find in the literature a law relating the Pd–Pd distances along the a- and c-axes in RPd2X2 to the magnetic properties (anti- and ferromagnetism), like the one for the Mn–Mn distances in RMn2X2 [71]; the latter reported on a critical value of the distance separating the regions of anti- and ferromagnetism for RMn2X2 if the Mn–Mn distance along the a-axis is correspondingly shorter or longer than a critical one. In the case of resembling material CePd2Si2 (a ¼ 4.2318 A˚ and b ¼ 9.9035 A˚) [59], it was found that a pressure-driven reduction in a cell volume and increase in the c/a ratio lead to a suppression of the antiferromagnetic state [72]. This fact agrees with the absence of magnetism at ambient conditions in YbPd2Si2; however, it does not hint at prospective modification of a dominant Pd–Pd exchange interaction under further reduction in the distances. The volume-collapse effect was shown to be an important indicator of possibility of existence of a superconducting state near the quantum transition [2]. So, according to Ref. [2], one of the necessary conditions for ‘‘spatially extended density fluctuations’’ superconductivity is a low-lying temperature endpoint of the transition—‘‘well below room temperature’’. Thus, if the feature we found is a valence transition with the DV effect, then probably YbPd2Si2 cannot form a superconducting state near this quantum transition at low temperatures [2]. A search for a pressure-driven superconductivity in YbPd2Si2 would help to clarify this general problem. Notice that at similar P values other Yb-based compounds exhibit a transition into the magnetically ordered Kondo lattice at cryogenic temperatures (T1–3 K), near P8–10 GPa in YbIr2Si2 [73], YbRh2Si2 [74], and YbCu2Si2 [63], and near P5 GPa in YbNi2Ge2 [23]; meanwhile, no features were detected at room temperature. However, the data for YbPd2Si2 from Ref. [75] hint at a different image: possible magnetic ordering below T ¼ 0.5 K at P ¼ 1 GPa. Moreover, Ref. [64] reported on an observation of an unknown weak magnetic phase below T1.4 K at ambient pressure. These findings point that a P–T diagram of YbPd2Si2 may be peculiar. Accounting for a sensitivity of the heavy fermion compounds to external influences, a small non-hydrostaticity in a pressure medium potentially could lead to a change in a pressurisation routine, distinguishing low- and high-pressure regimes. In Ref. [61] it was demonstrated that a moderate non-stoichiometricity (CeCu1.8Si2) results in an increase in the compressibility along the c-axis under pressurisation to P13–15 GPa, and then the c parameter shrinks in a similar manner as the one in the
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stoichiometric compound. The effect of non-stoichiometricity resulted in an obvious bend in a c(P) curve [61]—the resembling feature we observe in our Dh(P) dependencies curves (Fig. 4c).
5. Conclusion By the changes in the thermoelectric and the dilatometric properties, a phase transition in YbPd2Si2 was established at room temperature near P670.5 GPa. If this is a structural transition to a lattice with a different symmetry, it would be the first precedent for the RM2X2 family. One possible alternative explanation is a valence transition that should lead to the tiny volume-collapse effect (DV) because of a difference in the ionic radii of Yb3+ and Yb2+ ions (Fig. 1) [65]. As for the latter variant, it seems surprising that a potentially small variation in the ‘‘mean valence’’ (2.9 [66]-3) could result in such drastic variations in the properties (Fig. 4). However, this valence transition might be concurrent with the acquiring of magnetic properties by the initially non-magnetic material due to reduction in the Pb–Pd distances below some critical value. Note added in proof Recently, in a compound adopting the same ThCr2Si2-type structure, namely, a heavy fermion UMn2Ge2, a pressure-induced structural transition to a lattice of a different symmetry was detected near 16 GPa at room temperature [76]. The high-pressure phase was not refined. This finding supports our discussion about a possibility of a structural transformation in YbPd2Si2 near 6 GPa. Acknowledgements The authors thank Mr. A. Mezenin (IMP) for assistance in the experiment. The work was supported by the JSPS (P05312) and RFBR (Grant no. 07-08-00338).
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