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Electrical resistivity under extreme conditions in the Ce3Ir4Sn13 heavy fermion compound
Solid State Communications 177 (2014) 132–135
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Electrical resistivity under extreme conditions in the Ce3Ir4Sn13 heavy fermion compound J.R. Collave a,n, H.A. Borges a, S.M. Ramos b,c,1, E.N. Hering b,c,1, M.B. Fontes b, E. Baggio-Saitovitch b, A. Eichler d, E.M. Bittar b, P.G. Pagliuso e a
Departamento de Física, Pontifícia Universidade Católica do Rio de Janeiro, 22453-900 Rio de Janeiro, RJ, Brazil Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil c SPSMS, UMR-E CEA/UJF-Grenoble 1, INAC, 38054 Grenoble, France d Institut für Angewandte Physik, Technische Universität Braunschweig, Mendelssohnstrasse 2, D-38106 Braunschweig, Germany e Instituto de Física “Gleb Wataghin”, UNICAMP, 13083-859 Campinas, SP, Brazil b
art ic l e i nf o
a b s t r a c t
Article history: Received 9 August 2013 Received in revised form 30 September 2013 Accepted 11 October 2013 by prof. C. Lacroix Available online 21 October 2013
We have performed measurements of temperature dependent electrical resistivity ρðTÞ under pressures up to 27 kbar and down to 0.1 K on single crystals of the Ce3Ir4Sn13 heavy fermion compound. At ambient pressure (P ¼0) we have identified in the ρðTÞ data interesting features associated with the presence of crystalline field effects, magnetic correlations, Kondo single impurity scattering and, possibly, a low temperature structural phase transition. All these features were mapped as a function of pressure which allowed us to construct a pressure–temperature phase diagram with these temperature scales. We have also carried out measurements of ρðTÞ as a function of magnetic fields up to H ¼8 T and the important temperature scales in ρðTÞ were followed with field. Enlightened also by temperature dependent specific heat experiments we discuss the possible microscopic origins of the features found in our ρðTÞ data. & 2013 Elsevier Ltd. All rights reserved.
Keywords: A. Heavy fermion A. Ce3Ir4Sn13 C. Electrical resistivity C. Hydrostatic pressure
1. Introduction Firstly synthesized by Remeika et al. [1], for M¼Rh, in 1980, the intermetallic series of compounds R3M4Sn13, where R¼rare-earth ion and M¼ transition-metal (for example, Rh, Ir and Co) establishes a favorable system to study the interplay between interesting physical phenomena and their microscopic origins in structurally related materials. The intermetallic 3–4–13 series crystallizes in the cubic Yb3Rh4Sn13 type structure (space group Pm3n) which has 40 atoms per unit cell [2]. The structure contains a network of trigonal prisms MSn6 joined at their vertices, which generates two sites: an icosahedral and other an cubo-octahedral, occupied by Sn1 and R atoms, respectively. Actually, the cubo-octahedral rare earth site has a small distortion having really a local tetragonal symmetry [3]. Thus, this complex structure can induce interesting physical phenomena in these systems, which may have important effects on the transport properties [2,4]. These 3–4–13 compounds include, for instance, superconducting, magnetic and paramagnetic materials. Complex magnetic ordering, crystalline field (CF) effects and Ruderman–
n
Corresponding author. Tel.: þ 55 2180202633. E-mail addresses: [email protected], jacoga@fis.puc-rio.br (J.R. Collave). 1 “Science without Borders” (CNPq) scholarship.
0038-1098/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ssc.2013.10.015
Kittel–Kasuya–Yosida (RKKY) magnetic interaction are interesting physical phenomenal found in systems of these family, despite of their higher symmetry simple cubic structure. In most of these compounds the magnetism results mainly from the rare earth 4f electrons [4]. Examples of 3–4–13 intermetallic systems include type-II superconductors, for example, Ca3Rh4Sn13 ðT c 8:2 KÞ and Yb3Rh4Sn13 ðT c 8 KÞ [1]. There are antiferromagnetic materials such as Sm3Ir4Sn13 ðT N ¼ 5:8 KÞ [5], Gd3Co4Sn13 ðT N ¼ 14:5 KÞ [6] and Eu3Ir4Sn13 ðT N ¼ 10 KÞ, which presents valence fluctuations between Eu2 þ and Eu3 þ with an additional phase transition at 50 K [5,7,8]. Pr3Ir4Sn13 ðθCW ¼ 15 KÞ and Nd3Ir4Sn13 ðθCW ¼ 9 KÞ are paramagnetic metals, that obey the Curie–Weiss law down to 1.8 K [5]. Among other 3–4–13 variants, the In-based compounds include a conventional superconductor La3Pt4In13 ðT c ¼ 3:3 KÞ [9]. As for the metallic nature found for the electrical resistivity in most of the 3–4–13 compounds, R3Ru4Ge13 exhibits semiconducting behavior. Only for R ¼ Yb the resistivity has a metallic-like character. The Lu and Y samples undergoes to a superconducting transition at 2.3 and 1.8 K, respectively [10]. Recently, it was shown that the superconductor Sr3Ir4Sn13 ðT c ¼ 5 KÞ undergoes a structural transition at around 147 K from the Pm3n cubic structure to a superlattice which doubles the lattice parameter in respect to the higher temperature phase. Also,
J.R. Collave et al. / Solid State Communications 177 (2014) 132–135
it was claimed that the superlattice distortion is connected with a charge density wave transition of the conduction electrons. By combining chemical and physical pressure the superlattice transition temperature can be suppressed to zero, indicating a superlattice quantum phase transition [11]. Besides the interesting 3–4–13 intermetallics above, Ce-based compounds present an additional ingredient to the CF and RKKY energy scales which is the Kondo effect. In these materials, the Kondo interaction between Ce 4f1 electron spin and the conduction electrons sea gives rise to a singlet state, which enhances the electron effective mass and affects the electronic scattering. These compounds are commonly known as heavy fermions and present a variety of physical properties due to the interplay between these three characteristic temperatures. Some examples of Ce-based 3–4–13 compounds are Ce3Co4Sn13 [12,13], Ce3Rh4Sn13 [14,15] and Ce3Pt4In13 [9]. Both Ce3Co4Sn13 and Ce3Rh4Sn13 show no evidence for long range magnetic order and present a large increase in the specific heat at low temperatures yielding a high γ Sommerfeld coefficient [15]. On the other hand Ce3Pt4In13 orders antiferromagnetically at T N ¼ 0:95 K and at TN one can estimate γ 1000 mJ molCe 1 K 2 , indicating a Kondo temperature T K ¼ 5 K. In this work we investigate Ce3Ir4Sn13 which is a heavy fermion ðγ ¼ 670 mJ molCe 1 K 2 Þ [5,12] that exhibits two peaks, one at 0.6 K and another at 2 K, in specific heat data [16]. Measurements have indicated an antiferromagnetic transition at 0.6 K and a band structure, change at 2 K, accompanied by an expansion of the lattice parameter [17]. Here we show our temperature dependent electrical resistivity data on Ce3Ir4Sn13 single crystal measured under pressure and an external magnetic field. Some interesting features associated with the presence of CF effects, magnetic correlations, Kondo single impurity scattering and possibly a low temperature structural phase transition were seen. However, we have found no evidence of phase transition around 0.6 K.
2. Experiment details Sn flux-grown single crystals of Ce3Ir4Sn13, with typical dimensions of 0.5 0.5 0.5 cm3 were synthesized [18]. From room temperature the samples were heated at 200 1C/h up to 1100 1C, staying in this temperature for 2 h and then cooled at 5–650 1C where the excess of flux was spun. X-ray diffraction on powdered crystals indicates that the samples are single-phased. Specific heat measurements were performed in a Quantum Design DynaCool PPMS small-mass calorimeter that employs a quasiadiabatic thermal relaxation technique. As a reference compound, La3Ir4Sn13 was also grown and studied. For electrical resistivity measurements several samples were screened for Sn inclusions and average size of samples were approximately 0.8 0.3 0.4 mm3. We used a clamp-type Cu–Be cell, with Fluorinert FC70þFC77 as pressure transmitting medium, adapted to our AC resistance measurement system in a fourcontact configuration. The pressure cell was inserted in a He3– He4 dilution refrigerator which was able to go down to 50 mK. Lead and manganin were used as pressure manometers at low and room temperature, respectively. To determine the temperature, calibrated Cernox sensor, located at the bottom of the pressure cell in a cavity close to the sample space, was used. The temperature stability was better than 1% for the whole temperature range.
3. Results and discussion The temperature dependence of the electrical resistivity ρðTÞ for Ce3Ir4Sn13 single crystals at P ¼0 kbar is presented in Fig. 1.
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Fig. 1. Temperature dependent electrical resistivity for Ce3Ir4Sn13. Arrows indicate some characteristic features of the data. Open symbols identify the magnetic contribution to the electrical resistivity. Data for the non-magnetic reference La3Ir4Sn13 is also shown.
Among various measured crystals, the room temperature value of the resistivity ranges between 250 and 350 μΩ cm. The electrical resistivity data show interesting features in the whole temperature range. These features appear in greater details than previously reported which, along with the lower overall resistivity values, indicate a higher quality of the crystals studied in this work [5]. From 300 to 60 K ρðTÞ increases as temperature is lowered due to the Kondo single impurity scattering of the conduction electrons by the Ce3 þ local moments. Then, ρðTÞ reaches a maximum at around T CF ¼ 50 K that can be presumably associated to the CF effects [19,20]. This effect splits the degeneracy of the J ¼5/2 multiplet of the Ce3 þ ion into three Kramers doublets due to the tetragonal site symmetry of Ce3 þ ions [3]. The depopulation of the CF doublets can affect the Kondo single impurity scattering of the conduction electrons by the Ce3 þ local moments, creating a hump-like feature in the data which gives rise to a minimum at T min ¼ 16 K [21]. At lower temperature, ρðTÞ reaches a sharper maximum at Tmax as typically found in the Ce-based Kondo lattice compounds [22– 24]. However, just below Tmax, a clear kink can be seen at T ? ¼ 2 K indicating some sort of phase transition. This anomaly at T ? has been previously suggested to be due to a structural phase transition [17]. The reported antiferromagnetic transition at 0.6 K [16,17] is not observed in our electrical resistivity measurements. Fig. 2 shows the specific heat divided by temperature and the corresponding magnetic entropy in the temperature range 0 o T o 3:5 K for Ce3Ir4Sn13 single crystals. To calculate the magnetic entropy the phonon contribution was estimated from the non-magnetic specific heat data of La3Ir4Sn13 and subtracted from the total specific heat of the magnetic compound. The recovery magnetic entropy at T¼ 3.5 K is below the expected values for CF doublet indicating the existence of a partial Kondo compensation. At T ? ¼ 2 K the specific heat also show a broad peak associated with a possible phase transition. The pressure evolution of the electrical resistivity as a function of temperature for Ce3Ir4Sn13 single crystals is displayed in Fig. 3. These curves are representative of the qualitative behavior for all measured pressures. From these data we extract the relevant temperature scales for Ce3Ir4Sn13 and construct the pressure– temperature phase diagram presented in Fig. 4. The phase diagram clearly shows that Tmin shifts to higher temperatures reaching a value higher than 20 K for P ¼27 kbar. This effect occurs as a result of the suppression of the CF hump with pressure (see lower inset of Fig. 3) and suggests the strengthening of the hybridization
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J.R. Collave et al. / Solid State Communications 177 (2014) 132–135
Fig. 2. (Color online) Specific heat divided by temperature as a function of temperature for Ce3Ir4Sn13. Arrows indicate T ? and Tmax characteristic temperature scales of the electrical resistivity data (Fig. 1). Open symbols identify the magnetic contribution to the specific heat. Data for the non-magnetic reference La3Ir4Sn13 is also shown. Inset: calculated magnetic entropy of Ce3Ir4Sn13.
Fig. 3. (Color online) Representative pressure-dependent electrical resistivity curves as a function of temperature for Ce3Ir4Sn13. Upper and lower insets show in detail the pressure evolution of T ? and TCF, respectively.
Fig. 4. (Color online) Pressure–temperature phase diagram for Ce3Ir4Sn13 showing the pressure dependence of the Tmin, Tmax and T ? features seen in the electrical resistivity data. The dotted lines are guides for the eye.
Fig. 5. (Color online) Magnetic field dependence of the electrical resistivity as function of temperature for Ce3Ir4Sn13 at ambient pressure. (a) Tmin evolution with magnetic field. Inset: wider temperature range of the electric resistivity for different applied magnetic fields. (b) Tmax evolution with magnetic field.
between the Ce3 þ 4f electrons and the conduction bands as pressure is increased. This increase tends to mix the CF levels suppressing the CF hump and recovering the continuous increasing with decreasing temperature of ρðTÞ expected from the Kondo single impurity scattering regime. Typically, the CF levels for Cebased Kondo lattice compounds are broadened. As such, the increase of hybridization by pressure can intensify the CF levels broadening which tends to mix them and diminish their effect on the physical properties [25]. Regarding the behavior of Tmax, when this maximum is connected to the crossover from incoherent to coherent electronic scattering regime, it moves to higher temperatures under pressure, as it is the case for most Ce-based heavy fermion compounds [22–24]. On contrary, Tmax for Ce3Ir4Sn13 in Fig. 4 displays a small decrease as a function a pressure resembling the behavior of magnetic phase transitions in Ce-based Kondo lattice compounds. In fact, Tmax follows closely the pressure dependence of T ? ¼ 2 K suggesting that this two temperature scales may be connected. To gain further insights about the microscopic origin of the reported temperatures scales for Ce3Ir4Sn13 we have investigated the effect of an external magnetic field on the transport data for this compound. Fig. 5 shows the behavior under a magnetic field of the temperature dependent electrical resistivity of Ce3Ir4Sn13. Again the relevant temperature scales of the electrical resistivity data are mapped as a function of field at P ¼0 for Ce3Ir4Sn13 in order to construct a phase diagram as a function of magnetic field, as presented in Fig. 6. Here one can see that Tmax actually moves to higher temperature. This result is also inconsistent with the onset of Kondo lattice coherence at Tmax. Alternatively, this behavior of Tmax is expected if this temperature scale is associated with magnetic correlations of ferromagnetic nature. Interestingly, T ? does not follow the same field dependence of Tmax, showing, in fact, a small decrease as a function of magnetic field. This may indicate that the phase transition at T ? is in fact structural as previously suggested [17] and it is only weakly dependent on magnetic field. As such, the pressure dependence of T ? may be associated with variation of structural instabilities resembling the behavior of the high/low temperature structural transitions in the 3–4–13 families which always shifts to lower temperature as the lattice parameters decrease [3,26,27]. In particular, the Ce-based relative compound Ce3Co4Sn13 presents a high temperature structural transition at T ¼150 K which also shifts to lower temperatures as a function of pressure [26]. More broadly, many members of the R3(Co,Ir)4Sn13 (R¼Ce-Gd) series
J.R. Collave et al. / Solid State Communications 177 (2014) 132–135
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Acknowledgments This work was supported by FAPERJ, FAPESP, CNPq, FINEP and CAPES (Brazil).
References
Fig. 6. (Color online) Magnetic field-temperature phase diagram for Ce3Ir4Sn13 showing the magnetic field dependence of the Tmin, Tmax and T ? features seen in the electrical resistivity data at ambient pressure. The dotted lines are guides for the eye.
present such structural transition at high temperatures that moves to lower temperatures as a function of the decrease of the atomic radius of the R-ion [3]. Regarding the origin of Tmax it is plausible to speculate that it may be the result of short range ferromagnetic correlation that do not fully develop into a magnetic long range ordered state. This scenario may found support in the broad anomaly observed in the specific heat data for Ce3Ir4Sn13 compound (see Fig. 2). The presence of short range magnetic correlation in Ce-based Kondo lattice has been show to produce broad humps in the specific heat data near a phase transition [28–30]. Future experiments of field dependent heat capacity, 119Sn Mössbauer spectroscopy and pressure dependent magnetic susceptibility will be valuable to confirm such scenario. 4. Summary In summary, we report measurements of ρðTÞ under pressures up to 27 kbar and down to 0.1 K on single crystals of the Ce3Ir4Sn13 heavy fermion compound. The study was complemented by temperature dependent specific heat experiments at ambient pressure (P ¼0). Interesting features were identified in the ρðTÞ data and mapped as a function of pressure and as a function of magnetic field at P ¼0. We claim that the ρðTÞ data at higher temperatures are dominated by the interplay between the CF and Kondo single impurity scattering effects. At low temperatures the features observed in the data seem to be related to the presence of ferromagnetic short range magnetic correlations and, possibly, a low temperature structural phase transition.
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Electrical resistivity under extreme conditions in the Ce3Ir4Sn13 heavy fermion compound J.R. Collave a,n, H.A. Borges a, S.M. Ramos b,c,1, E.N. Hering b,c,1, M.B. Fontes b, E. Baggio-Saitovitch b, A. Eichler d, E.M. Bittar b, P.G. Pagliuso e a
Departamento de Física, Pontifícia Universidade Católica do Rio de Janeiro, 22453-900 Rio de Janeiro, RJ, Brazil Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil c SPSMS, UMR-E CEA/UJF-Grenoble 1, INAC, 38054 Grenoble, France d Institut für Angewandte Physik, Technische Universität Braunschweig, Mendelssohnstrasse 2, D-38106 Braunschweig, Germany e Instituto de Física “Gleb Wataghin”, UNICAMP, 13083-859 Campinas, SP, Brazil b
art ic l e i nf o
a b s t r a c t
Article history: Received 9 August 2013 Received in revised form 30 September 2013 Accepted 11 October 2013 by prof. C. Lacroix Available online 21 October 2013
We have performed measurements of temperature dependent electrical resistivity ρðTÞ under pressures up to 27 kbar and down to 0.1 K on single crystals of the Ce3Ir4Sn13 heavy fermion compound. At ambient pressure (P ¼0) we have identified in the ρðTÞ data interesting features associated with the presence of crystalline field effects, magnetic correlations, Kondo single impurity scattering and, possibly, a low temperature structural phase transition. All these features were mapped as a function of pressure which allowed us to construct a pressure–temperature phase diagram with these temperature scales. We have also carried out measurements of ρðTÞ as a function of magnetic fields up to H ¼8 T and the important temperature scales in ρðTÞ were followed with field. Enlightened also by temperature dependent specific heat experiments we discuss the possible microscopic origins of the features found in our ρðTÞ data. & 2013 Elsevier Ltd. All rights reserved.
Keywords: A. Heavy fermion A. Ce3Ir4Sn13 C. Electrical resistivity C. Hydrostatic pressure
1. Introduction Firstly synthesized by Remeika et al. [1], for M¼Rh, in 1980, the intermetallic series of compounds R3M4Sn13, where R¼rare-earth ion and M¼ transition-metal (for example, Rh, Ir and Co) establishes a favorable system to study the interplay between interesting physical phenomena and their microscopic origins in structurally related materials. The intermetallic 3–4–13 series crystallizes in the cubic Yb3Rh4Sn13 type structure (space group Pm3n) which has 40 atoms per unit cell [2]. The structure contains a network of trigonal prisms MSn6 joined at their vertices, which generates two sites: an icosahedral and other an cubo-octahedral, occupied by Sn1 and R atoms, respectively. Actually, the cubo-octahedral rare earth site has a small distortion having really a local tetragonal symmetry [3]. Thus, this complex structure can induce interesting physical phenomena in these systems, which may have important effects on the transport properties [2,4]. These 3–4–13 compounds include, for instance, superconducting, magnetic and paramagnetic materials. Complex magnetic ordering, crystalline field (CF) effects and Ruderman–
n
Corresponding author. Tel.: þ 55 2180202633. E-mail addresses: [email protected], jacoga@fis.puc-rio.br (J.R. Collave). 1 “Science without Borders” (CNPq) scholarship.
0038-1098/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ssc.2013.10.015
Kittel–Kasuya–Yosida (RKKY) magnetic interaction are interesting physical phenomenal found in systems of these family, despite of their higher symmetry simple cubic structure. In most of these compounds the magnetism results mainly from the rare earth 4f electrons [4]. Examples of 3–4–13 intermetallic systems include type-II superconductors, for example, Ca3Rh4Sn13 ðT c 8:2 KÞ and Yb3Rh4Sn13 ðT c 8 KÞ [1]. There are antiferromagnetic materials such as Sm3Ir4Sn13 ðT N ¼ 5:8 KÞ [5], Gd3Co4Sn13 ðT N ¼ 14:5 KÞ [6] and Eu3Ir4Sn13 ðT N ¼ 10 KÞ, which presents valence fluctuations between Eu2 þ and Eu3 þ with an additional phase transition at 50 K [5,7,8]. Pr3Ir4Sn13 ðθCW ¼ 15 KÞ and Nd3Ir4Sn13 ðθCW ¼ 9 KÞ are paramagnetic metals, that obey the Curie–Weiss law down to 1.8 K [5]. Among other 3–4–13 variants, the In-based compounds include a conventional superconductor La3Pt4In13 ðT c ¼ 3:3 KÞ [9]. As for the metallic nature found for the electrical resistivity in most of the 3–4–13 compounds, R3Ru4Ge13 exhibits semiconducting behavior. Only for R ¼ Yb the resistivity has a metallic-like character. The Lu and Y samples undergoes to a superconducting transition at 2.3 and 1.8 K, respectively [10]. Recently, it was shown that the superconductor Sr3Ir4Sn13 ðT c ¼ 5 KÞ undergoes a structural transition at around 147 K from the Pm3n cubic structure to a superlattice which doubles the lattice parameter in respect to the higher temperature phase. Also,
J.R. Collave et al. / Solid State Communications 177 (2014) 132–135
it was claimed that the superlattice distortion is connected with a charge density wave transition of the conduction electrons. By combining chemical and physical pressure the superlattice transition temperature can be suppressed to zero, indicating a superlattice quantum phase transition [11]. Besides the interesting 3–4–13 intermetallics above, Ce-based compounds present an additional ingredient to the CF and RKKY energy scales which is the Kondo effect. In these materials, the Kondo interaction between Ce 4f1 electron spin and the conduction electrons sea gives rise to a singlet state, which enhances the electron effective mass and affects the electronic scattering. These compounds are commonly known as heavy fermions and present a variety of physical properties due to the interplay between these three characteristic temperatures. Some examples of Ce-based 3–4–13 compounds are Ce3Co4Sn13 [12,13], Ce3Rh4Sn13 [14,15] and Ce3Pt4In13 [9]. Both Ce3Co4Sn13 and Ce3Rh4Sn13 show no evidence for long range magnetic order and present a large increase in the specific heat at low temperatures yielding a high γ Sommerfeld coefficient [15]. On the other hand Ce3Pt4In13 orders antiferromagnetically at T N ¼ 0:95 K and at TN one can estimate γ 1000 mJ molCe 1 K 2 , indicating a Kondo temperature T K ¼ 5 K. In this work we investigate Ce3Ir4Sn13 which is a heavy fermion ðγ ¼ 670 mJ molCe 1 K 2 Þ [5,12] that exhibits two peaks, one at 0.6 K and another at 2 K, in specific heat data [16]. Measurements have indicated an antiferromagnetic transition at 0.6 K and a band structure, change at 2 K, accompanied by an expansion of the lattice parameter [17]. Here we show our temperature dependent electrical resistivity data on Ce3Ir4Sn13 single crystal measured under pressure and an external magnetic field. Some interesting features associated with the presence of CF effects, magnetic correlations, Kondo single impurity scattering and possibly a low temperature structural phase transition were seen. However, we have found no evidence of phase transition around 0.6 K.
2. Experiment details Sn flux-grown single crystals of Ce3Ir4Sn13, with typical dimensions of 0.5 0.5 0.5 cm3 were synthesized [18]. From room temperature the samples were heated at 200 1C/h up to 1100 1C, staying in this temperature for 2 h and then cooled at 5–650 1C where the excess of flux was spun. X-ray diffraction on powdered crystals indicates that the samples are single-phased. Specific heat measurements were performed in a Quantum Design DynaCool PPMS small-mass calorimeter that employs a quasiadiabatic thermal relaxation technique. As a reference compound, La3Ir4Sn13 was also grown and studied. For electrical resistivity measurements several samples were screened for Sn inclusions and average size of samples were approximately 0.8 0.3 0.4 mm3. We used a clamp-type Cu–Be cell, with Fluorinert FC70þFC77 as pressure transmitting medium, adapted to our AC resistance measurement system in a fourcontact configuration. The pressure cell was inserted in a He3– He4 dilution refrigerator which was able to go down to 50 mK. Lead and manganin were used as pressure manometers at low and room temperature, respectively. To determine the temperature, calibrated Cernox sensor, located at the bottom of the pressure cell in a cavity close to the sample space, was used. The temperature stability was better than 1% for the whole temperature range.
3. Results and discussion The temperature dependence of the electrical resistivity ρðTÞ for Ce3Ir4Sn13 single crystals at P ¼0 kbar is presented in Fig. 1.
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Fig. 1. Temperature dependent electrical resistivity for Ce3Ir4Sn13. Arrows indicate some characteristic features of the data. Open symbols identify the magnetic contribution to the electrical resistivity. Data for the non-magnetic reference La3Ir4Sn13 is also shown.
Among various measured crystals, the room temperature value of the resistivity ranges between 250 and 350 μΩ cm. The electrical resistivity data show interesting features in the whole temperature range. These features appear in greater details than previously reported which, along with the lower overall resistivity values, indicate a higher quality of the crystals studied in this work [5]. From 300 to 60 K ρðTÞ increases as temperature is lowered due to the Kondo single impurity scattering of the conduction electrons by the Ce3 þ local moments. Then, ρðTÞ reaches a maximum at around T CF ¼ 50 K that can be presumably associated to the CF effects [19,20]. This effect splits the degeneracy of the J ¼5/2 multiplet of the Ce3 þ ion into three Kramers doublets due to the tetragonal site symmetry of Ce3 þ ions [3]. The depopulation of the CF doublets can affect the Kondo single impurity scattering of the conduction electrons by the Ce3 þ local moments, creating a hump-like feature in the data which gives rise to a minimum at T min ¼ 16 K [21]. At lower temperature, ρðTÞ reaches a sharper maximum at Tmax as typically found in the Ce-based Kondo lattice compounds [22– 24]. However, just below Tmax, a clear kink can be seen at T ? ¼ 2 K indicating some sort of phase transition. This anomaly at T ? has been previously suggested to be due to a structural phase transition [17]. The reported antiferromagnetic transition at 0.6 K [16,17] is not observed in our electrical resistivity measurements. Fig. 2 shows the specific heat divided by temperature and the corresponding magnetic entropy in the temperature range 0 o T o 3:5 K for Ce3Ir4Sn13 single crystals. To calculate the magnetic entropy the phonon contribution was estimated from the non-magnetic specific heat data of La3Ir4Sn13 and subtracted from the total specific heat of the magnetic compound. The recovery magnetic entropy at T¼ 3.5 K is below the expected values for CF doublet indicating the existence of a partial Kondo compensation. At T ? ¼ 2 K the specific heat also show a broad peak associated with a possible phase transition. The pressure evolution of the electrical resistivity as a function of temperature for Ce3Ir4Sn13 single crystals is displayed in Fig. 3. These curves are representative of the qualitative behavior for all measured pressures. From these data we extract the relevant temperature scales for Ce3Ir4Sn13 and construct the pressure– temperature phase diagram presented in Fig. 4. The phase diagram clearly shows that Tmin shifts to higher temperatures reaching a value higher than 20 K for P ¼27 kbar. This effect occurs as a result of the suppression of the CF hump with pressure (see lower inset of Fig. 3) and suggests the strengthening of the hybridization
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Fig. 2. (Color online) Specific heat divided by temperature as a function of temperature for Ce3Ir4Sn13. Arrows indicate T ? and Tmax characteristic temperature scales of the electrical resistivity data (Fig. 1). Open symbols identify the magnetic contribution to the specific heat. Data for the non-magnetic reference La3Ir4Sn13 is also shown. Inset: calculated magnetic entropy of Ce3Ir4Sn13.
Fig. 3. (Color online) Representative pressure-dependent electrical resistivity curves as a function of temperature for Ce3Ir4Sn13. Upper and lower insets show in detail the pressure evolution of T ? and TCF, respectively.
Fig. 4. (Color online) Pressure–temperature phase diagram for Ce3Ir4Sn13 showing the pressure dependence of the Tmin, Tmax and T ? features seen in the electrical resistivity data. The dotted lines are guides for the eye.
Fig. 5. (Color online) Magnetic field dependence of the electrical resistivity as function of temperature for Ce3Ir4Sn13 at ambient pressure. (a) Tmin evolution with magnetic field. Inset: wider temperature range of the electric resistivity for different applied magnetic fields. (b) Tmax evolution with magnetic field.
between the Ce3 þ 4f electrons and the conduction bands as pressure is increased. This increase tends to mix the CF levels suppressing the CF hump and recovering the continuous increasing with decreasing temperature of ρðTÞ expected from the Kondo single impurity scattering regime. Typically, the CF levels for Cebased Kondo lattice compounds are broadened. As such, the increase of hybridization by pressure can intensify the CF levels broadening which tends to mix them and diminish their effect on the physical properties [25]. Regarding the behavior of Tmax, when this maximum is connected to the crossover from incoherent to coherent electronic scattering regime, it moves to higher temperatures under pressure, as it is the case for most Ce-based heavy fermion compounds [22–24]. On contrary, Tmax for Ce3Ir4Sn13 in Fig. 4 displays a small decrease as a function a pressure resembling the behavior of magnetic phase transitions in Ce-based Kondo lattice compounds. In fact, Tmax follows closely the pressure dependence of T ? ¼ 2 K suggesting that this two temperature scales may be connected. To gain further insights about the microscopic origin of the reported temperatures scales for Ce3Ir4Sn13 we have investigated the effect of an external magnetic field on the transport data for this compound. Fig. 5 shows the behavior under a magnetic field of the temperature dependent electrical resistivity of Ce3Ir4Sn13. Again the relevant temperature scales of the electrical resistivity data are mapped as a function of field at P ¼0 for Ce3Ir4Sn13 in order to construct a phase diagram as a function of magnetic field, as presented in Fig. 6. Here one can see that Tmax actually moves to higher temperature. This result is also inconsistent with the onset of Kondo lattice coherence at Tmax. Alternatively, this behavior of Tmax is expected if this temperature scale is associated with magnetic correlations of ferromagnetic nature. Interestingly, T ? does not follow the same field dependence of Tmax, showing, in fact, a small decrease as a function of magnetic field. This may indicate that the phase transition at T ? is in fact structural as previously suggested [17] and it is only weakly dependent on magnetic field. As such, the pressure dependence of T ? may be associated with variation of structural instabilities resembling the behavior of the high/low temperature structural transitions in the 3–4–13 families which always shifts to lower temperature as the lattice parameters decrease [3,26,27]. In particular, the Ce-based relative compound Ce3Co4Sn13 presents a high temperature structural transition at T ¼150 K which also shifts to lower temperatures as a function of pressure [26]. More broadly, many members of the R3(Co,Ir)4Sn13 (R¼Ce-Gd) series
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Acknowledgments This work was supported by FAPERJ, FAPESP, CNPq, FINEP and CAPES (Brazil).
References
Fig. 6. (Color online) Magnetic field-temperature phase diagram for Ce3Ir4Sn13 showing the magnetic field dependence of the Tmin, Tmax and T ? features seen in the electrical resistivity data at ambient pressure. The dotted lines are guides for the eye.
present such structural transition at high temperatures that moves to lower temperatures as a function of the decrease of the atomic radius of the R-ion [3]. Regarding the origin of Tmax it is plausible to speculate that it may be the result of short range ferromagnetic correlation that do not fully develop into a magnetic long range ordered state. This scenario may found support in the broad anomaly observed in the specific heat data for Ce3Ir4Sn13 compound (see Fig. 2). The presence of short range magnetic correlation in Ce-based Kondo lattice has been show to produce broad humps in the specific heat data near a phase transition [28–30]. Future experiments of field dependent heat capacity, 119Sn Mössbauer spectroscopy and pressure dependent magnetic susceptibility will be valuable to confirm such scenario. 4. Summary In summary, we report measurements of ρðTÞ under pressures up to 27 kbar and down to 0.1 K on single crystals of the Ce3Ir4Sn13 heavy fermion compound. The study was complemented by temperature dependent specific heat experiments at ambient pressure (P ¼0). Interesting features were identified in the ρðTÞ data and mapped as a function of pressure and as a function of magnetic field at P ¼0. We claim that the ρðTÞ data at higher temperatures are dominated by the interplay between the CF and Kondo single impurity scattering effects. At low temperatures the features observed in the data seem to be related to the presence of ferromagnetic short range magnetic correlations and, possibly, a low temperature structural phase transition.
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