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High-pressure phase diagram of YbRh2Si2
ARTICLE IN PRESS
Physica B 359–361 (2005) 20–22 www.elsevier.com/locate/physb
High-pressure phase diagram of YbRh2Si2 G. Knebel, V. Glazkov, A. Pourret, P.G. Niklowitz, G. Lapertot, B. Salce, J. Flouquet De´partement de Recherche Fondamentale sur la Matie`re Condense´e, SPSMS, CEA Grenoble, 38054 Grenoble, France
Abstract We studied the high-pressure phase diagram of YbRh2Si2 by resistivity and specific heat measurements. The magnetic ordering temperature T N has a smooth maximum as function of pressure p at about 4 GPa. Above 9 GPa the magnetic structure is probably changing as T N ðpÞ is strongly increasing with pressure. Magnetoresistance measurements show a fundamental change between 2.3 and 6 GPa indicating different magnetic states. Further, we present specific heat measurements on mono-isotopic 174 YbRh2Si2 single crystals. r 2005 Elsevier B.V. All rights reserved. PACS: 71.10.Hf; 71.27.+a; 75.20.Hr Keywords: Heavy fermion; High pressure
In recent years, YbRh2Si2 has attracted much attention as this system is at ambient pressure ðpÞ very close to an antiferromagnetic quantum critical point [1]. This was inferred from the observation of a low ordering temperature ðT N ¼ 75 mKÞ which can be easily suppressed by the application of a small magnetic field or a negative pressure (small Ge doping on the Si site) [2]. The ordered state is characterized by a tiny moment ðmord ¼ 102 2103 mB Þ and the observation of antiferro- and ferromagnetic spin fluctuations below 200 mK [3,4]. At p ¼ 0 the system shows Corresponding author.
E-mail address: [email protected] (G. Knebel).
strong deviations from Fermi liquid properties in the paramagnetic regime over a large temperature range in resistivity ðDr / TÞ and in the electronic specific heat ðDC=T / ln TÞ: Despite the small magnetic moment, the signatures of the specific heat and resistivity anomalies at p ¼ 0 are very large in YbRh2Si2 in comparison to Ce compounds near a magnetic instability. The difference due to the strong localization of the 4f orbitals of Yb (0.25 A˚) compared to that of Ce (0.37 A˚) [5] leads to a different degree of hybridization with the conduction electrons and thus to a sizable difference in the magnetic properties. The local magnetic moments of Yb3þ can exist even much below the Kondo temperature, as observed
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.12.043
ARTICLE IN PRESS G. Knebel et al. / Physica B 359– 361 (2005) 20–22
by ESR studies [6]. If the hyperfine coupling is strong, these moments can couple with the nuclear spin I and a magnetic order can be induced (as observed e.g. in Pr metal [7]). From the seven Yb isotopes two exist with a nuclear moment (171 Yb; I ¼ 12; natural abundance 14.3%, and 173 Yb; I ¼ 52; natural abundance 16.1%). To test the influence of the hyperfine coupling on the magnetic ordering we have grown mono-isotopic 174 YbRh2 Si2 single crystals. CðTÞ=T and rðTÞ measured on these crystals are shown in Fig. 1. CðTÞ=T shows a very pronounced peak indicating the magnetic order at T N : The absolute value of CðTÞ=T at low temperature is somewhat lower than observed in Ref. [2]. The extrapolation T ! 0 gives g 1:2 J=mol K2 : Most interestingly we do not see a logarithmic increase of C=T above the magnetic transition but the C=T is only slightly increasing from 1 to 0.2 K. As shown in the inset of Fig. 1 rðTÞ of the mono-isotopic sample shows also a linear temperature dependence above the transition temperature. Previous r and C measurements in YbRh2Si2 inferred that T N increases up to 950 mK at p ¼ 2:5 GPa [8]. Mo¨ssbauer spectroscopy in quasihydrostatic pressure conditions shows that the low-moment (LM) magnetically ordered state persists up to about 10 GPa [9]. For 3 GPa opo 10 GPa T N ðpÞ 1 K is reported to be almost constant and at p ¼ 10 GPa a first-order phase
10 1.5 0.2
0.4 T (K)
1
0.6
ρ (H ) / ρ (H =0)
2.0
ρ (µΩcm)
ρ (µΩcm)
C/T (J/mol K2)
transition appears from the LM state to a high moment (HM) with mord ¼ 1:9mB at p ¼ 16:5 GPa: However, the reported p–T phase diagram is unique and the observed plateau cannot be explained in terms of a Doniach phase diagram. Here we present high-pressure resistivity and ac calorimetric measurements on YbRh2Si2 single crystals (not mono-isotopic) in a diamond anvil cell with argon as pressure transmitting medium. Argon deserves generally excellent hydrostatic conditions up to 10 GPa. At p ¼ 0 these single crystals have a resistivity ratio rð300 KÞ= rð0:1 KÞ 300 and they show a nice resistivity anomaly due to the onset of the antiferromagnetic order at T N 85 mK; somewhat higher than reported in Ref. [1]. Fig. 2 shows rðTÞ for different pressures. At T N ; rðTÞ shows a pronounced kink. The inset of Fig. 2 shows the magnetic field dependence rðHÞ=rðH ¼ 0Þ at 100 mK for p ¼ 2:3 and 6 GPa for Hkc: At p ¼ 2:3 GPa the magnetoresistance shows a very sharp decrease at H c ¼ 1:8 T and the magnetic order is suppressed for H4H c : In comparison to p ¼ 0; ðH c =T N Þ is about 5 times lower at 2.3 GPa. At p ¼ 2:3 GPa; an analysis of rðTÞ for To250 mK shows that the A-coefficient of the T 2 term of rðTÞ is almost constant as a function of H in the magnetic-ordered regime Ho1:8 T and is decreasing for H42 T from 10 mO cm=K2 to 7 mO cm=K2 at 6 T. However, rðT; HÞ has changed
2.5
TN = 80 mK 2
21
6 GPa
1.2 2.3
1.0 0
5
6 GPa
1.4
2.3 2
4 H (T)
6
1.3 YbRh2Si2
174YbRh Si 2 2
0 0.1
1 T (K)
Fig. 1. Specific heat as C=T vs. T on a logarithmic scale of mono-isotopic 174 YbRh2 Si2 : rðTÞ is linear in T above T N (see inset).
0 0.0
0.4
0.8
1.2
T (K)
Fig. 2. Electrical resistivity of YbRh2Si2 under high-pressure. The inset show the normalized magnetoresistance at 100 mK for p ¼ 2:3 and 6 GPa.
ARTICLE IN PRESS G. Knebel et al. / Physica B 359– 361 (2005) 20–22
22
4 YbRh2Si2 3 T (K)
Cac ρ
2
1
0
0
3
6 p (GPa)
9
12
Fig. 3. High-pressure phase diagram of YbRh2Si2 from AC calorimetry C AC and resistivity measurements r:
completely at p ¼ 6 GPa: Although T N is almost unchanged, at p ¼ 6 GPa H ¼ 6 T is not sufficient to suppress AFM at low temperatures. Here AðHÞ is decreasing linearly from 5:6 mO cm=K2 at H ¼ 0 to A ¼ 1:8 mO cm=K2 at H ¼ 6 T: The p–T phase diagram of YbRh2Si2 is summarized in Fig. 3. It is qualitatively in agreement with Ref. [9]. The phase diagram can be divided in three different regimes: (i) Initially T N ðpÞ increases with a rate of 0.37 GPa/K. In this regime the system may be dominated by the closeness to the magnetic instability. (ii) T N ðpÞ has a maximum at
about 4–5 GPa and is decreasing for higher pressures. Here the magnetoresistance is qualitatively completely different from the low-pressure phase. (iii) Above p49 GPa; T N is increasing with a rate of 0.1 GPa/K. Here, we observed very nice magnetic anomalies by ac calorimetry (not shown). However, the transition to the highpressure phase (mord ¼ 1:9mB at 16.5 GPa [9]) seems to be associated with a drastic change of the magnetic structure near 9 GPa which may be correlated to the entrance in the fully trivalent state Yb3þ : The pressure dependence of YbRh2Si2 appears quite different from that detected in Ce heavy fermion compounds what reflects differences in the degree of hybridization and consequently in the relation between valence occupation and the magnetic instability. References [1] [2] [3] [4] [5] [6] [7] [8]
O. Trovarelli, et al., Phys. Rev. Lett. 85 (2000) 626. J. Custers, et al., Nature 424 (2003) 524. K. Ishida, et al., Phys. Rev. Lett. 89 (2002) 107202. K. Ishida, et al., Phys. Rev. B 68 (2003) 184401. J.T. Waber, D.T. Cromer, J. Chem. Phys. 42 (1965) 4116. J. Sichelschmidt, et al., Phys. Rev. Lett. 91 (2003) 156401. H. Bjerrum Møller, et al., Phys. Rev. Lett. 49 (1982) 482. S. Mederle, et al., J. Magn. Magn. Matter. 226–230 (2001) 254. [9] J. Plessel, et al., Phys. Rev. B 67 (2003) 180403(R).
Physica B 359–361 (2005) 20–22 www.elsevier.com/locate/physb
High-pressure phase diagram of YbRh2Si2 G. Knebel, V. Glazkov, A. Pourret, P.G. Niklowitz, G. Lapertot, B. Salce, J. Flouquet De´partement de Recherche Fondamentale sur la Matie`re Condense´e, SPSMS, CEA Grenoble, 38054 Grenoble, France
Abstract We studied the high-pressure phase diagram of YbRh2Si2 by resistivity and specific heat measurements. The magnetic ordering temperature T N has a smooth maximum as function of pressure p at about 4 GPa. Above 9 GPa the magnetic structure is probably changing as T N ðpÞ is strongly increasing with pressure. Magnetoresistance measurements show a fundamental change between 2.3 and 6 GPa indicating different magnetic states. Further, we present specific heat measurements on mono-isotopic 174 YbRh2Si2 single crystals. r 2005 Elsevier B.V. All rights reserved. PACS: 71.10.Hf; 71.27.+a; 75.20.Hr Keywords: Heavy fermion; High pressure
In recent years, YbRh2Si2 has attracted much attention as this system is at ambient pressure ðpÞ very close to an antiferromagnetic quantum critical point [1]. This was inferred from the observation of a low ordering temperature ðT N ¼ 75 mKÞ which can be easily suppressed by the application of a small magnetic field or a negative pressure (small Ge doping on the Si site) [2]. The ordered state is characterized by a tiny moment ðmord ¼ 102 2103 mB Þ and the observation of antiferro- and ferromagnetic spin fluctuations below 200 mK [3,4]. At p ¼ 0 the system shows Corresponding author.
E-mail address: [email protected] (G. Knebel).
strong deviations from Fermi liquid properties in the paramagnetic regime over a large temperature range in resistivity ðDr / TÞ and in the electronic specific heat ðDC=T / ln TÞ: Despite the small magnetic moment, the signatures of the specific heat and resistivity anomalies at p ¼ 0 are very large in YbRh2Si2 in comparison to Ce compounds near a magnetic instability. The difference due to the strong localization of the 4f orbitals of Yb (0.25 A˚) compared to that of Ce (0.37 A˚) [5] leads to a different degree of hybridization with the conduction electrons and thus to a sizable difference in the magnetic properties. The local magnetic moments of Yb3þ can exist even much below the Kondo temperature, as observed
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.12.043
ARTICLE IN PRESS G. Knebel et al. / Physica B 359– 361 (2005) 20–22
by ESR studies [6]. If the hyperfine coupling is strong, these moments can couple with the nuclear spin I and a magnetic order can be induced (as observed e.g. in Pr metal [7]). From the seven Yb isotopes two exist with a nuclear moment (171 Yb; I ¼ 12; natural abundance 14.3%, and 173 Yb; I ¼ 52; natural abundance 16.1%). To test the influence of the hyperfine coupling on the magnetic ordering we have grown mono-isotopic 174 YbRh2 Si2 single crystals. CðTÞ=T and rðTÞ measured on these crystals are shown in Fig. 1. CðTÞ=T shows a very pronounced peak indicating the magnetic order at T N : The absolute value of CðTÞ=T at low temperature is somewhat lower than observed in Ref. [2]. The extrapolation T ! 0 gives g 1:2 J=mol K2 : Most interestingly we do not see a logarithmic increase of C=T above the magnetic transition but the C=T is only slightly increasing from 1 to 0.2 K. As shown in the inset of Fig. 1 rðTÞ of the mono-isotopic sample shows also a linear temperature dependence above the transition temperature. Previous r and C measurements in YbRh2Si2 inferred that T N increases up to 950 mK at p ¼ 2:5 GPa [8]. Mo¨ssbauer spectroscopy in quasihydrostatic pressure conditions shows that the low-moment (LM) magnetically ordered state persists up to about 10 GPa [9]. For 3 GPa opo 10 GPa T N ðpÞ 1 K is reported to be almost constant and at p ¼ 10 GPa a first-order phase
10 1.5 0.2
0.4 T (K)
1
0.6
ρ (H ) / ρ (H =0)
2.0
ρ (µΩcm)
ρ (µΩcm)
C/T (J/mol K2)
transition appears from the LM state to a high moment (HM) with mord ¼ 1:9mB at p ¼ 16:5 GPa: However, the reported p–T phase diagram is unique and the observed plateau cannot be explained in terms of a Doniach phase diagram. Here we present high-pressure resistivity and ac calorimetric measurements on YbRh2Si2 single crystals (not mono-isotopic) in a diamond anvil cell with argon as pressure transmitting medium. Argon deserves generally excellent hydrostatic conditions up to 10 GPa. At p ¼ 0 these single crystals have a resistivity ratio rð300 KÞ= rð0:1 KÞ 300 and they show a nice resistivity anomaly due to the onset of the antiferromagnetic order at T N 85 mK; somewhat higher than reported in Ref. [1]. Fig. 2 shows rðTÞ for different pressures. At T N ; rðTÞ shows a pronounced kink. The inset of Fig. 2 shows the magnetic field dependence rðHÞ=rðH ¼ 0Þ at 100 mK for p ¼ 2:3 and 6 GPa for Hkc: At p ¼ 2:3 GPa the magnetoresistance shows a very sharp decrease at H c ¼ 1:8 T and the magnetic order is suppressed for H4H c : In comparison to p ¼ 0; ðH c =T N Þ is about 5 times lower at 2.3 GPa. At p ¼ 2:3 GPa; an analysis of rðTÞ for To250 mK shows that the A-coefficient of the T 2 term of rðTÞ is almost constant as a function of H in the magnetic-ordered regime Ho1:8 T and is decreasing for H42 T from 10 mO cm=K2 to 7 mO cm=K2 at 6 T. However, rðT; HÞ has changed
2.5
TN = 80 mK 2
21
6 GPa
1.2 2.3
1.0 0
5
6 GPa
1.4
2.3 2
4 H (T)
6
1.3 YbRh2Si2
174YbRh Si 2 2
0 0.1
1 T (K)
Fig. 1. Specific heat as C=T vs. T on a logarithmic scale of mono-isotopic 174 YbRh2 Si2 : rðTÞ is linear in T above T N (see inset).
0 0.0
0.4
0.8
1.2
T (K)
Fig. 2. Electrical resistivity of YbRh2Si2 under high-pressure. The inset show the normalized magnetoresistance at 100 mK for p ¼ 2:3 and 6 GPa.
ARTICLE IN PRESS G. Knebel et al. / Physica B 359– 361 (2005) 20–22
22
4 YbRh2Si2 3 T (K)
Cac ρ
2
1
0
0
3
6 p (GPa)
9
12
Fig. 3. High-pressure phase diagram of YbRh2Si2 from AC calorimetry C AC and resistivity measurements r:
completely at p ¼ 6 GPa: Although T N is almost unchanged, at p ¼ 6 GPa H ¼ 6 T is not sufficient to suppress AFM at low temperatures. Here AðHÞ is decreasing linearly from 5:6 mO cm=K2 at H ¼ 0 to A ¼ 1:8 mO cm=K2 at H ¼ 6 T: The p–T phase diagram of YbRh2Si2 is summarized in Fig. 3. It is qualitatively in agreement with Ref. [9]. The phase diagram can be divided in three different regimes: (i) Initially T N ðpÞ increases with a rate of 0.37 GPa/K. In this regime the system may be dominated by the closeness to the magnetic instability. (ii) T N ðpÞ has a maximum at
about 4–5 GPa and is decreasing for higher pressures. Here the magnetoresistance is qualitatively completely different from the low-pressure phase. (iii) Above p49 GPa; T N is increasing with a rate of 0.1 GPa/K. Here, we observed very nice magnetic anomalies by ac calorimetry (not shown). However, the transition to the highpressure phase (mord ¼ 1:9mB at 16.5 GPa [9]) seems to be associated with a drastic change of the magnetic structure near 9 GPa which may be correlated to the entrance in the fully trivalent state Yb3þ : The pressure dependence of YbRh2Si2 appears quite different from that detected in Ce heavy fermion compounds what reflects differences in the degree of hybridization and consequently in the relation between valence occupation and the magnetic instability. References [1] [2] [3] [4] [5] [6] [7] [8]
O. Trovarelli, et al., Phys. Rev. Lett. 85 (2000) 626. J. Custers, et al., Nature 424 (2003) 524. K. Ishida, et al., Phys. Rev. Lett. 89 (2002) 107202. K. Ishida, et al., Phys. Rev. B 68 (2003) 184401. J.T. Waber, D.T. Cromer, J. Chem. Phys. 42 (1965) 4116. J. Sichelschmidt, et al., Phys. Rev. Lett. 91 (2003) 156401. H. Bjerrum Møller, et al., Phys. Rev. Lett. 49 (1982) 482. S. Mederle, et al., J. Magn. Magn. Matter. 226–230 (2001) 254. [9] J. Plessel, et al., Phys. Rev. B 67 (2003) 180403(R).