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Pressure dependence of the electrical resistivity of CeCu5.8Au0.2
Physica B 281&282 (2000) 363}364
Pressure dependence of the electrical resistivity of CeCu Au 5.8 0.2 C. P#eiderer, B. Will, O. Stockert, H. von LoK hneysen* Physikalisches Institut, Universita( t Karlsruhe, Engesserstrasse 7, D-76128 Karlsruhe, Germany
Abstract The resistivity o(¹) of the incommensurate antiferromagnet CeCu Au as measured along the a direction shows an 5.8 0.2 increase below the ordering temperature ¹ "0.25 K. ¹ decreases under hydrostatic pressure, reaching zero around N N p &5 kbar. Beyond p Fermi-liquid behavior o"o #A¹2 is recovered over a ¹ range increasing with p. The residual # # 0 resistivity o is found to decrease strongly from 93 to 66 l) cm between 0 and 9.8 kbar. ( 2000 Elsevier Science B.V. 0 All rights reserved. Keywords: Cerium compounds; Magnetic instability; Pressure e!ects; Quantum phase transition
The equivalent dependence of the speci"c heat C on pressure p or Au concentration x when tuning the magnetic}nonmagnetic quantum phase transition of CeCu Au , has long been a cornerstone guiding the 6~x x description of the non-Fermi-liquid characteristics of this system [1,2]. The linear coe$cient of the speci"c heat shows a universal temperature dependence, C/¹" a ln(¹/¹ ) with a+!0.6 J/mol K2 and ¹ +5.0 K at 0 0 the quantum critical point, i.e. for x"0.1 at p"0, for x"0.2 at p+4 kbar, and for x"0.3 at p+8 kbar. Here, we report on a study of the pressure dependence of the electrical resistivity o(¹) for x"0.2 in comparison to its concentration dependence [1]. The resistivity was measured on two x"0.2 single crystals with consistent results obtained on both for similar pressures. The samples were mounted in a Cu : Be hydrostatic pressure cell using a methanol/ethanol mixture as pressure transmitting medium, together with a Sn platelet whose pressuredependent superconducting transition temperature was measured inductively to serve as a pressure gauge. The resistivity was measured with the current applied parallel to the orthorhombic a direction. Fig. 1 shows o(¹) in the
* Corresponding author. Tel.: #49-721-608-3450; fax: #49721-608-6103. E-mail address: [email protected] (H. von LoK hneysen)
low-¹ range for pressures between 0 and 9.8 kbar. For p"0, the data show a strong increase below the NeH el temperature ¹ "0.25 K towards low ¹, as reported N before [3]. This increase is attributed to the magnetic ordering with an ordering wave vector Q having a component parallel to the current direction, i.e. Q" (0.625 0 0.275). The previous observation in the speci"c heat C of a decrease of ¹ with increasing p [2] is N supported by our o(¹) measurements as evident from Fig. 1. Our ¹ (p) data (Fig. 2) are compatible with N a linear decrease with a slightly larger critical pressure p +5 kbar where ¹ (p )"0 than found from C [3]. # N # There are several other important "ndings: (i) The residual resistivity o as roughly extrapolated for ¹P0 0 decreases strongly from 93 l) cm for p"0 to 66 l) cm for p"9.8 kbar. This very large change may not be understood in terms of a simple alloy-disorder scattering model. It may instead be taken as evidence for the local interplay of the Au atoms with the Ce atoms, since the former occupy exclusively the Cu(2) site for x)1 [4]. The Au atoms thus generate two types of Ce environments, one with and the other without the immediate vicinity of an Au atom. The e!ect of pressure may thus be seen as reducing the di!erence of these two states of the Ce atoms. (ii) While for p"9.8 kbar the data show a very gentle change of curvature between 0.1 and 0.5 K of an overall quasilinear ¹-dependence, o(¹) is dominated by a shallow maximum around 0.5 K for p"1.3 kbar. Our
0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 2 3 5 - 1
364
C. Pyeiderer et al. / Physica B 281&282 (2000) 363}364
Fig. 1. Pressure dependence of o(¹) of CeCu Au for i paral5.8 0.2 lel a. Curves correspond from top to bottom to ambient pressure, 1.3, 2.4, 3.5, 4.1, 5.1, 7.0, 8.1, 9.3 and 9.8 kbar. Filled arrows indicate the onset of magnetic order at ¹ , while open arrows N indicate the crossover temperature ¹ from a ¹2 behavior of #3 o at low ¹ to an assumed linear ¹-dependence of o at high ¹.
Fig. 2. Phase diagram of CeCu Au as derived from o(¹) 5.8 0.2 along a. ¹ marks the onset of magnetic order, while ¹ shows N #3 the onset of a ¹2 dependence of o as determined in Fig. 1. Shown in the inset is the pressure dependence of the coe$cient A of the ¹2 dependence of o.
measurements cover the range up to 4 K for the pressures indicated in Fig. 1, and up to 50 K for a few other selected pressures (not shown). All data for p*1.3 kbar show such a maximum of o(¹) which strongly increases under
p, e.g. to 8 K for p"9.8 kbar. By analogy with pure CeCu [5] this maximum is attributed to the onset of 6 coherence of the Kondo lattice. Decreasing p in turn may be viewed as drastically reducing the conduction}electron}4f-electron hybridization and hence the onset of Kondo coherence. This } by the way } is also the reason why with decreasing p antiferromagnetism appears in CeCu Au . A more detailed account on the concen5.8 0.2 tration and pressure dependence of the coherence maximum in CeCu Au will be presented elsewhere. 6~x x The strongly p-dependent features in o(¹) associated with the Kondo coherence render a straightforward interpretation of the ¹ dependence of o di$cult. Nevertheless, extrapolating the quasi-linear portion of the o(¹) curves above p to ¹"0 yields a temperature ¹ below # #3 which a distinct deviation towards a ¹2 behavior is found. Fig. 2 shows ¹ versus p which supports the #3 notion that the Fermi-liquid region shrinks to zero once the quantum-critical point is approached. Our data are compatible with a linear pressure dependence of ¹ (p) #3 this way determined. Fig. 2 moreover bears similarity with the generic phase diagram of itinerant fermions near a magnetic quantum critical point (QCP) [8] although the data of ¹ (p) and ¹ (p) are not precise enough to N #3 distinguish among di!erent universality classes. At the same time, the coe$cient A of the ¹2 resistivity o"o #A¹2, diverges as pPp from above, as shown 0 # in Fig. 2 as well. Turning "nally to the resistivity behavior close to the QCP, we note that the quasi-linear ¹-dependence extends to the lowest ¹ already for p+7 kbar. This is compatible with a ¹ dependence of o at the QCP as observed for x"0.1 at ambient pressure and explained in terms of two-dimensional #uctuations [6,7]. A more re"ned analysis of the o(¹) data with a single exponent, *o&¹. over the widest ¹ range possible, results in m+1.25 for ¹(0.25 K (i.e. over an order of magnitude in ¹). The latter form of o(¹), however, is well below the prediction of m"3 for a three-dimensional antifer2 romagnet, and yet slightly larger than that expected for a two-dimensional antiferromagnet [6]. References [1] [2] [3] [4] [5] [6] [7] [8]
H. von LoK hneysen, J. Phys.: Condens. Matter 8 (1996) 9689. M. Sieck et al., Physica B 230}232 (1997) 583. H. von LoK hneysen et al., Eur. Phys. J. B 5 (1998) 447. M. Ruck et al., Acta Crystallogr. B 49 (1993) 936. S. Yomo et al., J. Magn. Magn. Mater. 76&77 (1988) 257. A. Rosch et al., Phys. Rev. Lett. 79 (159) 1997. O. Stockert et al., Phys. Rev. Lett. 80 (1998) 5627. A.J. Millis, Phys. Rev. B 48 (1992) 7183.
Pressure dependence of the electrical resistivity of CeCu Au 5.8 0.2 C. P#eiderer, B. Will, O. Stockert, H. von LoK hneysen* Physikalisches Institut, Universita( t Karlsruhe, Engesserstrasse 7, D-76128 Karlsruhe, Germany
Abstract The resistivity o(¹) of the incommensurate antiferromagnet CeCu Au as measured along the a direction shows an 5.8 0.2 increase below the ordering temperature ¹ "0.25 K. ¹ decreases under hydrostatic pressure, reaching zero around N N p &5 kbar. Beyond p Fermi-liquid behavior o"o #A¹2 is recovered over a ¹ range increasing with p. The residual # # 0 resistivity o is found to decrease strongly from 93 to 66 l) cm between 0 and 9.8 kbar. ( 2000 Elsevier Science B.V. 0 All rights reserved. Keywords: Cerium compounds; Magnetic instability; Pressure e!ects; Quantum phase transition
The equivalent dependence of the speci"c heat C on pressure p or Au concentration x when tuning the magnetic}nonmagnetic quantum phase transition of CeCu Au , has long been a cornerstone guiding the 6~x x description of the non-Fermi-liquid characteristics of this system [1,2]. The linear coe$cient of the speci"c heat shows a universal temperature dependence, C/¹" a ln(¹/¹ ) with a+!0.6 J/mol K2 and ¹ +5.0 K at 0 0 the quantum critical point, i.e. for x"0.1 at p"0, for x"0.2 at p+4 kbar, and for x"0.3 at p+8 kbar. Here, we report on a study of the pressure dependence of the electrical resistivity o(¹) for x"0.2 in comparison to its concentration dependence [1]. The resistivity was measured on two x"0.2 single crystals with consistent results obtained on both for similar pressures. The samples were mounted in a Cu : Be hydrostatic pressure cell using a methanol/ethanol mixture as pressure transmitting medium, together with a Sn platelet whose pressuredependent superconducting transition temperature was measured inductively to serve as a pressure gauge. The resistivity was measured with the current applied parallel to the orthorhombic a direction. Fig. 1 shows o(¹) in the
* Corresponding author. Tel.: #49-721-608-3450; fax: #49721-608-6103. E-mail address: [email protected] (H. von LoK hneysen)
low-¹ range for pressures between 0 and 9.8 kbar. For p"0, the data show a strong increase below the NeH el temperature ¹ "0.25 K towards low ¹, as reported N before [3]. This increase is attributed to the magnetic ordering with an ordering wave vector Q having a component parallel to the current direction, i.e. Q" (0.625 0 0.275). The previous observation in the speci"c heat C of a decrease of ¹ with increasing p [2] is N supported by our o(¹) measurements as evident from Fig. 1. Our ¹ (p) data (Fig. 2) are compatible with N a linear decrease with a slightly larger critical pressure p +5 kbar where ¹ (p )"0 than found from C [3]. # N # There are several other important "ndings: (i) The residual resistivity o as roughly extrapolated for ¹P0 0 decreases strongly from 93 l) cm for p"0 to 66 l) cm for p"9.8 kbar. This very large change may not be understood in terms of a simple alloy-disorder scattering model. It may instead be taken as evidence for the local interplay of the Au atoms with the Ce atoms, since the former occupy exclusively the Cu(2) site for x)1 [4]. The Au atoms thus generate two types of Ce environments, one with and the other without the immediate vicinity of an Au atom. The e!ect of pressure may thus be seen as reducing the di!erence of these two states of the Ce atoms. (ii) While for p"9.8 kbar the data show a very gentle change of curvature between 0.1 and 0.5 K of an overall quasilinear ¹-dependence, o(¹) is dominated by a shallow maximum around 0.5 K for p"1.3 kbar. Our
0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 2 3 5 - 1
364
C. Pyeiderer et al. / Physica B 281&282 (2000) 363}364
Fig. 1. Pressure dependence of o(¹) of CeCu Au for i paral5.8 0.2 lel a. Curves correspond from top to bottom to ambient pressure, 1.3, 2.4, 3.5, 4.1, 5.1, 7.0, 8.1, 9.3 and 9.8 kbar. Filled arrows indicate the onset of magnetic order at ¹ , while open arrows N indicate the crossover temperature ¹ from a ¹2 behavior of #3 o at low ¹ to an assumed linear ¹-dependence of o at high ¹.
Fig. 2. Phase diagram of CeCu Au as derived from o(¹) 5.8 0.2 along a. ¹ marks the onset of magnetic order, while ¹ shows N #3 the onset of a ¹2 dependence of o as determined in Fig. 1. Shown in the inset is the pressure dependence of the coe$cient A of the ¹2 dependence of o.
measurements cover the range up to 4 K for the pressures indicated in Fig. 1, and up to 50 K for a few other selected pressures (not shown). All data for p*1.3 kbar show such a maximum of o(¹) which strongly increases under
p, e.g. to 8 K for p"9.8 kbar. By analogy with pure CeCu [5] this maximum is attributed to the onset of 6 coherence of the Kondo lattice. Decreasing p in turn may be viewed as drastically reducing the conduction}electron}4f-electron hybridization and hence the onset of Kondo coherence. This } by the way } is also the reason why with decreasing p antiferromagnetism appears in CeCu Au . A more detailed account on the concen5.8 0.2 tration and pressure dependence of the coherence maximum in CeCu Au will be presented elsewhere. 6~x x The strongly p-dependent features in o(¹) associated with the Kondo coherence render a straightforward interpretation of the ¹ dependence of o di$cult. Nevertheless, extrapolating the quasi-linear portion of the o(¹) curves above p to ¹"0 yields a temperature ¹ below # #3 which a distinct deviation towards a ¹2 behavior is found. Fig. 2 shows ¹ versus p which supports the #3 notion that the Fermi-liquid region shrinks to zero once the quantum-critical point is approached. Our data are compatible with a linear pressure dependence of ¹ (p) #3 this way determined. Fig. 2 moreover bears similarity with the generic phase diagram of itinerant fermions near a magnetic quantum critical point (QCP) [8] although the data of ¹ (p) and ¹ (p) are not precise enough to N #3 distinguish among di!erent universality classes. At the same time, the coe$cient A of the ¹2 resistivity o"o #A¹2, diverges as pPp from above, as shown 0 # in Fig. 2 as well. Turning "nally to the resistivity behavior close to the QCP, we note that the quasi-linear ¹-dependence extends to the lowest ¹ already for p+7 kbar. This is compatible with a ¹ dependence of o at the QCP as observed for x"0.1 at ambient pressure and explained in terms of two-dimensional #uctuations [6,7]. A more re"ned analysis of the o(¹) data with a single exponent, *o&¹. over the widest ¹ range possible, results in m+1.25 for ¹(0.25 K (i.e. over an order of magnitude in ¹). The latter form of o(¹), however, is well below the prediction of m"3 for a three-dimensional antifer2 romagnet, and yet slightly larger than that expected for a two-dimensional antiferromagnet [6]. References [1] [2] [3] [4] [5] [6] [7] [8]
H. von LoK hneysen, J. Phys.: Condens. Matter 8 (1996) 9689. M. Sieck et al., Physica B 230}232 (1997) 583. H. von LoK hneysen et al., Eur. Phys. J. B 5 (1998) 447. M. Ruck et al., Acta Crystallogr. B 49 (1993) 936. S. Yomo et al., J. Magn. Magn. Mater. 76&77 (1988) 257. A. Rosch et al., Phys. Rev. Lett. 79 (159) 1997. O. Stockert et al., Phys. Rev. Lett. 80 (1998) 5627. A.J. Millis, Phys. Rev. B 48 (1992) 7183.