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Field-induced quantum criticality in YbAgGe
ARTICLE IN PRESS
Physica B 403 (2008) 1230–1232 www.elsevier.com/locate/physb
Field-induced quantum criticality in YbAgGe S.L. Bud’ko, P.C. Canfield Ames Laboratory US DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA
Abstract YbAgGe is one of the very few stoichiometric, Yb-based, heavy fermion materials that exhibit field-induced quantum criticality. We will present an overview of thermodynamic and transport measurements in YbAgGe single crystals. Moderate magnetic field (45–90 kOe, depending on orientation) suppresses long range magnetic order, giving rise to non-Fermi-liquid behavior followed at higher field by a crossover to a heavy Fermi-liquid. Given the more accessible temperature and field scales, a non-Fermi liquid region rather than point for T ! 0 K may be detected. r 2007 Elsevier B.V. All rights reserved. PACS: 72.15.Qm; 75.20.Hr; 75.30.Mg; 75.40.s Keywords: YbAgGe; Quantum critical point; Magnetic field
For a number of heavy fermion materials a long range magnetic ordering temperature can be tuned by some control parameter to T ¼ 0, bringing the system to a quantum critical point (QCP). Recently magnetic field emerged as an experimentally convenient control parameter [1]. However, it is not clear if the theoretical models, used to describe QCP reached by pressure or doping, can be used without alterations for the case of the field-induced QCP (FIQCP). So far the number of materials that allegedly exhibit the FIQCP is rather small, with the stoichiometric compounds being even smaller subset. In the following we will briefly review the properties of a new, heavy fermion compound, YbAgGe, that can be driven to a quantum phase transition by moderate, less than 100 kOe, applied magnetic field. Due to space limitations, only Hka will be discussed. YbAgGe crystallizes in hexagonal ZrNiAl-type structure, its susceptibility and resistivity are fairly anisotropic. The material was identified as a moderate heavy fermion compound with the electronic specific heat coefficient, 150 mJ=mol K2 pgp1 J=mol K2 ; Kondo temperature, T K 20225 K and the Wilson ratio, R 1:8 [2,3]. It has two magnetic ordering transitions, second order, at 1 K and, Corresponding author. Tel.: +1 515 294 3986; fax: +1 515 294 0689.
E-mail address: [email protected] (S.L. Bud’ko). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.10.112
first order, at 0:65 K [2–4]. Applied magnetic field suppresses the long range magnetic order at H crit 45 kOe. A region of the logarithmic divergency, C magn = T / ln T, is seen in the magnetic specific heat data measured in applied field (Fig. 1), with the largest, over a decade in temperature, range of such behavior observed for H ¼ 80 kOe, considerably above H crit . Scaling of ½CðHÞ Cð0Þ=T vs. H=T b with b 1:15 is observed for HX60 kOe (Fig. 1, inset). Analysis of the low temperature part of the temperature dependent resistivity, rðTÞ, measured in different applied fields [3,5], shows that, at least above T ¼ 70 mK, there is a rather large, spanning over 25 kOe, region (Fig. 2), where rðTÞ is linear in temperature, indicating a non-Fermiliquid behavior, and only in higher fields, Ho100 kOe, after a crossover region, a Fermi-liquid-like resistivity, rðTÞ ¼ r0 þ AT 2 , is recovered. In addition to the aforementioned properties, observed in the vicinity of the FIQCP, a distinct feature in fielddependent Hall resistivity (Fig. 3), that sharpens on decrease of temperature and defines a distinct line in the H2T phase diagram, was detected [6]. At low temperatures this Hall line approaches the critical field for the suppression of the long range magnetic order. The existence of a distinct feature in Hall coefficient in the vicinity of a FIQCP was also reported in YbRh2Si2 [7]. At
ARTICLE IN PRESS S.L. Bud’ko, P.C. Canfield / Physica B 403 (2008) 1230–1232
1.0
-0.5
4 2 0
-1.0 1
0.5
YbAgGe H||a
6
ρH (μΩ m)
0.0
10 1.15
H/T
dρH/dH (nΩ cm/Oe)
Cmagn/T (J/mol K2)
1.5
8 YbAgGe H||a (C(H)-C(0))/T (J/mol K2)
H=0 10kOe 20kOe 40kOe 60kOe 80kOe 100kOe 120kOe 140kOe
1231
100 1.05
(kOe/K
)
0.0 1
10
0.4
T=50 mK
0.2 0.0 -0.2
T (K)
50
0
Fig. 1. Semi-log plot of the magnetic part of heat capacity for different magnetic fields, dashed line is a guide for an eye, arrows mark the region of logarithmic divergency. Inset: semi-log plot of ½CðHÞ Cð0Þ=T vs. H=T 1:15 (after Ref. [3]).
150
Fig. 3. Field-dependent Hall resistivity, rH and Hall coefficient, drH =dH, measured at T ¼ 50 mK. Dashed lines mark QCP-related, and coherenceline-related features (after Ref. [6]).
YbAgGe H||a
3
100 H (kOe)
3 YbAgGe H||a
2
Hall line
T (K)
n
2
LRMO
1 1 n
FL
NFL
fit: ρ = ρ0 + cT
0 0
50
100
150
H (kOe) Fig. 2. Low temperature exponent, n, results from single-power-law, rðTÞ ¼ r0 þ AT n , fits of low temperature resistivity (after Ref. [5]).
low temperatures the functional form of the field-dependent Hall coefficient in YbAgGe is complex beyond existing simple models [8] thus reflecting the multicomponent Fermi surface of the material and its nontrivial modification at the QCP. Fig. 4 shows H2T phase diagram (Hka) constructed from aforementioned thermodynamic and transport measurements, with the additional low temperature magnetization data [9] included. Magnetization data confirm the magnetic phase lines suggested by the electrical transport (including Hall effect) and specific heat measurements in applied field. Magnetization measurements suggest that the Yb magnetic moment saturation is not associated with the FIQCP in this material. The propagation vectors and H2T lines for two distinct magnetically ordered phases (A and B in Fig. 4) were determined by neutron scattering [10] and further scattering work is in progress.
0 0
50
100
150
H (kOe) Fig. 4. H2T phase diagram for YbAgGe (Hka) based on thermodynamic and transport measurements discussed in the text.
To summarize, YbAgGe presents an example of heavy fermion material with (anisotropic) FIQCP, clear feature in Hall coefficient, that defines a distinct phase line on the H2T phase diagram and, possibly, a non-Fermi-liquid region rather than point in the T ! 0 limit. Ames Laboratory is operated for the US DOE by ISU under Contract no. DE-AC02-07CH11358. Work at Ames Laboratory was supported by the Director for Energy Research, Office of Basic Energy Sciences. References [1] P. Gegenwart, et al., J. Low Temp. Phys. 133 (2003) 3; P. Gegenwart, et al., New J. Phys. 8 (2006) 171.
ARTICLE IN PRESS 1232 [2] [3] [4] [5] [6]
S.L. Bud’ko, P.C. Canfield / Physica B 403 (2008) 1230–1232 E. Morosan, et al., J. Magn. Magn. Mater. 277 (2004) 298. S.L. Bud’ko, et al., Phys. Rev. B. 69 (2004) 014415. K. Umeo, et al., J. Phys. Soc. Jpn. 73 (2004) 537. P.G. Niklowitz, et al., Phys. Rev. B. 73 (2006) 125101. S.L. Bud’ko, et al., Phys. Rev. B. 71 (2005) 054408; S.L. Bud’ko, et al., Phys. Rev. B. 72 (2005) 172413.
[7] [8] [9] [10]
S. Paschen, et al., Nature 432 (2004) 881. P. Coleman, et al., J. Phys.: Condens. Matter 13 (2001) R723. Y. Tokiwa, et al., Phys. Rev. B 73 (2006) 094435. B. Fa˚k, et al., J. Phys.: Condens. Matter 17 (2005) 301; B. Fa˚k, et al., Physica B 378–380 (2006) 669.
Physica B 403 (2008) 1230–1232 www.elsevier.com/locate/physb
Field-induced quantum criticality in YbAgGe S.L. Bud’ko, P.C. Canfield Ames Laboratory US DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA
Abstract YbAgGe is one of the very few stoichiometric, Yb-based, heavy fermion materials that exhibit field-induced quantum criticality. We will present an overview of thermodynamic and transport measurements in YbAgGe single crystals. Moderate magnetic field (45–90 kOe, depending on orientation) suppresses long range magnetic order, giving rise to non-Fermi-liquid behavior followed at higher field by a crossover to a heavy Fermi-liquid. Given the more accessible temperature and field scales, a non-Fermi liquid region rather than point for T ! 0 K may be detected. r 2007 Elsevier B.V. All rights reserved. PACS: 72.15.Qm; 75.20.Hr; 75.30.Mg; 75.40.s Keywords: YbAgGe; Quantum critical point; Magnetic field
For a number of heavy fermion materials a long range magnetic ordering temperature can be tuned by some control parameter to T ¼ 0, bringing the system to a quantum critical point (QCP). Recently magnetic field emerged as an experimentally convenient control parameter [1]. However, it is not clear if the theoretical models, used to describe QCP reached by pressure or doping, can be used without alterations for the case of the field-induced QCP (FIQCP). So far the number of materials that allegedly exhibit the FIQCP is rather small, with the stoichiometric compounds being even smaller subset. In the following we will briefly review the properties of a new, heavy fermion compound, YbAgGe, that can be driven to a quantum phase transition by moderate, less than 100 kOe, applied magnetic field. Due to space limitations, only Hka will be discussed. YbAgGe crystallizes in hexagonal ZrNiAl-type structure, its susceptibility and resistivity are fairly anisotropic. The material was identified as a moderate heavy fermion compound with the electronic specific heat coefficient, 150 mJ=mol K2 pgp1 J=mol K2 ; Kondo temperature, T K 20225 K and the Wilson ratio, R 1:8 [2,3]. It has two magnetic ordering transitions, second order, at 1 K and, Corresponding author. Tel.: +1 515 294 3986; fax: +1 515 294 0689.
E-mail address: [email protected] (S.L. Bud’ko). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.10.112
first order, at 0:65 K [2–4]. Applied magnetic field suppresses the long range magnetic order at H crit 45 kOe. A region of the logarithmic divergency, C magn = T / ln T, is seen in the magnetic specific heat data measured in applied field (Fig. 1), with the largest, over a decade in temperature, range of such behavior observed for H ¼ 80 kOe, considerably above H crit . Scaling of ½CðHÞ Cð0Þ=T vs. H=T b with b 1:15 is observed for HX60 kOe (Fig. 1, inset). Analysis of the low temperature part of the temperature dependent resistivity, rðTÞ, measured in different applied fields [3,5], shows that, at least above T ¼ 70 mK, there is a rather large, spanning over 25 kOe, region (Fig. 2), where rðTÞ is linear in temperature, indicating a non-Fermiliquid behavior, and only in higher fields, Ho100 kOe, after a crossover region, a Fermi-liquid-like resistivity, rðTÞ ¼ r0 þ AT 2 , is recovered. In addition to the aforementioned properties, observed in the vicinity of the FIQCP, a distinct feature in fielddependent Hall resistivity (Fig. 3), that sharpens on decrease of temperature and defines a distinct line in the H2T phase diagram, was detected [6]. At low temperatures this Hall line approaches the critical field for the suppression of the long range magnetic order. The existence of a distinct feature in Hall coefficient in the vicinity of a FIQCP was also reported in YbRh2Si2 [7]. At
ARTICLE IN PRESS S.L. Bud’ko, P.C. Canfield / Physica B 403 (2008) 1230–1232
1.0
-0.5
4 2 0
-1.0 1
0.5
YbAgGe H||a
6
ρH (μΩ m)
0.0
10 1.15
H/T
dρH/dH (nΩ cm/Oe)
Cmagn/T (J/mol K2)
1.5
8 YbAgGe H||a (C(H)-C(0))/T (J/mol K2)
H=0 10kOe 20kOe 40kOe 60kOe 80kOe 100kOe 120kOe 140kOe
1231
100 1.05
(kOe/K
)
0.0 1
10
0.4
T=50 mK
0.2 0.0 -0.2
T (K)
50
0
Fig. 1. Semi-log plot of the magnetic part of heat capacity for different magnetic fields, dashed line is a guide for an eye, arrows mark the region of logarithmic divergency. Inset: semi-log plot of ½CðHÞ Cð0Þ=T vs. H=T 1:15 (after Ref. [3]).
150
Fig. 3. Field-dependent Hall resistivity, rH and Hall coefficient, drH =dH, measured at T ¼ 50 mK. Dashed lines mark QCP-related, and coherenceline-related features (after Ref. [6]).
YbAgGe H||a
3
100 H (kOe)
3 YbAgGe H||a
2
Hall line
T (K)
n
2
LRMO
1 1 n
FL
NFL
fit: ρ = ρ0 + cT
0 0
50
100
150
H (kOe) Fig. 2. Low temperature exponent, n, results from single-power-law, rðTÞ ¼ r0 þ AT n , fits of low temperature resistivity (after Ref. [5]).
low temperatures the functional form of the field-dependent Hall coefficient in YbAgGe is complex beyond existing simple models [8] thus reflecting the multicomponent Fermi surface of the material and its nontrivial modification at the QCP. Fig. 4 shows H2T phase diagram (Hka) constructed from aforementioned thermodynamic and transport measurements, with the additional low temperature magnetization data [9] included. Magnetization data confirm the magnetic phase lines suggested by the electrical transport (including Hall effect) and specific heat measurements in applied field. Magnetization measurements suggest that the Yb magnetic moment saturation is not associated with the FIQCP in this material. The propagation vectors and H2T lines for two distinct magnetically ordered phases (A and B in Fig. 4) were determined by neutron scattering [10] and further scattering work is in progress.
0 0
50
100
150
H (kOe) Fig. 4. H2T phase diagram for YbAgGe (Hka) based on thermodynamic and transport measurements discussed in the text.
To summarize, YbAgGe presents an example of heavy fermion material with (anisotropic) FIQCP, clear feature in Hall coefficient, that defines a distinct phase line on the H2T phase diagram and, possibly, a non-Fermi-liquid region rather than point in the T ! 0 limit. Ames Laboratory is operated for the US DOE by ISU under Contract no. DE-AC02-07CH11358. Work at Ames Laboratory was supported by the Director for Energy Research, Office of Basic Energy Sciences. References [1] P. Gegenwart, et al., J. Low Temp. Phys. 133 (2003) 3; P. Gegenwart, et al., New J. Phys. 8 (2006) 171.
ARTICLE IN PRESS 1232 [2] [3] [4] [5] [6]
S.L. Bud’ko, P.C. Canfield / Physica B 403 (2008) 1230–1232 E. Morosan, et al., J. Magn. Magn. Mater. 277 (2004) 298. S.L. Bud’ko, et al., Phys. Rev. B. 69 (2004) 014415. K. Umeo, et al., J. Phys. Soc. Jpn. 73 (2004) 537. P.G. Niklowitz, et al., Phys. Rev. B. 73 (2006) 125101. S.L. Bud’ko, et al., Phys. Rev. B. 71 (2005) 054408; S.L. Bud’ko, et al., Phys. Rev. B. 72 (2005) 172413.
[7] [8] [9] [10]
S. Paschen, et al., Nature 432 (2004) 881. P. Coleman, et al., J. Phys.: Condens. Matter 13 (2001) R723. Y. Tokiwa, et al., Phys. Rev. B 73 (2006) 094435. B. Fa˚k, et al., J. Phys.: Condens. Matter 17 (2005) 301; B. Fa˚k, et al., Physica B 378–380 (2006) 669.