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Quantum criticality in Ce(Al1−xCox)2
ARTICLE IN PRESS
Physica B 403 (2008) 824–825 www.elsevier.com/locate/physb
Quantum criticality in Ce(Al1xCox)2 A.V. Bogacha,, V.V. Glushkova, S.V. Demisheva, G.S. Burkhanovb, O.D. Chistyakovb, N.E. Sluchankoa a A.M. Prokhorov General Physics Institute of RAS, Vavilov Street 38, Moscow 119991, Russia A.A. Baikov Institute of Metallurgy and Materials Science of RAS, Leninskii pr. 49, Moscow 119991, Russia
b
Abstract To search for the quantum critical point (QCP) in the transit from antiferromagnetic metal CeAl2 to paramagnetic superconductor CeCo2, transport (Hall coefficient, resistivity) and magnetic properties have been studied on the high-quality polycrystalline samples of solid solutions Ce(Al1xMx)2 (xo0.1, M–Co, Ni) in a wide temperature range 1.8–300 K. The analysis of Hall mobility and magnetic susceptibility parameters shows the significant anomalies in the vicinity of Co impurity concentration xE1.5–2 at%, that possibly may be considered as a QCP in these strongly correlated electron systems. r 2007 Elsevier B.V. All rights reserved. Keywords: Quantum criticality; Heavy fermions
Among the features of Ce-based heavy fermion compounds, the anomalous transport and magnetic properties, and especially anomalous Hall effect have been certainly established [1–3]. For so-called magnetic Kondo-lattice CeAl2, recent studies revealed a complicated activation type behavior of the Hall coefficient RHexp(Ea1,2/kBT) with activation energy values Ea1/kB=1270.5 K and Ea2/ kB=7.670.2 K attributed to the bonding energies of the many-body states in the vicinity of Fermi level EF [4]. Moreover, the investigation of Ce(Al1xMx)2 solid solutions, with xo0.1 and M ¼ Co, Ni, shows the dramatic increase of Hall coefficient at low temperatures (more than three times in the range xp0.08) and significant elevation of activation energy Ea1 from Ea1(CeAl2)/kB ¼ 1270.5 K to Ea1(Ce(Al0.92Co0.08)2)/kB ¼ 4073 K [5]. At the same time, a substitution of Al with Co in the family Ce(Al1xCox)2 induces the transition from antiferromagnetic (AF) metal CeAl2 (TN ¼ 3.8 K; [4]) to paramagnetic superconductor CeCo2 (TC ¼ 1.5 K; [6]). Thus, in the vicinity of antiferromagnetic instability in Ce(Al1xCox)2 solid solution series, one should expect the realization of quantum critical behavior (see e.g.
Corresponding author. Tel.: +7 499 503 8253; fax: +7 495 135 8129.
E-mail address: [email protected] (A.V. Bogach). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.10.039
Refs. [7,8]) and following onset of anomalies of physical properties. To search for the QCP in this system, the resistivity, Hall coefficient and magnetic susceptibility measurements of high-quality polycrystalline samples of substitutional solid solutions Ce(Al1xCox)2 (xo0.1) and Ce(Al0.95Ni0.05)2 (for comparison) were investigated over a wide temperature range 1.8–300 K in low magnetic fields Ho5 kOe. The temperature dependencies of resistivity r(T) of the alloys Ce(Al1xMx)2 (xo0.1, M=Co, Ni) are shown in Fig. 1. Distinct features resulting from both the crystal field splitting of Ce3+ 2F5/2-ground state (for CeAl2, D1 ¼ 100 K and D2 ¼ 170 K; [9]) and spin fluctuation effects (Tsf(CeAl2)E5 K; [10]) can be clearly detected by r(T) curves (see Fig. 1) for all samples under investigation. At the same time, the bulk AF-transition (see Fig. 1, kink on the CeAl2 curve) is happened to be completely suppressed when impurity concentration increases up to x ¼ 0.03 in Ce(Al1xCox)2 series. Fig. 2a shows the concentration dependencies of the Hall coefficient RH ðxÞjT¼T max and resistivity rðxÞjT¼T max of Ce(Al1xCox)2 taken in low-temperature maximums of these characteristics. Additionally, Fig. 2a also shows RH jT¼T max and rjT¼T max parameters for solid solution Ce(Al0.95Ni0.05)2 (empty symbols). The values of RH and r at T ¼ Tmax obtained for Ce(Al0.95Ni0.05)2 very well
ARTICLE IN PRESS A.V. Bogach et al. / Physica B 403 (2008) 824–825
825
w(Ce(Al0.95Ni0.05)2) are also plotted on the concentration dependencies of Hall mobility m(x) ¼ RH(x)/r(x) and magnetic susceptibility w(x) of Ce(Al1xCox)2 series presented in Fig. 2b. The anomalies of these parameters that can be clearly seen in Fig. 2b at Co concentration xE1.5–2 at% possibly could be attributed to the realization of QCP in SCES Ce(Al1xCox)2. This work was supported by RFBR ] 04-02-16721, INTAS ] 03-51-3036 and the Program ‘‘Strongly Correlated Electrons’’ in semiconductors, metals, superconductors and magnetic materials of RAS and Russian Science Support Foundation. References Fig. 1. Temperature dependencies of the resistivity r(T) of substitution solid solutions Ce(Al1xMx)2 (xo0.1, M ¼ Co, Ni).
Fig. 2. Concentration dependencies of (a) Hall coefficient RH(x) and resistivity r(x), (b) Hall mobility m(x) ¼ RH(x)/r(x) and magnetic susceptibility w(x) of Ce(Al1xCox)2 series (empty symbols correspond to the data for Ce(Al0.95Ni0.05)2, see text).
comply with those of Ce(Al1xCox)2 with cobalt impurity x ¼ 0.012 (see shaded area in Fig. 2a). Using this assumption, the values of m(Ce(Al0.95Ni0.05)2) and
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
P. Coleman, et al., Phys. Rev. Lett. 55 (1985) 414. M. Hadzic-Leroux, et al., Europhys. Lett. 1 (1986) 579. M.I. Ignatov, et al., Physica B 363 (2005) 252. N.E. Sluchanko, et al., JETP 98 (2004) 793. A.V. Bogach, et al., JETP 104 (2007) 120. H. Sugawara, et al., Physica B 230 (1997) 179. Q. Si, et al., Nature 413 (2001) 804. H.V. Lohneysen, et al., Phys. Rev. Lett. 72 (1994) 3262. M. Loewenhaupt, et al., Phys. Rev. Lett. 42 (1979) 1709. F. Steglich, et al., J. Phys. Coll. C5-Suppl. 40 (1979) 301.
Physica B 403 (2008) 824–825 www.elsevier.com/locate/physb
Quantum criticality in Ce(Al1xCox)2 A.V. Bogacha,, V.V. Glushkova, S.V. Demisheva, G.S. Burkhanovb, O.D. Chistyakovb, N.E. Sluchankoa a A.M. Prokhorov General Physics Institute of RAS, Vavilov Street 38, Moscow 119991, Russia A.A. Baikov Institute of Metallurgy and Materials Science of RAS, Leninskii pr. 49, Moscow 119991, Russia
b
Abstract To search for the quantum critical point (QCP) in the transit from antiferromagnetic metal CeAl2 to paramagnetic superconductor CeCo2, transport (Hall coefficient, resistivity) and magnetic properties have been studied on the high-quality polycrystalline samples of solid solutions Ce(Al1xMx)2 (xo0.1, M–Co, Ni) in a wide temperature range 1.8–300 K. The analysis of Hall mobility and magnetic susceptibility parameters shows the significant anomalies in the vicinity of Co impurity concentration xE1.5–2 at%, that possibly may be considered as a QCP in these strongly correlated electron systems. r 2007 Elsevier B.V. All rights reserved. Keywords: Quantum criticality; Heavy fermions
Among the features of Ce-based heavy fermion compounds, the anomalous transport and magnetic properties, and especially anomalous Hall effect have been certainly established [1–3]. For so-called magnetic Kondo-lattice CeAl2, recent studies revealed a complicated activation type behavior of the Hall coefficient RHexp(Ea1,2/kBT) with activation energy values Ea1/kB=1270.5 K and Ea2/ kB=7.670.2 K attributed to the bonding energies of the many-body states in the vicinity of Fermi level EF [4]. Moreover, the investigation of Ce(Al1xMx)2 solid solutions, with xo0.1 and M ¼ Co, Ni, shows the dramatic increase of Hall coefficient at low temperatures (more than three times in the range xp0.08) and significant elevation of activation energy Ea1 from Ea1(CeAl2)/kB ¼ 1270.5 K to Ea1(Ce(Al0.92Co0.08)2)/kB ¼ 4073 K [5]. At the same time, a substitution of Al with Co in the family Ce(Al1xCox)2 induces the transition from antiferromagnetic (AF) metal CeAl2 (TN ¼ 3.8 K; [4]) to paramagnetic superconductor CeCo2 (TC ¼ 1.5 K; [6]). Thus, in the vicinity of antiferromagnetic instability in Ce(Al1xCox)2 solid solution series, one should expect the realization of quantum critical behavior (see e.g.
Corresponding author. Tel.: +7 499 503 8253; fax: +7 495 135 8129.
E-mail address: [email protected] (A.V. Bogach). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.10.039
Refs. [7,8]) and following onset of anomalies of physical properties. To search for the QCP in this system, the resistivity, Hall coefficient and magnetic susceptibility measurements of high-quality polycrystalline samples of substitutional solid solutions Ce(Al1xCox)2 (xo0.1) and Ce(Al0.95Ni0.05)2 (for comparison) were investigated over a wide temperature range 1.8–300 K in low magnetic fields Ho5 kOe. The temperature dependencies of resistivity r(T) of the alloys Ce(Al1xMx)2 (xo0.1, M=Co, Ni) are shown in Fig. 1. Distinct features resulting from both the crystal field splitting of Ce3+ 2F5/2-ground state (for CeAl2, D1 ¼ 100 K and D2 ¼ 170 K; [9]) and spin fluctuation effects (Tsf(CeAl2)E5 K; [10]) can be clearly detected by r(T) curves (see Fig. 1) for all samples under investigation. At the same time, the bulk AF-transition (see Fig. 1, kink on the CeAl2 curve) is happened to be completely suppressed when impurity concentration increases up to x ¼ 0.03 in Ce(Al1xCox)2 series. Fig. 2a shows the concentration dependencies of the Hall coefficient RH ðxÞjT¼T max and resistivity rðxÞjT¼T max of Ce(Al1xCox)2 taken in low-temperature maximums of these characteristics. Additionally, Fig. 2a also shows RH jT¼T max and rjT¼T max parameters for solid solution Ce(Al0.95Ni0.05)2 (empty symbols). The values of RH and r at T ¼ Tmax obtained for Ce(Al0.95Ni0.05)2 very well
ARTICLE IN PRESS A.V. Bogach et al. / Physica B 403 (2008) 824–825
825
w(Ce(Al0.95Ni0.05)2) are also plotted on the concentration dependencies of Hall mobility m(x) ¼ RH(x)/r(x) and magnetic susceptibility w(x) of Ce(Al1xCox)2 series presented in Fig. 2b. The anomalies of these parameters that can be clearly seen in Fig. 2b at Co concentration xE1.5–2 at% possibly could be attributed to the realization of QCP in SCES Ce(Al1xCox)2. This work was supported by RFBR ] 04-02-16721, INTAS ] 03-51-3036 and the Program ‘‘Strongly Correlated Electrons’’ in semiconductors, metals, superconductors and magnetic materials of RAS and Russian Science Support Foundation. References Fig. 1. Temperature dependencies of the resistivity r(T) of substitution solid solutions Ce(Al1xMx)2 (xo0.1, M ¼ Co, Ni).
Fig. 2. Concentration dependencies of (a) Hall coefficient RH(x) and resistivity r(x), (b) Hall mobility m(x) ¼ RH(x)/r(x) and magnetic susceptibility w(x) of Ce(Al1xCox)2 series (empty symbols correspond to the data for Ce(Al0.95Ni0.05)2, see text).
comply with those of Ce(Al1xCox)2 with cobalt impurity x ¼ 0.012 (see shaded area in Fig. 2a). Using this assumption, the values of m(Ce(Al0.95Ni0.05)2) and
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
P. Coleman, et al., Phys. Rev. Lett. 55 (1985) 414. M. Hadzic-Leroux, et al., Europhys. Lett. 1 (1986) 579. M.I. Ignatov, et al., Physica B 363 (2005) 252. N.E. Sluchanko, et al., JETP 98 (2004) 793. A.V. Bogach, et al., JETP 104 (2007) 120. H. Sugawara, et al., Physica B 230 (1997) 179. Q. Si, et al., Nature 413 (2001) 804. H.V. Lohneysen, et al., Phys. Rev. Lett. 72 (1994) 3262. M. Loewenhaupt, et al., Phys. Rev. Lett. 42 (1979) 1709. F. Steglich, et al., J. Phys. Coll. C5-Suppl. 40 (1979) 301.