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Local magnetization measurements of the first-order transition of CeCoIn5
ARTICLE IN PRESS
Physica B 403 (2008) 871–873 www.elsevier.com/locate/physb
Local magnetization measurements of the first-order transition of CeCoIn5 H. Shishidoa,, R. Okazakia, T. Shibauchia, Y. Matsudaa,b, ¯ nukid M. Konczykowskic, R. Settaid, Y. O a Department of Physics, Kyoto University, Kyoto 606-8502, Japan Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan c CNRS, URA 1380, Laboratoire des Solides Irradie´s, E´cole Polyte´chnique, 91128 Palaiseau, France d Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan b
Abstract We measured the local magnetization in CeCoIn5 with a micro-Hall probe for magnetic fields H along the [0 0 1] and [1 0 0] directions. We observed a sharp jump in the local magnetization at T c ðHÞ below 0.77 K for H k [0 0 1] and 0.79 K for H k [1 0 0], indicating the firstorder phase transitions at upper critical fields. We also observed a dip structure in the local magnetization at the first-order phase transitions for H k [0 0 1], below which the FFLO state is realized. We infer that the dip structure is consistent with the development of planar nodes in the FFLO state. r 2007 Elsevier B.V. All rights reserved. PACS: 74.70.Tx; 74.25.Dw; 74.25.Ha Keywords: CeCoIn5; FFLO; Local magnetization
Some cerium and uranium compounds, in which the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction and the Kondo effect compete, form heavy fermions at low temperatures. The compound CeCoIn5 is a heavy fermion superconductor with a superconducting transition temperature of T c ¼ 2:3 K [1]. A first-order superconducting phase transition at low temperatures and high magnetic fields was observed along both the [0 0 1] and [1 0 0] directions [2–4]. It is believed that the first-order phase transition (FOPT) is due to the Pauli paramagnetic limit. Experimental results indicating the existence of a Fulde– Ferrel–Larkin–Ovchinnikov(FFLO) [5,6] state in the vicinity of H c2 have been reported for H perpendicular and parallel to the c-axis by the specific heat [4], ultrasound velocity [7], NMR [8,9] and magnetization measurements [10]. Here we investigate the superconducting phase diagram of CeCoIn5 by a local probe that can detect clear signature Corresponding author. Tel./fax: +81 75 753 3777.
E-mail address: [email protected] (H. Shishido). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.10.051
of the FOPT even in the presence of large-scale vortex distributions, which some times may mask the first-order nature in the global bulk measurements [11]. In this paper, we observed the FOPT in CeCoIn5 for H k [0 0 1] and H k [1 0 0] by means of the local magnetization measurements with a micro-Hall probe of two-dimensional-electron-gas GaAs/AlGaAs with active area of 10 10 mm2 . We measured the temperature dependence of the Hall resistance in the field-cooling condition, which is proportional to the local magnetic induction B. Fig. 1 shows the temperature dependence of local magnetic induction changes DB, which is defined as DB ¼ B Bnormal , where Bnormal is a linear fit of BðTÞ in normal state, for H along the [1 0 0] direction at various magnetic fields. We observed a sharp jump in DB: jump of 1.93 G with the transition width of 20 mK at T c ¼ 0:46 K in H ¼ 111 kOe. This is clear evidence of the FOPT at T c by a local probe. The step height decreases with decreasing H below 111 kOe, and the step disappears below 105 kOe. Superconducting phase transitions above 111 kOe, which were measured in temperature-sweep conditions, are
ARTICLE IN PRESS H. Shishido et al. / Physica B 403 (2008) 871–873
872
H = 114 kOe
H = 48.5 kOe CeCoIn5 H // [100]
113.8 113.5
48.3
113
CeCoIn5 H // [001]
48.1 3G
112
47.9
111 108 1st
47.7
ΔB
ΔB
110
47.5
106 105
47.3
3G
47.0
104
46.5
2nd
1.0
0.9
Fig. 2. Temperature dependence of the local magnetization changes for H k [0 0 1]. Each curve is shifted vertically for clarity.
120
60 CeCoIn5 H // [100]
120
60
110
100
0 0
H // [001] 40 50 H (kOe)
broad. This may be due to broadening of the transition by the flat phase line in this region. In contrast, the previous measurements, which were measured by sweeping fields, indicated a clear FOPT [2,3]. From these facts, we can conclude that the FOPT appears below T cr ¼ 0:77 K of 0.33 T c ð0Þ, where T c ð0Þ ¼ 2:3 K is the superconducting transition temperature at 0 kOe. Fig. 2 shows the temperature dependence of DB for H k [0 0 1] at various magnetic fields. The sharp steps according to the FOPT at T c were observed in DBðTÞ, and the step height decreases with decreasing the magnetic fields, as the same as that in H k [1 0 0]. These results indicate that the FOPT changes into second-order phase transition above T cr ¼ 0:79 Kð0:34T c Þ. An important difference from the H k [1 0 0] case is that DBðTÞ has a dip structure above 47.5 kOe. We note that such a structure has not been resolved by the bulk magnetization measurements [3]. The origin of the dip structure is discussed below. We show the superconducting phase diagrams for H k [1 0 0] in Fig. 3a and H k [0 0 1] in Fig. 3b. Open and filled symbols represent first- and second-order phase transitions, respectively. Present results are well consistent with previous ones: T ccr of 0.77 K ð0:33T c Þ and T acr ¼ 0:79 K ð0:34T c Þ for H k [1 0 0] and [0 0 1], respectively. We will discuss the origin of the dip structure on DB. DB for H k [0 0 1] has a dip structure at the FOPT, just below which the FFLO state was reported [9,10], as shown in the inset of Fig. 3b. In contrast, the dip structure was not observed for H k [1 0 0] at the FOPT, where a standard (d-wave) superconducting state occurs just below H c2 in magnetic field range of 105 to 113 kOe. These results imply that the dip structure observed for H k [0 0 1] is caused by a development of nodal-planes with the FFLO transition which should have additional paramagnetic contribution.
0.7 Temperature (K)
Magnetic Field (kOe)
Fig. 1. Temperature dependence of the local magnetization changes under various magnetic fields for H k [1 0 0]. Each curve is shifted vertically for clarity.
0.5
H (kOe)
0.5 Temperature (K)
Magnetic Field (kOe)
0
20
FFLO 45 BCS 40
0
0.5 T (K)
0
1.0
1 2 Temperature (K)
1 T (K)
0 0
1 2 Temperature (K)
Fig. 3. Superconducting phase diagrams determined by the present work (, K), together with the global magnetization(&, ’) [3] and the specific heat measurements (n, m) [4] in (a) H k [1 0 0] and (b) H k [0 0 1], respectively. Open symbols indicate the first-order phase transition.
The dip structure was, however, not observed above 113 kOe, where the FFLO state was reported [4,7,8,10] below the FOPT for H k [1 0 0]. It seems to be due to broadening of the transition discussed above. A consistent result was reported in the temperature dependence of the Knight shift at 115In-site which is related to the spin susceptibility [9]. The Knight shift increases steeply with decreasing the temperature in the vicinity of T c , decreases in low temperatures. In conclusion, we measured the temperature dependence of DB via the micro-Hall probe in a heavy-fermion superconductor CeCoIn5 for H along the [0 0 1] and [1 0 0] directions. We observed the clear local magnetization jump at T c indicating the FOPT. The FOPT exists below T ccr ¼ 0:77 K ð0:33T c Þ for H k [1 0 0] and T acr ¼ 0:79 K ð0:34T c Þ for H k [0 0 1], respectively. The dip structure appeared in DB for H k [0 0 1] at the FOPT. It may be
ARTICLE IN PRESS H. Shishido et al. / Physica B 403 (2008) 871–873
related to the development of nodal-planes expected in the FFLO phase.
[2] [3] [4] [5] [6]
This work was partly supported by a Grant in-Aid for Scientific Research from the MEXT and by Japan-France Integrated Action Program SAKURA. One of the authors (H. S.) was supported by the Research Fellowships of the JSPS for Young Scientists.
[7] [8] [9] [10] [11]
References [1] C. Petrovic, et al., J. Phys. Condens. Matter 13 (2001) L337.
873
K. Izawa, et al., Phys. Rev. Lett. 87 (2001) 057002. T. Tayama, et al., Phys. Rev. B 65 (2002) 180504. A. Bianchi, et al., Phys. Rev. Lett. 91 (2003) 187004. P. Fulde, R.A. Ferrell, Phys. Rev. 135 (1964) A550. A.I. Larkin, Y.N. Ovchinnikov, Sov. Phys. J. Exp. Theoret. Phys. 20 (1965) 762. T. Watanabe, et al., Phys. Rev. B 70 (2004) 020506(R). K. Kakuyanagi, et al., Phys. Rev. Lett. 94 (2005) 047602. K. Kumagai, et al., Phys. Rev. Lett. 97 (2006) 227002. X. Gratens, et al, cond-mat/0608722. E. Zeldov, et al., Nature 375 (1995) 373.
Physica B 403 (2008) 871–873 www.elsevier.com/locate/physb
Local magnetization measurements of the first-order transition of CeCoIn5 H. Shishidoa,, R. Okazakia, T. Shibauchia, Y. Matsudaa,b, ¯ nukid M. Konczykowskic, R. Settaid, Y. O a Department of Physics, Kyoto University, Kyoto 606-8502, Japan Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan c CNRS, URA 1380, Laboratoire des Solides Irradie´s, E´cole Polyte´chnique, 91128 Palaiseau, France d Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan b
Abstract We measured the local magnetization in CeCoIn5 with a micro-Hall probe for magnetic fields H along the [0 0 1] and [1 0 0] directions. We observed a sharp jump in the local magnetization at T c ðHÞ below 0.77 K for H k [0 0 1] and 0.79 K for H k [1 0 0], indicating the firstorder phase transitions at upper critical fields. We also observed a dip structure in the local magnetization at the first-order phase transitions for H k [0 0 1], below which the FFLO state is realized. We infer that the dip structure is consistent with the development of planar nodes in the FFLO state. r 2007 Elsevier B.V. All rights reserved. PACS: 74.70.Tx; 74.25.Dw; 74.25.Ha Keywords: CeCoIn5; FFLO; Local magnetization
Some cerium and uranium compounds, in which the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction and the Kondo effect compete, form heavy fermions at low temperatures. The compound CeCoIn5 is a heavy fermion superconductor with a superconducting transition temperature of T c ¼ 2:3 K [1]. A first-order superconducting phase transition at low temperatures and high magnetic fields was observed along both the [0 0 1] and [1 0 0] directions [2–4]. It is believed that the first-order phase transition (FOPT) is due to the Pauli paramagnetic limit. Experimental results indicating the existence of a Fulde– Ferrel–Larkin–Ovchinnikov(FFLO) [5,6] state in the vicinity of H c2 have been reported for H perpendicular and parallel to the c-axis by the specific heat [4], ultrasound velocity [7], NMR [8,9] and magnetization measurements [10]. Here we investigate the superconducting phase diagram of CeCoIn5 by a local probe that can detect clear signature Corresponding author. Tel./fax: +81 75 753 3777.
E-mail address: [email protected] (H. Shishido). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.10.051
of the FOPT even in the presence of large-scale vortex distributions, which some times may mask the first-order nature in the global bulk measurements [11]. In this paper, we observed the FOPT in CeCoIn5 for H k [0 0 1] and H k [1 0 0] by means of the local magnetization measurements with a micro-Hall probe of two-dimensional-electron-gas GaAs/AlGaAs with active area of 10 10 mm2 . We measured the temperature dependence of the Hall resistance in the field-cooling condition, which is proportional to the local magnetic induction B. Fig. 1 shows the temperature dependence of local magnetic induction changes DB, which is defined as DB ¼ B Bnormal , where Bnormal is a linear fit of BðTÞ in normal state, for H along the [1 0 0] direction at various magnetic fields. We observed a sharp jump in DB: jump of 1.93 G with the transition width of 20 mK at T c ¼ 0:46 K in H ¼ 111 kOe. This is clear evidence of the FOPT at T c by a local probe. The step height decreases with decreasing H below 111 kOe, and the step disappears below 105 kOe. Superconducting phase transitions above 111 kOe, which were measured in temperature-sweep conditions, are
ARTICLE IN PRESS H. Shishido et al. / Physica B 403 (2008) 871–873
872
H = 114 kOe
H = 48.5 kOe CeCoIn5 H // [100]
113.8 113.5
48.3
113
CeCoIn5 H // [001]
48.1 3G
112
47.9
111 108 1st
47.7
ΔB
ΔB
110
47.5
106 105
47.3
3G
47.0
104
46.5
2nd
1.0
0.9
Fig. 2. Temperature dependence of the local magnetization changes for H k [0 0 1]. Each curve is shifted vertically for clarity.
120
60 CeCoIn5 H // [100]
120
60
110
100
0 0
H // [001] 40 50 H (kOe)
broad. This may be due to broadening of the transition by the flat phase line in this region. In contrast, the previous measurements, which were measured by sweeping fields, indicated a clear FOPT [2,3]. From these facts, we can conclude that the FOPT appears below T cr ¼ 0:77 K of 0.33 T c ð0Þ, where T c ð0Þ ¼ 2:3 K is the superconducting transition temperature at 0 kOe. Fig. 2 shows the temperature dependence of DB for H k [0 0 1] at various magnetic fields. The sharp steps according to the FOPT at T c were observed in DBðTÞ, and the step height decreases with decreasing the magnetic fields, as the same as that in H k [1 0 0]. These results indicate that the FOPT changes into second-order phase transition above T cr ¼ 0:79 Kð0:34T c Þ. An important difference from the H k [1 0 0] case is that DBðTÞ has a dip structure above 47.5 kOe. We note that such a structure has not been resolved by the bulk magnetization measurements [3]. The origin of the dip structure is discussed below. We show the superconducting phase diagrams for H k [1 0 0] in Fig. 3a and H k [0 0 1] in Fig. 3b. Open and filled symbols represent first- and second-order phase transitions, respectively. Present results are well consistent with previous ones: T ccr of 0.77 K ð0:33T c Þ and T acr ¼ 0:79 K ð0:34T c Þ for H k [1 0 0] and [0 0 1], respectively. We will discuss the origin of the dip structure on DB. DB for H k [0 0 1] has a dip structure at the FOPT, just below which the FFLO state was reported [9,10], as shown in the inset of Fig. 3b. In contrast, the dip structure was not observed for H k [1 0 0] at the FOPT, where a standard (d-wave) superconducting state occurs just below H c2 in magnetic field range of 105 to 113 kOe. These results imply that the dip structure observed for H k [0 0 1] is caused by a development of nodal-planes with the FFLO transition which should have additional paramagnetic contribution.
0.7 Temperature (K)
Magnetic Field (kOe)
Fig. 1. Temperature dependence of the local magnetization changes under various magnetic fields for H k [1 0 0]. Each curve is shifted vertically for clarity.
0.5
H (kOe)
0.5 Temperature (K)
Magnetic Field (kOe)
0
20
FFLO 45 BCS 40
0
0.5 T (K)
0
1.0
1 2 Temperature (K)
1 T (K)
0 0
1 2 Temperature (K)
Fig. 3. Superconducting phase diagrams determined by the present work (, K), together with the global magnetization(&, ’) [3] and the specific heat measurements (n, m) [4] in (a) H k [1 0 0] and (b) H k [0 0 1], respectively. Open symbols indicate the first-order phase transition.
The dip structure was, however, not observed above 113 kOe, where the FFLO state was reported [4,7,8,10] below the FOPT for H k [1 0 0]. It seems to be due to broadening of the transition discussed above. A consistent result was reported in the temperature dependence of the Knight shift at 115In-site which is related to the spin susceptibility [9]. The Knight shift increases steeply with decreasing the temperature in the vicinity of T c , decreases in low temperatures. In conclusion, we measured the temperature dependence of DB via the micro-Hall probe in a heavy-fermion superconductor CeCoIn5 for H along the [0 0 1] and [1 0 0] directions. We observed the clear local magnetization jump at T c indicating the FOPT. The FOPT exists below T ccr ¼ 0:77 K ð0:33T c Þ for H k [1 0 0] and T acr ¼ 0:79 K ð0:34T c Þ for H k [0 0 1], respectively. The dip structure appeared in DB for H k [0 0 1] at the FOPT. It may be
ARTICLE IN PRESS H. Shishido et al. / Physica B 403 (2008) 871–873
related to the development of nodal-planes expected in the FFLO phase.
[2] [3] [4] [5] [6]
This work was partly supported by a Grant in-Aid for Scientific Research from the MEXT and by Japan-France Integrated Action Program SAKURA. One of the authors (H. S.) was supported by the Research Fellowships of the JSPS for Young Scientists.
[7] [8] [9] [10] [11]
References [1] C. Petrovic, et al., J. Phys. Condens. Matter 13 (2001) L337.
873
K. Izawa, et al., Phys. Rev. Lett. 87 (2001) 057002. T. Tayama, et al., Phys. Rev. B 65 (2002) 180504. A. Bianchi, et al., Phys. Rev. Lett. 91 (2003) 187004. P. Fulde, R.A. Ferrell, Phys. Rev. 135 (1964) A550. A.I. Larkin, Y.N. Ovchinnikov, Sov. Phys. J. Exp. Theoret. Phys. 20 (1965) 762. T. Watanabe, et al., Phys. Rev. B 70 (2004) 020506(R). K. Kakuyanagi, et al., Phys. Rev. Lett. 94 (2005) 047602. K. Kumagai, et al., Phys. Rev. Lett. 97 (2006) 227002. X. Gratens, et al, cond-mat/0608722. E. Zeldov, et al., Nature 375 (1995) 373.