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Anisotropic superconductivity in borocarbide superconductors and spin disorder
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) 158–159
Anisotropic superconductivity in borocarbide superconductors and spin disorder J.P. Brisona,*, N. Luchiera, A. Sulpicea, H. Suderowb, P. Martinez-Samperb, S. Vieirab, A.I. Buzdinc, P.C. Canfieldd a
b
Centre de Recherches sur les Trs Basses Tempratures, CNRS, BP 166, 38042 Grenoble Cedex 9, France ! Laboratorio de Bajas Temperaturas, Departamento de Fisica de la Materia Condensada, Instituto de Ciencia de Materiales Nicolas ! Cabrera, Facultad de Ciencias, C-III, Universidad Autonoma de Madrid, 28049 Madrid, Spain c Laboratoire de Physique Th!eorique, Universit!e de Bordeaux, CNRS URA 764, 33175 Gradignan-Cedex, France d Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA
Abstract We present microscopic measurements indicating that the superconducting gap of borocarbide superconductors is strongly anisotropic. They are compared to macroscopic Bc2 measurements on TmNi2 B2 C; which allow a direct estimation of spin disorder and of coupling strength anisotropy (strong coupling two-band model). r 2004 Elsevier B.V. All rights reserved. PACS: 74.25.Ha; 74.25.Op; 74.70.Dd Keywords: TmNi2 B2 C; Borocarbide; Tunnelling spectroscopy; Bc2
An appreciable feature of the borocarbide superconductors is that almost all microscopic and macroscopic measurements can be performed, and compared together. Here we first summarize the results of tunnelling spectroscopy on various members of the series, and then we discuss new results on spin disorder in the magnetic TmNi2 B2 C: We have performed scanning tunnelling spectroscopy on the Lu, Y [1] and Tm [2] borocarbides: for all systems, we get zero conductance within the gap at low temperature (0.5–0:8 K), and we clearly observe the quasiparticle excitation peak at the gap edge, asserting the good quality of the measurements (see Fig. 1). But there are important differences between the nonmagnetic (Lu, Y) and the magnetic (Tm) system. In the first two cases, the data change quantitatively depending on the position on the sample surface: zero conductance is always observed at low voltage, but the gap amplitude as well as the critical temperature may be *Corresponding author. Tel.: +33-4-76-88-12-70; fax: +334-76-87-50-60. E-mail address: [email protected] (J.P. Brison).
reduced, which has been interpreted as the influence of surface disorder on a very anisotropic gap [1]. This is also confirmed on individual measurements by the smearing of the gap edge (Fig. 1). By contrast, in the case of Tm, the spectroscopy is independent of the position on the surface, and it can be fitted by standard BCS formula with just a subtle modification: additional thermal smearing (T ¼ 1 K instead of 0:8 K) should be introduced: this is the only sign of a gap anisotropy in this system, which might be strongly washed out by spin disorder. Indeed, TmNi2 B2 C has the peculiarity of showing magnetic order only deep within the superconducting phase (TN E1:5 K5Tc E11 K). However, the strong paramagnetism above TN has been recognized as a probable key factor for the control of its upper critical field Bc2 [3] and of the decrease of Tc with respect to the Lu or Y systems [4]. We have made these points quantitative, taking advantage of the large ratio (Tc =TN ) to make ‘‘single impurity’’ approximations for the Tm ions, and of their rather low-crystalline electric field (CEF) anisotropies [5] to neglect CEF effects altogether.
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.1380
ARTICLE IN PRESS J.P. Brison et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 158–159
Table 1 Parameters of the fits of Fig. 2. vF1 and vF2 are the Fermi velocities of the two bands, l11 ; l12 ¼ l21 ¼ l22 the inter- and intra-band strong coupling parameters (see Ref. [6])
2.5
2
Normalized conductance
159
1.5
Bjjc B>c
l11
l12 ; l21 ; l22
vF1 ð106 m=sÞ
vF2 ð106 m=sÞ
I (K)
0.8 0.8
0.3 0.3
0.07 0.052
0.23 0.26
37 45
1
0.5
0 -6
-4
-2
0
2
4
6
into the form: M Hz ¼ 2 mB Bapp þ ðgJ 1ÞI J sz ; Msat
ð1Þ
V (mV)
Fig. 1. Conductance normalized to its value at high bias voltage, obtained with scanning tunnelling spectroscopy on LuNi2 B2 C (dash–dotted line, 0:5 K), YNi2 B2 C (dashed line, 0:5 K), and TmNi2 B2 C (circles, 0:8 K) The anisotropy is washed out in the Tm compound, which can be fitted with conventional BCS theory (full line).
3 Bapp//c Bint //c
2.5
Bapp⊥c
Bc2 (T)
Bint⊥c
TmNi 2 B2C
2
fit Bapp
1.5
1
0.5
0 0
2
4
6 T (K)
8
10
12
Fig. 2. Upper critical field of TmNi2 B2 C (from resistivity experiments) for an applied field Bapp jjc (full circles) and >c (full squares). Open symbols show the internal field (Bint ¼ Bapp þ m0 M). Full lines is the fit for both directions including internal field corrections and Pauli limitation with exchange coupling (see text).
Bc2 has been deduced from resistive transitions, and analysed using our magnetization measurements and an effective two-band model [6]. The magnetization of TmNi2 B2 C has two different effects on Bc2 ; which have been both included in the fit. The orbital limitation is controlled not by the applied field Bapp ; but by the internal field Bint ¼ Bapp þ m0 M; a large correction for Bjjc (see Fig. 2). The paramagnetic limitation is controlled by an effective Zeeman Hamiltonian cast
where I is the exchange parameter (per Tm ion) between conduction electrons and Tm3þ ; M (resp. Msat ) the measured (resp. saturation) magnetization for Bapp ; J ¼ 6; gJ ¼ 76 (Lande g-factor) for Tm3þ : The two-band model accounts for the positive curvature of Bc2 observed in the non-magnetic Y and Lu superconductors which is also present (although less pronounced) in the Tm, particularly for fields Bapp >c (see Fig. 2). Its parameters are close to those of Ref. [6] (see Table 1), and the strong coupling constants have been adjusted to the Tc of Lu (16:5 K): the reduction down to 11 K (the value of Tc in TmNi2 B2 C) is obtained by addition of magnetic scattering, with the same value of 1=ts (E7:9 K) for inter- and intra-band scattering. From this value, according to standard expressions [7] a value of IE77 K is deduced. The fit of Bc2 gives IE40 K for both directions (Table 1). The low anisotropy between the two crystallographic directions is quite satisfying. In fact, Tm3þ is known to break ‘‘de Gennes scaling’’ in the borocarbide compounds [8], so the estimate of I from Tc reduction should be considered as an upper limit of this parameter: the estimation from the fit of Bc2 should be much more reliable. This analysis does give quantitative support to the role of spin disorder in the superconducting state of TmNi2 B2 C; encouraging further investigations on its influence on the gap anisotropy and in the other magnetic borocarbides.
References [1] [2] [3] [4] [5] [6] [7] [8]
P. Martinez-Samper, et al., Phys. Rev. B 67 (2003) 014526. H. Suderow, et al., Phys. Rev. B 64 (2001) 020503(R). B.K. Cho, et al., Phys. Rev. B 52 (1995) 3676. P.C. Canfield, et al., Phys. Tod. 51 (10) (1998) 40. B.D. Dunlap, Phys. Rev. B 34 (1986) 1496. S.V. Shulga, et al., Phys. Rev. Lett. 80 (1998) 1730. M.B. Maple, Physica B 215 (1995) 110. J. Freudenberger, et al., Physica C 339 (2000) 1995.
Journal of Magnetism and Magnetic Materials 272–276 (2004) 158–159
Anisotropic superconductivity in borocarbide superconductors and spin disorder J.P. Brisona,*, N. Luchiera, A. Sulpicea, H. Suderowb, P. Martinez-Samperb, S. Vieirab, A.I. Buzdinc, P.C. Canfieldd a
b
Centre de Recherches sur les Trs Basses Tempratures, CNRS, BP 166, 38042 Grenoble Cedex 9, France ! Laboratorio de Bajas Temperaturas, Departamento de Fisica de la Materia Condensada, Instituto de Ciencia de Materiales Nicolas ! Cabrera, Facultad de Ciencias, C-III, Universidad Autonoma de Madrid, 28049 Madrid, Spain c Laboratoire de Physique Th!eorique, Universit!e de Bordeaux, CNRS URA 764, 33175 Gradignan-Cedex, France d Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA
Abstract We present microscopic measurements indicating that the superconducting gap of borocarbide superconductors is strongly anisotropic. They are compared to macroscopic Bc2 measurements on TmNi2 B2 C; which allow a direct estimation of spin disorder and of coupling strength anisotropy (strong coupling two-band model). r 2004 Elsevier B.V. All rights reserved. PACS: 74.25.Ha; 74.25.Op; 74.70.Dd Keywords: TmNi2 B2 C; Borocarbide; Tunnelling spectroscopy; Bc2
An appreciable feature of the borocarbide superconductors is that almost all microscopic and macroscopic measurements can be performed, and compared together. Here we first summarize the results of tunnelling spectroscopy on various members of the series, and then we discuss new results on spin disorder in the magnetic TmNi2 B2 C: We have performed scanning tunnelling spectroscopy on the Lu, Y [1] and Tm [2] borocarbides: for all systems, we get zero conductance within the gap at low temperature (0.5–0:8 K), and we clearly observe the quasiparticle excitation peak at the gap edge, asserting the good quality of the measurements (see Fig. 1). But there are important differences between the nonmagnetic (Lu, Y) and the magnetic (Tm) system. In the first two cases, the data change quantitatively depending on the position on the sample surface: zero conductance is always observed at low voltage, but the gap amplitude as well as the critical temperature may be *Corresponding author. Tel.: +33-4-76-88-12-70; fax: +334-76-87-50-60. E-mail address: [email protected] (J.P. Brison).
reduced, which has been interpreted as the influence of surface disorder on a very anisotropic gap [1]. This is also confirmed on individual measurements by the smearing of the gap edge (Fig. 1). By contrast, in the case of Tm, the spectroscopy is independent of the position on the surface, and it can be fitted by standard BCS formula with just a subtle modification: additional thermal smearing (T ¼ 1 K instead of 0:8 K) should be introduced: this is the only sign of a gap anisotropy in this system, which might be strongly washed out by spin disorder. Indeed, TmNi2 B2 C has the peculiarity of showing magnetic order only deep within the superconducting phase (TN E1:5 K5Tc E11 K). However, the strong paramagnetism above TN has been recognized as a probable key factor for the control of its upper critical field Bc2 [3] and of the decrease of Tc with respect to the Lu or Y systems [4]. We have made these points quantitative, taking advantage of the large ratio (Tc =TN ) to make ‘‘single impurity’’ approximations for the Tm ions, and of their rather low-crystalline electric field (CEF) anisotropies [5] to neglect CEF effects altogether.
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.1380
ARTICLE IN PRESS J.P. Brison et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 158–159
Table 1 Parameters of the fits of Fig. 2. vF1 and vF2 are the Fermi velocities of the two bands, l11 ; l12 ¼ l21 ¼ l22 the inter- and intra-band strong coupling parameters (see Ref. [6])
2.5
2
Normalized conductance
159
1.5
Bjjc B>c
l11
l12 ; l21 ; l22
vF1 ð106 m=sÞ
vF2 ð106 m=sÞ
I (K)
0.8 0.8
0.3 0.3
0.07 0.052
0.23 0.26
37 45
1
0.5
0 -6
-4
-2
0
2
4
6
into the form: M Hz ¼ 2 mB Bapp þ ðgJ 1ÞI J sz ; Msat
ð1Þ
V (mV)
Fig. 1. Conductance normalized to its value at high bias voltage, obtained with scanning tunnelling spectroscopy on LuNi2 B2 C (dash–dotted line, 0:5 K), YNi2 B2 C (dashed line, 0:5 K), and TmNi2 B2 C (circles, 0:8 K) The anisotropy is washed out in the Tm compound, which can be fitted with conventional BCS theory (full line).
3 Bapp//c Bint //c
2.5
Bapp⊥c
Bc2 (T)
Bint⊥c
TmNi 2 B2C
2
fit Bapp
1.5
1
0.5
0 0
2
4
6 T (K)
8
10
12
Fig. 2. Upper critical field of TmNi2 B2 C (from resistivity experiments) for an applied field Bapp jjc (full circles) and >c (full squares). Open symbols show the internal field (Bint ¼ Bapp þ m0 M). Full lines is the fit for both directions including internal field corrections and Pauli limitation with exchange coupling (see text).
Bc2 has been deduced from resistive transitions, and analysed using our magnetization measurements and an effective two-band model [6]. The magnetization of TmNi2 B2 C has two different effects on Bc2 ; which have been both included in the fit. The orbital limitation is controlled not by the applied field Bapp ; but by the internal field Bint ¼ Bapp þ m0 M; a large correction for Bjjc (see Fig. 2). The paramagnetic limitation is controlled by an effective Zeeman Hamiltonian cast
where I is the exchange parameter (per Tm ion) between conduction electrons and Tm3þ ; M (resp. Msat ) the measured (resp. saturation) magnetization for Bapp ; J ¼ 6; gJ ¼ 76 (Lande g-factor) for Tm3þ : The two-band model accounts for the positive curvature of Bc2 observed in the non-magnetic Y and Lu superconductors which is also present (although less pronounced) in the Tm, particularly for fields Bapp >c (see Fig. 2). Its parameters are close to those of Ref. [6] (see Table 1), and the strong coupling constants have been adjusted to the Tc of Lu (16:5 K): the reduction down to 11 K (the value of Tc in TmNi2 B2 C) is obtained by addition of magnetic scattering, with the same value of 1=ts (E7:9 K) for inter- and intra-band scattering. From this value, according to standard expressions [7] a value of IE77 K is deduced. The fit of Bc2 gives IE40 K for both directions (Table 1). The low anisotropy between the two crystallographic directions is quite satisfying. In fact, Tm3þ is known to break ‘‘de Gennes scaling’’ in the borocarbide compounds [8], so the estimate of I from Tc reduction should be considered as an upper limit of this parameter: the estimation from the fit of Bc2 should be much more reliable. This analysis does give quantitative support to the role of spin disorder in the superconducting state of TmNi2 B2 C; encouraging further investigations on its influence on the gap anisotropy and in the other magnetic borocarbides.
References [1] [2] [3] [4] [5] [6] [7] [8]
P. Martinez-Samper, et al., Phys. Rev. B 67 (2003) 014526. H. Suderow, et al., Phys. Rev. B 64 (2001) 020503(R). B.K. Cho, et al., Phys. Rev. B 52 (1995) 3676. P.C. Canfield, et al., Phys. Tod. 51 (10) (1998) 40. B.D. Dunlap, Phys. Rev. B 34 (1986) 1496. S.V. Shulga, et al., Phys. Rev. Lett. 80 (1998) 1730. M.B. Maple, Physica B 215 (1995) 110. J. Freudenberger, et al., Physica C 339 (2000) 1995.