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Electron transport and superconducting properties of ZrB12 and YB6
Physica C 460–462 (2007) 623–625 www.elsevier.com/locate/physc
Electron transport and superconducting properties of ZrB12 and YB6 Vitaly Gasparov
a,*
, Ilya Sheikin b, Shigeki Otani
c
a
c
Institute of Solid State Physics RAS, 142432, Chernogolovka, Russian Federation b Grenoble High Magnetic Field Laboratory, 38042 Grenoble Cedex 9, France National Institute for Research in Inorganic Materials, Tsukuba, Ibaraki 305, Japan Available online 14 April 2007
Abstract We report the measurements of the temperature dependence of the resistivity, q(T), magnetic penetration depth, k(T), the lower, H c1 (T), and upper, H c2 (T), critical magnetic fields, for single crystals of dodecaboride ZrB12 and hexaboride YB6. We observe a number of deviations from conventional behavior in these cluster materials. Although both borides behaves like a simple metal in the normal state, the resistive Debye temperature TR for ZrB12 (TR = 300 K) is three times smaller relative to that calculated from the specific heat data. At the same time TR = 60 K is anomalously small for YB6. Superfluid density of ZrB12 displays unconventional temperature dependence with pronounced shoulder at T/Tc equal to 0.6. Contrary to conventional theories we found a linear temperature dependence of H c2 (T) from Tc down to 0.35 K for both cluster borides. We suggest that both k(T) and H c2 (T) dependencies can be explained by two band BCS model with different superconducting gap and Tc. First de Haas-van Alphen oscillations in ZrB12 single crystals are also presented. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Superconductivity; Two gap model; ZrB12; YB6
1. Introduction The discovery of superconductivity in MgB2 initiated a search for superconductivity in other borides [1]. However, it was observed only in the non-stoichiometric compounds (MoB2.5, NbB2.5, Mo2B, W2B, BeB2.75) (see references in [2,3,5]). Although it is accepted that the layered structure is crucial for high-Tc superconductivity, one can argue that clusters of light atoms are important for high Tc. It was suggested (see in [3]) that the superconductivity in ZrB12 is due to the effect of a cluster of boron atoms. While the superconductivity in ZrB12 and YB6 was discovered long time ago (see in [2,3,5]), there has been little and controversial efforts devoted to study the electron transport and superconducting properties in these compounds. Here, we report unusual superconducting properties of ZrB12 and
*
Corresponding author. Tel.: +7 495 9932755; fax: +7 496 5249701. E-mail address: [email protected] (V. Gasparov).
0921-4534/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.04.134
YB6. Recently observed de Haas-van Alphen oscillations in ZrB12 are also discussed. 2. Results and discussion Under ambient conditions, ZrB12 crystallizes in the UB12 type fcc structure. In this structure, Zr atoms are located among the close-packed B12 clusters [2]. In the cubic structure of YB6, the Y atom is located at the center of a lattice surrounded by B6 clusters with icosahedral symmetry. The ZrB12 single crystals have been grown by the floating-zone method by the Kiev group [3]. The metallographic and X-ray analysis indicated that some parts of the ingot contained needle like phase of non-superconducting ZrB2. Thus special care was taken to cut the ZrB2-free h1 0 0i – oriented rectangular ZrB12 bars. The YB6 single crystals were grown by aid of the RF-heated floating-zone method by Tsukuba group [4]. Fig. 1 shows the temperature dependence of the resistivity of ZrB12 and YB6 single crystal samples. The transition temperature in ZrB12 (Tc0 = 6.0 K) and in YB6
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V. Gasparov et al. / Physica C 460–462 (2007) 623–625
Fig. 1. Temperature dependence of q(T) for ZrB12 and YB6. The solid lines are the BG t5 model.
(Tc0 = 7.7 K) is consistent with the previously reported values (see Ref. in [1–3,5]) and is larger than that of ZrB2 polycrystalline samples (5.5 K) [1]. Above 25 K the Bloch–Gru¨neisen (BG) model describes the q(T) dependence of both borides fairly well [3] and shows that the electron–phonon interaction dominates at this temperature range. The resistive Debye temperature TR, is equal to 300 K and 60 K for ZrB12 and YB6, respectively. The former one is very close to TR = 280 K observed on polycrystalline ZrB12 samples [2]. At the same time, TR for ZrB12 calculated from the specific heat C(T) data on a rather large sample [6], is three times higher, possibly due to presence of ZrB2 phase. The deviations of q(T) from the BG model at low temperatures relates to possible effect of electron–electron interaction on conductivity [3]. The radio frequency LC techniques [2,5] have been used for the penetration depth k(T) measurements. Fig. 2 shows k2(0)/k2(T) versus reduced temperature T/Tc for the ZrB12 single crystals as determined from this technique [2,5]. The
1.0
2
0.6
2
λ (0)/ λ (T)
0.8
0.4
p-
0.2 0.0 0.0
Fig. 3. Temperature dependence of H c2 in ZrB12 and YB6 (squares) extracted from: k(H) – bold points; q(H) – circles. The dashed line represents the BCS dependence.
unconventional behavior of ZrB12 superfluid density with pronounced shoulder at T/Tc = 0.65 is easily noticed. This feature can be explained by the two band model [5], which assumes the existence of two independent p- and d-bands with the different gaps, D’s, and transition temperatures, Tc’s [5]. Fitting of the experimental data as 1=k2 ¼ 1=k2p þ 1=k2d gives the following p- and d-band parameters: T pc ¼ 6:0 K, Dp(0) = 0.73 meV, kp(0) = 170 nm and T dc ¼ 4:2 K, Dd(0) = 2.1 meV, kd(0) = 260 nm [5]. Fig. 3 presents the H c2 (T) dependence obtained from the onsets of the q(H) and k(H) in the normal state for ZrB12 and YB6. In contrast to the BCS theory, the H c2 (T) dependence is linear over an extended temperature range with no evidence of a saturation down to 0.35 K. We explain this behavior in the frames of the two band model described above. From the k(T) data for ZrB12, we found that the diffusivities in the p- and d-bands are equal to Dp = 57 cm2/s and Dd = 10 cm2/s, respectively. According to [7], the large ratio Dp/Dd 6 leads to enhancement of the H c2 (0) value. Thus we can speculate that the limiting value of H c2 (0) is dominated by the d-band with the lower Dd, while the derivative dH c2 /dT in the vicinity of Tc is governed by the p-band with the larger Dp. We successfully detect three dHvA frequencies in ZrB12 in the fields from 14 T up to 28 T by aid of cantilever technique, in spite of the low resistivity ratio of our samples (q300 K/q6 K 10). The effective mass corresponding to one of these frequencies is rather low (0.5me). Although the observed two-gap behavior of k(T) in ZrB12 is similar to that in MgB2, discovery of two different Tc is unconventional.
d0.2
0.4
0.6
0.8
1.0
T/T c Fig. 2. The superfluid density of the ZrB12 (circles). The two band model calculations are shown by the dashed (p-band term), dotted (d-band term), and solid (total) lines.
Acknowledgements We are grateful Yu.B. Paderno, V.B. Filipov, A.B. Lyashenko for the ZrB12 single crystals. This work was supported by the Grants MSh-2169.2003.2, RAS Program: New Materials and Structures, and GHMFL Ref. SM0606.
V. Gasparov et al. / Physica C 460–462 (2007) 623–625
References [1] V.A. Gasparov et al., JETP Lett. 73 (2001) 601. [2] V.A. Gasparov et al., JETP 101 (2005) 98. [3] V.A. Gasparov et al., JETP Lett. 80 (2004) 330.
[4] [5] [6] [7]
S. Otani et al., J. Cryst. Growth 217 (2000) 378. V.A. Gasparov et al., Phys. Rev. B 73 (2006) 094510. R. Lortz et al., Phys. Rev. B 72 (2005) 024547. A. Gurevich, Phys. Rev. B 67 (2003) 184515.
625
Electron transport and superconducting properties of ZrB12 and YB6 Vitaly Gasparov
a,*
, Ilya Sheikin b, Shigeki Otani
c
a
c
Institute of Solid State Physics RAS, 142432, Chernogolovka, Russian Federation b Grenoble High Magnetic Field Laboratory, 38042 Grenoble Cedex 9, France National Institute for Research in Inorganic Materials, Tsukuba, Ibaraki 305, Japan Available online 14 April 2007
Abstract We report the measurements of the temperature dependence of the resistivity, q(T), magnetic penetration depth, k(T), the lower, H c1 (T), and upper, H c2 (T), critical magnetic fields, for single crystals of dodecaboride ZrB12 and hexaboride YB6. We observe a number of deviations from conventional behavior in these cluster materials. Although both borides behaves like a simple metal in the normal state, the resistive Debye temperature TR for ZrB12 (TR = 300 K) is three times smaller relative to that calculated from the specific heat data. At the same time TR = 60 K is anomalously small for YB6. Superfluid density of ZrB12 displays unconventional temperature dependence with pronounced shoulder at T/Tc equal to 0.6. Contrary to conventional theories we found a linear temperature dependence of H c2 (T) from Tc down to 0.35 K for both cluster borides. We suggest that both k(T) and H c2 (T) dependencies can be explained by two band BCS model with different superconducting gap and Tc. First de Haas-van Alphen oscillations in ZrB12 single crystals are also presented. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Superconductivity; Two gap model; ZrB12; YB6
1. Introduction The discovery of superconductivity in MgB2 initiated a search for superconductivity in other borides [1]. However, it was observed only in the non-stoichiometric compounds (MoB2.5, NbB2.5, Mo2B, W2B, BeB2.75) (see references in [2,3,5]). Although it is accepted that the layered structure is crucial for high-Tc superconductivity, one can argue that clusters of light atoms are important for high Tc. It was suggested (see in [3]) that the superconductivity in ZrB12 is due to the effect of a cluster of boron atoms. While the superconductivity in ZrB12 and YB6 was discovered long time ago (see in [2,3,5]), there has been little and controversial efforts devoted to study the electron transport and superconducting properties in these compounds. Here, we report unusual superconducting properties of ZrB12 and
*
Corresponding author. Tel.: +7 495 9932755; fax: +7 496 5249701. E-mail address: [email protected] (V. Gasparov).
0921-4534/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.04.134
YB6. Recently observed de Haas-van Alphen oscillations in ZrB12 are also discussed. 2. Results and discussion Under ambient conditions, ZrB12 crystallizes in the UB12 type fcc structure. In this structure, Zr atoms are located among the close-packed B12 clusters [2]. In the cubic structure of YB6, the Y atom is located at the center of a lattice surrounded by B6 clusters with icosahedral symmetry. The ZrB12 single crystals have been grown by the floating-zone method by the Kiev group [3]. The metallographic and X-ray analysis indicated that some parts of the ingot contained needle like phase of non-superconducting ZrB2. Thus special care was taken to cut the ZrB2-free h1 0 0i – oriented rectangular ZrB12 bars. The YB6 single crystals were grown by aid of the RF-heated floating-zone method by Tsukuba group [4]. Fig. 1 shows the temperature dependence of the resistivity of ZrB12 and YB6 single crystal samples. The transition temperature in ZrB12 (Tc0 = 6.0 K) and in YB6
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V. Gasparov et al. / Physica C 460–462 (2007) 623–625
Fig. 1. Temperature dependence of q(T) for ZrB12 and YB6. The solid lines are the BG t5 model.
(Tc0 = 7.7 K) is consistent with the previously reported values (see Ref. in [1–3,5]) and is larger than that of ZrB2 polycrystalline samples (5.5 K) [1]. Above 25 K the Bloch–Gru¨neisen (BG) model describes the q(T) dependence of both borides fairly well [3] and shows that the electron–phonon interaction dominates at this temperature range. The resistive Debye temperature TR, is equal to 300 K and 60 K for ZrB12 and YB6, respectively. The former one is very close to TR = 280 K observed on polycrystalline ZrB12 samples [2]. At the same time, TR for ZrB12 calculated from the specific heat C(T) data on a rather large sample [6], is three times higher, possibly due to presence of ZrB2 phase. The deviations of q(T) from the BG model at low temperatures relates to possible effect of electron–electron interaction on conductivity [3]. The radio frequency LC techniques [2,5] have been used for the penetration depth k(T) measurements. Fig. 2 shows k2(0)/k2(T) versus reduced temperature T/Tc for the ZrB12 single crystals as determined from this technique [2,5]. The
1.0
2
0.6
2
λ (0)/ λ (T)
0.8
0.4
p-
0.2 0.0 0.0
Fig. 3. Temperature dependence of H c2 in ZrB12 and YB6 (squares) extracted from: k(H) – bold points; q(H) – circles. The dashed line represents the BCS dependence.
unconventional behavior of ZrB12 superfluid density with pronounced shoulder at T/Tc = 0.65 is easily noticed. This feature can be explained by the two band model [5], which assumes the existence of two independent p- and d-bands with the different gaps, D’s, and transition temperatures, Tc’s [5]. Fitting of the experimental data as 1=k2 ¼ 1=k2p þ 1=k2d gives the following p- and d-band parameters: T pc ¼ 6:0 K, Dp(0) = 0.73 meV, kp(0) = 170 nm and T dc ¼ 4:2 K, Dd(0) = 2.1 meV, kd(0) = 260 nm [5]. Fig. 3 presents the H c2 (T) dependence obtained from the onsets of the q(H) and k(H) in the normal state for ZrB12 and YB6. In contrast to the BCS theory, the H c2 (T) dependence is linear over an extended temperature range with no evidence of a saturation down to 0.35 K. We explain this behavior in the frames of the two band model described above. From the k(T) data for ZrB12, we found that the diffusivities in the p- and d-bands are equal to Dp = 57 cm2/s and Dd = 10 cm2/s, respectively. According to [7], the large ratio Dp/Dd 6 leads to enhancement of the H c2 (0) value. Thus we can speculate that the limiting value of H c2 (0) is dominated by the d-band with the lower Dd, while the derivative dH c2 /dT in the vicinity of Tc is governed by the p-band with the larger Dp. We successfully detect three dHvA frequencies in ZrB12 in the fields from 14 T up to 28 T by aid of cantilever technique, in spite of the low resistivity ratio of our samples (q300 K/q6 K 10). The effective mass corresponding to one of these frequencies is rather low (0.5me). Although the observed two-gap behavior of k(T) in ZrB12 is similar to that in MgB2, discovery of two different Tc is unconventional.
d0.2
0.4
0.6
0.8
1.0
T/T c Fig. 2. The superfluid density of the ZrB12 (circles). The two band model calculations are shown by the dashed (p-band term), dotted (d-band term), and solid (total) lines.
Acknowledgements We are grateful Yu.B. Paderno, V.B. Filipov, A.B. Lyashenko for the ZrB12 single crystals. This work was supported by the Grants MSh-2169.2003.2, RAS Program: New Materials and Structures, and GHMFL Ref. SM0606.
V. Gasparov et al. / Physica C 460–462 (2007) 623–625
References [1] V.A. Gasparov et al., JETP Lett. 73 (2001) 601. [2] V.A. Gasparov et al., JETP 101 (2005) 98. [3] V.A. Gasparov et al., JETP Lett. 80 (2004) 330.
[4] [5] [6] [7]
S. Otani et al., J. Cryst. Growth 217 (2000) 378. V.A. Gasparov et al., Phys. Rev. B 73 (2006) 094510. R. Lortz et al., Phys. Rev. B 72 (2005) 024547. A. Gurevich, Phys. Rev. B 67 (2003) 184515.
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