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Optical properties of the borocarbide superconductors
ELSEVIER
Physica B 230-232 (1997) 879 881
Optical properties of the borocarbide superconductors F. Bommeli a'*, L. Degiorgi a, P. Wachter a, B.K. C h o b, P.C. Canfield b, R. Chau c, M.B. Maple ~ Laboratorium fiir Festk6rperphysik, ETH-Zurich. CH-8093 Zurich, Switzerland hAmes Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA Department of Physics and Institute for Pure and Applied Physical Sciences, University of California at San Diego, La Jolla, CA 92093, USA
Abstract
We have measured the optical reflectivityof LuNi2B2C and YNizBEC compounds, and have evaluated the optical conductivity both above and below the superconducting transition temperature. The normal state optical properties suggest that these superconductors are almost in the clean limit. Our results below Tc give, however, evidence of a superconducting gap signature, and are in agreement with a moderate-to-strong coupling limit of the BCS theory. Keywords: Superconductivity;Optical properties; LuNi2B2C; YNizB2C
The discovery [ 1, 2] of superconductivity at relatively high temperatures in the new family of quaternary intermetallic compounds LnNi/BzC (Ln = Lu, Tin, Er, Ho, Dy, Y, with Tc = 15.6 and 16.6 K for the Y and Lu compound, respectively) raised a lot of interest both experimentally and theoretically. The striking layered-like crystallographic similarity of the LnNi2BzC compound with the cuprate-oxide superconductors [3], and the fact that superconductivity is observed not only for the non-magnetic rare-earth elements but also for the heavy magnetic rare earths, Tm, Er, Ho and Dy [1, 2] raised the expectation for the occurrence of competition between magnetism and superconductivity [4] and led to speculation that some exotic pairing mechanism is responsible for their relatively high To's. Even though these systems were extensively characterized by transport and magnetic measurements [1, 2, 4, 5], the mechanism of superconduc*Correspondingauthor.
tivity still remains to be settled. In this respect, an important intrinsic parameter is the superconducting gap. Optical spectroscopic methods are in principle a powerful experimental tool for the determination of such a relevant energy scale which has important implications in connection with the excitations mediating superconductivity and the strength of the coupling mechanism (electronphonon or electron-electron). The Lu-single-crystal sample used in the present experiment was prepared following the method described in Refs. [1, 5]. The sample was polished in order to achieve smooth and shiny optical surface. The optical properties were obtained by measuring the reflectivity R(~o) of the Lu-single crystal in the ab-plane, as a function of temperature between 15 and 105 cm 1, using four different spectrometers [6]. By performing the Kramers-Kronig transformation with standard extrapolations, we obtain the complete set of optical properties expressed in term of the complete optical conductivity [6]. Below T~, R(o~) at T > 6 K was completed with an
0921-4526/97/$17.00 Copyright ~-~ c 1997 ElsevierScienceB.V.All rights reserved Pll S092 1-4526(96)00465-6
F. Bommeli et al. / Physica B 230-232 (1997) 879-881
880
/9
'
1O0 ,~ .
1.0.
200 .
[cm-t ]
'
8000
~
\~'~ %0.5 m-
~\ vc,.~ 6000
r "-,:.,f g
.,..~
,,,,,\,,,000 \
~4000
\,\'~""7: ........ ,_27~
\\ \,\'-'
,,,
~ . ~ i 0~" - 6K ~'~'~ . . . . 10 K _
,, 2000
,~ r
/\/1
,~ \ . \
.,,~
',
,'"" ""
/
\..
/
"~'-.......
0.01
_
. . . . !4 - . - 20 K - .... 50K
0.02
0.03
Photon Energy [eV]
Fig. 1. Temperature dependence of ¢1 (~) in the FIR spectral range for the Lu compound.The insetdisplaysal,(co)/crln(e0 at 6 and 10 K compared with the BCS theory (solid line).
"ad hoc" Hagen-Rubens extrapolation for frequencies smaller than 10 cm- 1 in order to impose a metallic-like behaviour (i.e., R(co) --* 100% for co --* 0). At 6 K we set R(o) = 100% below 15 cm -1 down to zero frequency. These extrapolations do not affect al (co) in the far infrared (FIR) above 15 crn-1 [6]. The temperature dependence of the real part of the optical conductivity in FIR for LuNizB/C is presented in Fig. 1 (equivalent results are found for YNizBzC). There is a clear temperature dependence, which bears a striking similarity with the results found for the superconducting alkali-metal doped fullerenes A3C6o [6]. By decreasing the temperature there is first a narrowing of the Drude component in the normal state and for temperatures below Tc we find a progressive suppression of the optical conductivity in FIR, which is very reminiscent of the expected scenario for the opening of a gap. The normal state properties deviate rather remarkably from the simple Drude picture, for which a constant al (co) is expected in the FIR spectral range. Indeed, a shallow minimum is seen at about 200 cm-*, which is basically the consequence of a mid-IR absorption at 500 cm-~ [7]. Previous investigation [8] also hints to a two-component picture (i.e., a low-frequency Drude and a broad mid-IR excitation). The resulting narrow Drude component of al (co) at T < 100 K is characterized by a small scattering rate F, which is even
smaller than the expected superconducting gap. Only the high-frequency tail of the Drude resonance merges in the spectral range where the superconducting energy gap should manifest (Fig. 1). Even though F < 2A, the materials are not yet in the extreme clean limit, which would completely prevent the detection of the gap. The optical conductivity between 6 and 10 K is basically zero up to a threshold frequency of about 5.6 meV. We ascribe the onset of absorption in al (09) to the optical identification of the superconducting gap. The gap value corresponds to a reduced gap ratio of 2A/kBTc ,-, 3.9 ( ,-, 5.2 for the Y compound [7]). These ratios suggest that the borocarbide superconductors should be placed within the moderate-to-strong coupling limit. This also agrees with the specific heat discontinuity at the superconducting transition in the Lu compound which implies a strong coupling, as well [9]. The experimental electrodynamic response can be directly compared with the BCS theoretical prediction [10]. The inset of Fig. 1 shows the ratio of the superconducting over the normal state optical conductivity als (co)/al n (CO) for the Lu compound at 6 and 10 K. There is an excellent agreement between experiment and theory,-suggesting that LnNi2B2C are BCS-like superconductors. The analysis of the experimental data in terms of the BCS approach can be extended to all measured temperatures below To, allowing us to extract the temperature dependence of the order parameter A(T). Fig. 2 shows A(T) for both Lu and Y compounds and the agreement with the BCS prediction is satisfactory, though in the moderate-to-strong coupling limit. Nevertheless, close to Tc the error bars associated to the determination of A(T) are quite large. In summary, our first attempt to optically investigate the electrodynamic response of the borocarbide superconductors allows us to establish that the Lu compound is very close to the clean limit, showing nevertheless the optical signature for the opening of a gap below T¢. The data are consistent with the BCS scenario in the moderate-to-strong coupling limit. This would suggest that the relevant excitation responsible for the superconductivity pairing might be associated with low-frequency phonon modes (e.g., optical phonons [8]).
[1 Bommeli et al. /Physica B 230-232 (1997) 879-881
881
References
z~
1,0
0.8
~ 0.6 0.4 -
0.2
0.0 0.0
-
BCS
YNi2B2CA(0) = 3.46 meV, Tc = 15.6 K A
LuNi2B2C, A(0) = 2.68 meV, To= 16.6 K
o'.2
i
o.,
#.6
i
I
o.s
i
1.o
TIT e
Fig. 2. Temperature dependence of the superconducting energy gap A for both LuNi2B2C and YNi2B2C, compared with the BCS prediction.
The authors wish to thank D.B. Tanner for fruitful discussion and J. Miiller for technical assistance. Ames Laboratory is operated for the US Department of Energy by Iowa State University under Contract No. W-7405-Eng-82. This work was supported by the Director for Energy Research, Office of Basic Energy Sciences. The work at UCSD was supported by a NSF Grant. One of us (L.D.) thanks the Swiss National Foundation for the Scientific Research for the financial support.
[1] R.J. Cava, H. Takagi, H.W. Zandbergen, J.J. Krajewski, W.F. Peck Jr., T. Siegrist, B. Batlogg, R.B. van Dover, R.J. Felder, K. Mizuhashi, J.O. Lee, H. Eisaki and S. Uchida, Nature 367 (1994) 252. [2] B.K. Cho, P.C. Canfield and D.C. Johnston, Phys. Rev. B 52 (1995) R3844. [3] T. Siegrist, H.W. Zandbergen, R.J. Cava, J.J. Krajewski and W.F. Peck Jr., Nature 367 (1994) 254. [4] H. Eisaki, H. Takagi, R.J. Cava, B. Batlogg, J.J. Krajewski, W.F. Peck Jr., K. Mizuhashi, J.O. Lee and S. Uchida, Phys. Rev. B 50 (1994) 647. [5] B.K. Cho, P.C. Canfield, L.L. Miller, D.C. Johnston, W.P. Beyermann and A. Yatskar, Phys. Rev. B 52 (1995) 3684 [6] L. Degiorgi, E.J. Nicol, O. Klein, G. Griiner, P. Wachter, S.-M. Huang, J. Wiley and R.B. Kaner, Phys. Rev. B 49 (1994) 7012. [7] F. Bommeli, L. Degiorgi, P. Wachter, B.K. Cho, PC. Canfield, R. Chau and M.B. Maple, Phys. Rev. Lett., in press. [8] K. Widder, D. Berner, A. Zibold, H.P. Geserich, M. Knupfer, M. Kielwein, M. Buchgeister and J. Fink, Europhys. Lett. 30 (1995) 55. [9] A. Yatskar, N.K. Budraa, W.P. Beyermann, P.C. Canfield and S.L. Bud'ko, Phys. Rev. B 54 (1996) R3772. [10] D.C. Mattis and J. Bardeen, Phys. Rev. 111 (1958) 412.
Physica B 230-232 (1997) 879 881
Optical properties of the borocarbide superconductors F. Bommeli a'*, L. Degiorgi a, P. Wachter a, B.K. C h o b, P.C. Canfield b, R. Chau c, M.B. Maple ~ Laboratorium fiir Festk6rperphysik, ETH-Zurich. CH-8093 Zurich, Switzerland hAmes Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA Department of Physics and Institute for Pure and Applied Physical Sciences, University of California at San Diego, La Jolla, CA 92093, USA
Abstract
We have measured the optical reflectivityof LuNi2B2C and YNizBEC compounds, and have evaluated the optical conductivity both above and below the superconducting transition temperature. The normal state optical properties suggest that these superconductors are almost in the clean limit. Our results below Tc give, however, evidence of a superconducting gap signature, and are in agreement with a moderate-to-strong coupling limit of the BCS theory. Keywords: Superconductivity;Optical properties; LuNi2B2C; YNizB2C
The discovery [ 1, 2] of superconductivity at relatively high temperatures in the new family of quaternary intermetallic compounds LnNi/BzC (Ln = Lu, Tin, Er, Ho, Dy, Y, with Tc = 15.6 and 16.6 K for the Y and Lu compound, respectively) raised a lot of interest both experimentally and theoretically. The striking layered-like crystallographic similarity of the LnNi2BzC compound with the cuprate-oxide superconductors [3], and the fact that superconductivity is observed not only for the non-magnetic rare-earth elements but also for the heavy magnetic rare earths, Tm, Er, Ho and Dy [1, 2] raised the expectation for the occurrence of competition between magnetism and superconductivity [4] and led to speculation that some exotic pairing mechanism is responsible for their relatively high To's. Even though these systems were extensively characterized by transport and magnetic measurements [1, 2, 4, 5], the mechanism of superconduc*Correspondingauthor.
tivity still remains to be settled. In this respect, an important intrinsic parameter is the superconducting gap. Optical spectroscopic methods are in principle a powerful experimental tool for the determination of such a relevant energy scale which has important implications in connection with the excitations mediating superconductivity and the strength of the coupling mechanism (electronphonon or electron-electron). The Lu-single-crystal sample used in the present experiment was prepared following the method described in Refs. [1, 5]. The sample was polished in order to achieve smooth and shiny optical surface. The optical properties were obtained by measuring the reflectivity R(~o) of the Lu-single crystal in the ab-plane, as a function of temperature between 15 and 105 cm 1, using four different spectrometers [6]. By performing the Kramers-Kronig transformation with standard extrapolations, we obtain the complete set of optical properties expressed in term of the complete optical conductivity [6]. Below T~, R(o~) at T > 6 K was completed with an
0921-4526/97/$17.00 Copyright ~-~ c 1997 ElsevierScienceB.V.All rights reserved Pll S092 1-4526(96)00465-6
F. Bommeli et al. / Physica B 230-232 (1997) 879-881
880
/9
'
1O0 ,~ .
1.0.
200 .
[cm-t ]
'
8000
~
\~'~ %0.5 m-
~\ vc,.~ 6000
r "-,:.,f g
.,..~
,,,,,\,,,000 \
~4000
\,\'~""7: ........ ,_27~
\\ \,\'-'
,,,
~ . ~ i 0~" - 6K ~'~'~ . . . . 10 K _
,, 2000
,~ r
/\/1
,~ \ . \
.,,~
',
,'"" ""
/
\..
/
"~'-.......
0.01
_
. . . . !4 - . - 20 K - .... 50K
0.02
0.03
Photon Energy [eV]
Fig. 1. Temperature dependence of ¢1 (~) in the FIR spectral range for the Lu compound.The insetdisplaysal,(co)/crln(e0 at 6 and 10 K compared with the BCS theory (solid line).
"ad hoc" Hagen-Rubens extrapolation for frequencies smaller than 10 cm- 1 in order to impose a metallic-like behaviour (i.e., R(co) --* 100% for co --* 0). At 6 K we set R(o) = 100% below 15 cm -1 down to zero frequency. These extrapolations do not affect al (co) in the far infrared (FIR) above 15 crn-1 [6]. The temperature dependence of the real part of the optical conductivity in FIR for LuNizB/C is presented in Fig. 1 (equivalent results are found for YNizBzC). There is a clear temperature dependence, which bears a striking similarity with the results found for the superconducting alkali-metal doped fullerenes A3C6o [6]. By decreasing the temperature there is first a narrowing of the Drude component in the normal state and for temperatures below Tc we find a progressive suppression of the optical conductivity in FIR, which is very reminiscent of the expected scenario for the opening of a gap. The normal state properties deviate rather remarkably from the simple Drude picture, for which a constant al (co) is expected in the FIR spectral range. Indeed, a shallow minimum is seen at about 200 cm-*, which is basically the consequence of a mid-IR absorption at 500 cm-~ [7]. Previous investigation [8] also hints to a two-component picture (i.e., a low-frequency Drude and a broad mid-IR excitation). The resulting narrow Drude component of al (co) at T < 100 K is characterized by a small scattering rate F, which is even
smaller than the expected superconducting gap. Only the high-frequency tail of the Drude resonance merges in the spectral range where the superconducting energy gap should manifest (Fig. 1). Even though F < 2A, the materials are not yet in the extreme clean limit, which would completely prevent the detection of the gap. The optical conductivity between 6 and 10 K is basically zero up to a threshold frequency of about 5.6 meV. We ascribe the onset of absorption in al (09) to the optical identification of the superconducting gap. The gap value corresponds to a reduced gap ratio of 2A/kBTc ,-, 3.9 ( ,-, 5.2 for the Y compound [7]). These ratios suggest that the borocarbide superconductors should be placed within the moderate-to-strong coupling limit. This also agrees with the specific heat discontinuity at the superconducting transition in the Lu compound which implies a strong coupling, as well [9]. The experimental electrodynamic response can be directly compared with the BCS theoretical prediction [10]. The inset of Fig. 1 shows the ratio of the superconducting over the normal state optical conductivity als (co)/al n (CO) for the Lu compound at 6 and 10 K. There is an excellent agreement between experiment and theory,-suggesting that LnNi2B2C are BCS-like superconductors. The analysis of the experimental data in terms of the BCS approach can be extended to all measured temperatures below To, allowing us to extract the temperature dependence of the order parameter A(T). Fig. 2 shows A(T) for both Lu and Y compounds and the agreement with the BCS prediction is satisfactory, though in the moderate-to-strong coupling limit. Nevertheless, close to Tc the error bars associated to the determination of A(T) are quite large. In summary, our first attempt to optically investigate the electrodynamic response of the borocarbide superconductors allows us to establish that the Lu compound is very close to the clean limit, showing nevertheless the optical signature for the opening of a gap below T¢. The data are consistent with the BCS scenario in the moderate-to-strong coupling limit. This would suggest that the relevant excitation responsible for the superconductivity pairing might be associated with low-frequency phonon modes (e.g., optical phonons [8]).
[1 Bommeli et al. /Physica B 230-232 (1997) 879-881
881
References
z~
1,0
0.8
~ 0.6 0.4 -
0.2
0.0 0.0
-
BCS
YNi2B2CA(0) = 3.46 meV, Tc = 15.6 K A
LuNi2B2C, A(0) = 2.68 meV, To= 16.6 K
o'.2
i
o.,
#.6
i
I
o.s
i
1.o
TIT e
Fig. 2. Temperature dependence of the superconducting energy gap A for both LuNi2B2C and YNi2B2C, compared with the BCS prediction.
The authors wish to thank D.B. Tanner for fruitful discussion and J. Miiller for technical assistance. Ames Laboratory is operated for the US Department of Energy by Iowa State University under Contract No. W-7405-Eng-82. This work was supported by the Director for Energy Research, Office of Basic Energy Sciences. The work at UCSD was supported by a NSF Grant. One of us (L.D.) thanks the Swiss National Foundation for the Scientific Research for the financial support.
[1] R.J. Cava, H. Takagi, H.W. Zandbergen, J.J. Krajewski, W.F. Peck Jr., T. Siegrist, B. Batlogg, R.B. van Dover, R.J. Felder, K. Mizuhashi, J.O. Lee, H. Eisaki and S. Uchida, Nature 367 (1994) 252. [2] B.K. Cho, P.C. Canfield and D.C. Johnston, Phys. Rev. B 52 (1995) R3844. [3] T. Siegrist, H.W. Zandbergen, R.J. Cava, J.J. Krajewski and W.F. Peck Jr., Nature 367 (1994) 254. [4] H. Eisaki, H. Takagi, R.J. Cava, B. Batlogg, J.J. Krajewski, W.F. Peck Jr., K. Mizuhashi, J.O. Lee and S. Uchida, Phys. Rev. B 50 (1994) 647. [5] B.K. Cho, P.C. Canfield, L.L. Miller, D.C. Johnston, W.P. Beyermann and A. Yatskar, Phys. Rev. B 52 (1995) 3684 [6] L. Degiorgi, E.J. Nicol, O. Klein, G. Griiner, P. Wachter, S.-M. Huang, J. Wiley and R.B. Kaner, Phys. Rev. B 49 (1994) 7012. [7] F. Bommeli, L. Degiorgi, P. Wachter, B.K. Cho, PC. Canfield, R. Chau and M.B. Maple, Phys. Rev. Lett., in press. [8] K. Widder, D. Berner, A. Zibold, H.P. Geserich, M. Knupfer, M. Kielwein, M. Buchgeister and J. Fink, Europhys. Lett. 30 (1995) 55. [9] A. Yatskar, N.K. Budraa, W.P. Beyermann, P.C. Canfield and S.L. Bud'ko, Phys. Rev. B 54 (1996) R3772. [10] D.C. Mattis and J. Bardeen, Phys. Rev. 111 (1958) 412.