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or density of states effect in YxLu1−xNi2B2C
Physica B 283}284 (2000) 491}492
Disorder and/or density of states e!ect in Y Lu Ni B C V \V H. Michor*, S. Manalo, M. El-Hagary, G. Hilscher Institut fu( r Experimentalphysik, Technische Universitat Wien, Wiedner Hauptstr. 8-10, A-1040 Wien, Austria
Abstract The role of disorder and/or lattice strain due to the size mismatch between Y and Lu in the solid solution Y Lu Ni B C was studied by speci"c heat measurements in magnetic "elds up to 9 T. Thereby, the analysis of the V \V superconducting and normal state heat capacity as well as the temperature dependence of the upper critical "eld H shows that the reported reduction of ¹ within the solid solution correlates with a reduction of the electronic density of states N(E ). Thus, the major e!ect of Y/Lu substitution upon superconductivity is due to a band broadening arising from the R-ion size mismatch rather than from disorder scattering of Cooper electrons. 2000 Elsevier Science B.V. All rights reserved. Keywords: Borocarbides; Speci"c heat
1. Introduction Investigations on pseudo-quaternary borocarbides R R Ni B C were motivated by the complex inter\V V play between superconductivity (SC) and magnetism when in Y- or LuNi B C with ¹ K16 K the non magnetic rare-earth R is gradually substituted with magnetic ions, R"Gd}Tm. In this context, Freudenberger et al. [1] reported a breakdown of the expected linear relation between ¹ and the concentration of magnetic moments even in the paramagnetic regime of Lu Ho Ni B C while the linear relation is well ful"l\V V led in Y Ho Ni B C. In order to analyze the in#u\V V ence of disorder due to the size mismatch between the R and R ions they [2] studied solid solutions of purely non-magnetic rare-earth elements, namely Y Lu Ni B C, and found a roughly parabolic dip in V \V ¹ (x) which is well con"rmed by the present investiga tion as shown in Fig. 1. The lattice parameters follow Vegard's law (linear change with x) without any line broadening or superstructure re#ections in the X-ray pattern. Freudenberger et al. [2] reported a rough correlation of the ¹ reduction with an increase of the
* Corresponding author. E-mail address: [email protected] (H. Michor)
residual resistivity indicative for electron scattering on spatial inhomogeneities of the periodic potential (&disorder scattering'), however, they pointed out that this e!ect is neither su$cient to explain well ¹ (x) nor the change of the temperature dependence of the upper critical "eld, H (¹)/H (0)K(1!¹/¹ )?, where the expo nent a is also a function of x with a minimum value aK1.1 at x"0.5 and maximum values aK1.25 for the unalloyed compounds Y- and LuNi B C. 2. Results and discussion In order to investigate possible changes of the electronic density of states (EDOS) and an eventual lattice sti!ening within the solid solution we performed speci"c heat measurements on YNi B C, Y Lu Ni B C, Y Lu Ni B C, and LuNi B C where *¹ /*x is large. The normal state speci"c heat shown in Fig. 2 could be recovered by applying an external magnetic "eld of 9 T yielding the linear coe$cient of the electronic speci"c heat c which is a measure for the EDOS at the Fermi level N(E ). The thermodynamic mean transition temperature ¹ and the speci"c heat jump *C were determined from the zero "eld measurements. The results summarized in Table 1 reveal a linear correlation between ¹ and the c-value while the BCS ratio *C/c¹ which is a measure for the electron phonon
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 0 8 4 - 0
492
H. Michor et al. / Physica B 283}284 (2000) 491}492
Table 1 Comparison of ¹ , the c-value and the BCS ratio *C/c¹ of Y Lu Ni B C V \V x
¹ (K)
c (mJ/mol K)
*C/c¹
1.0 0.8 0.1 0.0
15.5 14.8 15.5 16.0
19.7 (2) 18.5 (2) 19.7 (3) 20.6 (2)
1.83 1.91 2.03 2.10
Fig. 2. The normal state heat capacities as C/¹ versus ¹ obtained by applying a magnetic "eld of 9 T.
Fig. 1. The superconducting transition temperature ¹ versus x of Y Lu Ni B C obtained by AC susceptibility measureV \V ments.
On the other hand, there is a clear correlation of ¹ and c which both depend on N(E ) as it was shown by Ni-site substitutions in YNi B C as well as in La Ni B N \B [4]. Thus, we conclude that the reduction of N(E ) and the corresponding drop of ¹ and the c-value is most likely due to a band broadening arising from the R-ion size mismatch which washes out the EDOS maximum at the Fermi level.
Acknowledgements coupling strength (i.e. the ratio of ¹ to the characteristic mean phonon frequency u ) increases linearly from Y to LuNi B C. The latter is in line with our analysis of the lattice heat capacity data (2 } 140 K) indicating that the phonon density of states of Y Lu - and Y Lu Ni B C is nearly a linear combination by that of Y- and LuNi B C, i.e. the dip in ¹ (x) can hardly be attributed to a phonon e!ect. We further estimated the in#uence of disorder scattering by analyzing the H (¹) data with the Eliashberg theory (see Ref. [3]) yielding e.g. for Y Lu Ni B C an upper limit for the scattering potential t>)1 meV which is more than one order of magnitude too small to account for the reduction of ¹ .
The work was supported by the Austrian Science Foundation Fonds under project P-11090-PHY.
References [1] J. Freudenberger et al., J. Magn. Magn. Mater. 187 (1998) 309. [2] J. Freudenberger et al., Physica C 306 (1998) 1. [3] M. Prohammer, E. Schachinger, Phys. Rev. B 36 (1987) 8353. [4] H. Michor et al., Phys. Rev. B 58 (1998) 15045.
Disorder and/or density of states e!ect in Y Lu Ni B C V \V H. Michor*, S. Manalo, M. El-Hagary, G. Hilscher Institut fu( r Experimentalphysik, Technische Universitat Wien, Wiedner Hauptstr. 8-10, A-1040 Wien, Austria
Abstract The role of disorder and/or lattice strain due to the size mismatch between Y and Lu in the solid solution Y Lu Ni B C was studied by speci"c heat measurements in magnetic "elds up to 9 T. Thereby, the analysis of the V \V superconducting and normal state heat capacity as well as the temperature dependence of the upper critical "eld H shows that the reported reduction of ¹ within the solid solution correlates with a reduction of the electronic density of states N(E ). Thus, the major e!ect of Y/Lu substitution upon superconductivity is due to a band broadening arising from the R-ion size mismatch rather than from disorder scattering of Cooper electrons. 2000 Elsevier Science B.V. All rights reserved. Keywords: Borocarbides; Speci"c heat
1. Introduction Investigations on pseudo-quaternary borocarbides R R Ni B C were motivated by the complex inter\V V play between superconductivity (SC) and magnetism when in Y- or LuNi B C with ¹ K16 K the non magnetic rare-earth R is gradually substituted with magnetic ions, R"Gd}Tm. In this context, Freudenberger et al. [1] reported a breakdown of the expected linear relation between ¹ and the concentration of magnetic moments even in the paramagnetic regime of Lu Ho Ni B C while the linear relation is well ful"l\V V led in Y Ho Ni B C. In order to analyze the in#u\V V ence of disorder due to the size mismatch between the R and R ions they [2] studied solid solutions of purely non-magnetic rare-earth elements, namely Y Lu Ni B C, and found a roughly parabolic dip in V \V ¹ (x) which is well con"rmed by the present investiga tion as shown in Fig. 1. The lattice parameters follow Vegard's law (linear change with x) without any line broadening or superstructure re#ections in the X-ray pattern. Freudenberger et al. [2] reported a rough correlation of the ¹ reduction with an increase of the
* Corresponding author. E-mail address: [email protected] (H. Michor)
residual resistivity indicative for electron scattering on spatial inhomogeneities of the periodic potential (&disorder scattering'), however, they pointed out that this e!ect is neither su$cient to explain well ¹ (x) nor the change of the temperature dependence of the upper critical "eld, H (¹)/H (0)K(1!¹/¹ )?, where the expo nent a is also a function of x with a minimum value aK1.1 at x"0.5 and maximum values aK1.25 for the unalloyed compounds Y- and LuNi B C. 2. Results and discussion In order to investigate possible changes of the electronic density of states (EDOS) and an eventual lattice sti!ening within the solid solution we performed speci"c heat measurements on YNi B C, Y Lu Ni B C, Y Lu Ni B C, and LuNi B C where *¹ /*x is large. The normal state speci"c heat shown in Fig. 2 could be recovered by applying an external magnetic "eld of 9 T yielding the linear coe$cient of the electronic speci"c heat c which is a measure for the EDOS at the Fermi level N(E ). The thermodynamic mean transition temperature ¹ and the speci"c heat jump *C were determined from the zero "eld measurements. The results summarized in Table 1 reveal a linear correlation between ¹ and the c-value while the BCS ratio *C/c¹ which is a measure for the electron phonon
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 0 8 4 - 0
492
H. Michor et al. / Physica B 283}284 (2000) 491}492
Table 1 Comparison of ¹ , the c-value and the BCS ratio *C/c¹ of Y Lu Ni B C V \V x
¹ (K)
c (mJ/mol K)
*C/c¹
1.0 0.8 0.1 0.0
15.5 14.8 15.5 16.0
19.7 (2) 18.5 (2) 19.7 (3) 20.6 (2)
1.83 1.91 2.03 2.10
Fig. 2. The normal state heat capacities as C/¹ versus ¹ obtained by applying a magnetic "eld of 9 T.
Fig. 1. The superconducting transition temperature ¹ versus x of Y Lu Ni B C obtained by AC susceptibility measureV \V ments.
On the other hand, there is a clear correlation of ¹ and c which both depend on N(E ) as it was shown by Ni-site substitutions in YNi B C as well as in La Ni B N \B [4]. Thus, we conclude that the reduction of N(E ) and the corresponding drop of ¹ and the c-value is most likely due to a band broadening arising from the R-ion size mismatch which washes out the EDOS maximum at the Fermi level.
Acknowledgements coupling strength (i.e. the ratio of ¹ to the characteristic mean phonon frequency u ) increases linearly from Y to LuNi B C. The latter is in line with our analysis of the lattice heat capacity data (2 } 140 K) indicating that the phonon density of states of Y Lu - and Y Lu Ni B C is nearly a linear combination by that of Y- and LuNi B C, i.e. the dip in ¹ (x) can hardly be attributed to a phonon e!ect. We further estimated the in#uence of disorder scattering by analyzing the H (¹) data with the Eliashberg theory (see Ref. [3]) yielding e.g. for Y Lu Ni B C an upper limit for the scattering potential t>)1 meV which is more than one order of magnitude too small to account for the reduction of ¹ .
The work was supported by the Austrian Science Foundation Fonds under project P-11090-PHY.
References [1] J. Freudenberger et al., J. Magn. Magn. Mater. 187 (1998) 309. [2] J. Freudenberger et al., Physica C 306 (1998) 1. [3] M. Prohammer, E. Schachinger, Phys. Rev. B 36 (1987) 8353. [4] H. Michor et al., Phys. Rev. B 58 (1998) 15045.