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Superconductivity and magnetism in the pseudo-quaternary system (ErxTb1−x)Ni2B2C
Physica C 317–318 Ž1999. 441–443
Superconductivity and magnetism in the pseudo-quaternary system žEr xTb 1yx /Ni 2 B 2 C Z.Q. Peng ) , K. Krug, K. Winzer I. Physikalisches Institut der UniÕersitat Bunsenstrasse 9, 37073 Gottingen, Germany ¨ Gottingen, ¨ ¨
Abstract Magnetic phase diagram and superconductivity in the ŽEr xTb1yx .Ni 2 B 2 C system were studied by measurements of resistivity and susceptibility as a function of temperature and magnetic field. In the range 0.45 F x F 0.75, antiferromagnetic transition temperature T N exhibits an anomalous minimum. The suppression of superconductivity in the ŽEr xTb1yx .Ni 2 B 2 C system can be explained using the AG pair breaking theory. The possible reason for the absence of superconductivity in TbNi 2 B 2 C is discussed. q 1999 Elsevier Science B.V. All rights reserved. PACS: 74.72Ny; 74.25.Dw; 74.25.Ha Keywords: Borocarbides; ŽEr xTb1yx .Ni 2 B 2 C; Superconductivity; Magnetic pair-breaking
For superconducting members of RNi 2 B 2 C ŽR s Lu, Y, Tm, Er, Ho and Dy., the superconducting transition temperature Tc scales roughly with the de Gennes ŽdG. factor w1–3x, seemingly consistent well with the Abrikosov–Gor’kov ŽAG. pair breaking theory in the dilute magnetic impurity limit. According to this dG scaling, it was expected that Tc for TbNi 2 B 2 C would be about 1.2 K w3,4x. However, it has been proved that TbNi 2 B 2 C is not superconducting at temperatures above 7 mK w5x. It was suggested that the absence of superconductivity in TbNi 2 B 2 C would be due to the influence from the weak ferromagnetic phase ŽWFM. w6x. Here we present our measurements of the resistivity and susceptibility on the ŽEr xTb1yx .Ni 2 B 2 C system. The results of these
)
Corresponding author. E-mail: [email protected]
measurements indicate that the condition of the dilute magnetic impurity limit is not strictly fulfilled in ŽEr xTb1yx .Ni 2 B 2 C and the pure superconducting members. The possible reason for the absence of superconductivity in TbNi 2 B 2 C is discussed. Polycrystalline samples of ŽEr xTb1yx .Ni 2 B 2 C were prepared using the arc-melting method under argon gas. The samples were annealed at 10008C for 24 h in evacuated quartz tubes. Single crystals of ŽEr xTb1yx .Ni 2 B 2 C were grown using the standard flux method with Ni 2 B as flux w7x. Resistivity and susceptibility measurements, X-ray Laue backscattering, X-ray diffraction were used for sample characterization. Susceptibility and resistivity measurements were performed in an adiabatic demagnetization cryostat at temperatures between 50 mK and 14 K with magnetic fields up to 5 T. The magnetic and superconducting transition temperatures as a function of the concentration x in
0921-4534r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 9 . 0 0 0 9 4 - 5
442
Z.Q. Peng et al.r Physica C 317–318 (1999) 441–443
ŽEr xTb1yx .Ni 2 B 2 C are shown in Fig. 1. Taking the point x s 0.9 as an example, the superconducting transition occurs at Tc f 9.3 K; the Neel ´ temperature TN f 6.8 K; at T WFM f 1.1 K, the sample undergoes a transition from AFM phase to WFM phase. With decreasing x, T WF M increases monotonously, while TN exhibits an unexpected minimum at x f 0.6. From our susceptibility measurement on ŽEr0.6Tb 0.4 .Ni 2 B 2 C, no antiferromagnetic transition can be resolved, the sample seems to take a direct transition from paramagnetic state ŽPM. to WFM phase. In ranges x F 0.45 and x G 0.75, T N decreases almost linearly with increasing x. The behaviour of TN in the middle concentration range 0.45 F x F 0.75 might result from the competing exchange interactions between Er–Er, Er–Tb and Tb–Tb. Another possible origin is that it may be due to changes in the conduction electron concentration influencing RKKY-type interactions, as in the ternary system TbŽIn x Sn 1yx . 3 w8x. Detailed investigation is in progress. As shown in Fig. 1, Tc decreases with increasing concentration of Tb. Fig. 2 shows the dependence of Tc on dG factor. For comparison, we include in Fig. 2 also the pure superconducting members in the RNi 2 B 2 C system. It is seen that the superconducting transition temperatures for ŽEr xTb1yx .Ni 2 B 2 C do not obey the dG scaling deduced from the pure superconducting members Žthe dashed line in Fig. 2..
Fig. 1. Low-temperature phase diagram for the ŽEr xTb1yx .Ni 2 B 2 C system.
Fig. 2. The dependence of Tc on dG factor for the ŽEr xTb 1yx .Ni 2 B 2 C and pure superconducting members in RNi 2 B 2 C ŽR s Lu, Y, Tm, Er, Ho and Dy..
In order to explain the behaviour of Tc in the ŽEr xTb1yx .Ni 2 B 2 C system, we fitted our results to the AG equations: ln
Tc
1
ž / ž/ ž Tc 0
sc
2
yc
1 q
0.14a Tc 0
a cr Tc
2 2
/
a s "y1 cN Ž EF . Jex2 Ž g J y 1 . Ž J q 1 . J
,
Ž 1. Ž 2.
where c is the concentration of magnetic ions, N Ž EF . is the density of states Žfor one spin direction. at Fermi level, Jex is the s–f exchange integral, dG s Ž g J y 1. 2 Ž J q 1. J is the dG factor, Tc0 corresponds to a s 0, a cr s k B Tc0r4"g Žln g is Euler’s constant.. Tc s 0 corresponds to a s a cr . In the limit a ™ 0, AG equations is reduced to a simple relation: DTc ; Jex2 dG, this is the theoretical basis for the expectation of dG scaling. For the ŽEr xTb1yx .Ni 2 B 2 C system, if we take Tc0 f 16.6 K ŽTc for R s Lu., DTcrTc0 G 36%, we believe the condition of a ™ 0 is no longer fulfilled, so the full AG equations should be applied to account for our results. First we fit the AG equations to the Tc s for pure RNi 2 B 2 C ŽR s Tm, Er, Ho, Dy. with different Jex . N Ž E F . s 4.8 eVy1 per unit cell. Tc0 ŽLu. s 16.6 K. The results are shown as dotted lines in Fig. 2, each line corresponds to a different value of Jex . Jex ŽEr. ˚ 3. is obtained to be about 0.87 eV A
Z.Q. Peng et al.r Physica C 317–318 (1999) 441–443
Then we take a for ŽEr xTb1yx .Ni 2 B 2 C as:
a s a Er x q a Tb Ž 1 y x . ,
Ž 3.
a Er s "y1 cN Ž EF . Jex2 Ž Er . dG Ž Er . ,
Ž 4.
y1
a Tb s "
cN Ž EF .
Jex2
Ž Tb . dG Ž Tb. .
Ž 5.
The fitting result is shown as solid lines in Figs. 1 ˚ 3. and 2. The obtained Jex ŽTb. s 0.89 eV A The fitting curve in Fig. 1 displays that for x F 0.65, the superconductivity is totally suppressed. Our measurement on a sample with x s 0.65 confirmed this prediction. As shown in Fig. 1, all the superconducting transition temperatures under consideration are above the WFM phase, no effect of WFM phase is considered in the above fitting procedure. Hence, it is reasonable to believe that for TbNi 2 B 2 C the pair breaking parameter a ) a cr . The magnetic pair breaking by Tb ions alone is strong enough to destroy the superconductivity, and the influence of
443
WFM is not necessary to be included in the explanation of the absence of superconductivity in TbNi 2 B 2 C. References w1x H. Eisaki, H. Takagi, R.J. Cava, B. Batlogg, J.J. Krajewski, W.F. Peck Jr., K. Mizuhashi, J.O. Lee, S. Uchida, Phys. Rev. B 50 Ž1994. 647. w2x B.K. Cho, P.C. Canfield, D.C. Johnston, Phys. Rev. B 52 Ž1995. 3844. w3x L.C. Gupta, Physica B 223–224 Ž1996. 56. w4x B.K. Cho, P.C. Canfield, D.C. Johnston, Phys. Rev. B 53 Ž1996. 8499. w5x H. Bitterlich, Diplomarbeit, Gottingen Ž1997.. ¨ w6x C.V. Tomy, L.A. Afalfiz, M.R. Lees, J.M. Martin, D.Mck. Paul, D.T. Adroja, Phys. Rev. B 53 Ž1996. 307. w7x M. Xu, P.C. Canfield, J.E. Ostenson, D.K. Finnemore, B.K. Cho, Z.R. Wang, D.C. Johnston, Physica C 227 Ž1994. 321. w8x P. Lethuillier, J. Pierre, G. Fillion, B. Barbara, Phys. Status Solidi 15a Ž1973. 613.
Superconductivity and magnetism in the pseudo-quaternary system žEr xTb 1yx /Ni 2 B 2 C Z.Q. Peng ) , K. Krug, K. Winzer I. Physikalisches Institut der UniÕersitat Bunsenstrasse 9, 37073 Gottingen, Germany ¨ Gottingen, ¨ ¨
Abstract Magnetic phase diagram and superconductivity in the ŽEr xTb1yx .Ni 2 B 2 C system were studied by measurements of resistivity and susceptibility as a function of temperature and magnetic field. In the range 0.45 F x F 0.75, antiferromagnetic transition temperature T N exhibits an anomalous minimum. The suppression of superconductivity in the ŽEr xTb1yx .Ni 2 B 2 C system can be explained using the AG pair breaking theory. The possible reason for the absence of superconductivity in TbNi 2 B 2 C is discussed. q 1999 Elsevier Science B.V. All rights reserved. PACS: 74.72Ny; 74.25.Dw; 74.25.Ha Keywords: Borocarbides; ŽEr xTb1yx .Ni 2 B 2 C; Superconductivity; Magnetic pair-breaking
For superconducting members of RNi 2 B 2 C ŽR s Lu, Y, Tm, Er, Ho and Dy., the superconducting transition temperature Tc scales roughly with the de Gennes ŽdG. factor w1–3x, seemingly consistent well with the Abrikosov–Gor’kov ŽAG. pair breaking theory in the dilute magnetic impurity limit. According to this dG scaling, it was expected that Tc for TbNi 2 B 2 C would be about 1.2 K w3,4x. However, it has been proved that TbNi 2 B 2 C is not superconducting at temperatures above 7 mK w5x. It was suggested that the absence of superconductivity in TbNi 2 B 2 C would be due to the influence from the weak ferromagnetic phase ŽWFM. w6x. Here we present our measurements of the resistivity and susceptibility on the ŽEr xTb1yx .Ni 2 B 2 C system. The results of these
)
Corresponding author. E-mail: [email protected]
measurements indicate that the condition of the dilute magnetic impurity limit is not strictly fulfilled in ŽEr xTb1yx .Ni 2 B 2 C and the pure superconducting members. The possible reason for the absence of superconductivity in TbNi 2 B 2 C is discussed. Polycrystalline samples of ŽEr xTb1yx .Ni 2 B 2 C were prepared using the arc-melting method under argon gas. The samples were annealed at 10008C for 24 h in evacuated quartz tubes. Single crystals of ŽEr xTb1yx .Ni 2 B 2 C were grown using the standard flux method with Ni 2 B as flux w7x. Resistivity and susceptibility measurements, X-ray Laue backscattering, X-ray diffraction were used for sample characterization. Susceptibility and resistivity measurements were performed in an adiabatic demagnetization cryostat at temperatures between 50 mK and 14 K with magnetic fields up to 5 T. The magnetic and superconducting transition temperatures as a function of the concentration x in
0921-4534r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 9 . 0 0 0 9 4 - 5
442
Z.Q. Peng et al.r Physica C 317–318 (1999) 441–443
ŽEr xTb1yx .Ni 2 B 2 C are shown in Fig. 1. Taking the point x s 0.9 as an example, the superconducting transition occurs at Tc f 9.3 K; the Neel ´ temperature TN f 6.8 K; at T WFM f 1.1 K, the sample undergoes a transition from AFM phase to WFM phase. With decreasing x, T WF M increases monotonously, while TN exhibits an unexpected minimum at x f 0.6. From our susceptibility measurement on ŽEr0.6Tb 0.4 .Ni 2 B 2 C, no antiferromagnetic transition can be resolved, the sample seems to take a direct transition from paramagnetic state ŽPM. to WFM phase. In ranges x F 0.45 and x G 0.75, T N decreases almost linearly with increasing x. The behaviour of TN in the middle concentration range 0.45 F x F 0.75 might result from the competing exchange interactions between Er–Er, Er–Tb and Tb–Tb. Another possible origin is that it may be due to changes in the conduction electron concentration influencing RKKY-type interactions, as in the ternary system TbŽIn x Sn 1yx . 3 w8x. Detailed investigation is in progress. As shown in Fig. 1, Tc decreases with increasing concentration of Tb. Fig. 2 shows the dependence of Tc on dG factor. For comparison, we include in Fig. 2 also the pure superconducting members in the RNi 2 B 2 C system. It is seen that the superconducting transition temperatures for ŽEr xTb1yx .Ni 2 B 2 C do not obey the dG scaling deduced from the pure superconducting members Žthe dashed line in Fig. 2..
Fig. 1. Low-temperature phase diagram for the ŽEr xTb1yx .Ni 2 B 2 C system.
Fig. 2. The dependence of Tc on dG factor for the ŽEr xTb 1yx .Ni 2 B 2 C and pure superconducting members in RNi 2 B 2 C ŽR s Lu, Y, Tm, Er, Ho and Dy..
In order to explain the behaviour of Tc in the ŽEr xTb1yx .Ni 2 B 2 C system, we fitted our results to the AG equations: ln
Tc
1
ž / ž/ ž Tc 0
sc
2
yc
1 q
0.14a Tc 0
a cr Tc
2 2
/
a s "y1 cN Ž EF . Jex2 Ž g J y 1 . Ž J q 1 . J
,
Ž 1. Ž 2.
where c is the concentration of magnetic ions, N Ž EF . is the density of states Žfor one spin direction. at Fermi level, Jex is the s–f exchange integral, dG s Ž g J y 1. 2 Ž J q 1. J is the dG factor, Tc0 corresponds to a s 0, a cr s k B Tc0r4"g Žln g is Euler’s constant.. Tc s 0 corresponds to a s a cr . In the limit a ™ 0, AG equations is reduced to a simple relation: DTc ; Jex2 dG, this is the theoretical basis for the expectation of dG scaling. For the ŽEr xTb1yx .Ni 2 B 2 C system, if we take Tc0 f 16.6 K ŽTc for R s Lu., DTcrTc0 G 36%, we believe the condition of a ™ 0 is no longer fulfilled, so the full AG equations should be applied to account for our results. First we fit the AG equations to the Tc s for pure RNi 2 B 2 C ŽR s Tm, Er, Ho, Dy. with different Jex . N Ž E F . s 4.8 eVy1 per unit cell. Tc0 ŽLu. s 16.6 K. The results are shown as dotted lines in Fig. 2, each line corresponds to a different value of Jex . Jex ŽEr. ˚ 3. is obtained to be about 0.87 eV A
Z.Q. Peng et al.r Physica C 317–318 (1999) 441–443
Then we take a for ŽEr xTb1yx .Ni 2 B 2 C as:
a s a Er x q a Tb Ž 1 y x . ,
Ž 3.
a Er s "y1 cN Ž EF . Jex2 Ž Er . dG Ž Er . ,
Ž 4.
y1
a Tb s "
cN Ž EF .
Jex2
Ž Tb . dG Ž Tb. .
Ž 5.
The fitting result is shown as solid lines in Figs. 1 ˚ 3. and 2. The obtained Jex ŽTb. s 0.89 eV A The fitting curve in Fig. 1 displays that for x F 0.65, the superconductivity is totally suppressed. Our measurement on a sample with x s 0.65 confirmed this prediction. As shown in Fig. 1, all the superconducting transition temperatures under consideration are above the WFM phase, no effect of WFM phase is considered in the above fitting procedure. Hence, it is reasonable to believe that for TbNi 2 B 2 C the pair breaking parameter a ) a cr . The magnetic pair breaking by Tb ions alone is strong enough to destroy the superconductivity, and the influence of
443
WFM is not necessary to be included in the explanation of the absence of superconductivity in TbNi 2 B 2 C. References w1x H. Eisaki, H. Takagi, R.J. Cava, B. Batlogg, J.J. Krajewski, W.F. Peck Jr., K. Mizuhashi, J.O. Lee, S. Uchida, Phys. Rev. B 50 Ž1994. 647. w2x B.K. Cho, P.C. Canfield, D.C. Johnston, Phys. Rev. B 52 Ž1995. 3844. w3x L.C. Gupta, Physica B 223–224 Ž1996. 56. w4x B.K. Cho, P.C. Canfield, D.C. Johnston, Phys. Rev. B 53 Ž1996. 8499. w5x H. Bitterlich, Diplomarbeit, Gottingen Ž1997.. ¨ w6x C.V. Tomy, L.A. Afalfiz, M.R. Lees, J.M. Martin, D.Mck. Paul, D.T. Adroja, Phys. Rev. B 53 Ž1996. 307. w7x M. Xu, P.C. Canfield, J.E. Ostenson, D.K. Finnemore, B.K. Cho, Z.R. Wang, D.C. Johnston, Physica C 227 Ž1994. 321. w8x P. Lethuillier, J. Pierre, G. Fillion, B. Barbara, Phys. Status Solidi 15a Ž1973. 613.